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• Int J Clin Exp Med
• v.6(8); 2013

The effect of water temperature and voluntary drinking on the post rehydration sweating

Abdollah hosseinlou.

1 Faculty of Medicine, Urmia University of Medical Sciences, Urmia, Iran

Saeed Khamnei

2 Department of Physiology, Azad Islamic University, Tabriz Branch, Tabriz, Iran

Masumeh Zamanlu

3 Neuroscience Research Center, Student Research Committee, Tabriz University of Medical Sciences, Tabriz, Iran

During heat stress and dehydration, thermoregulation is partly suppressed to save body fluid and circulation. Drinking induces the recovery of thermoregulatory responses including sweating. Our objective is to investigate the effect of water temperature and voluntary drinking on the extent of the drinking-induced sweating . Six healthy subjects 23.7 ± 0.6 yr old and 80.7 ± 5.7 kg wt were dehydrated by performing mild exercise (ergometer cycling) in a hot and humid chamber (38-40°C, 20-28% relative humidity). After dehydration, subjects were allowed to drink water with temperatures of 5, 16, 26, 58°C on four separate days. The sweating rate was measured on the forehead area before and after drinking. Also, blood samples were collected during the experiments and plasma osmolality was measured. Sweating increased markedly just a few minutes after the onset of drinking. The rate of this response was lower in ingested water temperature of 5°C (0.43 ± 0.03 g, p = 0.000). Different intake occurred with different water temperatures (respectively 4.2, 6.4, 3.1, 1.8 ml/kg). Water at 16°C induced higher intake (6.4 ml/kg) together with lower sweating (0.54 ± 0.03 g), which can result in optimum level of hydration. Conclusion- When dehydrated subjects drink water with different temperatures, there are different sweating responses together with different voluntary intakes. According to our results, consuming 16°C water, cool tap water, could be suggested in dehydration.

Introduction

During heat stress –either by heat exposure, exercise, or other physical activities and pressures– balancing and regulating thermal state, fluid state and circulation is an important challenge. Heat stress induces thermoregulatory responses including sweating, coetaneous vasodilatation and panting (in animals). These responses induce dehydration which can go beyond compensatability and impose cardiovascular strain. Therefore, when the central nervous system senses dehydration via hypovolemia and hyperosmolarity in dorsal preoptic region, it distributes inhibitory signals to effectors of the thermoregulatory responses, as if the ‘physiologic thermostat’ has been reset to a higher point and thus the body temperature rises [ 1 - 5 ]. Fluid intake (ingestion or even injection) ameliorates the dehydration and eliminates, at least partially, the inhibition of the thermoregulatory responses; so there are phenomena called ‘drinking induced thermoregulatory responses’ [ 6 - 8 ] and one of them is ‘drinking induced sweating’ . This phenomenon was introduced in 1965 [ 9 ] and has been the stuff of various studies since then. It has been reported that drink temperature influences thermoregulatory responses [ 10 - 12 ] and one study has reported that drinking induced sweating rate is lower in lower drink temperatures [ 12 ]. But the studies in question have investigated the effects of forced hydration by instructing subjects to drink specific amounts of the beverages, which could be stressful, especially in higher temperatures, inducing sympathetic activity, and thus affecting sweating in an interfering way. We hypothesize that what happens naturally is that dehydrated subjects voluntarily drink different amounts of beverages with different temperatures [ 13 - 15 ] and their sweating response would result from reflex effects of both the amount of intake [ 18 ] and beverage temperature. So we have investigated and compared sweating response following different water temperatures when subjects drank their desired amounts.

Materials and methods

Six healthy male volunteers, age 23.7 ± 0.6 years and weight 80.7 ± 5.7 kg participated in this study. The study was reviewed and approved by the Investigation Committee of Tabriz University of Medical Sciences. All subjects gave their informed written consent for their participation.

Pretest instructions included eating a light lunch, refraining from drinking any beverage several hours before the experiment, and no exercise on the day of the experiments. Before each experiment, subjects entered a chamber and rested in the sitting position for 30 min at a thermoneutral temperature (28°C, 20-28% relative humidity (rh)). Body weight was measured with light clothing. After drawing a blood sample by venopuncture as the first control sample, subjects entered another chamber (38-40°C, 20-28% rh). They performed a mild exercise (ergometer cycling) by alternating 10-min rest and 20 min exercise periods for 60 min, then exercise continued for the last 30-min period to induce a reduction in total body weight through sweating. Total heat exposure time was 120 min. During heat exposure, subjects were under constant observation for indications of any inability to tolerate the experimental conditions (e.g., elevated heart rate, nausea or confusion).

After the cessation of exercise, subjects dried their body and their forehead, and were then weighed. An indwelling cannula was inserted into a large superficial vein in the forearm to collect free-flowing blood samples. Second control blood sample was drawn through the indwelling cannula. The first control blood sample compares the plasma concentrations of sodium before and after heat exposure while second control blood sample is considered as a control to compare them before and after drinking.

Before drinking (The point of 0 min in Figure 1 ), sweat rate was measured as control, then subjects were allowed to drink water at temperatures of 5, 16, 26 and 58°C in voluntary volumes. Blood samples were drawn through the indwelling cannula at the start of drinking (0 min) and at 3, 9, 12, and 15 minutes after drinking.

Sweat rates during trials with different water temperatures shown as mean ± SD. The point of 0 min represents the time of drinking. Error bars have been moved slightly to be discriminated.

Measurements

Forehead sweat rate was chosen to represent a localized area of sweating and was measured by the weight gain of a covered filter paper disk (96 cm²) placed on the skin over the forehead. The front sides of the disks were covered with waterproof tape to prevent evaporation. The disk was left on the skin each 3 minutes. It was enough to reliably detect weight gain and for saturation of the filter paper. The weight of a filter paper disk was gauged using EK-500 G beam balance, accurate to ± 0.01 g. Body weight was measured using a Secca beam balance, accurate to ± 100 g. As a result of experimental conditions, a decrease in weight primarily reflects water loss by thermoregulatory responses, mainly sweating.

Plasma sodium concentration was determined by Eppendorf flame photometry (model EFOX 5054, Instrumentation Laboratory). Sodium concentrations were measured as milliequivalents per kilogram of water by correcting for total solids. Because sodium and its associated anions account for about 94 percent of the solute in the extracellular compartment (including plasma), plasma osmolality can be roughly approximated as:

Posm = 2.1 * Plasma sodium concentration [ 16 ].

We applied this formula for the estimation of plasma osmolality from plasma sodium concentration.

Data were analyzed by SPSS16. The difference in variables was assessed using paired t test (one measurement) and repeated measures analysis of variance (multiple measurements). Values of P<0.05 were considered statistically significant, and all data are presented as means ± SD.

Subjects became dehydrated (2.37 ± 0.08% reduction of initial body weight which accords 24.3 ± 1.2 ml/kg), therefore, and as plasma assessments showed, a highly significant (P = 0.000 and 0.001) rise occurred in Posm and then no significant change in Posm occurred up to 15 min after drinking. The Posm changes did not differ statistically on different days. Plasma osmolalities of subjects during the experiments are shown in Table 1 .

Plasma osmolality (mosmol/kg H 2 O) of subjects while they drink water with different temperatures

Sweating rates in different water temperatures are shown in Figure 1 . Maximum sweating in all temperatures occurred 3minutes after drinking, which was significantly more than the rate in the time of drinking (p = 0.000). As illustrated in Figure 1 , the 58°C trial showed higher sweat rate at this point (0.86 ± 0.04 g). Total sweat rate of the 5°C trial was statistically lower compared to the other trials, and the difference was highly significant (mean: 0.43 ± 0.03 g, P = 0.000). Sweat rate of other trials were not statically different.

We tested the effect of ingested water temperature on the extent of rehydration induced sweating response, assessing both the effect of different water temperatures and different water volumes (due to various voluntary intakes). The temperatures were defined by subjects as cold (5°C), cool (16°C), tepid (26°C) and warm (58°C). Therefore the investigation tested the effect of these senses on the sweating response. These temperatures are commonly used in daily life as refrigerated water (5°C), cool tap water (16°C), water approximately at room temperature (26°C), and water at the temperature of a hot drink e.g. coffee (58°C).

Our results indicated that sweating was aggravated significantly in all subjects within the first 3 minutes after drinking, and this thermoregulatory response varied according to ingested water temperature; being the lowest in trial of cold water (5°C) compared with other trials. The sweating rate did not differ statistically in other trials. It has been reported that compared to ingestion of warm water (38°C), cold water (0.5°C) attenuates the increments in sweat rate of the whole body and the forearm (local), but in the case of cool water this reduction was true just for the whole body sweating and not for the local one [ 12 ]. As our measurement defined the localized sweat rate (forehead), similar to the study mentioned, cold water (5°C) induced significantly lower increments in sweat rate but cool water did not. Studies have shown that when dehydrated subjects intake fluid, their core temperature declines and the ultimate temperature is not influenced by the temperature of beverage, but colder water induces faster correction of core temperature [ 10 - 12 ]. In practice, cold drink acts as a heat sink [ 17 ], thus there is lower need for heat dissipation, and less sweating. Also for warmer drinks, it has been demonstrated that although some heat load is imposed to the subject, due to appropriate thermoregulatory reflexes, the core temperature is adjusted properly [ 10 - 12 ], and one of these reflexes, as we have described here, is higher drinking-induced sweating . It seems, in Figure 1 , that the sweating rate at the peak point (3 min after drinking) is higher in 58°C water, but the difference was not statistically significant. Measuring whole body sweating and also forced hydration and higher intake of warm water would probably result in significant differences of sweat rate on this score.

The abrupt sweating response to drinking (within 3 min of the beginning of drinking), before any considerable change in plasma osmolality indicates that an osmotic signal acting on the brain via the blood osmoreceptors cannot account for the rapid onset of sweating [ 5 ]. Therefore some signals associated with the act of drinking, possibly from receptors in the oropharynx, could be involved in the recovery of thermoregulatory evaporation. These receptors appear to discriminate the temperature of received fluid as in thermoreceptors . Actually, as we sense the thermal content of what we drink, the physiological regulations of our body take it into account. Studies assessing drinking-induced thermoregulatory responses conclude that the phenomenon are not initiated by changes in plasma osmolality (Posm) or in blood volume and appear to depend upon oropharyngeal receptors [ 6 , 7 , 18 - 21 ].

The most useful application of researches about dehydration and drinking is about fluid balance in athletes [ 22 ] and soldiers [ 12 , 13 ]. Our results show 16°C water induces much more intake, meanwhile sweating response is much lower, and therefore the most efficient hydration occurs. So water temperature of 16°C could be recommended for consumption of dehydrated athletes and soldiers.

When dehydrated subjects drink water with different temperatures, the sweating response is influenced both by the water temperature and the volume of voluntary intake. The sweating response in cold water differs significantly compared to other water temperatures. Water temperature of 16°C, as in cool tap water, is the most optimum point for acquiring hydration in dehydrated athletes or other subjects.

Acknowledgements

We express our deep appreciation to our subjects who voluntarily participated in this experiment. We also make a point of our gratitude to Dr Y. Hadidi for agreeing to edit the English text of this paper. The current investigation was financially supported in the Drug Applied Research Center, Tabriz University of Medical Sciences, Tabriz, Iran.

Disclosure of conflict of interest

The authors declare that they have no conflict of interest.

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• Published: 24 November 2016

Questioning the Mpemba effect: hot water does not cool more quickly than cold

• Henry C. Burridge 1 , 2 &
• Paul F. Linden 1  

Scientific Reports volume  6 , Article number:  37665 ( 2016 ) Cite this article

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• Fluid dynamics
• Thermodynamics

The Mpemba effect is the name given to the assertion that it is quicker to cool water to a given temperature when the initial temperature is higher. This assertion seems counter-intuitive and yet references to the effect go back at least to the writings of Aristotle. Indeed, at first thought one might consider the effect to breach fundamental thermodynamic laws, but we show that this is not the case. We go on to examine the available evidence for the Mpemba effect and carry out our own experiments by cooling water in carefully controlled conditions. We conclude, somewhat sadly, that there is no evidence to support meaningful observations of the Mpemba effect.

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Introduction

The statement “hot water does not cool more quickly than cold” is vague and imprecise; hot water can be made to cool more quickly than cold by supplying more energy to the cooling of hot water, but it is under such a non-specific premise that the Mpemba effect has become an artefact in popular science. More precisely, we show that for two samples of water, identical except for a difference in initial temperature, cooled under the same conditions to a prescribed temperature (for example, the freezing temperature of water) the initially hotter sample will take longer to cool — contrary to the assertion of the Mpemba effect. Despite the non-specific nature of the effect, the Mpemba effect has been the subject of numerous articles in international broadsheet newspapers (e.g. refs 1 , 2 , 3 ) and was the focus of a competition organised in 2012 by the Royal Society of Chemistry (RSC) which received substantial publicity, for example a special report on the BBC’s Newsnight programme. As such the Mpemba effect cannot simply be disregarded. Moreover, both The Telegraph 2 and The Daily Mail 4 have reported that the scientific work of a group of chemists working in Singapore 5 provides a molecular mechanism to explain the effect. These findings, and those of ref. 6 , concern the molecular interactions and hydrogen bonding within liquid water. While the findings of these studies are of great interest in their own right, we note that small-scale molecular effects are parameterised within the thermal and fluid properties of water — properties which are known to a reasonable degree of accuracy and do indeed vary with temperature. Such findings therefore offer a route to explaining the Mpemba effect only if they result in a meaningful hysteresis in the thermal or fluid properties of water. A model exhibiting a hysteresis in the cooling of water is presented by ref. 5 which is compared to an observation of the Mpemba effect documented as part of a popular science competition organised by the RSC 7 — we include the experimental observations by ref. 7 within the data analysed in the present study. It is our aim to present an investigation of the history behind the Mpemba effect, examine the scientific evidence for it, consider the underlying physical mechanisms for the effect and determine whether the effect actually exists in any meaningful manner.

There is no clear universally accepted scientific definition of the ‘Mpemba effect’. Mpemba & Osborne 8 document the time for freezing to commence while others include the freezing process (for example see ref. 9 ). This lack of clarity is reflected by the level of discrepancies in the literature, which offers a number of different explanations. Broadly speaking, when two samples of water are cooled to the same temperature, in the same manner with the two samples being identical except for their initial temperature, and the initially hotter sample cools in less time, one can consider the Mpemba effect to have been observed. The temperature at which cooling times are compared has often been chosen to be 0 °C (or below) making careful measurements more difficult because of the phase change that occurs as water freezes.

Observations of hot water freezing in less time than cold water date back to classical science. Aristotle 10 noted that the ancient Greeks of Pontus exploited the effects when they encamped on the ice to fish, and similar observations have been repeated by Bacon 11 and Descartes 12 . More modern awareness of this apparent anomaly range from the accidental experiments of the Tanzanian school boy, Mpemba (after whom the phenomenon is popularly known 8 ), to the competition calling for explanations of the phenomenon by the RSC.

The Mpemba effect is an oft cited scientific anomaly and has been widely used in high-school and undergraduate physics projects 13 , 14 . The effect may appear anomalous since on first consideration one might regard the first law of thermodynamics to be breached. An interpretation of the first law is that the change in the internal energy of a closed system is equal to the amount of heat supplied (accounting for any work done on or by the system). Thus, in the absence of work, for a constant heat flux one naturally expects hot water to take longer to cool to freezing than cooler water. However, typically the cooling does not occur in environments which can be regarded as inducing a constant heat flux, instead most cooling occurs in (near) constant temperature environments. One example of this being the widespread domestic formation of ice-cubes within ice-trays, for which the ice-trays typically sit on a cold plate within a freezer and are cooled by the thermostatically controlled freezer which acts to maintain an approximately constant temperature. Hence, an ice-tray filled with warm water experiences a larger temperature difference and, therefore, a larger initial heat flux compared with an ice-tray filled with cooler water. Moreover, in the presence of an initially hot sample the freezer may remain on, and doing work, to drive the cooling for longer. This, however, by no means explains the Mpemba effect — the hot water must take some time to cool to the initial temperature of the cooler sample of water, after which all else being equal one would expect the further cooling of the warm sample to take the same time as the cooling of the colder sample. Hence the warm water, in total, would take longer to cool. Thus for the Mpemba effect to be observed there must be some difference in the chemistry of the samples or the physics of their cooling either initially or when at equivalent temperatures — understanding and examining the various mechanisms that might give rise to such differences remains the focus of scientific debate.

The winning entry to the RSC competition, for example, cites four factors as possibly contributing to the Mpemba effect, namely: (a) evaporation, (b) dissolved gases, (c) mixing by convective currents, and (d) supercooling 7 . No doubt all four processes affect the cooling rate of water, albeit to differing extents, and crucially their effects may be strongly coupled. For example, in two volumes of water, only differing in initial temperature and then cooled in identical conditions, one would expect that different convective currents might develop. Therefore, for significantly different initial temperatures the characteristic times that a given water particle remains in contact with an imperfection in the container or impurity within the water (e.g. dissolved gases) would vary between the two samples and so the level of supercooling required to form ice crystals would vary also. Thus it can be reasoned that the observed variations in the extent to which supercooling occurs must arise, at least in part, due to differences in convective currents and the relative levels of dissolved gases (further affected if evaporation occurs). Hence all the factors which have been proposed to individually cause the Mpemba effect may alter the extent of supercooling required to cause water to freeze.

A reasonable start to analysing the problem is to consider the process in two stages; first, cooling the water to an average temperature of 0 °C (or enthalpy equivalent thereof), and second, freezing the water to form solid ice. In so doing any effects associated with the supercooling of water are entirely contained within the second stage. We restrict our definition of the Mpemba effect to the first stage of the process, i.e. the process of cooling a sample of warm water to 0 °C in less time than it takes to cool a sample of water, which is notionally identical except that it is initially at a lower temperature, to 0 °C.

Three widely cited historical references to Mpemba-like effects in water

The cooling and freezing of water has intrigued some great scientific minds. Aristotle, Sir Francis Bacon and René Descartes have all been credited with consideration of the Mpemba effect 15 and, although this list is by no means comprehensive, it is worth documenting the precise observations of these three renowned scientists.

In his treatise on earth sciences (therein “Meteorology”) Aristotle 10 , book I part 12 is concerned with the freezing of water and contains the following text: The fact that the water has previously been warmed contributes to its freezing quickly: for so it cools sooner. Hence many people, when they want to cool hot water quickly, begin by putting it in the sun. So the inhabitants of Pontus when they encamp on the ice to fish ( they cut a hole in the ice and then fish ) pour warm water round their reeds that it may freeze the quicker, for they use the ice like lead to fix the reeds.

The reference to ice as ‘like lead’ in connection to fishing potentially raises confusion since the use of lead to weight fishing lines is widespread in traditional fishing; ice being less dense than water clearly makes it unsuitable for weighting fishing lines. It is our interpretation of the description ‘like lead to fix the reeds’ that it refers to the stiffening of the reeds by the formation of ice so that the reeds can be plunged beneath the water, hence avoiding the need to weight the reeds so that they might sink. It would, therefore, seem that Aristotle and the peoples of ancient Greece believed that warming water did make it freeze faster.

The second book (section L in ref. 11 ) of Sir Francis Bacon’s “Aphorisms on the interpretation of nature or on the kingdom of man”, includes a lengthy discourse regarding “Mans works on natural bodies” including a discussion of heat and cold; within which, while concerned with matters of medicine, he states: We should also deal with the preparation of substances to receive cold: for example, slightly warm water will freeze more easily than water which is altogether cold, and so on.

No further discussion nor details are provided. Indeed, it is not clear whether any of Bacon’s experiments actually concerned the freezing of water 16 and hence the observations leading to, or the source of, his stated belief that warm water cools faster than cold is also unclear.

In his essay on Meteorology, near the end of his first discourse, René Descartes 12 describes some experiments in which both hot and cold water are frozen within a beaker and states: we can also see by experiment that water which has been kept hot for a long time freezes faster than any other sort, because those of its parts which can least cease to bend evaporate while it is being heated.

The ‘bending’ which he describes, refers to his hypothesis for the motion of particles and although he credits evaporation for hot water freezing faster, his description of the experimental beaker indicates it has a long thin neck (which aided his observations of the expansion and contraction of water as it was heated and cooled) but would have restricted the area of the free-surface and hence evaporation. It is, therefore, unlikely that evaporation was the dominant physical effect leading to Descartes’ observation. However, like Aristotle and Bacon, Descartes does seem to document observations or convictions that can be fairly described as indicating that they would have supported assertions that the ‘Mpemba effect’ is genuine.

More recent scientific investigations of the Mpemba effect

The, now popular, adoption of the name ‘Mpemba effect’ is owed to the lack of freezer space at a Tanzanian school. While making ice-cream one pupil placed his mixture of milk and sugar in the freezer without first boiling it; another pupil, Mpemba, worried that he would not find space in the freezer and put his boiling mixture straight into the freezer without first allowing it to cool. Both pupils returned an hour and a half later to find Mpemba’s mixture had frozen while the other had not 8 . Mpemba did not brush this curious observation aside, instead he asked friends (some of whom made a living selling ice-cream and apparently exploited the time saving effects of this anomalous behaviour) and teachers to explain his observations but to no avail. Mpemba eventually asked a visiting lecturer from the University of Dar es Salaam to explain his observations. The open-minded Dr Osborne was intrigued by Mpemba’s observation and later began investigating the effect with his students, ultimately publishing a scientific paper with Mpemba on the observed effect 8 . The ‘Mpemba effect’ also appears to be widely accepted in the Northern Americas 17 . In the same month that Mpemba & Osborne 8 published their findings a chemist working in Canada 18 published an article on the very same subject. In his article, Kell describes centuries-old Canadian ‘folklore’ of wooden pails being left out to freeze, and the pails containing the hot water freezing fastest.

Certain subsequent studies report being unable to observe the effect, for example, Ahtee 19 who examined the fraction of ice formed and Hsu 9 who considered the time taken for the samples to form solid ice. However, other studies report being able to reproduce the effect, typically, using domestic style ice formation. Numerous differences exist between the experimental conditions of these various studies. These variations include: altering the nature of the cooling supplied, e.g. insulating the base 8 , 20 , submerging samples in cooling baths (for example 21 , 22 ) and radiative cooling 23 ; degassing or deionising the samples (for example see refs 14 and 24 ); the addition of dissolved gases 25 and controlling or monitoring evaporation from the sample (see ref. 23 ). Despite this wealth of experimental data, detailed analysis is typically lacking; for example, almost all studies present the absolute sample temperature rather than the sample temperature relative to the cooling environment and typically no consideration is given to the volume (mass) of water being cooled nor the geometry of the cooling vessel. A notable exception is the study of Maciejewski 17 who analysed his data in terms of nondimensional parameters, the Grashof ( Gr ), Prandtl ( Pr ) and Rayleigh ( Ra ) numbers, concluding that the key parameter is GrPr 3 and that the Mpemba effect may be driven by convection.

A number of studies have proposed physical models for the freezing of water in connection with the Mpemba effect. Katz 26 developed a freezing front model based on a ‘Stefan problem’ with a moving boundary condition which is unable to predict the effect, while the models of Kell 18 , Vynnycky and co-workers 27 , 28 consider the effects of evaporative cooling, suggesting that evaporation alone is sufficient to observe the Mpemba effect. Vynnycky and co-workers include an experimental observation of the Mpemba effect based on temperature measurements near the water surface. However, they also note that different cooling curves were obtained for samples with identical initial temperatures and that they had difficulty in repeatedly reproducing any observations of the Mpemba effect, citing uncontrollable “micro-physical processes” as the cause of such variations. Vynnycky and Kimura 29 present results from a detailed experimental examination, and a theoretical model, for the cooling of water in the context of the Mpemba effect. Their experimental results reporting the time at which solidification begins, show no evidence to support the Mpemba effect. However, their data reporting results for the time at which the layer of ice had grown to a particular thickness (therein 25 mm) “hinted at a freezing time inversion, and hence the Mpemba effect”. They attribute such effects to supercooling and they go on to suggest that their experimental data indicates that supercooling is more likely to occur with lower initial temperatures — a suggestion that would promote Mpemba-like effects in water.

Recent advances in the understanding of the bonding of water molecules have been suggested as a potential route to explaining the Mpemba effect which requires a hysteresis within the molecular interactions dependent on the initial temperature. A model accounting for the relaxation dynamics of the hydrogen bonds in liquid water has been proposed 5 in which a ‘cell’ of water is considered to comprise of the ‘bulk’ (90% of its volume) and the ‘skin’ (10% of its volume). For selected values of the ratio of thermal diffusivity between the skin and bulk (approximately a 50% difference in diffusivity), termed ‘skin supersolidity’, the model exhibits cooling akin to the Mpemba effect. The results of the model are qualitatively compared to an experimental observation of the Mpemba effect documented as part of the 2012 competition organised by the RSC 7 . Through an experimental investigation of the behaviour during cooling of tetrahydrofuran hydrate (a clathrate hydrate) 30 , it is reported that the “formation kinetics of [tetrahydrofuran] hydrate therefore might depend on its initial temperature” and suggest this is Mpemba-like behaviour. The advances in the understanding of the molecular interactions within water, and clathrate hydrates, may be of some significance in understanding the Mpemba effect. However, for this to be the case it would require that the bulk thermal and/or fluid properties of water are significantly influenced by the initial, i.e. the history of the, temperature of the water — it is not yet clear that this is the case. Should it be shown to be necessary it would, indeed, be a result of real significance; for example, standard reference tables for the properties of water would need to be updated to account for not only the current temperature but also the route to the said temperature.

Analysis of our ‘Mpemba style’ data and the data from other studies

Figure 1 plots the variation in the time t 0 , to cool samples to 0 °C, with the initial temperature from a variety of studies including our ‘Mpemba-type’ experiments. We have attempted to represent a broad selection of published experimental data regarding the Mpemba effect. We note that the data from the careful experiments of  29 reporting the time to cool to 0 °C (their Fig. 5), which exhibited no evidence of the Mpemba effect, could not be included due to difficulties in accurately obtaining data from their printed figure. Their results for the time to for the ice layer to grow to a depth of 25 mm cannot be fairly included in our analysis, since we exclude the freezing process; however, we discuss these results when drawing our conclusions. The mass of water, the geometry of its container and indeed the nature of the cooling varied widely between the different datasets and this variation is reflected in the spread of the data. From Fig. 1 it is difficult to draw any conclusions from the data, except that broadly speaking the cooling time increases with initial temperature. The only exception, which reports data (across a broad range of temperatures) that exhibit a decreasing trend in cooling time with increasing initial temperature, is that of Mpemba & Osborne 8 .

The time t 0 to cool to 0 °C, plotted against the initial temperature, T i for the ‘Mpemba-type’ experiments.

The data show a broad trend of increasing cooling time with increasing initial temperature, with the notable exception being the data of Mpemba & Osborne 8 .

Figure 2 shows the variation in the cooling time t 0 , scaled by the convective time scale, with the temperature averaged Rayleigh number from the various studies detailed in Fig. 1 (for details of the convective time scale and the temperature averaged Rayleigh number see the Methods section). Some of the studies included in Fig. 2 did not explicitly provide all the details required to scale the data, and in such cases we made reasonable estimates based on the information provided (details of which are also provided in our Methods section). The experimental conditions vary widely between the eight independent studies from which data are included within the figure. There is no obvious systematic bias for the cooling times based on the geometry of the cooling vessel, despite the aspect ratio of width to height, D/H , varying by a factor of fifteen and the depth of water being cooled varying by a factor of eight within the data — indicating that the geometry may be appropriately reflected by the length scales within the temperature averaged Rayleigh number Ra T . There is, however, an obvious bias in the cooling times based on the nature of the cooling and we broadly split the data into two datasets. The first set we describe as ‘convectively dominated’ data (marked by the solid symbols in Fig. 2 ) which broadly consists of samples where the base was insulated or cooling from below was inhibited in some manner (see the legend in Fig. 2 for details). In such cases there is no direct heat transfer between the freezer base (or cooling plate) and the sample of water is predominately cooled through the sides or top of the sample and unstable density stratifications are promoted. In such cases, the heat transfer is inhibited by the addition of insulation and hence the cooling times are typically increased, despite the increased role of convection. The second dataset we describe as ‘stably cooled’ (marked by the blue hollow symbols in Fig. 2 ) which consists of data for which the heat flux through the base of the sample is expected to have been significant (e.g. where the sample was placed directly on a cooling plate), and the cooling is expect to have promoted stably stratified sample of water (at least above 4 °C).

The data from Fig. 1 scaled to show variation of t 0 / t conv (the time to cool to 0 °C in units of the convective time scale) with Rayleigh number, Ra T  =  t cond / t conv .

The ‘stably cooled’ data are marked by blue open symbols and ‘convectively dominated’ data are marked by solid symbols. The black solid line marks the scaling for high-Rayleigh number convective cooling, (5).

We note that we scaled the data in Fig. 1 using a number of alternative definitions for the Rayleigh number, for example taking all parameters at the initial conditions or combining individually temperature-averaged parameters to form the Rayleigh number, cf. Equation (7) . The different definitions of the Rayleigh number that we tested all resulted in the various datasets exhibiting trends well approximated by (1).

Considerations of high Rayleigh number convection, in which the assumption that the heat flux is independent of the depth of the fluid, imply that

(for example, see ref. 31 ) where Nu =  Q /( κ Δ T/H ) is the Nusselt number, with κ the thermal diffusivity of the fluid, Q being proportional to the flux of heat and Δ T being a characteristic temperature difference between the fluid and the cooled surface. The time rate of change of temperature for a given sample is then proportional to the heat flux, i.e. Q , and given that Ra   ∼   β Δ TgH 3 /( κv ), from equation (2) we can write

where β and v are the coefficient of thermal expansion and the kinematic viscosity of the fluid, and A is the cooled surface area of the fluid. Hence

We note that crucially, in deriving (5) we assumed that the convection exhibited behaviour associated with that of asymptotically high Rayleigh number convection. The data investigating the Mpemba effect, plotted in Fig. 2 (obtained at initial Rayleigh numbers up to O (10 10 )), fits well with the trend predicted by (5) suggesting that the experimental data can be regarded as high Rayleigh number. As such, if the data plotted in Fig. 2 are shown not to exhibit the Mpemba effect, as indeed we go on to argue, then one must expect that data obtained at higher Rayleigh numbers would also not exhibit the Mpemba effect.

Analysis of the occurrence of the Mpemba effect

The above analysis, although informative as to the physics of cooling water, does not explicitly address when the Mpemba effect has been observed. In order to establish a single observation of the Mpemba effect, one must compare two experiments which are identical in every manner except for a difference in the initial temperatures of the water samples. One can then state that the Mpemba effect may be regarded to have been observed if the sample of water initially at the higher temperature reaches the desired cooling temperature first. To illustrate when the Mpemba effect may be reported to have been observed we consider the average rate at which heat is transferred Q from the initially hot Q H and initially cold Q C samples, where for a given sample Q  = Δ E/t 0  = ( E i  −  E 0 )/ t 0   ∝  Δ T/t 0  = ( T i  −  T 0 )/ t 0 with E i and E 0 denoting the initial and final enthalpy of the samples, respectively.

The Mpemba effect can be reported as having been observed when the inequality Q H / Q C  > Δ E H /Δ E C is satisfied, since Q H / Q C  > Δ E H /Δ E C   ⇒   t c  >  t H , where t c and t H denote the cooling time of the cold and hot samples, respectively. Figure 3(a) plots the variation in the ratio Q H / Q C with Δ E H /Δ E C (or equivalently Δ T H /Δ T C ) for the various pairs of data shown in Fig. 1 and the results of our experiments of the ‘second-type’ (see the Methods section). Figure 3(b) highlights the results of our experiments of the ‘second-type’, with an allowance for spatial variation in the temperature measurements. The relationship Q H / Q C  = Δ E H /Δ E C is marked by solid black lines within Fig. 3 . Hence, any data lying above this line may be reasonably reported as an observation of the Mpemba effect.

The variation in the ratio of mean heat transfer rates with initial temperature (or equivalently enthalpy) for pairs of otherwise identical samples of hot and cold water.

We have made efforts to contact both of the authors, Mr Erasto B. Mpemba and Dr Denis Osborne. In our attempts to contact Dr Osborne we were saddened to be informed of his death in September 2014. It seems that throughout his life, Dr Osborne continued to make extremely positive contributions to both science and politics. We have so far failed in our attempt to contact Mr Mpemba although we understand he was the principal game officer in the Tanzanian Ministry of Natural Resources and Tourism, Wildlife Division (he is now retired). We have been unable to deduce the source of any systematic error in the experimental procedure or experimental set-up of Mpemba & Osborne 8 that could feasibly have led to such extreme data being recorded.

Discussion and Conclusions

We conclude that despite our best efforts, we were not able to make observations of any physical effects which could reasonably be described as the Mpemba effect. Moreover, we have shown that all data (with the only exceptions coming from a single study) reporting to be observations of the Mpemba effect within existing studies fall just above the Mpemba effect line, i.e. the difference in the cooling times between the hot and cold samples is marginal. We have shown ( Fig. 3 ) that much of the data reporting to be observations of the Mpemba effect were from studies not reporting the height at which temperatures were measured 7 , 14 , 20 , 21 , 22 , 23 and that the conclusions drawn from these data could have been altered by simply recording temperatures without precisely monitoring the height. Indeed, all the data which lie just above the Mpemba effect line in Fig. 3 (including data for which the temperautre measurement height was carefully monitored and reported 17 , 24 , 28 ) are, by the very nature of experiments, subject to some degree of uncertainty which may ultimately affect whether the observed results are recorded as an apparent observation of the Mpemba effect or not. To be precise regarding our meaning by this statement, let us now consider the reported observations of the Mpemba effect from, arguably, the two most careful sets of experiments within the literature 28 , 29 . The study 28 does present data for one observation of the Mpemba effect but also reports obtaining “different cooling curves even if the initial temperatures were identical”, furthermore they state “[c]areful and precise experiments to probe the Mpemba effect can be tried by cooling hot and cool water in two similar containers simultaneously, but it is extremely difficult to obtain scientifically meaningful and reproducible results”. The study 29 shows a potential observation of the Mpemba effect (in the times for the ice layer to grow to a thickness of 25 mm, their figure 19) for a single pair of initial temperatures (from a possible 21 initial temperature pairings), namely the pair of initial temperatures 10 °C and 15 °C. From data recorded at a fixed height (for example, 5 mm) the samples cooling from 15 °C exhibit a mean cooling time of approximately 95 minutes while those cooling from 10 °C the mean is approximately 105 minutes — hence in taking only the mean of the data for this particular temperature pairing one could describe the Mpemba effect as having been observed. However, the variation in notionally identical experiments is significant. At the same recording height, for samples cooling from 15 °C the recorded time spans the range 95–105 minutes while for samples cooling from 10 °C the recorded time spans the range 100–110 minutes. As such, the variation in notionally identical experiments is at least large enough to render any conclusion that the Mpemba effect has been observed in the mean data as highly questionable, and so this cannot be regarded as a meaningful observation of the effect.

The only exception to our above statements, the single study in which some data is reported that shows dramatically warmer samples cooling in substantially less time (i.e. data points that are far above the line Q H / Qc  = Δ T H /Δ Tc in Fig. 3 ) is the data reported by Mpemba & Osborne 8 . If these data could be reproduced in a repeatable fashion and the underlying mechanism understood then it would be of real significance to a multitude of applications relying on the transfer of heat. For example ref. 8 , report cooling a sample from 90 °C to freezing point in 30 minutes while a sample at 20 °C took 100 minutes to cool to freezing point, i.e. the average heat transfer rate during cooling was observed to increase by a factor of 15 by simply increasing the initial temperature of the sample. With the use of modern heat-exchangers such a result would have profound implications for the efficiency of any number of common industrial processes. However, over the subsequent 47 years, numerous studies have attempted to demonstrate the ‘effect’ on a scale comparable to that reported by Mpemba & Osborne. Despite these efforts, including our own, none have succeeded. We must therefore assert that this particular dataset may be fundamentally flawed and thus, unless it can be shown to be reproducible and repeatable, this dataset must be regarded as erroneous.

We must highlight that our primary focus has been to examine the cooling of water to the freezing point (observed under standard atmospheric conditions), i.e. an enthalpy equivalent of 0 °C. In so doing we have been able to show that much of the published experimental data exhibit a scaling behaviour associated with asymptotically high Rayleigh number convection. Thus one cannot expect to observe samples of hot water cooling to 0 °C faster than colder samples by carrying out experiments at higher Rayleigh numbers. Under our definition of the Mpemba effect, akin to the definition in the ‘original’ paper by Mpemba & Osborne 8 (in which they documented “the time for water to start freezing”) we are forced to conclude that the ‘Mpemba effect’ is not a genuine physical effect and is a scientific fallacy.

If one extends the definition of the Mpemba effect to include the freezing process then one can examine the experimental evidence presented by a number of scientific studies which have sought to include the effect of freezing, e.g. refs 9 , 21 , 22 , 28 and 29 . The freezing of water to ice is a thermodynamically intensive process. For example, the energy required to change the phase of a given mass of water at 0 °C, into ice at 0 °C is approximately equal to the energy required to cool the same mass of water from 80 °C to 0 °C in the liquid state. Intuition, therefore, guides one to expect the time to completely freeze a sample of water could depend only weakly on the initial water temperature. Moreover, freezing is initiated by a nucleation process and as such it is susceptible to variations at the smallest physical scales, e.g. imperfections in the surface of containers or impurities within the water samples — the physical scales of which are extremely difficult to control in even the most precise experiments. Such intuition is entirely born out in the experimental evidence, with no single study able to report repeatable observations of the Mpemba effect when the freezing process is included 9 , 21 , 22 , 28 , 29 . Experimental observations of a particular example of warm water cooling and freezing in less time than a particular example of initially cooler water have been made — what is yet to be reported is any experimental evidence that samples of water can be consistently cooled and frozen in less time (the time being less by a repeatable and statistically significant amount) by simply initiating the cooling from a higher temperature. As such we can conclude that even with the freezing process included within the definition of the Mpemba effect, the Mpemba effect is not observable in any meaningful way.

We are not gladdened by such a conclusion, indeed quite the opposite. The Mpemba effect has proved to be a wonderful puzzle with which to engage and interest people of all ages and backgrounds in the pursuit of scientific understanding. However, the role of scientists is to objectively examine facts and further knowledge by reporting the conclusions, and as such we feel compelled to disseminate our findings. Finally, we want to give hope to the educators who may have previously relied on the Mpemba effect as a useful tool with which to inspire their students. There are numerous genuine artefacts of science which can continue to provide such inspiration. For example, try filling two identical glasses, one with fresh water and one with salty water (both of equal temperature), place a few cubes of ice in each and observe which melts first — many students will be surprised by the result, finding it counter to their experience and intuition. Equally one could try placing a thin sheet of card on top of a glass of water, turn the glass upside down and then remove your hand from the card — watch as the atmospheric air pressure allows the water to be held in the glass — repeat this, replacing the card by just a rigid gauze with holes of up to a few millimetres and still the water will be held within the glass 32 . We hope that these examples serve to act as catalysts for those seeking other examples of genuine science and that these help to inspire scientific interest within future generations.

Dimensional considerations

The physics of cooling water within a regular three dimensional vessel, all surfaces of which are held at a uniform temperature, can be described in the terms of a thermal buoyancy potential g  ′, three length scales L x , L y , L Z , and the kinematic viscosity v and thermal diffusivity κ for water. It is common in both the practical cooling of water (e.g. the domestic formation of ice-cubes) and the experiments reported in the literature that the two horizontal length scales are of similar magnitude, and herein we assume L x  ≈  L y  =  D (where D is a characteristic width or diameter of the cooling vessel) and denote the vertical length scale L z  =  H , where H is the depth of water being cooled. As such, the problem can be described by three non-dimensional variables and it is appropriate to select the Grashof number, G r  =  g  ′ H 3 / v 2 (cf. the Reynolds number for inertial flows); Prandtl number, P r  =  v/κ ; and the aspect ratio D/H . These three non-dimensional parameters can all be combined within a Rayleigh number for the cooling.

Within a fluid heat may be transported either by advection (convection) or thermal diffusion (conduction); the Rayleigh number can be interpreted as a ratio of the time scales for conduction, t cond , and convection, t conv . Suitable length scales for the Rayleigh number can be identified by consideration of these time scales. Conduction, or thermal diffusion, acts to distribute heat in all directions and so t cond   ∝  L 2 / κ   ∝  min( H 2 , D 2 )/ κ , as conduction will predominantly occur over the shortest length scale of the cooling vessel (since this must be the direction of the strongest temperature gradients). Convection is generated when thermal effects give rise to gravitationally unstable distributions of density and so it is appropriate to consider only the vertical length scale H in the convective time scale. Hence an appropriate Rayleigh number for the cooling is Ra  =  g  ′ H 3 min(1, D/H ) 2 /( κv ) = G r  × P r  × min(1, D/H ) 2 .

A suitable representation for the thermal buoyancy potential g ′ is worthy of consideration. It is natural to define the buoyancy as the gravitational acceleration scaled by the normalised density difference between two relevant fluids. One might argue that it is appropriate to take the difference between the density of water at the initial temperature and at some other temperature, e.g. 0 °C (see the definition of the Grashof number in ref. 17 ); however, so doing highlights two particular issues. First, the buoyancy can only ever be an indicative scale of the driving cooling potential since one would not expect that, within a given sample, water still at the initial temperature would directly interact with water at 0 °C. Second, such a definition does not account for the differences in the cooling times that one would expect if the same sample were placed in a cooling environment held at 0 °C or in an environment at a far lower temperature, e.g. −50 °C. Consequently, it is more appropriate to accept g  ′ as an indicative scale for the driving cooling potential and, as such, define the thermal buoyancy potential by

where T f is the temperature of the cooling environment, T is the characteristic instantaneous temperature of the water being cooled, and β  =  β(T ) is the coefficient of thermal expansion for water at the temperature T . Given the density maximum of water at about 4 °C, over the relevant temperature range, 0 °C ≤  T  ≤ 100 °C, the coefficient of thermal expansion and hence the buoyancy will change sign if a given sample cools below 4 °C. Furthermore, both the kinematic viscosity and thermal diffusivity of water vary with temperature, in the case of the viscosity by factor of six over the temperature range of cooling 33 . In order to account for varying physical properties of water as it cools we consider a temperature averaged Rayleigh number, which incorporates values of β(T ) calculated from the variations in the density of water with temperature from 34 , values of κ(T ) calculated from the density 34 , thermal conductivity 35 and specific heat capacity 36 of water, and v(T ) taken from 33 .

We define the temperature averaged Rayleigh number Ra T , for water cooling from an initial temperature T i to a final temperature T 0 , as

the time scale for conduction as

and maintaining the Rayleigh number as the ratio of times scales for conduction and convection gives the time scale for convection as

Experiments

We carried out two types of experiments: the first was designed to mimic the experiments of Mpemba & Osborne 8 , and the second was designed to avoid any formation of ice, and thereby avoid issues associated with phase change, by keeping the cooling plate at 0.3 °C. For both sets of experiments temperatures were digitally recorded and stored using up to eight thermocouples, with a data-logger connected to a computer running LabVIEW. The thermocouples were calibrated using a refrigerated circulator providing temperatures accurate to within 0.01 °C.

In the first set of experiments, our ‘Mpemba style’ experiments, three samples of water each of mass 400 g (measured to an accuracy of within 0.1%) were placed within glass beakers of approximate diameter D  = 9.0 cm; filling the beaker with a water depth of approximately H  = 6.3 cm. All the samples of water were boiled, to remove some of the dissolved gases, and then left to cool for varying amounts of time so that the three samples were at different initial temperatures T i  = {21.8, 57.3, 84.7} °C, respectively. The samples were then placed on a 5 cm thick sheet of expanded polystyrene sitting inside a standard domestic chest-freezer. All three samples were placed inside the freezer at the same time in order to ensure that the samples were exposed to the same cooling from the thermostatically controlled chest-freezer. The thermostat on the freezer was set to −18 °C. On placing the samples into the freezer the ambient air temperature within was observed to rise but, after approximately 15 minutes, the freezer temperature had cooled back down to −18 °C. Subsequently, the freezer temperature gradually increased (due to the imperfect insulation of the freezer) until it reached approximately −15 °C at which point the thermostat activated the freezer refrigeration unit and the freezer temperature was cooled once again to −18 °C. This periodic cooling and warming of the freezer, in the temperature range −18 °C ≤  T f  ≤ −15 °C, continued throughout the experiment. Prior to being placed inside the freezer a thermocouple was located and carefully fixed centrally within each sample of water. The temperature of the thermocouples within each water samples were recorded at 1 second intervals throughout the experiment and the time taken for the temperature of each sample to first fall to 0 °C denoted as t 0  = {6397, 9504, 10812}s, respectively.

In the second set of experiments we filled a perspex tank, of horizontal cross-section 20 cm × 20 cm, with fresh water to a depth of 10 cm. Expanded polystyrene sheets (5 cm thick) were attached to the base and the four sides of the tank to act as insulation. The water was then cooled by carefully suspending a brass cooling plate such that the cooling plate was in direct contact with the upper surface of the water. The cooling plate had been carefully machined so that it contained a continuous channel, entirely housed within the plate except for openings at two of its corners which were connected to insulated pipes. The channel meandered within the plate so that by passing ethylene glycol solutions (continuously cooled by a Thermo Haake refrigerated circulator, Phoenix-line, model PII-C41P) through the channel the entire plate was held at an approximately uniform and constant temperature. The refrigerated circulator included a reservoir containing 15 000 cm 3 of ethylene glycol solution cooled by a refrigeration cycle of power of approximately 1 kW. The circulator passed the solution through insulated pipes and around the machined channel (of cross-section less than 1 cm 2 ) at approximately 400 cm 3 /s.

In these experiments of ‘the second type’, to avoid the formation of ice the cooling plate was held at a temperature of 0.3 °C. Prior to our experiments, seven T-type thermocouples (Omega, HSTC-TT-TI-24 S-5 M) were carefully positioned and clamped in place at specified heights within the tank. The thermocouples had been calibrated, to an accuracy of 0.01 °C using the refrigerated circulator, over a temperature range of −20 °C and 100 °C. Throughout each experiment, temperatures were recorded from each of the thermocouples at a frequency of 1 Hz using a National Instruments 9213 measurement system and digitally stored in csv files for later analysis within Matlab. The characteristic temperature of the water at any instant was determined by spatially averaging the temperatures recorded at the thermocouples positioned at the carefully measured heights. Experiments were run until the water within the tank reached a steady temperature which took approximately one day to occur. Since in these experiments the temperature of the samples were intended to remain above freezing point, we defined the cooling time based on the time taken to cool to 4 °C (this temperature being selected to maximise the role of convection), the times to cool to this temperature were in the range 12–17 hrs. It is important to note that since our experiments of ‘the second type’ were deliberately never cooled to 0 °C data from these experiments cannot be included in Figs 1 or 2 , and is only included in Fig. 3 in which only the relative cooling times of hot and cold samples are compared. As such, our results are not affected by the choice (in our experiments of the second-type) to measure the time to cool to 4 °C — identical trends in our data are observed with any reasonable variation in this choice of the target temperature. During these experiments the initial temperature T i of the fresh water was systematically varied between experiments in the range 18 °C ≤  T i  ≤ 75 °C.

Assumptions made in sourcing the data of other studies

In order to be able to scale the data published in other studies it was necessary to have sufficient information in order to be able to calculate the Rayleigh number, i.e. T i , T f , H and D , see equation (7) . For certain studies 9 , 17 , 20 , 28 the required information was explicitly provided. Table 1 provides details of information not explicitly provided by the remaining studies for which we report data. In each case, details of our assumptions and the data on which these assumptions was based is provided. It should be noted that the sensitivity of our results to the assumptions detailed in the table is by no means dramatic. Indeed, any reasonable variations to our assumptions does not alter any of our findings.

Additional Information

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Acknowledgements

HCB gratefully acknowledges Dr Nick Daish for his encouragement to complete and report this study. In addition, the authors would like to thank Prof. Grae Worster for his insight and advice, and Prof. Graham Hughes for his comments on the high Rayleigh number scaling. The authors further acknowledge the skills and expertise provided by the technical staff at the G. K. Batchelor laboratory. This work was supported, in part, by the Leverhulme Trust Research Programme Grant RP2013-SL-008, and by the Royal Society.

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H.C.B. carried out the experiments, wrote the main manuscript text and prepared the Figures. P.F.L. reviewed and edited the manuscript.

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Burridge, H., Linden, P. Questioning the Mpemba effect: hot water does not cool more quickly than cold. Sci Rep 6 , 37665 (2016). https://doi.org/10.1038/srep37665

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Barry M Popkin, Kristen E D'Anci, Irwin H Rosenberg, Water, hydration, and health, Nutrition Reviews , Volume 68, Issue 8, 1 August 2010, Pages 439–458, https://doi.org/10.1111/j.1753-4887.2010.00304.x

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This review examines the current knowledge of water intake as it pertains to human health, including overall patterns of intake and some factors linked with intake, the complex mechanisms behind water homeostasis, and the effects of variation in water intake on health and energy intake, weight, and human performance and functioning. Water represents a critical nutrient, the absence of which will be lethal within days. Water's importance for the prevention of nutrition-related noncommunicable diseases has received more attention recently because of the shift toward consumption of large proportions of fluids as caloric beverages. Despite this focus, there are major gaps in knowledge related to the measurement of total fluid intake and hydration status at the population level; there are also few longer-term systematic interventions and no published randomized, controlled longer-term trials. This review provides suggestions for ways to examine water requirements and encourages more dialogue on this important topic.

Water is essential for life. From the time that primeval species ventured from the oceans to live on land, a major key to survival has been the prevention of dehydration. The critical adaptations cross an array of species, including man. Without water, humans can survive only for days. Water comprises from 75% body weight in infants to 55% in the elderly and is essential for cellular homeostasis and life. 1 Nevertheless, there are many unanswered questions about this most essential component of our body and our diet. This review attempts to provide some sense of our current knowledge of water, including overall patterns of intake and some factors linked with intake, the complex mechanisms behind water homeostasis, the effects of variation in water intake on health and energy intake, weight, and human performance and functioning.

Recent statements on water requirements have been based on retrospective recall of water intake from food and beverages among healthy, noninstitutionalized individuals. Provided here are examples of water intake assessment in populations to clarify the need for experimental studies. Beyond these circumstances of dehydration, it is not fully understood how hydration affects health and well-being, even the impact of water intakes on chronic diseases. Recently, Jéquier and Constant 2 addressed this question based on human physiology, but more knowledge is required about the extent to which water intake might be important for disease prevention and health promotion.

As noted later in the text, few countries have developed water requirements and those that exist are based on weak population-level measures of water intake and urine osmolality. 3 , 4 The European Food Safety Authority (EFSA) was recently asked to revise existing recommended intakes of essential substances with a physiological effect, including water since this nutrient is essential for life and health. 5

The US Dietary Recommendations for water are based on median water intakes with no use of measurements of the dehydration status of the population to assist. One-time collection of blood samples for the analysis of serum osmolality has been used by the National Health and Nutrition Examination Survey program. At the population level, there is no accepted method of assessing hydration status, and one measure some scholars use, hypertonicity, is not even linked with hydration in the same direction for all age groups. 6 Urine indices are used often but these reflect the recent volume of fluid consumed rather than a state of hydration. 7 Many scholars use urine osmolality to measure recent hydration status. 8 , – 12 Deuterium dilution techniques (isotopic dilution with D 2 O, or deuterium oxide) allow measurement of total body water but not water balance status. 13 Currently, there are no completely adequate biomarkers to measure hydration status at the population level.

In discussing water, the focus is first and foremost on all types of water, whether it be soft or hard, spring or well, carbonated or distilled. Furthermore, water is not only consumed directly as a beverage; it is also obtained from food and to a very small extent from oxidation of macronutrients (metabolic water). The proportion of water that comes from beverages and food varies according to the proportion of fruits and vegetables in the diet. The ranges of water content in various foods are presented in Table 1 . In the United States it is estimated that about 22% of water intake comes from food while the percentages are much higher in European countries, particularly a country like Greece with its higher intake of fruits and vegetables, or in South Korea. 3 , – 15 The only in-depth study performed in the United States of water use and water intrinsic to food found a 20.7% contribution from food water; 16 , 17 however, as shown below, this research was dependent on poor overall assessment of water intake.

Ranges of water content for selected foods.

Data from the USDA national nutrient database for standard reference, release 21, as provided in Altman. 126

This review considers water requirements in the context of recent efforts to assess water intake in US populations. The relationship between water and calorie intake is explored both for insights into the possible displacement of calories from sweetened beverages by water and to examine the possibility that water requirements would be better expressed in relation to calorie/energy requirements with the dependence of the latter on age, size, gender, and physical activity level. Current understanding of the exquisitely complex and sensitive system that protects land animals against dehydration is covered and commentary is provided on the complications of acute and chronic dehydration in man, against which a better expression of water requirements might complement the physiological control of thirst. Indeed, the fine intrinsic regulation of hydration and water intake in individuals mitigates prevalent underhydration in populations and its effects on function and disease.

Regulation of fluid intake

To prevent dehydration, reptiles, birds, vertebrates, and all land animals have evolved an exquisitely sensitive network of physiological controls to maintain body water and fluid intake by thirst. Humans may drink for various reasons, particularly for hedonic ones, but drinking is most often due to water deficiency that triggers the so-called regulatory or physiological thirst. The mechanism of thirst is quite well understood today and the reason nonregulatory drinking is often encountered is related to the large capacity of the kidneys to rapidly eliminate excesses of water or to reduce urine secretion to temporarily economize on water. 1 But this excretory process can only postpone the necessity of drinking or of ceasing to drink an excess of water. Nonregulatory drinking is often confusing, particularly in wealthy societies that have highly palatable drinks or fluids that contain other substances the drinker seeks. The most common of these are sweeteners or alcohol for which water is used as a vehicle. Drinking these beverages is not due to excessive thirst or hyperdipsia, as can be shown by offering pure water to individuals instead and finding out that the same drinker is in fact hypodipsic (characterized by abnormally diminished thirst). 1

Fluid balance of the two compartments

Maintaining a constant water and mineral balance requires the coordination of sensitive detectors at different sites in the body linked by neural pathways with integrative centers in the brain that process this information. These centers are also sensitive to humoral factors (neurohormones) produced for the adjustment of diuresis, natriuresis, and blood pressure (angiotensin mineralocorticoids, vasopressin, atrial natriuretic factor). Instructions from the integrative centers to the “executive organs” (kidney, sweat glands, and salivary glands) and to the part of the brain responsible for corrective actions such as drinking are conveyed by certain nerves in addition to the above-mentioned substances. 1

Most of the components of fluid balance are controlled by homeostatic mechanisms responding to the state of body water. These mechanisms are sensitive and precise, and are activated with deficits or excesses of water amounting to only a few hundred milliliters. A water deficit produces an increase in the ionic concentration of the extracellular compartment, which takes water from the intracellular compartment causing cells to shrink. This shrinkage is detected by two types of brain sensors, one controlling drinking and the other controlling the excretion of urine by sending a message to the kidneys, mainly via the antidiuretic hormone vasopressin to produce a smaller volume of more concentrated urine. 18 When the body contains an excess of water, the reverse processes occur: the lower ionic concentration of body fluids allows more water to reach the intracellular compartment. The cells imbibe, drinking is inhibited, and the kidneys excrete more water.

The kidneys thus play a key role in regulating fluid balance. As discussed later, the kidneys function more efficiently in the presence of an abundant water supply. If the kidneys economize on water and produce more concentrated urine, they expend a greater amount of energy and incur more wear on their tissues. This is especially likely to occur when the kidneys are under stress, e.g., when the diet contains excessive amounts of salt or toxic substances that need to be eliminated. Consequently, drinking a sufficient amount of water helps protect this vital organ.

Regulatory drinking

Most drinking occurs in response to signals of water deficit. Apart from urinary excretion, the other main fluid regulatory process is drinking, which is mediated through the sensation of thirst. There are two distinct mechanisms of physiological thirst: the intracellular and the extracellular mechanisms. When water alone is lost, ionic concentration increases. As a result, the intracellular space yields some of its water to the extracellular compartment. Once again, the resulting shrinkage of cells is detected by brain receptors that send hormonal messages to induce drinking. This association with receptors that govern extracellular volume is accompanied by an enhancement of appetite for salt. Thus, people who have been sweating copiously prefer drinks that are relatively rich in Na+ salts rather than pure water. When excessive sweating is experienced, it is also important to supplement drinks with additional salt.

The brain's decision to start or stop drinking and to choose the appropriate drink is made before the ingested fluid can reach the intra- and extracellular compartments. The taste buds in the mouth send messages to the brain about the nature, and especially the salt content, of the ingested fluid, and neuronal responses are triggered as if the incoming water had already reached the bloodstream. These are the so-called anticipatory reflexes: they cannot be entirely “cephalic reflexes” because they arise from the gut as well as the mouth. 1

The anterior hypothalamus and pre-optic area are equipped with osmoreceptors related to drinking. Neurons in these regions show enhanced firing when the inner milieu gets hyperosmotic. Their firing decreases when water is loaded in the carotid artery that irrigates the neurons. It is remarkable that the same decrease in firing in the same neurons takes place when the water load is applied on the tongue instead of being injected into the carotid artery. This anticipatory drop in firing is due to communication from neural pathways that depart from the mouth and converge onto neurons that simultaneously sense the blood's inner milieu.

Nonregulatory drinking

Although everyone experiences thirst from time to time, it plays little role in the day-to-day control of water intake in healthy people living in temperate climates. In these regions, people generally consume fluids not to quench thirst, but as components of everyday foods (e.g., soup, milk), as beverages used as mild stimulants (tea, coffee), and for pure pleasure. A common example is alcohol consumption, which can increase individual pleasure and stimulate social interaction. Drinks are also consumed for their energy content, as in soft drinks and milk, and are used in warm weather for cooling and in cold weather for warming. Such drinking seems to also be mediated through the taste buds, which communicate with the brain in a kind of “reward system”, the mechanisms of which are just beginning to be understood. This bias in the way human beings rehydrate themselves may be advantageous because it allows water losses to be replaced before thirst-producing dehydration takes place. Unfortunately, this bias also carries some disadvantages. Drinking fluids other than water can contribute to an intake of caloric nutrients in excess of requirements, or in alcohol consumption that, in some people, may insidiously bring about dependence. For example, total fluid intake increased from 79 fluid ounces in 1989 to 100 fluid ounces in 2002 among US adults, with the difference representing intake of caloric beverages. 19

Effects of aging on fluid intake regulation

The thirst and fluid ingestion responses of older persons to a number of stimuli have been compared to those of younger persons. 20 Following water deprivation, older individuals are less thirsty and drink less fluid compared to younger persons. 21 , 22 The decrease in fluid consumption is predominantly due to a decrease in thirst, as the relationship between thirst and fluid intake is the same in young and old persons. Older persons drink insufficient amounts of water following fluid deprivation to replenish their body water deficit. 23 When dehydrated older persons are offered a highly palatable selection of drinks, this also fails to result in increased fluid intake. 23 The effects of increased thirst in response to an osmotic load have yielded variable responses, with one group reporting reduced osmotic thirst in older individuals 24 and one failing to find a difference. In a third study, young individuals ingested almost twice as much fluid as old persons, even though the older subjects had a much higher serum osmolality. 25

Overall, these studies support small changes in the regulation of thirst and fluid intake with aging. Defects in both osmoreceptors and baroreceptors appear to exist as do changes in the central regulatory mechanisms mediated by opioid receptors. 26 Because the elderly have low water reserves, it may be prudent for them to learn to drink regularly when not thirsty and to moderately increase their salt intake when they sweat. Better education on these principles may help prevent sudden hypotension and stroke or abnormal fatigue, which can lead to a vicious circle and eventually hospitalization.

Thermoregulation

Hydration status is critical to the body's process of temperature control. Body water loss through sweat is an important cooling mechanism in hot climates and in periods of physical activity. Sweat production is dependent upon environmental temperature and humidity, activity levels, and type of clothing worn. Water losses via skin (both insensible perspiration and sweating) can range from 0.3 L/h in sedentary conditions to 2.0 L/h in high activity in the heat, and intake requirements range from 2.5 to just over 3 L/day in adults under normal conditions, and can reach 6 L/day with high extremes of heat and activity. 27 , 28 Evaporation of sweat from the body results in cooling of the skin. However, if sweat loss is not compensated for with fluid intake, especially during vigorous physical activity, a hypohydrated state can occur with concomitant increases in core body temperature. Hypohydration from sweating results in a loss of electrolytes, as well as a reduction in plasma volume, and this can lead to increased plasma osmolality. During this state of reduced plasma volume and increased plasma osmolality, sweat output becomes insufficient to offset increases in core temperature. When fluids are given to maintain euhydration, sweating remains an effective compensation for increased core temperatures. With repeated exposure to hot environments, the body adapts to heat stress and cardiac output and stroke volume return to normal, sodium loss is conserved, and the risk for heat-stress-related illness is reduced. 29 Increasing water intake during this process of heat acclimatization will not shorten the time needed to adapt to the heat, but mild dehydration during this time may be of concern and is associated with elevations in cortisol, increased sweating, and electrolyte imbalances. 29

Children and the elderly have differing responses to ambient temperature and different thermoregulatory concerns than healthy adults. Children in warm climates may be more susceptible to heat illness than adults due to their greater surface area to body mass ratio, lower rate of sweating, and slower rate of acclimatization to heat. 30 , 31 Children may respond to hypohydration during activity with a higher relative increase in core temperature than adults, 32 and with a lower propensity to sweat, thus losing some of the benefits of evaporative cooling. However, it has been argued that children can dissipate a greater proportion of body heat via dry heat loss, and the concomitant lack of sweating provides a beneficial means of conserving water under heat stress. 30 Elders, in response to cold stress, show impairments in thermoregulatory vasoconstriction, and body water is shunted from plasma into the interstitial and intracellular compartments. 33 , 34 With respect to heat stress, water lost through sweating decreases the water content of plasma, and the elderly are less able to compensate for increased blood viscosity. 33 Not only do they have a physiological hypodipsia, but this can be exaggerated by central nervous system disease 35 and by dementia. 36 In addition, illness and limitations in daily living activities can further limit fluid intake. When reduced fluid intake is coupled with advancing age, there is a decrease in total body water. Older individuals have impaired renal fluid conservation mechanisms and, as noted above, have impaired responses to heat and cold stress. 33 , 34 All of these factors contribute to an increased risk of hypohydration and dehydration in the elderly.

With regard to physiology, the role of water in health is generally characterized in terms of deviations from an ideal hydrated state, generally in comparison to dehydration. The concept of dehydration encompasses both the process of losing body water and the state of dehydration. Much of the research on water and physical or mental functioning compares a euhydrated state, usually achieved by provision of water sufficient to overcome water loss, to a dehydrated state, which is achieved via withholding of fluids over time and during periods of heat stress or high activity. In general, provision of water is beneficial in individuals with a water deficit, but little research supports the notion that additional water in adequately hydrated individuals confers any benefit.

Physical performance

The role of water and hydration in physical activity, particularly in athletes and in the military, has been of considerable interest and is well-described in the scientific literature. 37 , – 39 During challenging athletic events, it is not uncommon for athletes to lose 6–10% of body weight through sweat, thus leading to dehydration if fluids have not been replenished. However, decrements in the physical performance of athletes have been observed under much lower levels of dehydration, i.e., as little as 2%. 38 Under relatively mild levels of dehydration, individuals engaging in rigorous physical activity will experience decrements in performance related to reduced endurance, increased fatigue, altered thermoregulatory capability, reduced motivation, and increased perceived effort. 40 , 41 Rehydration can reverse these deficits and reduce the oxidative stress induced by exercise and dehydration. 42 Hypohydration appears to have a more significant impact on high-intensity and endurance activity, such as tennis 43 and long-distance running, 44 than on anaerobic activities, 45 such as weight lifting, or on shorter-duration activities, such as rowing. 46

During exercise, individuals may not hydrate adequately when allowed to drink according to thirst. 32 After periods of physical exertion, voluntary fluid intake may be inadequate to offset fluid deficits. 1 Thus, mild-to-moderate dehydration can persist for some hours after the conclusion of physical activity. Research performed on athletes suggests that, principally at the beginning of the training season, they are at particular risk for dehydration due to lack of acclimatization to weather conditions or suddenly increased activity levels. 47 , 48 A number of studies show that performance in temperate and hot climates is affected to a greater degree than performance in cold temperatures. 41 , – 50 Exercise in hot conditions with inadequate fluid replacement is associated with hyperthermia, reduced stroke volume and cardiac output, decreases in blood pressure, and reduced blood flow to muscle. 51

During exercise, children may be at greater risk for voluntary dehydration. Children may not recognize the need to replace lost fluids, and both children as well as coaches need specific guidelines for fluid intake. 52 Additionally, children may require more time to acclimate to increases in environmental temperature than adults. 30 , 31 Recommendations are for child athletes or children in hot climates to begin athletic activities in a well-hydrated state and to drink fluids over and above the thirst threshold.

Cognitive performance

Water, or its lack (dehydration), can influence cognition. Mild levels of dehydration can produce disruptions in mood and cognitive functioning. This may be of special concern in the very young, very old, those in hot climates, and those engaging in vigorous exercise. Mild dehydration produces alterations in a number of important aspects of cognitive function such as concentration, alertness, and short-term memory in children (10–12 y), 32 young adults (18–25 y), 53 , – 56 and the oldest adults (50–82 y). 57 As with physical functioning, mild-to-moderate levels of dehydration can impair performance on tasks such as short-term memory, perceptual discrimination, arithmetic ability, visuomotor tracking, and psychomotor skills. 53 , – 56 However, mild dehydration does not appear to alter cognitive functioning in a consistent manner. 53 , – 58 In some cases, cognitive performance was not significantly affected in ranges from 2% to 2.6% dehydration. 56 , 58 Comparing across studies, performance on similar cognitive tests was divergent under dehydration conditions. 54 , 56 In studies conducted by Cian et al., 53 , 54 participants were dehydrated to approximately 2.8% either through heat exposure or treadmill exercise. In both studies, performance was impaired on tasks examining visual perception, short-term memory, and psychomotor ability. In a series of studies using exercise in conjunction with water restriction as a means of producing dehydration, D'Anci et al. 56 observed only mild decrements in cognitive performance in healthy young men and women athletes. In these experiments, the only consistent effect of mild dehydration was significant elevations of subjective mood score, including fatigue, confusion, anger, and vigor. Finally, in a study using water deprivation alone over a 24-h period, no significant decreases in cognitive performance were seen with 2.6% dehydration. 58 It is therefore possible that heat stress may play a critical role in the effects of dehydration on cognitive performance.

Reintroduction of fluids under conditions of mild dehydration can reasonably be expected to reverse dehydration-induced cognitive deficits. Few studies have examined how fluid reintroduction may alleviate the negative effects of dehydration on cognitive performance and mood. One study 59 examined how water ingestion affected arousal and cognitive performance in young people following a period of 12-h water restriction. While cognitive performance was not affected by either water restriction or water consumption, water ingestion affected self-reported arousal. Participants reported increased alertness as a function of water intake. Rogers et al. 60 observed a similar increase in alertness following water ingestion in both high- and low-thirst participants. Water ingestion, however, had opposite effects on cognitive performance as a function of thirst. High-thirst participants' performance on a cognitively demanding task improved following water ingestion, but low-thirst participants' performance declined. In summary, hydration status consistently affected self-reported alertness, but effects on cognition were less consistent.

Several recent studies have examined the utility of providing water to school children on attentiveness and cognitive functioning in children. 61 , – 63 In these experiments, children were not fluid restricted prior to cognitive testing, but were allowed to drink as usual. Children were then provided with a drink or no drink 20–45 min before the cognitive test sessions. In the absence of fluid restriction and without physiological measures of hydration status, the children in these studies should not be classified as dehydrated. Subjective measures of thirst were reduced in children given water, 62 and voluntary water intake in children varied from 57 mL to 250 mL. In these studies, as in the studies in adults, the findings were divergent and relatively modest. In the research led by Edmonds et al., 61 , 62 children in the groups given water showed improvements in visual attention. However, effects on visual memory were less consistent, with one study showing no effects of drinking water on a spot-the-difference task in 6–7-year-old children 61 and the other showing a significant improvement in a similar task in 7–9-year-old children. 62 In the research described by Benton and Burgess, 63 memory performance was improved by provision of water but sustained attention was not altered with provision of water in the same children.

Taken together, these studies indicate that low-to-moderate dehydration may alter cognitive performance. Rather than indicating that the effects of hydration or water ingestion on cognition are contradictory, many of the studies differ significantly in methodology and in measurement of cognitive behaviors. These variances in methodology underscore the importance of consistency when examining relatively subtle chances in overall cognitive performance. However, in those studies in which dehydration was induced, most combined heat and exercise; this makes it difficult to disentangle the effects of dehydration on cognitive performance in temperate conditions from the effects of heat and exercise. Additionally, relatively little is known about the mechanism of mild dehydration's effects on mental performance. It has been proposed that mild dehydration acts as a physiological stressor that competes with and draws attention from cognitive processes. 64 However, research on this hypothesis is limited and merits further exploration.

Dehydration and delirium

Dehydration is a risk factor for delirium and for delirium presenting as dementia in the elderly and in the very ill. 65 , – 67 Recent work shows that dehydration is one of several predisposing factors for confusion observed in long-term-care residents 67 ; however, in this study, daily water intake was used as a proxy measure for dehydration rather than other, more direct clinical assessments such as urine or plasma osmolality. Older people have been reported as having reduced thirst and hypodipsia relative to younger people. In addition, fluid intake and maintenance of water balance can be complicated by factors such as disease, dementia, incontinence, renal insufficiency, restricted mobility, and drug side effects. In response to primary dehydration, older people have less thirst sensation and reduced fluid intakes in comparison to younger people. However, in response to heat stress, while older people still display a reduced thirst threshold, they do ingest comparable amounts of fluid to younger people. 20

Gastrointestinal function

Fluids in the diet are generally absorbed in the proximal small intestine, and the absorption rate is determined by the rate of gastric emptying to the small intestine. Therefore, the total volume of fluid consumed will eventually be reflected in water balance, but the rate at which rehydration occurs is dependent upon factors affecting the rate of delivery of fluids to the intestinal mucosa. The gastric emptying rate is generally accelerated by the total volume consumed and slowed by higher energy density and osmolality. 68 In addition to water consumed in food (1 L/day) and beverages (circa 2–3 L/day), digestive secretions account for a far greater portion of water that passes through and is absorbed by the gastrointestinal tract (circa 8 L/day). 69 The majority of this water is absorbed by the small intestine, with a capacity of up to 15 L/day with the colon absorbing some 5 L/day. 69

Constipation, characterized by slow gastrointestinal transit, small, hard stools, and difficulty in passing stool, has a number of causes, including medication use, inadequate fiber intake, poor diet, and illness. 70 Inadequate fluid consumption is touted as a common culprit in constipation, and increasing fluid intake is a frequently recommended treatment. Evidence suggests, however, that increasing fluids is only useful to individuals in a hypohydrated state, and is of little utility in euhydrated individuals. 70 In young children with chronic constipation, increasing daily water intake by 50% did not affect constipation scores. 71 For Japanese women with low fiber intake, concomitant low water intake in the diet is associated with increased prevalence of constipation. 72 In older individuals, low fluid intake is a predictor for increased levels of acute constipation, 73 , 74 with those consuming the least amount of fluid having over twice the frequency of constipation episodes than those consuming the most fluid. In one trial, researchers compared the utility of carbonated mineral water in reducing functional dyspepsia and constipation scores to tap water in individuals with functional dyspepsia. 75 When comparing carbonated mineral water to tap water, participants reported improvements in subjective gastric symptoms, but there were no significant improvements in gastric or intestinal function. The authors indicate it is not possible to determine to what degree the mineral content of the two waters contributed to perceived symptom relief, as the mineral water contained greater levels of magnesium and calcium than the tap water. The available evidence suggests that increased fluid intake should only be indicated in individuals in a hypohydrated state. 69 , 71

Significant water loss can occur through the gastrointestinal tract, and this can be of great concern in the very young. In developing countries, diarrheal diseases are a leading cause of death in children, resulting in approximately 1.5–2.5 million deaths per year. 76 Diarrheal illness results not only in a reduction in body water, but also in potentially lethal electrolyte imbalances. Mortality in such cases can many times be prevented with appropriate oral rehydration therapy, by which simple dilute solutions of salt and sugar in water can replace fluid lost by diarrhea. Many consider application of oral rehydration therapy to be one of the significant public health developments of the last century. 77

Kidney function

As noted above, the kidney is crucial in regulating water balance and blood pressure as well as removing waste from the body. Water metabolism by the kidney can be classified into regulated and obligate. Water regulation is hormonally mediated, with the goal of maintaining a tight range of plasma osmolality (between 275 and 290 mOsm/kg). Increases in plasma osmolality and activation of osmoreceptors (intracellular) and baroreceptors (extracellular) stimulate hypothalamic release of arginine vasopressin (AVP). AVP acts at the kidney to decrease urine volume and promote retention of water, and the urine becomes hypertonic. With decreased plasma osmolality, vasopressin release is inhibited, and the kidney increases hypotonic urinary output.

In addition to regulating fluid balance, the kidneys require water for the filtration of waste from the bloodstream and excretion via urine. Water excretion via the kidney removes solutes from the blood, and a minimum obligate urine volume is required to remove the solute load with a maximum output volume of 1 L/h. 78 This obligate volume is not fixed, but is dependent upon the amount of metabolic solutes to be excreted and levels of AVP. Depending on the need for water conservation, basal urine osmolality ranges from 40 mOsm/kg to a maximum of 1,400 mOsm/kg. 78 The ability to both concentrate and dilute urine decreases with age, with a lower value of 92 mOsm/kg and an upper range falling between 500 and 700 mOsm/kg for individuals over the age of 70 years. 79 , – 81 Under typical conditions, in an average adult, urine volume of 1.5 to 2.0 L/day would be sufficient to clear a solute load of 900 to 1,200 mOsm/day. During water conservation and the presence of AVP, this obligate volume can decrease to 0.75–1.0 L/day and during maximal diuresis up to 20 L/day can be required to remove the same solute load. 78 , – 81 In cases of water loading, if the volume of water ingested cannot be compensated for with urine output, having overloaded the kidney's maximal output rate, an individual can enter a hyponatremic state.

Heart function and hemodynamic response

Blood volume, blood pressure, and heart rate are closely linked. Blood volume is normally tightly regulated by matching water intake and water output, as described in the section on kidney function. In healthy individuals, slight changes in heart rate and vasoconstriction act to balance the effect of normal fluctuations in blood volume on blood pressure. 82 Decreases in blood volume can occur, through blood loss (or blood donation), or loss of body water through sweat, as seen with exercise. Blood volume is distributed differently relative to the position of the heart, whether supine or upright, and moving from one position to the other can lead to increased heart rate, a fall in blood pressure, and, in some cases, syncope. This postural hypotension (or orthostatic hypotension) can be mediated by drinking 300–500 mL of water. 83 , 84 Water intake acutely reduces heart rate and increases blood pressure in both normotensive and hypertensive individuals. 85 These effects of water intake on the pressor effect and heart rate occur within 15–20 min of drinking water and can last for up to 60 min. Water ingestion is also beneficial in preventing vasovagal reaction with syncope in blood donors at high risk for post-donation syncope. 86 The effect of water intake in these situations is thought to be due to effects on the sympathetic nervous system rather than to changes in blood volume. 83 , 84 Interestingly, in rare cases, individuals may experience bradycardia and syncope after swallowing cold liquids. 87 , – 89 While swallow syncope can be seen with substances other than water, swallow syncope further supports the notion that the result of water ingestion in the pressor effect has both a neural component as well as a cardiac component.

Water deprivation and dehydration can lead to the development of headache. 90 Although this observation is largely unexplored in the medical literature, some observational studies indicate that water deprivation, in addition to impairing concentration and increasing irritability, can serve as a trigger for migraine and can also prolong migraine. 91 , 92 In those with water deprivation-induced headache, ingestion of water provided relief from headache in most individuals within 30 min to 3 h. 92 It is proposed that water deprivation-induced headache is the result of intracranial dehydration and total plasma volume. Although provision of water may be useful in relieving dehydration-related headache, the utility of increasing water intake for the prevention of headache is less well documented.

The folk wisdom that drinking water can stave off headaches has been relatively unchallenged, and has more traction in the popular press than in the medical literature. Recently, one study examined increased water intake and headache symptoms in headache patients. 93 In this randomized trial, patients with a history of different types of headache, including migraine and tension headache, were either assigned to a placebo condition (a nondrug tablet) or the increased water condition. In the water condition, participants were instructed to consume an additional volume of 1.5 L water/day on top of what they already consumed in foods and fluids. Water intake did not affect the number of headache episodes, but it was modestly associated with reduction in headache intensity and reduced duration of headache. The data from this study suggest that the utility of water as prophylaxis is limited in headache sufferers, and the ability of water to reduce or prevent headache in the broader population remains unknown.

One of the more pervasive myths regarding water intake is its relation to improvements of the skin or complexion. By improvement, it is generally understood that individuals are seeking to have a more “moisturized” look to the surface skin, or to minimize acne or other skin conditions. Numerous lay sources such as beauty and health magazines as well as postings on the Internet suggest that drinking 8–10 glasses of water a day will “flush toxins from the skin” and “give a glowing complexion” despite a general lack of evidence 94 , 95 to support these proposals. The skin, however, is important for maintaining body water levels and preventing water loss into the environment.

The skin contains approximately 30% water, which contributes to plumpness, elasticity, and resiliency. The overlapping cellular structure of the stratum corneum and lipid content of the skin serves as “waterproofing” for the body. 96 Loss of water through sweat is not indiscriminate across the total surface of the skin, but is carried out by eccrine sweat glands, which are evenly distributed over most of the body surface. 97 Skin dryness is usually associated with exposure to dry air, prolonged contact with hot water and scrubbing with soap (both strip oils from the skin), medical conditions, and medications. While more serious levels of dehydration can be reflected in reduced skin turgor, 98 , 99 with tenting of the skin acting as a flag for dehydration, overt skin turgor in individuals with adequate hydration is not altered. Water intake, particularly in individuals with low initial water intake, can improve skin thickness and density as measured by sonogram, 100 offsets transepidermal water loss, and can improve skin hydration. 101 Adequate skin hydration, however, is not sufficient to prevent wrinkles or other signs of aging, which are related to genetics and to sun and environmental damage. Of more utility to individuals already consuming adequate fluids is the use of topical emollients; these will improve skin barrier function and improve the look and feel of dry skin. 102 , 103

Many chronic diseases have multifactorial origins. In particular, differences in lifestyle and the impact of environment are known to be involved and constitute risk factors that are still being evaluated. Water is quantitatively the most important nutrient. In the past, scientific interest with regard to water metabolism was mainly directed toward the extremes of severe dehydration and water intoxication. There is evidence, however, that mild dehydration may also account for some morbidities. 4 , 104 There is currently no consensus on a “gold standard” for hydration markers, particularly for mild dehydration. As a consequence, the effects of mild dehydration on the development of several disorders and diseases have not been well documented.

There is strong evidence showing that good hydration reduces the risk of urolithiasis (see Table 2 for evidence categories). Less strong evidence links good hydration with reduced incidence of constipation, exercise asthma, hypertonic dehydration in the infant, and hyperglycemia in diabetic ketoacidosis. Good hydration is associated with a reduction in urinary tract infections, hypertension, fatal coronary heart disease, venous thromboembolism, and cerebral infarct, but all these effects need to be confirmed by clinical trials. For other conditions such as bladder or colon cancer, evidence of a preventive effect of maintaining good hydration is not consistent (see Table 3 ).

Categories of evidence used in evaluating the quality of reports.

Data adapted from Manz. 104

Summary of evidence for association of hydration status with chronic diseases.

Categories of evidence: described in Table 2 .

Water consumption, water requirements, and energy intake are linked in fairly complex ways. This is partially because physical activity and energy expenditures affect the need for water but also because a large shift in beverage consumption over the past century or more has led to consumption of a significant proportion of our energy intake from caloric beverages. Nonregulatory beverage intake, as noted earlier, has assumed a much greater role for individuals. 19 This section reviews current patterns of water intake and then refers to a full meta-analysis of the effects of added water on energy intake. This includes adding water to the diet and water replacement for a range of caloric and diet beverages, including sugar-sweetened beverages, juice, milk, and diet beverages. The third component is a discussion of water requirements and suggestions for considering the use of mL water/kcal energy intake as a metric.

Patterns and trends of water consumption

Measurement of total fluid water consumption in free-living individuals is fairly new in focus. As a result, the state of the science is poorly developed, data are most likely fairly incomplete, and adequate validation of the measurement techniques used is not available. Presented here are varying patterns and trends of water intake for the United States over the past three decades followed by a brief review of the work on water intake in Europe.

There is really no existing information to support an assumption that consumption of water alone or beverages containing water affects hydration differentially. 3 , 105 Some epidemiological data suggest water might have different metabolic effects when consumed alone rather than as a component of caffeinated or flavored or sweetened beverages; however, these data are at best suggestive of an issue deserving further exploration. 106 , 107 As shown below, the research of Ershow et al. indicates that beverages not consisting solely of water do contain less than 100% water.

One study in the United States has attempted to examine all the dietary sources of water. 16 , 17 These data are cited in Table 4 as the Ershow study and were based on National Food Consumption Survey food and fluid intake data from 1977–1978. These data are presented in Table 4 for children aged 2–18 years (Panel A) and for adults aged 19 years and older (Panel B). Ershow et al. 16 , 17 spent a great deal of time working out ways to convert USDA dietary data into water intake, including water absorbed during the cooking process, water in food, and all sources of drinking water.

Beverage pattern trends in the United States for children aged 2–18 years and adults aged 19 years and older, (nationally representative).

Note: The data are age and sex adjusted to 1965.

Values stem from the Ershow calculations. 16

These researchers created a number of categories and used a range of factors measured in other studies to estimate the water categories. The water that is found in food, based on food composition table data, was 393 mL for children. The water that was added as a result of cooking (e.g., rice) was 95 mL. Water consumed as a beverage directly as water was 624 mL. The water found in other fluids, as noted, comprised the remainder of the milliliters, with the highest levels in whole-fat milk and juices (506 mL). There is a small discrepancy between the Ershow data regarding total fluid intake measures for these children and the normal USDA figures. That is because the USDA does not remove milk fats and solids, fiber, and other food constituents found in beverages, particularly juice and milk.

A key point illustrated by these nationally representative US data is the enormous variability between survey waves in the amount of water consumed (see Figure 1 , which highlights the large variation in water intake as measured in these surveys). Although water intake by adults and children increased and decreased at the same time, for reasons that cannot be explained, the variation was greater among children than adults. This is partly because the questions the surveys posed varied over time and there was no detailed probing for water intake, because the focus was on obtaining measures of macro- and micronutrients. Dietary survey methods used in the past have focused on obtaining data on foods and beverages containing nutrient and non-nutritive sweeteners but not on water. Related to this are the huge differences between the the USDA surveys and the National Health and Nutrition Examination Survey (NHANES) performed in 1988–1994 and in 1999 and later. In addition, even the NHANES 1999–2002 and 2003–2006 surveys differ greatly. These differences reflect a shift in the mode of questioning with questions on water intake being included as part of a standard 24-h recall rather than as stand-alone questions. Water intake was not even measured in 1965, and a review of the questionnaires and the data reveals clear differences in the way the questions have been asked and the limitations on probes regarding water intake. Essentially, in the past people were asked how much water they consumed in a day and now they are asked for this information as part of a 24-h recall survey. However, unlike for other caloric and diet beverages, there are limited probes for water alone. The results must thus be viewed as crude approximations of total water intake without any strong research to show if they are over- or underestimated. From several studies of water and two ongoing randomized controlled trials performed by us, it is clear that probes that include consideration of all beverages and include water as a separate item result in the provision of more complete data.

Water consumption trends from USDA and NHANES surveys (mL/day/capita), nationally representative. Note: this includes water from fluids only, excluding water in foods. Sources for 1965, 1977–1978, 1989–1991, and 1994–1998, are USDA. Others are NHANES and 2005–2006 is joint USDA and NHANES.

Water consumption data for Europe are collected far more selectively than even the crude water intake questions from NHANES. A recent report from the European Food Safety Agency provides measures of water consumption from a range of studies in Europe. 4 , – 109 Essentially, what these studies show is that total water intake is lower across Europe than in the United States. As with the US data, none are based on long-term, carefully measured or even repeated 24-h recall measures of water intake from food and beverages. In an unpublished examination of water intake in UK adults in 1986–1987 and in 2001–2002, Popkin and Jebb have found that although intake increased by 226 mL/day over this time period, it was still only 1,787 mL/day in the latter period (unpublished data available from BP); this level is far below the 2,793 mL/day recorded in the United States for 2005–2006 or the earlier US figures for comparably aged adults.

A few studies have been performed in the United States and Europe utilizing 24-h urine and serum osmolality measures to determine total water turnover and hydration status. Results of these studies suggest that US adults consume over 2,100 mL of water per day while adults in Europe consume less than half a liter. 4 , 110 Data on total urine collection would appear to be another useful measure for examining total water intake. Of course, few studies aside from the Donald Study of an adolescent cohort in Germany have collected such data on population levels for large samples. 109

Effects of water consumption on overall energy intake

There is an extensive body of literature that focuses on the impact of sugar-sweetened beverages on weight and the risk of obesity, diabetes, and heart disease; however, the perspective of providing more water and its impact on health has not been examined. The literature on water does not address portion sizes; instead, it focuses mainly on water ad libitum or in selected portions compared with other caloric beverages. A detailed meta-analysis of the effects of water intake alone (i.e., adding additional water) and as a replacement for sugar-sweetened beverages, juice, milk, and diet beverages appears elsewhere. 111

In general, the results of this review suggest that water, when consumed in place of sugar-sweetened beverages, juice, and milk, is linked with reduced energy intake. This finding is mainly derived from clinical feeding studies but also from one very good randomized, controlled school intervention and several other epidemiological and intervention studies. Aside from the issue of portion size, factors such as the timing of beverage and meal intake (i.e., the delay between consumption of the beverage and consumption of the meal) and types of caloric sweeteners remain to be considered. However, when beverages are consumed in normal free-living conditions in which five to eight daily eating occasions are the norm, the delay between beverage and meal consumption may matter less. 112 , – 114

The literature on the water intake of children is extremely limited. However, the excellent German school intervention with water suggests the effects of water on the overall energy intake of children might be comparable to that of adults. 115 In this German study, children were educated on the value of water and provided with special filtered drinking fountains and water bottles in school. The intervention schoolchildren increased their water intake by 1.1 glasses/day ( P  < 0.001) and reduced their risk of overweight by 31% (OR = 0.69, P  = 0.40).

Classically, water data are examined in terms of milliliters (or some other measure of water volume consumed per capita per day by age group). This measure does not link fluid intake and caloric intake. Disassociation of fluid and calorie intake is difficult for clinicians dealing with older persons with reduced caloric intake. This milliliter water measure assumes some mean body size (or surface area) and a mean level of physical activity – both of which are determinants of not only energy expenditure but also water balance. Children are dependent on adults for access to water, and studies suggest that their larger surface area to volume ratio makes them susceptible to changes in skin temperatures linked with ambient temperature shifts. 116 One option utilized by some scholars is to explore food and beverage intake in milliliters per kilocalorie (mL/kcal), as was done in the 1989 US recommended dietary allowances. 4 , 117 This is an option that is interpretable for clinicians and which incorporates, in some sense, body size or surface area and activity. Its disadvantage is that water consumed with caloric beverages affects both the numerator and the denominator; however, an alternative measure that could be independent of this direct effect on body weight and/or total caloric intake is not presently known.

Despite its critical importance in health and nutrition, the array of available research that serves as a basis for determining requirements for water or fluid intake, or even rational recommendations for populations, is limited in comparison with most other nutrients. While this deficit may be partly explained by the highly sensitive set of neurophysiological adaptations and adjustments that occur over a large range of fluid intakes to protect body hydration and osmolarity, this deficit remains a challenge for the nutrition and public health community. The latest official effort at recommending water intake for different subpopulations occurred as part of the efforts to establish Dietary Reference Intakes in 2005, as reported by the Institute of Medicine of the National Academies of Science. 3 As a graphic acknowledgment of the limited database upon which to express estimated average requirements for water for different population groups, the Committee and the Institute of Medicine stated: “While it might appear useful to estimate an average requirement (an EAR) for water, an EAR based on data is not possible.” Given the extreme variability in water needs that are not solely based on differences in metabolism, but also on environmental conditions and activities, there is not a single level of water intake that would assure adequate hydration and optimum health for half of all apparently healthy persons in all environmental conditions. Thus, an adequate intake (AI) level was established in place of an EAR for water.

The AIs for different population groups were set as the median water intakes for populations, as reported in the National Health and Nutrition Examination Surveys; however, the intake levels reported in these surveys varied greatly based on the survey years (e.g., NHANES 1988–1994 versus NHANES 1999–2002) and were also much higher than those found in the USDA surveys (e.g., 1989–1991, 1994–1998, or 2005–2006). If the AI for adults, as expressed in Table 5 , is taken as a recommended intake, the wisdom of converting an AI into a recommended water or fluid intake seems questionable. The first problem is the almost certain inaccuracy of the fluid intake information from the national surveys, even though that problem may also exist for other nutrients. More importantly, from the standpoint of translating an AI into a recommended fluid intake for individuals or populations, is the decision that was made when setting the AI to add an additional roughly 20% of water intake, which is derived from some foods in addition to water and beverages. While this may have been a legitimate effort to use total water intake as a basis for setting the AI, the recommendations that derive from the IOM report would be better directed at recommendations for water and other fluid intake on the assumption that the water content of foods would be a “passive” addition to total water intake. In this case, the observations of the dietary reference intake committee that it is necessary for water intake to meet needs imposed by metabolism and environmental conditions must be extended to consider three added factors, namely body size, gender, and physical activity. Those are the well-studied factors that allow a rather precise measurement and determination of energy intake requirements. It is, therefore, logical that those same factors might underlie recommendations to meet water intake needs in the same populations and individuals. Consideration should also be given to the possibility that water intake needs would best be expressed relative to the calorie requirements, as is done regularly in the clinical setting, and data should be gathered to this end through experimental and population research.

Water requirements expressed in relation to energy recommendations.

AI for total fluids derived from dietary reference intakes for water, potassium, sodium, chloride, and sulphate.

Ratios for water intake based on the AI for water in liters/day calculated using EER for each range of physical activity. EER adapted from the Institute of Medicine Dietary Reference Intakes Macronutrients Report, 2002.

It is important to note that only a few countries include water on their list of nutrients. 118 The European Food Safety Authority is developing a standard for all of Europe. 105 At present, only the United States and Germany provide AI values for water. 3 , 119

Another approach to the estimation of water requirements, beyond the limited usefulness of the AI or estimated mean intake, is to express water intake requirements in relation to energy requirements in mL/kcal. An argument for this approach includes the observation that energy requirements for each age and gender group are strongly evidence-based and supported by extensive research taking into account both body size and activity level, which are crucial determinants of energy expenditure that must be met by dietary energy intake. Such measures of expenditure have used highly accurate methods, such as doubly labeled water; thus, estimated energy requirements have been set based on solid data rather than the compromise inherent in the AIs for water. Those same determinants of energy expenditure and recommended intake are also applicable to water utilization and balance, and this provides an argument for pegging water/fluid intake recommendations to the better-studied energy recommendations. The extent to which water intake and requirements are determined by energy intake and expenditure is understudied, but in the clinical setting it has long been practice to supply 1 mL/kcal administered by tube to patients who are unable to take in food or fluids. Factors such as fever or other drivers of increased metabolism affect both energy expenditure and fluid loss and are thus linked in clinical practice. This concept may well deserve consideration in the setting of population intake goals.

Finally, for decades there has been discussion about expressing nutrient requirements per 1,000 kcal so that a single number would apply reasonably across the spectrum of age groups. This idea, which has never been adopted by the Institute of Medicine and the National Academies of Science, may lend itself to an improved expression of water/fluid intake requirements, which must eventually replace the AIs. Table 5 presents the IOM water requirements and then develops a ratio of mL/kcal based on them. The European Food Safety Agency refers positively to the possibility of expressing water intake recommendations in mL/kcal as a function of energy requirements. 105 Outliers in the adult male categories, which reach ratios as high as 1.5, may well be based on the AI data from the United States, which are above those in the more moderate and likely more accurate European recommendations.

The topic of utilizing mL/kcal to examine water intake and water gaps is explored in Table 6 , which takes the full set of water intake AIs for each age-gender grouping and examines total intake. The data suggest a high level of fluid deficiency. Since a large proportion of fluids in the United States is based on caloric beverages and this proportion has changed markedly over the past 30 years, fluid intake increases both the numerator and the denominator of this mL/kcal relationship. Nevertheless, even using 1 mL/kcal as the AI would leave a gap for all children and adolescents. The NHANES physical activity data were also translated into METS/day to categorize all individuals by physical activity level and thus varying caloric requirements. Use of these measures reveals a fairly large fluid gap, particularly for adult males as well as children ( Table 6 ).

Water intake and water intake gaps based on US Water Adequate Intake Recommendations (based on utilization of water and physical activity data from NHANES 2005–2006).

Note: Recommended water intake for actual activity level is the upper end of the range for moderate and active.

A weighted average for the proportion of individuals in each METS-based activity level.

This review has pointed out a number of issues related to water, hydration, and health. Since water is undoubtedly the most important nutrient and the only one for which an absence will prove lethal within days, understanding of water measurement and water requirements is very important. The effects of water on daily performance and short- and long-term health are quite clear. The existing literature indicates there are few negative effects of water intake while the evidence for positive effects is quite clear.

Little work has been done to measure total fluid intake systematically, and there is no understanding of measurement error and best methods of understanding fluid intake. The most definitive US and European documents on total water requirements are based on these extant intake data. 3 , 105 The absence of validation methods for water consumption intake levels and patterns represents a major gap in knowledge. Even varying the methods of probing in order to collect better water recall data has been little explored.

On the other side of the issue is the need to understand total hydration status. There are presently no acceptable biomarkers of hydration status at the population level, and controversy exists about the current knowledge of hydration status among older Americans. 6 , 120 Thus, while scholars are certainly focused on attempting to create biomarkers for measuring hydration status at the population level, the topic is currently understudied.

As noted, the importance of understanding the role of fluid intake on health has emerged as a topic of increasing interest, partially because of the trend toward rising proportions of fluids being consumed in the form of caloric beverages. The clinical, epidemiological, and intervention literature on the effects of added water on health are covered in a related systematic review. 111 The use of water as a replacement for sugar-sweetened beverages, juice, or whole milk has clear effects in that energy intake is reduced by about 10–13% of total energy intake. However, only a few longer-term systematic interventions have investigated this topic and no randomized, controlled, longer-term trials have been published to date. There is thus very minimal evidence on the effects of just adding water to the diet and of replacing water with diet beverages.

There are many limitations to this review. One certainly is the lack of discussion of potential differences in the metabolic functioning of different types of beverages. 121 Since the literature in this area is sparse, however, there is little basis for delving into it at this point. A discussion of the potential effects of fructose (from all caloric sweeteners when consumed in caloric beverages) on abdominal fat and all of the metabolic conditions directly linked with it (e.g., diabetes) is likewise lacking. 122 , – 125 A further limitation is the lack of detailed review of the array of biomarkers being considered to measure hydration status. Since there is no measurement in the field today that covers more than a very short time period, except for 24-hour total urine collection, such a discussion seems premature.

Some ways to examine water requirements have been suggested in this review as a means to encourage more dialogue on this important topic. Given the significance of water to our health and of caloric beverages to our total energy intake, as well as the potential risks of nutrition-related noncommunicable diseases, understanding both the requirements for water in relation to energy requirements, and the differential effects of water versus other caloric beverages, remain important outstanding issues.

This review has attempted to provide some sense of the importance of water to our health, its role in relationship to the rapidly increasing rates of obesity and other related diseases, and the gaps in present understanding of hydration measurement and requirements. Water is essential to our survival. By highlighting its critical role, it is hoped that the focus on water in human health will sharpen.

The authors wish to thank Ms. Frances L. Dancy for administrative assistance, Mr. Tom Swasey for graphics support, Dr. Melissa Daniels for assistance, and Florence Constant (Nestle's Water Research) for advice and references.

This work was supported by the Nestlé Waters, Issy-les-Moulineaux, France, 5ROI AGI0436 from the National Institute on Aging Physical Frailty Program, and NIH R01-CA109831 and R01-CA121152.

Declaration of interest

The authors have no relevant interests to declare.

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• dehydration
• energy intake
• water drinking
• fluid intake
• water requirements

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Heat waves: a hot topic in climate change research

• Original Paper
• Open access
• Published: 03 September 2021
• Volume 146 , pages 781–800, ( 2021 )

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• Werner Marx   ORCID: orcid.org/0000-0002-1763-5753 1 ,
• Robin Haunschild   ORCID: orcid.org/0000-0001-7025-7256 1 &
• Lutz Bornmann   ORCID: orcid.org/0000-0003-0810-7091 1 , 2  

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Research on heat waves (periods of excessively hot weather, which may be accompanied by high humidity) is a newly emerging research topic within the field of climate change research with high relevance for the whole of society. In this study, we analyzed the rapidly growing scientific literature dealing with heat waves. No summarizing overview has been published on this literature hitherto. We developed a suitable search query to retrieve the relevant literature covered by the Web of Science (WoS) as complete as possible and to exclude irrelevant literature ( n  = 8,011 papers). The time evolution of the publications shows that research dealing with heat waves is a highly dynamic research topic, doubling within about 5 years. An analysis of the thematic content reveals the most severe heat wave events within the recent decades (1995 and 2003), the cities and countries/regions affected (USA, Europe, and Australia), and the ecological and medical impacts (drought, urban heat islands, excess hospital admissions, and mortality). An alarming finding is that the limit for survivability may be reached at the end of the twenty-first century in many regions of the world due to the fatal combination of rising temperatures and humidity levels measured as “wet-bulb temperature” (WBT). Risk estimation and future strategies for adaptation to hot weather are major political issues. We identified 104 citation classics, which include fundamental early works of research on heat waves and more recent works (which are characterized by a relatively strong connection to climate change).

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1 Introduction

As a consequence of the well-documented phenomenon of global warming, climate change has become a major research field in the natural and medical sciences, and more recently also in the social and political sciences. The scientific community has contributed extensively to a comprehensive understanding of the earth’s climate system, providing various data and projections on the future climate as well as on the effects and risks of anticipated global warming (IPCC 2014; CSSR 2017; NCA4 2018; and the multitude of references cited therein). During recent decades, climate change has also become a major political, economic, and environmental issue and a central theme in political and public debates.

One consequence of global warming is the increase of extreme weather events such as heat waves, droughts, floods, cyclones, and wildfires. Some severe heat waves occurring within the last few decades made heat waves a hot topic in climate change research, with “hot” having a dual meaning: high temperature and high scientific activity. “More intense, more frequent, and longer lasting heat waves in the twenty-first century” is the title of a highly cited paper published 2004 in Science (Meehl and Tebaldi 2004 ). This title summarizes in short what most climate researchers anticipate for the future. But what are heat waves (formerly also referred to as “heatwaves”)? In general, a heat wave is a period of excessively hot weather, which may be accompanied by high humidity. Since heat waves vary according to region, there is no universal definition, but only definitions relative to the usual weather in the area and relative to normal temperatures for the season. The World Meteorological Organization (WMO) defines a heat wave as 5 or more consecutive days of prolonged heat in which the daily maximum temperature is higher than the average maximum temperature by 5 °C (9 °F) or more ( https://www.britannica.com/science/heat-wave-meteorology ).

Europe, for example, has suffered from a series of intense heat waves since the beginning of the twenty-first century. According to the World Health Organization (WHO) and various national reports, the extreme 2003 heat wave caused about 70,000 excess deaths, primarily in France and Italy. The 2010 heat wave in Russia caused extensive crop loss, numerous wildfires, and about 55,000 excess deaths (many in the city of Moscow). Heat waves typically occur when high pressure systems become stationary and the winds on their rear side continuously pump hot and humid air northeastward, resulting in extreme weather conditions. The more intense and more frequently occurring heat waves cannot be explained solely by natural climate variations and without human-made climate change (IPCC 2014; CSSR 2017; NCA4 2018). Scientists discuss a weakening of the polar jet stream caused by global warming as a possible reason for an increasing probability for the occurrence of stationary weather, resulting in heavy rain falls or heat waves (Broennimann et al. 2009 ; Coumou et al. 2015 ; Mann 2019 ). This jet stream is one of the most important factors for the weather in the middle latitude regions of North America, Europe, and Asia.

Until the end of the twentieth century, heat waves were predominantly seen as a recurrent meteorological fact with major attention to drought, being almost independent from human activities and unpredictable like earthquakes. However, since about 1950, distinct changes in extreme climate and weather events have been increasingly observed. Meanwhile, climate change research has revealed that these changes are clearly linked to the human influence on the content of greenhouse gases in the earth’s atmosphere. Climate-related extremes, such as heat waves, droughts, floods, cyclones, and wildfires, reveal significant vulnerability to climate change as a result of global warming.

In recent years, research on heat waves has been established as an emerging research topic within the large field of current climate change research. Bibliometric analyses are very suitable in order to have a systematic and quantitative overview of the literature that can be assigned to an emerging topic such as research dealing with heat waves (e.g., Haunschild et al. 2016 ). No summarizing overview on the entire body of heat wave literature has been published until now. However, a bibliometric analysis of research on urban heat islands as a more specific topic in connection with heat waves has been performed (Huang and Lu 2018 ).

In this study, we analyzed the publications dealing with heat waves using appropriate bibliometric methods and tools. First, we determined the amount and time evolution of the scientific literature dealing with heat waves. The countries contributing the most papers are presented. Second, we analyzed the thematic content of the publications via keywords assigned by the WoS. Third, we identified the most important (influential) publications (and also the historical roots). We identified 104 citation classics, which include fundamental early works and more recent works with a stronger connection to climate change.

2 Heat waves as a research topic

The status of the current knowledge on climate change is summarized in the Synthesis Report of the Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change (IPCC) (IPCC 2014, https://www.ipcc.ch/report/ar5/syr/ ). This panel is the United Nations body for assessing the science related to climate change. The Synthesis Report is based on the reports of the three IPCC Working Groups , including relevant Special Reports . In its Summary for Policymakers , it provides an integrated view of climate change as the final part of the Fifth Assessment Report (IPCC 2014, https://www.ipcc.ch/site/assets/uploads/2018/02/AR5_SYR_FINAL_SPM.pdf ).

In the chapter Extreme Events , it is stated that “changes in many extreme weather and climate events have been observed since about 1950. Some of these changes have been linked to human influences, including a decrease in cold temperature extremes, an increase in warm temperature extremes, an increase in extreme high sea levels and an increase in the number of heavy precipitation events in a number of regions … It is very likely that the number of cold days and nights has decreased and the number of warm days and nights has increased on the global scale. It is likely that the frequency of heat waves has increased in large parts of Europe, Asia and Australia. It is very likely that human influence has contributed to the observed global scale changes in the frequency and intensity of daily temperature extremes since the mid-twentieth century. It is likely that human influence has more than doubled the probability of occurrence of heat waves in some locations” (p. 7–8). Under Projected Changes , the document summarizes as follows: “Surface temperature is projected to rise over the twenty-first century under all assessed emission scenarios. It is very likely that heat waves will occur more often and last longer, and that extreme precipitation events will become more intense and frequent in many regions” (p. 10).

With regard to the USA, the Climate Science Special Report of the U.S. Global Change Research Program (CSSR 2017, https://science2017.globalchange.gov/ ) mentions quite similar observations and states unambiguously in its Fourth National Climate Assessment (Volume I) report ( https://science2017.globalchange.gov/downloads/CSSR2017_FullReport.pdf ) under Observed Changes in Extremes that “the frequency of cold waves has decreased since the early 1900s, and the frequency of heat waves has increased since the mid-1960s (very high confidence). The frequency and intensity of extreme heat and heavy precipitation events are increasing in most continental regions of the world (very high confidence). These trends are consistent with expected physical responses to a warming climate [p. 19]. Heavy precipitation events in most parts of the United States have increased in both intensity and frequency since 1901 (high confidence) [p. 20]. There are important regional differences in trends, with the largest increases occurring in the northeastern United States (high confidence). Recent droughts and associated heat waves have reached record intensity in some regions of the United States … (very high confidence) [p. 21]. Confidence in attribution findings of anthropogenic influence is greatest for extreme events that are related to an aspect of temperature” (p. 123).

Among the key findings in the chapter on temperature changes in the USA, the report states that “there have been marked changes in temperature extremes across the contiguous United States. The frequency of cold waves has decreased since the early 1900s, and the frequency of heat waves has increased since the mid-1960s (very high confidence). Extreme temperatures in the contiguous United States are projected to increase even more than average temperatures. The temperatures of extremely cold days and extremely warm days are both expected to increase. Cold waves are projected to become less intense while heat waves will become more intense (very high confidence) [p. 185]. Most of this methodology as applied to extreme weather and climate event attribution, has evolved since the European heat wave study of Stott et al.” (p. 128).

Heat waves are also discussed in the Fourth National Climate Assessment (Volume II) report (NCA4 2018, https://nca2018.globalchange.gov/ ). The Report-in-Brief ( https://nca2018.globalchange.gov/downloads/NCA4_Report-in-Brief.pdf ) for example states: “More frequent and severe heat waves and other extreme events in many parts of the United States are expected [p. 38]. Heat waves and heavy rainfalls are expected to increase in frequency and intensity [p. 93]. The season length of heat waves in many U.S. cities has increased by over 40 days since the 1960s [p. 30]. Cities across the Southeast are experiencing more and longer summer heat waves [p. 123]. Exposure to hotter temperatures and heat waves already leads to heat-associated deaths in Arizona and California. Mortality risk during a heat wave is amplified on days with high levels of ground-level ozone or particulate air pollution” (p. 150).

In summary, climate change research expects more frequent and more severe heat wave events as a consequence of global warming. It is likely that the more frequent and longer lasting heat waves will significantly increase excess mortality, particularly in urban regions with high air pollution. Therefore, research around heat waves will become increasingly important and is much more than a temporary research fashion.

3 Methodology

3.1 dataset used.

This analysis is based on the relevant literature retrieved from the following databases accessible under the Web of Science (WoS) of Clarivate Analytics: Web of Science Core Collection: Citation Indexes, Science Citation Index Expanded (SCI-EXPANDED), Social Sciences Citation Index (SSCI), Arts & Humanities Citation Index (A&HCI), Conference Proceedings Citation Index—Science (CPCI-S), Conference Proceedings Citation Index—Social Science & Humanities (CPCI-SSH), Book Citation Index—Science (BKCI-S), Book Citation Index—Social Sciences & Humanities (BKCI-SSH), Emerging Sources Citation Index (ESCI).

We applied the search query given in Appendix 1 to cover the relevant literature as completely as possible and to exclude irrelevant literature. We practiced an iterative query optimization by identifying and excluding the WoS subject categories with most of the non-relevant papers. For example, heat waves are also mentioned in the field of materials science but have nothing to do with climate and weather phenomena. Unfortunately, WoS obviously assigned some heat wave papers related to climate to materials science-related subject categories. Therefore, these subject categories were not excluded. By excluding the other non-relevant subject categories, 597 out of 8,568 papers have been removed, resulting in a preliminary publication set of 7,971 papers (#2 of the search query). But this is no safe method, since the excluded categories may well include some relevant papers. Therefore, we have combined these 597 papers with search terms related to climate or weather and retrieved 62 relevant papers in addition, which we added to our preliminary paper subset, eventually receiving 8,033 publications (#3 to #5 of the search query).

Commonly, publication sets for bibliometric analyses are limited to articles, reviews, and conference proceedings as the most relevant document types and are restricted to complete publication years. In this study, however, we have included all relevant WoS document types for a better literature coverage of the research topic analyzed. For example, conference meetings and early access papers may well be interesting for the content analysis of the literature under study. Such literature often anticipates important results, which are published later as regular articles. Furthermore, we have included the literature until the date of search for considering the recent rapid growth of the field. Our search retrieved a final publication set of 8,011 papers indexed in WoS until the date of search (July 1, 2021) and dealing with heat waves (#6 of the search query). We have combined this publication set with climate change-related search terms from a well-proven search query (Haunschild et al. 2016 ) resulting in 4,588 papers dealing with heat waves in connection with climate change or global warming (# 11 of the search query). Also, we have selected a subset of 2,373 papers dealing with heat waves and mortality (#13 of the search query). The complete WoS search query is given in Appendix 1.

The final publication set of 8,011 papers dealing with heat waves still contains some non-relevant papers primarily published during the first half of the twentieth century, such as some Nature papers within the WoS category Multidisciplinary Sciences . Since these papers are assigned only to this broad subject category and have no abstracts and no keywords included, they cannot be excluded using the WoS search and refinement functions. We do not expect any bias through these papers, because their keywords do not appear in our maps. Also, they normally contain very few (if any) cited references, which could bias/impact our reference analysis.

3.2 Networks

We used the VOSviewer software (Van Eck and Waltman 2010 ) to map co-authorship with regard to the countries of authors (88 countries considered) of the papers dealing with heat waves ( www.vosviewer.com ). The map of the cooperating countries presented is based on the number of joint publications. The distance between two nodes is proportionate to the number of co-authored papers. Hence, largely cooperating countries are positioned closer to each other. The size of the nodes is proportionate to the number of papers published by authors of the specific countries.

The method that we used for revealing the thematic content of the publication set retrieved from the WoS is based on the analysis of keywords. For better standardization, we chose the keywords allocated by the database producer (keywords plus) rather than the author keywords. We also used the VOSviewer for mapping the thematic content of the 104 key papers selected by reference analysis. This map is also based on keywords plus.

The term maps (keywords plus) are based on co-occurrence for positioning the nodes on the maps. The distance between two nodes is proportionate to the co-occurrence of the terms. The size of the nodes is proportionate to the number of papers with a specific keyword. The nodes on the map are assigned by VOSviewer to clusters based on a specific cluster algorithm (the clusters are highlighted in different colors). These clusters identify closely related (frequently co-occurring) nodes, where each node is assigned to only one cluster.

3.3 Reference Publication Year Spectroscopy

A bibliometric method called “Reference Publication Year Spectroscopy” (RPYS, Marx et al. 2014 ) in combination with the tool CRExplorer ( http://www.crexplorer.net , Thor et al. 2016a , b ) has proven useful for exploring the cited references within a specific publication set, in order to detect the most important publications of the relevant research field (and also the historical roots). In recent years, several studies have been published, in which the RPYS method was basically described and applied (Marx et al. 2014 ; Marx and Bornmann 2016 ; Comins and Hussey 2015 ). In previous studies, Marx et al. have analyzed the roots of research on global warming (Marx et al. 2017a ), the emergence of climate change research in combination with viticulture (Marx et al. 2017b ), and tea production (Marx et al. 2017c ) from a quantitative (bibliometric) perspective. In this study, we determined which references have been most frequently cited by the papers dealing with heat waves.

RPYS is based on the assumption that peers produce a useful database by their publications, in particular by the references cited therein. This database can be analyzed statistically with regard to the works most important for their specific research field. Whereas individual scientists judge their research field more or less subjectively, the overall community can deliver a more objective picture (based on the principle of “the wisdom of the crowds”). The peers effectively “vote” via their cited references on which works turned out to be most important for their research field (Bornmann and Marx 2013 ). RPYS implies a normalization of citation counts (here: reference counts) with regard to the research area and the time of publication, which both impact the probability to be cited frequently. Basically, the citing and cited papers analyzed were published in the same research field and the reference counts are compared with each other only within the same publication year.

RPYS relies on the following observation: the analysis of the publication years of the references cited by all the papers in a specific research topic shows that publication years are not equally represented. Some years occur particularly frequently among the cited references. Such years appear as distinct peaks in the distribution of the reference publication years (i.e., the RPYS spectrogram). The pronounced peaks are frequently based on a few references that are more frequently cited than other references published in the same year. The frequently cited references are—as a rule—of specific significance to the research topic in question (here: heat waves) and the earlier references among them represent its origins and intellectual roots (Marx et al. 2014 ).

The RPYS changes the perspective of citation analysis from a times cited to a cited reference analysis (Marx and Bornmann 2016 ). RPYS does not identify the most highly cited papers of the publication set being studied (as is usually done by bibliometric analyses in research evaluation). RPYS aims to mirror the knowledge base of research (here: on heat waves).

With time, the body of scientific literature of many research fields is growing rapidly, particularly in climate change research (Haunschild et al. 2016 ). The growth rate of highly dynamic research topics such as research related to heat waves is even larger. As a consequence, the number of potentially citable papers is growing substantially. Toward the present, the peaks of individual publications lie over a broad continuum of newer publications and are less numerous and less pronounced. Due to the many publications cited in the more recent years, the proportion of individual highly cited publications in specific reference publication years falls steadily. Therefore, the distinct peaks in an RPYS spectrogram reveal only the most highly cited papers, in particular the earlier references comprising the historical roots. Further inspection and establishing a more entire and representative list of highly cited works requires consulting the reference table provided by the CRExplorer. The most important references within a specific reference publication year can be identified by sorting the cited references according to the reference publication year (RPY) and subsequently according to the number of cited references (N_CR) in a particular publication year.

The selection of important references in RPYS requires the consideration of two opposing trends: (1) the strongly growing number of references per reference publication year and (2) the fall off near present due to the fact that the newest papers had not sufficient time to accumulate higher citation counts. Therefore, we decided to set different limits for the minimum number of cited references for different periods of reference publication years (1950–1999: N_CR ≥ 50, 2000–2014: N_CR ≥ 150, 2015–2020: N_CR ≥ 100). This is somewhat arbitrary, but is helpful in order to adapt and limit the number of cited references to be presented and discussed.

In order to apply RPYS, all cited references ( n  = 408,247) of 216,932 unique reference variants have been imported from the papers of our publication set on heat waves ( n  = 8,011). The cited reference publication years range from 1473 to 2021. We removed all references (297 different cited reference variants) with reference publication years prior to 1900. Due to the very low output of heat wave-related papers published before 1990, no relevant literature published already in the nineteenth century can be expected. Also, global warming was no issue before 1900 since the Little Ice Age (a medieval cold period) lasted until the nineteenth century. The references were sorted according to RPY and N_CR for further inspection.

The CRExplorer offers the possibility to cluster and merge variants of the same cited reference (Thor et al. 2016a , b ). We clustered and merged the associated reference variants in our dataset (which are mainly caused by misspelled references) using the corresponding CRExplorer module, clustering the reference variants via volume and page numbers and subsequently merging aggregated 374 cited references (for more information on using the CRExplorer see “guide and datasets” at www.crexplorer.net ).

After clustering and merging, we applied a further cutback: to focus the RPYS on the most pronounced peaks, we removed all references ( n  = 212,324) with reference counts below 10 (resulting in a final number of 3,937 cited references) for the detection of the most frequently cited works. A minimum reference count of 10 has proved to be reasonable, in particular for early references (Marx et al. 2014 ). The cited reference publication years now range from 1932 to 2020.

In this study, we have considered all relevant WoS document types for a preferably comprehensive coverage of the literature of the research topic analyzed. The vast majority of the papers of our publication set, however, have been assigned to the document types “article” ( n  = 6.738, 84.1%), “proceedings paper” ( n  = 485, 6.1%), and “review” ( n  = 395 papers, 4.9%). Note that some papers belong to more than one document type.

4.1 Time evolution of literature

In Fig.  1 , the time evolution between 1990 and 2020 of the publications dealing with heat waves is shown (there are only 109 pre-1990 publications dealing with heat waves and covered by the WoS).

Time evolution of the overall number of heat wave publications, of heat wave publications in connection with climate change, and of heat wave publications in connection with mortality, each between 1990 and 2020. For comparison, the overall number of publications (scaled down) in the field of climate change research and the total number of publications covered by the WoS database (scaled down, too) are included

According to Fig.  1 , research dealing with heat waves is a highly dynamic research topic, currently doubling within about 5 years. The number of papers published per year shows a strong increase: since around 2000, the publication output increased by a factor of more than thirty, whereas in the same period, the overall number of papers covered by the WoS increased only by a factor of around three. Also, the portion of heat wave papers dealing with climate change increased substantially: from 16.1 in the period 1990–1999 to 25.7% in 2000, reaching 66.9% in 2020. The distinct decrease of the overall number of papers covered by the WoS between 2019 and 2020 might be a result of the Covid-19 pandemic.

With regard to the various impacts of heat waves, excess mortality is one of the most frequently analyzed and discussed issues in the scientific literature (see below). Whereas the subject specific literature on heat waves increased from 2000 to 2020 by a factor of 33.6, literature on heat waves dealing with mortality increased from 2000 to 2020 by a factor of 51.5. The dynamics of the research topic dealing with heat waves is mirrored by the WoS Citation Report , which shows the time evolution of the overall citation impact of the papers of the publication set (not presented). The citation report curve shows no notable citation impact before 2005, corresponding to the increase of the publication rate since about 2003 as shown in Fig.  1 .

4.2 Countries of authors

In Table 1 , the number of papers assigned to the countries of authors with more than 100 publications dealing with heat waves is presented, showing the national part of research activities on this research topic. For comparative purposes, the percentage of overall papers in WoS of each country is shown. As a comparison with the overall WoS, we only considered WoS papers published between 2000 and 2020, because the heat wave literature started to grow substantially around 2000.

The country-specific percentages from Table 1 are visualized in Fig.  2 . Selected countries are labeled. Countries with a higher relative percentage of more than two percentage points in heat wave research than in WoS overall output are marked blue (blue circle). Countries with a relative percentage at least twice as high in heat wave research than in overall WoS output are marked green (green cross), whereas countries with a relative percentage at most half as much in heat wave research than in overall WoS output are marked with a yellow cross. Only Japan has a much lower output in heat wave research than in WoS overall output, as indicated by the red circle and yellow cross. Most countries are clustered around the bisecting line and are marked gray (gray circle). China and the USA are outside of the plot region. Both countries are rather close to the bisecting line. Some European countries show a much larger activity in heat wave research than in overall WoS output. Australia shows the largest difference and ratio in output percentages as shown by the blue circle and green cross.

Publication percentages of countries in Table 1 . Countries with large deviations between heat wave output and overall WoS output are labeled. Countries with an absolute percentage of more than two percentage points higher (lower) in heat wave research than in overall WoS output are marked blue (red). Countries with a relative percentage at least twice as high (at most half as much) in heat wave research than in overall WoS output are marked green (yellow)

The results mainly follow the expectations of such bibliometric analyses, with one distinct exception: Australia increasingly suffers from extreme heat waves and is comparatively active in heat wave research—compared with its proportion of scientific papers in general. The growth factor of the Australian publication output since 2010 is 8.5, compared to 5.3 for the USA and 3.3 for Germany.

Figure  3 shows the co-authorship network with regard to the countries of authors of the papers dealing with heat waves using the VOSviewer software.

Co-authorship overlay map with regard to the countries of authors and their average publication years from the 8,011 papers dealing with heat waves. The minimum number of co-authored publications of a country is 5; papers with more than 25 contributing countries are neglected; of the 135 countries, 89 meet the threshold, and 88 out of 89 countries are connected and are considered (one country, Armenia, that is disconnected from the network has been removed). The co-authorship network of a single country can be depicted by clicking on the corresponding node in the interactive map. Readers interested in an in-depth analysis can use VOSviewer interactively and zoom into the map via the following URL: https://tinyurl.com/3ywkwv8t

According to Fig.  3 and in accordance with Table 1 , the USA is most productive in heat wave research. This is not unexpected, because the US publication output is at the top for most research fields. However, this aside, the USA has been heavily affected by heat wave events and is leading with regard to the emergence of the topic. Australia appears as another major player and is strongly connected with the US publications within the co-authorship network and thus appears as a large node near the US node in the map. Next, the leading European countries England, France, Germany, Italy, and Spain appear.

The overlay version of the map includes the time evolution of the research activity in the form of coloring of the nodes. The map shows the mean publication year of the publications for each specific author country. As a consequence, the time span of the mean publication years ranges only from 2014 to 2018. Nevertheless, the early activity in France and the USA and the comparatively recent activity in Australia and China, with the European countries in between, become clearly visible.

4.3 Topics of the heat wave literature

Figure  4 shows the keywords (keywords plus) map for revealing the thematic content of our publication set using the VOSviewer software. This analysis is based on the complete publication set ( n  = 8,011). The minimum number of occurrences of keywords is 10; of the 10,964 keywords, 718 keywords met the threshold. For each of the 718 keywords, the total strength of the co-occurrence links with other keywords was calculated. The keywords with the greatest total link strength were selected for presentation in the map.

Co-occurrence network map of the keywords plus from the 8,011 papers dealing with heat waves for a rough analysis of the thematic content. The minimum number of occurrences of keywords is 10; of the 10,964 keywords, 718 meet the threshold. Readers interested in an in-depth analysis can use VOSviewer interactively and zoom into the map via the following URL: https://tinyurl.com/enrdbw

According to Fig.  4 , the major keywords are the following: climate change, temperature, mortality, impact, heat waves (searched), and variability. The colored clusters identify closely related (frequently co-occurring) nodes. The keywords marked red roughly originate from fundamental climate change research focused on the hydrological cycle (particularly on drought), the keywords of the green cluster are around heat waves and moisture or precipitation, the keywords marked blue result from research concerning impacts of heat waves on health, the keywords marked yellow are focused on the various other impacts of heat waves, and the keywords of the magenta cluster are around adaptation and vulnerability in connection with heat waves.

The clustering by the VOSviewer algorithm provides basic categorizations, but many related keywords also appear in different clusters. For example, severe heat wave events are marked in different colors. For a better overview of the thematic content of the publications dealing with heat waves, we have assigned the keywords of Fig.  4 (with a minimum number of occurrences of 50) to ten subject categories (each arranged in the order of occurrence):

Countries/regions: United-States, Europe, France, China, Pacific, Australia, London, England

Cities: cities, city, US cities, Chicago, communities

Events: 2003 heat-wave, 1995 heat-wave

Impacts: impact, impacts, air-pollution, drought, soil-moisture, exposure, heat-island, urban, islands, photosynthesis, pollution, heat-island, air-quality, environment, precipitation extremes, biodiversity, emissions

Politics: risk, responses, vulnerability, adaptation, management, mitigation, risk-factors, scenarios

Biology: vegetation, forest, diversity, stomatal conductance

Medicine: mortality, health, stress, deaths, morbidity, hospital admissions, public-health, thermal comfort, population, heat, sensitivity, human health, disease, excess mortality, heat-stress, heat-related mortality, comfort, behavior, death, stroke

Climate research: climate change, temperature, climate, model, simulation, energy, projections, simulations, cmip5, ozone, el-nino, parametrization, elevated CO 2 , models, climate variability, carbon, carbon-dioxide

Meteorology: heat waves, variability, precipitation, summer, heat-wave, weather, ambient-temperature, waves, extremes, wave, cold, water, rainfall, circulation, heat, air-temperature, extreme heat, climate extremes, heatwaves, temperature extremes, temperatures, temperature variability, high-temperature, ocean, extreme temperatures, atmospheric circulation, interannual variability, sea-surface temperature, oscillation, surface temperature, surface

Broader terms (multi-meaning): trends, events, patterns, growth, performance, time-series, indexes, system, dynamics, association, index, tolerance, productivity, ensemble, resilience, increase, quality, prediction, frequency, particulate matter, future, framework, 20 th -century, time, reanalysis, systems

Although allocated by the database provider, the keywords are not coherent. For example, the same keyword may appear as singular or plural, and complex keywords are written with and without hyphens.

In order to compare the thematic content of the complete publication set with the earlier literature on heat waves, we have analyzed the pre-2000 publications ( n  = 297) separately. Figure  5 shows the keywords (keywords plus) map for revealing the thematic content of the pre-2000 papers.

Co-occurrence network map of the keywords plus from the 297 pre-2000 papers dealing with heat waves for a rough analysis of the thematic content. The minimum number of occurrences of keywords is 1; of the 389 keywords, 277 keywords are connected, and all items are shown. Readers interested in an in-depth analysis can use VOSviewer interactively and zoom into the map via the following URL: https://tinyurl.com/u2zzr399

The major nodes in Fig.  5 are heat waves (searched), temperature, United States, and mortality, with climate change appearing only as a smaller node here. Obviously, the connection between heat waves and climate change was not yet pronounced, which can also be seen from Fig.  1 . Compared with Fig.  4 , the thematic content of the clusters is less clear and the clusters presented in Fig.  5 can hardly be assigned to specific research areas. For a better overview of the thematic content of the early publications dealing with heat waves, we have assigned the connected keywords of Fig.  5 to seven subject categories:

Countries/regions: United-States, Great-Plains

Cities: St-Louis, Athens, Chicago

Events: 1980 heat-wave, 1995 heat-wave

Impacts: impacts, responses, drought, precipitation, comfort, sultriness

Climate research: climate, climate change, model, temperature, variability

Medicine: cardiovascular deaths, mortality, air pollution

Meteorology: atmospheric flow, weather, heat, humidity index

4.4 Important publications

Figures  6 – 8 show the results of the RPYS analysis performed with the CRExplorer and present the distribution of the number of cited references across the reference publication years. Figure  6 shows the RPYS spectrogram of the full range of reference publication years since 1925. Figure  7 presents the spectrogram for the reference publication year period 1950–2000 for better resolving the historical roots. Figure  8 shows the spectrogram for the period 2000–2020, comprising the cited references from the bulk of the publication set analyzed.

Annual distribution of cited references throughout the time period 1925–2020, which have been cited in heat wave-related papers (published between 1964 and 2020). Only references with a minimum reference count of 10 are considered

Annual distribution of cited references throughout the time period 1950–2000, which have been cited in heat wave-related papers (published between 1972 and 2020). Only references with a minimum reference count of 10 are considered

Annual distribution of cited references throughout the time period 2000–2020, which have been cited in heat wave-related papers (published between 2000 and 2020). Only references with a minimum reference count of 10 are considered

The gray bars (Fig.  6 ) and red lines (Figs. 7 – 8 ) in the graphs visualize the number of cited references per reference publication year. In order to identify those publication years with significantly more cited references than other years, the (absolute) deviation of the number of cited references in each year from the median of the number of cited references in the two previous, the current, and the two following years (t − 2; t − 1; t; t + 1; t + 2) is also visualized (blue lines). This deviation from the 5-year median provides a curve smoother than the one in terms of absolute numbers. We inspected both curves for the identification of the peak papers.

Which papers are most important for the scientific community performing research on heat waves? We use the number of cited references (N_CR) as a measure of the citation impact within the topic-specific literature of our publication set. N_CR should not be confused with the overall number of citations of the papers as given by the WoS citation counts (times cited). These citation counts are based on all citing papers covered by the complete database (rather than a topic-specific publication set) and are usually much higher.

Applying the selection criteria mentioned above (minimum number of cited references between 50 and 150 in three different periods), 104 references have been selected as key papers (important papers most frequently referenced within the research topic analyzed) and are presented in Table 2 in Appendix 2. The peak papers corresponding to reference publication years below about 2000 can be seen as the historical roots of the research topic analyzed. Since around 2000, the number of references with the same publication year becomes increasingly numerous, usually with more than one highly referenced (cited) paper at the top. Although there are comparatively fewer distinct peaks visible in the RPYS spectrogram of Fig.  8 , the most frequently referenced papers can easily be identified via the CRE reference listing. Depending on the specific skills and needs (i.e., the expert knowledge and the intended depth of the analysis), the number of top-referenced papers considered key papers can be defined individually.

Table 2 lists the first authors and titles of the 104 key papers selected, their number of cited references (N_CR), and the DOIs for easy access. Some N_CR values are marked by an asterisk, indicating a high value of the N_TOP10 indicator implemented in the CRExplorer. The N_TOP10 indicator value is the number of reference publication years in which a focal cited reference belongs to the 10% most referenced publications. In the case of about half of the cited references in Table 2 ( n  = 58), the N_TOP10 value exceeded a value of 9. The three highest values in our dataset are 24, 21, and 20.

Out of the 104 key papers from Table 2 , 101 have a DOI of which we found 101 papers in the WoS. Three papers have no DOI but could be retrieved from WoS. The altogether 104 papers were exported and their keywords (keywords plus) were displayed in Fig.  9 for revealing the thematic content of the key papers from the RPYS analysis at a glance.

Co-occurrence network map of the keywords plus of the 104 key papers dealing with heat waves selected applying RPYS via CRE software and listed in Table 2 . The minimum number of occurrences of keywords is 2; of the 310 keywords, 91 meet the threshold. Readers interested in an in-depth analysis can use VOSviewer interactively and zoom into the map via the following URL: https://tinyurl.com/4vwpc4t2

Overall, the keywords mapped in Fig.  9 are rather similar to the keywords presented in Fig.  4 . Besides climate change, temperature, weather, and air-pollution, the keywords deaths, health, mortality, and United-States appear as the most pronounced terms.

The key papers presented in Table 2 can be categorized as follows: (1) papers dealing with specific heat wave events, (2) the impact of heat waves on human health, (3) heat wave-related excess mortality and implications for prevention, (4) the interaction between air pollution and high temperature, (5) circulation pattern and the meteorological basis, (6) future perspectives and risks, and (7) climate models, indicators, and statistics.

5 Discussion

Today, the hypothesis of a human-induced climate change is no longer abstract but has become a clear fact, at least for the vast majority of the scientific community (IPCC 2014; CSSR 2017; NCA4 2018; and the multitude of references cited therein). The consequences of a warmer climate are already obvious. The rapidly growing knowledge regarding the earth’s climate system has revealed the connection between global warming and extreme weather events. Heat waves impact people directly and tangibly and many people are pushing for political actions. Research on heat waves came up with the occurrence of some severe events in the second half of the twentieth century and was much stimulated by the more numerous, more intense, and longer lasting heat waves that have occurred since the beginning of the twenty-first century.

As already mentioned in Sect.  1 , the more intense and more frequently occurring heat waves cannot be explained solely by natural climate variations but only with human-made climate change. As a consequence, research on heat waves has become embedded into meteorology and climate change research and has aimed to understand the specific connection with global warming. Scientists discuss a weakening of the polar jet stream as a possible reason for an increasing probability for the occurrence of heat waves (e.g., Broennimann et al. 2009 ; Coumou et al. 2015 ; Mann 2019 ). Climate models are used for projections of temperature and rainfall variability in the future, based on various scenarios of greenhouse gas emissions. As a result, the corresponding keywords appear in the maps of Figs. 4 and 9 . Also, the application of statistics plays a major role in the papers of our publication set; some of the most highly referenced (early) papers in Table 2 primarily deal with statistical methods. These methods provide the basis for research on heat waves.

Our analysis shows that research on heat waves has become extremely important in the medical area, since severe heat waves have caused significant excess mortality (e.g., Kalkstein and Davis 1989 ; Fouillet et al. 2006 ; Anderson and Bell 2009 , 2011 ). The most alarming is that the limit for survivability may be reached at the end of the twenty-first century in many regions of the world due to the fatal combination of rising temperatures and humidity levels (e.g., Pal and Eltahir 2016 ; Im et al. 2017 ; Kang and Eltahir 2018 ). The combination of heat and humidity is measured as the “wet-bulb temperature” (WBT), which is the lowest temperature that can be reached under current ambient conditions by the evaporation of water. At 100% relative humidity, the wet-bulb temperature is equal to the air temperature and is different at lower humidity levels. For example, an ambient temperature of 46 °C and a relative humidity of 50% correspond to 35 °C WBT, which is the upper limit that can kill even healthy people within hours. By now, the limit of survivability has almost been reached in some places. However, if global warming is not seriously tackled, deadly heat waves are anticipated for many regions that have contributed little to climate change.

According to high-resolution climate change simulations, North China and South Asia are particularly at risk, because the annual monsoon brings hot and humid air to these regions (Im et al. 2017 ; Kang and Eltahir 2018 ). The fertile plain of North China has experienced vast expansion of irrigated agriculture, which enhances the intensity of heat waves. South Asia, a region inhabited by about one-fifth of the global human population, is likely to approach the critical threshold by the late twenty-first century, if greenhouse gas emissions are not lowered significantly. In particular, the densely populated agricultural regions of the Ganges and Indus river basins are likely to be affected by extreme future heat waves. Also, the Arabic-speaking desert countries of the Gulf Region in the Middle East and the French-speaking parts of Africa are expected to suffer from heat waves beyond the limit of human survival. But to date, only 12 papers have been published on heat waves in connection with wet-bulb temperature (#15 of the search query); no paper was published before 2016. Some papers report excess hospital admissions during heat wave events (e.g., Semenza et al. 1999 ; Knowlton et al. 2009 ), with the danger of a temporary capacity overload of local medical systems in the future. Presumably, this will be an increasingly important issue in the future, when more and larger urban areas are affected by heat waves beyond the limit of human survival indicated by wet-bulb temperatures above 35° C.

The importance of heat waves for the medical area is underlined by the large portion of papers discussing excess hospital admissions and excess mortality during intense heat wave events, particularly in urban areas with a high population density. As was the case during the boom phase of the Covid-19 pandemic, local medical health care systems may become overstressed by long-lasting heat wave events and thus adaptation strategies are presented and discussed. Finally, the analysis of the keywords in this study reveals the connection of heat wave events with air pollution in urban regions. There seems to be evidence of an interaction between air pollution and high temperatures in the causation of excess mortality (e.g., Katsouyanni et al. 1993 ). Two more recent papers discuss the global risk of deadly heat (Mora et al. 2017 ) and the dramatically increasing chance of extremely hot summers since the 2003 European heat wave (Christidis et al. 2015 ).

Another important topic of the heat wave papers is related to the consequences for agriculture and forestry. Reduced precipitation and soil moisture result in crop failure and put food supplies at risk. Unfortunately, large regions of the world that contribute least to the emission of greenhouse gases are affected most by drought, poor harvests, and hunger. Some more recent papers discuss the increasing probability of marine heat waves (Oliver et al. 2018 ) and the consequences for the marine ecosystem (Smale et al. 2019 ).

The results of this study should be interpreted in terms of its limitations:

We tried to include in our bibliometric analyses all relevant heat wave papers covered by the database. Our long-standing experience in professional information retrieval has shown, however, that it is sheer impossible to get complete and clean results by search queries against the backdrop of the search functions provided by literature databases like WoS or others. Also, the transition from relevant to non-relevant literature is blurred and is a question of the specific needs. In this study, we used bibliometric methods that are relatively robust with regard to the completeness and precision of the publication sets analyzed. For example, it is an advantage of RPYS that a comparatively small portion of relevant publications (i.e., an incomplete publication set) contains a large amount of the relevant literature as cited references. The number of cited references is indeed lowered as a consequence of an incomplete publication set. However, this does not significantly affect the results, since the reference counts are only used as a relative measure within specific publication years.

As most literature databases, the WoS does not cover each and every scientific journal but only a carefully selected set of core journals most important for scientific disciplines. The coverage or comprehensiveness of the database can be estimated by comparing the number of all cited references with the number of the linked cited references (i.e., the references, which correspond to papers appearing in publications covered by the database as publication records). Based on the publication years 1990, 1995, 2000, 2005, and 2010, about 70% of all references in the natural sciences are linked references (Marx and Bornmann 2015 ). Thus, about 30% of the cited literature of these disciplines is not covered by the database in the form of paper records, presumably many non-English publications. It may be true that the publication set analyzed is biased toward mid-latitude developed countries, disadvantaging countries with most people suffering from humid heat waves. Parts of the most extreme heat waves occur in the French-speaking parts of Africa and the Arabic-speaking desert countries. Presumably, relevant literature like national reports discussing for example the local impact of extreme heat waves is not included in this analysis. However, if such documents were highly relevant, they should be cited in the literature covered by the WoS. In this case, our RPYS analysis would have discovered them. Therefore, we are confident that at least the highly relevant documents of the heat wave literature are considered in our analysis.

Two other limitations of this study refer to the RPYS of the heat wave paper set:

There are numerous rather highly cited references retrieved by RPYS via CRExplorer but not considered in the listing of Table 2 due to the selection criteria applied. Many of these non-selected papers have N_CR values just below the limits that we have set. Therefore, papers not included in our listing are not per se qualified as much less important or even unimportant.

In the interpretation of cited references counts, one should have in mind that they rely on the “popularity” of a publication being cited in subsequent research. The counts measure impact but not scientific importance or accuracy (Tahamtan and Bornmann 2019 ). Note that there are many reasons why authors cite publications (Tahamtan and Bornmann 2018 ), thus introducing a lot of “noise” in the data (this is why RPYS focuses on the cited reference peaks).

Our suggestions for future empirical analysis refer to the impact of the scientific heat wave discourse on social networks and funding of basic research on heat waves around topics driven by political pressure. Whereas this paper focuses on the scientific discourse around heat waves, it would be interesting if future studies were to address the policy relevance of the heat waves research.

Data availability

Not applicable.

Code availability

Change history, 23 february 2022.

The original version of this paper was updated to add the missing compact agreement Open Access funding note.

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Werner Marx, Robin Haunschild & Lutz Bornmann

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All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Werner Marx, Robin Haunschild, and Lutz Bornmann. The first draft of the manuscript was written by Werner Marx and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Marx, W., Haunschild, R. & Bornmann, L. Heat waves: a hot topic in climate change research. Theor Appl Climatol 146 , 781–800 (2021). https://doi.org/10.1007/s00704-021-03758-y

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Received : 29 August 2020

Accepted : 14 August 2021

Published : 03 September 2021

Issue Date : October 2021

DOI : https://doi.org/10.1007/s00704-021-03758-y

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