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11.15: Homework Exercises

• Last updated
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• Page ID 10216

• Roland Stull
• University of British Columbia

11.15.1. Broaden Knowledge & Comprehension

B1. From hemispheric weather maps of winds near the tropopause (which you can access via the internet), identify locations of major global-circulation features including the jet stream, monsoon circulations, tropical cyclones and the ITCZ.

B2. Same as the previous exercise, except using water-vapor or infrared image loops from geostationary satellites to locate the features.

B3. From the web, find a rawinsonde sounding at a location in the trade-wind region, and confirm the wind reversal between low and high altitudes.

B4. Use a visible, whole-disk image from a geostationary satellite to view and quantify the cloud-cover fraction as a function of latitude. Speculate on how insolation at the Earth’s surface is affected.

B5. Download a series of rawinsonde soundings for different latitudes between the equator and a pole. Find the tropopause from each sounding, and then plot the variation of tropopause height vs. latitude.

B6. Download a map of sea-surface temperature (SST), and discuss how SST varies with latitude.

B7. Most satellite images in the infrared show greys or colors that are related to brightness temperature (see the legend in whole-disk IR images that you acquired from the internet). Use these temperatures as a function of latitude to estimate the corresponding meridional variation of IR-radiation out. Hint, consider the Stefan-Boltzmann law.

B8. Download satellite-derived images that show the climatological average incoming and outgoing radiation at the top of the atmosphere. How does it relate to the idealized descriptions in this chapter?

B9. Download satellite-derived or buoy & ship-derived ocean currents for the global oceans, and discuss how they transport heat meridionally, and why the oceanic transport of heat is relatively small at mid to high latitudes in the N. Hemisphere.

B10. Use a satellite image to locate a strong portion of the ITCZ over a rawinsonde site, and then download the rawinsonde data. Plot (compute if needed) the variation of pressure with altitude, and discuss how it does or doesn’t deviate from hydrostatic.

B11. Search the web for sites where you can plot “reanalysis data”, such as the NCEP/NCAR reanalysis or any of the ECMWF reanalyses. Pick a month during late summer from some past year in this database, and plot the surface pressure map. Explain how this “real” result relates to a combination of the “idealized” planetary and monsoonal circulations.

B12. Same as B11, but for monthly average vertical cross sections that can be looped as movies. Display fields such as zonal wind, meridional wind, and vertical velocity, and see how they vary over a year.

B13. Capture a current map showing 85 kPa temperatures, and assume that those temperatures are surrogates for the actual average virtual temperature between 100 and 70 kPa. Compute the thermal wind magnitude and direction for a location assigned by your teacher, and see if this theoretical relationship successfully explains the wind shear between 100 and 70 kPa. Justify your reasoning.

B14 Capture a current map showing the thickness between 100 and 50 kPa, and estimate the thermal wind direction and magnitude across that layer.

B15. Use rawinsonde soundings from stations that cross the jet stream. Create your own contour plots of the jet-stream cross section for (a) heights of key isobaric surfaces; (b) potential temperature; and (c) wind magnitude. Compare your plots with idealized sketches presented in this chapter.

B16. What are the vertical and horizontal dimensions of the jet stream, based on weather maps you acquire from the internet.

B17. Acquire a 50 kPa vorticity chart, and determine if the plotted vorticity is isentropic, absolute, relative, or potential. Where are positive-vorticity maxima relative to fronts and foul weather?

B18. Calculate the values for the four types of vorticity at a location identified by your instructor, based on data for winds and temperatures. Namely, acquire the raw data used for vorticity calculations; do not use vorticity maps captured from the web.

B19. For the 20 kPa geopotential heights, use the wavy pattern of height contours and their relative packing to identify ridges and troughs in the jet stream. Between two troughs, or between two ridges, estimate the wavelength of the Rossby wave. Use that measured length as if it were the dominant wavelength to estimate the phase speed for baroclinic and barotropic waves.

B20. Confirm that the theoretical relationship between horizontal winds, temperatures, vertical velocities, and heights for baroclinic waves is consistent with the corresponding weather maps you acquire from the internet. Explain any discrepancies.

B21. Confirm the three-band nature of the global circulation using IR satellite image movie loops. In the tropics, compare the motion of low (warm) and high (cold) clouds, and relate this motion to the trade winds and Hadley circulation. In mid-latitudes, find the regions of meandering jet stream with its corresponding high and low-pressure centers. In polar regions, relate cloud motions to the polar cell.

B22. Are the ocean-surface current directions consistent with near-surface wind directions as observed in maps or animations acquired from the internet, given the dynamics describe for the Ekman spiral?

11.15.2. Apply

A1(§). For the “toy” model, make a graph of zonally-averaged temperature (°C) vs. latitude for the altitude (km) above ground level (AGL) given here:

A2(§). For the “toy” model, make a graph of zonallyaveraged ∆T/∆y (°C km –1 ) vs. latitude for the altitude (km AGL) given here:

A3. Estimate the annual average insolation (W m –2 ) at the following latitude:

A4. Estimate the annual average amount of incoming solar radiation (W m –2 ) that is absorbed in the Earth-ocean-atmosphere system at latitude:

A5. Using the idealized temperature near the middle of the troposphere (at z = 5.5 km), estimate the outgoing infrared radiation (W m –2 ) from the atmosphere at the following latitude:

A6. Using the results from the previous two exercises, find the net radiation magnitude (W m –2 ) that is input to the atmosphere at latitude:

A7. Using the results from the previous exercise, find the latitude-compensated net radiation magnitude (W m –2 ; i.e., the differential heating) at latitude:

A8. Assuming a standard atmosphere, find the internal Rossby deformation radius (km) at latitude:

A9. Given the following virtual temperatures at your location (20°C) and at another location, find the change of geostrophic wind with height [(m s –1 )/ km]. Relative to your location, the other locations are:

A10. Find the thermal wind (m s –1 ) components, given a 100 to 50 kPa thickness change of 0.1 km across the following distances:

A11. Find the magnitude of the thermal wind (m s –1 ) for the following thickness gradients:

A12. For the toy model temperature distribution, find the wind speed (m s –1 ) of the jet stream at the following heights (km) for latitude 30°:

A13. If an air parcel from the starting latitude 5° has zero initial velocity relative to the Earth, then find its U component of velocity (m s –1 ) relative to the Earth when it reaches the following latitude, assuming conservation of angular momentum.

A14. Find the relative vorticity (s –1 ) for the change of (U , V) wind speed (m s –1 ), across distances of ∆x = 300 km and ∆y = 600 km respectively given below.

A15. Given below a radial shear (∆M/∆R) in [(m s –1 )/ km] and tangential wind speed M (m s –1 ) around radius R (km), find relative vorticity (s –1 ):

A16. If the air rotates as a solid body of radius 500 km, find the relative vorticity (s –1 ) for tangential speeds (m s –1 ) of:

A17. If the relative vorticity is 5x10 –5 s –1 , find the absolute vorticity at the following latitude:

A18. If absolute vorticity is 5x10 –5 s –1 , find the potential vorticity (m –1 ·s –1 ) for a layer of thickness (km) of:

A19. The potential vorticity is 1x10 –8 m –1 ·s –1 for a 10 km thick layer of air at latitude 48°N. What is the change of relative vorticity (s –1 ) if the thickness (km) of the rotating air changes to:

A20. If the absolute vorticity is 3x10 –5 s –1 at 12 km altitude, find the isentropic potential vorticity (PVU) for a potential temperature change of ___ °C across a height increase of 1 km.

A21. Find the horizontal circulation associated with average relative vorticity 5x10 –5 s –1 over area (km 2 ):

A22. For the latitude given below, what is the value of the beta parameter (m –1 s –1 ):

A23. Suppose the average wind speed is 60 m s –1 from the west at the tropopause. For a barotropic Rossby wave at 50° latitude, find both the intrinsic phase speed (m s –1 ) and the phase speed (m s –1 ) relative to the ground for wavelength (km) of:

A24. Plot the barotropic wave (y’ vs x’) from the previous exercise, assuming amplitude 2000 km.

A25. Same as exercise A23, but for a baroclinic Rossby wave in an atmosphere where air temperature decreases with height at 4°C km –1 .

A26(§). Plot the baroclinic wave (y’ vs x’) from the previous exercise, assuming amplitude 2000 km and a height (km):

A27. What is the fastest growing wavelength (km) for a baroclinic wave in a standard atmosphere at latitude:

A28. For the baroclinic Rossby wave of exercise A25 with amplitude 2000 km, find the wave amplitudes of the:

• vertical-displacement perturbation
• potential-temperature perturbation
• pressure perturbation
• U-wind perturbation
• V-wind perturbation
• W-wind perturbation

A29(§). For a vertical slice through the atmosphere, plot baroclinic Rossby-wave perturbation amount for conditions assigned in exercise A28.

A30. Find the latitude-weighted a·u’ momentum value (m s –1 ) for air that reaches destination latitude 50° from source latitude:

A31. Suppose the ____ cell upward and downward speeds are ___ and ___ mm s –1 , respectively, and the north-south wind speeds are 3 m s –1 at the top and bottom of the cell. The cell is about __ km high by ___ km wide, and is centered at about ___ latitude. Temperature in the atmosphere decreases from about 15°C near the surface to –57°C at 11 km altitude. Find the vertical circulation.

A32. Find the friction velocity at the water surface if the friction velocity (m s –1 ) in the air (at sea level for a standard atmosphere) is:

A33. Find the Ekman-spiral depth scale at latitude 50°N for eddy viscosity (m 2 s –1 ) of:

A34(§). Create a graph of Ekman-spiral wind components (U, V) components for depths from the surface down to where the velocities are near zero, for near-surface wind speed of 8 m s –1 at 40°N latitude.

11.15.3. Evaluate & Analyze

E1. During months when the major Hadley cell exists, trade winds cross the equator. If there are no forces at the equator, explain why this is possible.

E2. In regions of surface high pressure, descending air in the troposphere is associated with dry (nonrainy) weather. These high-pressure belts are where deserts form. In addition to the belts at ±30° latitude, semi-permanent surface highs also exist at the poles. Are polar regions deserts? Explain.

E3. The subtropical jet stream for Earth is located at about 30° latitude. Due to Coriolis force, this is the poleward limit of outflow air from the top of the ITCZ. If the Earth were to spin faster, numerical experiments suggest that the poleward limit (and thus the jet location) would be closer to the equator. Based on the spins of the other planets (get this info from the web or a textbook) compared to Earth, at what latitudes would you expect the subtropical jets to be on Jupiter? Do your predictions agree with photos of Jupiter?

E4. Horizontal divergence of air near the surface tends to reduce or eliminate horizontal temperature gradients. Horizontal convergence does the opposite. Fronts (as you will learn in the next chapter) are regions of strong local temperature gradients. Based on the general circulation of Earth, at what latitudes would you expect fronts to frequently exist, and at what other latitudes would you expect them to rarely exist? Explain.

E5. In the global circulation, what main features can cause mixing of air between the Northern and Southern Hemispheres? Based on typical velocities and cross sectional areas of these flows, over what length of time would be needed for the portion 1/e of all the air in the N. Hemisphere to be replaced by air that arrived from the S. Hemisphere?

E6. In Fig. 11.4, the average declination of the sun was listed as 14.9° to 15° for the 4-month periods listed in those figures. Confirm that those are the correct averages, based on the equations from the Solar & Infrared Radiation chapter for solar declination angle vs. day of the year.

E7. Thunderstorms are small-diameter (15 km) columns of cloudy air from near the ground to the tropopause. They are steered by the environmental winds at an altitude of roughly 1/4 to 1/3 the troposphere depth. With that information, in what direction would you expect thunderstorms to move as a function of latitude (do this for every 10° latitude)?

E8. The average meridional wind at each pole is zero. Why? Also, does your answer apply to instantaneous winds such as on a weather map? Why?

E9. Can you detect monsoonal (monthly or seasonal average) pressure centers on a normal (instantaneous) weather map analysis or forecast? Explain.

E10. Figs. 11.3a & 11.5a showed idealized surface wind & pressure patterns. Combine these and draw a sketch of the resulting idealized global circulation including both planetary and monsoon effects.

E11. Eqs. (11.1-11.3) represent an idealized (“toy model”) meridional variation of zonally averaged temperature. Critically analyze this model and discuss. Is it reasonable at the ends (boundaries) of the curve; are the units correct; is it physically justifiable; does it satisfy any budget constraints (e.g., conservation of heat, if appropriate), etc. What aspects of it are too simplified, and what aspects are OK?

E12. (a) Eq. (11.4) has the 3 rd power of the sine times the 2 nd power of the cosine. If you could arbitrarily change these powers, what values would lead to reasonable temperature gradients (∆T/∆y) at the surface and which would not (Hint: use a spreadsheet and experiment with different powers)?

(b) Of the various powers that could be reasonable, which powers would you recommend as fitting the available data the best? (Hint: consider not only the temperature gradient, but the associated meridional temperature profile and the associated jet stream.) Also, speculate on why I chose the powers that I did for this toy model.

E13. Concerning differential heating, Fig. 11.9 shows the annual average insolation vs. latitude. Instead, compute the average insolation over the two-month period of June and July, and plot vs. latitude. Use the resulting graph to explain why the jet stream and weather patterns are very weak in the summer hemisphere, and strong in the winter hemisphere.

E14. At mid- and high-latitudes, Fig. 11.9 shows that each hemisphere has one full cycle of insolation annually (i.e., there is one maximum and one minimum each year).

But look at Fig. 11.9 near the equator.

• Based on the data in this graph (or even better, based on the eqs. from the Solar & Infrared Radiation chapter), plot insolation vs. relative Julian day for the equator.
• How many insolation cycles are there each year at the equator?
• At the equator, speculate on when would be the hottest and coldest “seasons”.
• Within what range of latitudes near the equator is this behavior observed?

E15. Just before idealized eq. (11.6), I mentioned my surprise that E 2 was approximately constant with latitude. I had estimated E 2 by subtracting my toy-model values for E insol from the actual observed values of E in . Speculate about what physical processes could cause E 2 to be constant with latitude all the way from the equator to the poles.

E16. How sensitive is the toy model for E out (i.e., eq. 11.7) to the choice of average emission altitude z m ? Recall that z m , when used as the altitude z in eqs. (11.1-11.3), affects T m . Hint: for your sensitivity analysis, use a spreadsheet to experiment with different z m and see how the resulting plots of E out vs. latitude change. (See the “A SCIENTIFIC PERSPECTIVE” box about model sensitivity.)

E17(§). Solve the equations to reproduce the curves in figure:

E18. We recognize the global circulation as a response of the atmosphere to the instability caused by differential heating, as suggested by LeChatelier’s Principle . But the circulation does not totally undo the instability; namely, the tropics remain slightly warmer than the poles. Comment on why this remaining, unremoved instability is required to exist, for the global circulation to work.

E19. In Fig. 11.12, what would happen if the surplus area exceeded the deficit area? How would the global circulation change, and what would be the end result for Fig. 11.12?

E20. Check to see if the data in Fig. 11.12 does give zero net radiation when averaged from pole to pole.

E21. The observation data that was used in Fig. 11.14 was based on satellite-measured radiation and differential heating to get the total needed heat transport, and on estimates of heat transport by the oceans . The published “observations” for net atmospheric heat transport were, in fact, estimated as the difference (i.e., residual) between the total and the ocean curves. What could be some errors in this atmosphere curve? (Hint: see the A SCIENTIFIC PERSPECTIVE box about Residuals.)

E22. Use the total heat-transport curve from Fig. 11.60. At what latitude is the max transport? For that latitude, convert the total meridional heat-flux value to horsepower.

E23. For Fig. 11.15, explain why it is p’ vs. z that drive vertical winds, and not P column vs. z.

• Redraw Figs. 11.16 for downdraft situations.
• Figs. 11.16 both show updraft situations, but they have opposite pressure couplets. As you already found from part (a) both pressure couplets can be associated with downdrafts. What external information (in addition to the pressure-couplet sign) do you always need to decide whether a pressure couplet causes an updraft or a downdraft? Why?
• For the thermal circulation of Fig. 11.17(iv), what needs to happen for this circulation to be maintained? Namely, what prevents it from dying out?
• For what real-atmosphere situations can thermal circulations be maintained for several days?
• Study Fig. 11.18 closely, and explain why the wind vectors to/from the low- and high-pressure centers at the equator differ from the winds near pressure centers at mid-latitudes.
• Redraw Fig. 11.5a, but with continents and oceans at the equator. Discuss what monsoonal pressures and winds might occur during winter and summer, and why.
• Redraw Fig. 11.19, but for the case of geostrophic wind decreasing from its initial equilibrium value. Discuss the resulting evolution of wind and pressure fields during this geostrophic adjustment.
• Redraw Fig. 11.19, but for flow around a lowpressure center (i.e., look at gradient winds instead of geostrophic winds). Discuss how the wind and pressure fields adjust when the geostrophic wind is increased above its initial equilibrium value.

E28. How would the vertical potential temperature gradient need to vary with latitude for the “internal Rossby radius of deformation” to be invariant? Assume constant troposphere depth.

E29. In the Regional Winds chapter, gap winds and coastally-trapped jets are explained. Discuss how these flows relate to geostrophic adjustment.

E30. At the top of hurricanes (see the Tropical Cyclones chapter), so much air is being continuously pumped to the top of the troposphere that a highpressure center is formed over the hurricane core there. This high is so intense and localized that it violates the conditions for gradient winds; namely, the pressure gradient around this high is too steep (see the Forces & Winds chapter).

Discuss the winds and pressure at the top of a hurricane, using what you know about geostrophic adjustment. Namely, what happens to the winds and air mass if the wind field is not in geostrophic or gradient balance with the pressure field?

E31. In the thermal-wind relationship (eqs. 11.13), which factors on the right side are constant or vary by only a small amount compared to their magnitude, and which factors vary more (and are thus more important in the equations)?

E32. In Fig. 11.20, how would it change if the bottom isobaric surface were tilted; namely, if there were already a horizontal pressure gradient at the bottom?

E33. Draw a sketch similar to Fig. 11.20 for the thermalwind relationship for the Southern Hemisphere.

E34. In maps such as Fig. 11.21, explain why thickness is related to average temperature.

E35. Redraw Fig. 11.22 for the case cold air in the west and warm air in the east. Assume no change to the bottom isobaric surface.

E36. Copy Fig. 11.24.

• On your copy, draw the G 1 and G 2 vectors, and the M TH vector at point B. Confirm that the thermal wind relationship is qualitatively satisfied via vector addition. Discuss why point B is an example of veering or backing.
• Same as (a) but calculate the actual magnitude of each vector at point B based on the spacing between isobars, thickness contours, or height contours. Again, confirm that the thermal wind relationship is satisfied. (1° latitude = 111 km)

E37. Using a spreadsheet, start with an air parcel at rest at the tropopause over the equator. Assume a realistic pressure gradient between the equator and 30° latitude. Use dynamics to solve for acceleration of the parcel over a short time step, and then iterate over many time steps to find parcel speed and position. How does the path of this parcel compare to the idealized paths drawn in Fig. 11.26d? Discuss.

E38. In the thunderstorms at the ITCZ, copious amounts of water vapor condense and release latent heat. Discuss how this condensation affects the average lapse rate in the tropics, the distribution of heat, and the strength of the equatorial high-pressure belt at the tropopause.

E39. Summarize in a list or an outline all the general-circulation factors that make the mid-latitude weather different from tropical weather.

E40. Explain the surface pressure patterns in Figs. 11.31 in terms of a combination of idealized monsoon and planetary circulations.

E41. Figs. 11.31 show mid-summer and mid-winter conditions in each hemisphere. Speculate on what the circulation would look like in April or October.

E42. Compare Figs. 11.32 with the idealized planetary and monsoon circulations, and discuss similarities and differences.

E43. Based on Figs. 11.32, which hemisphere would you expect to have strong subtropical jets in both summer and winter, and which would not. What factors might be responsible for this difference?

E44. For the Indian monsoon sketched in Fig. 11.33, where are the updraft and downdraft portions of the major Hadley cell for that month? Also, what is the relationship between the trade winds at that time, and the Indian monsoon winds?

E45. What are the dominant characteristics you see in Fig. 11.34, regarding jet streams in the Earth’s atmosphere? Where don’t jet streams go?

E46. In Figs. 11.35, indicate if the jet-stream winds would be coming out of the page or into the page, for the:

• N. Hemisphere,
• S. Hemisphere.

E47. Although Figs. 11.36 are for different months than Figs. 11.32, they are close enough in months to still both describe summer and winter flows.

• Do the near-tropopause winds in Figs. 11.36 agree with the pressure gradients (or height gradients) in Figs. 11.32?
• Why are there easterly winds at the tropopause over/near the equator, even though there is negligible pressure gradient there?

E48. Describe the mechanism that drives the polar jet, and explain how it differs from the mechanism that drives the subtropical jet.

E49. In Fig. 11.37b, we see a very strong pressure gradient in the vertical (indicated by the different isobars), but only small pressure gradients in the horizontal (indicated by the slope of any one isobar). Yet the strongest average winds are horizontal, not vertical. Why?

E50. Why does the jet stream wind speed decrease with increasing height above the tropopause?

E51. a. Knowing the temperature field given by the toy model earlier in this chapter, show the steps needed to create eq. (11.17) by utilizing eqs. (11.2, 11.4 and 11.13). b. For what situations might this jetwind-speed equation not be valid? c. Explain what each term in eq. (11.17) represents physically.

E52. Why does an air parcel at rest (i.e., calm winds) near the equator possess large angular momentum?

What about for air parcels that move from the east at typical trade wind speeds?

E53. At the equator, air at the bottom of the troposphere has a smaller radius of curvature about the Earth’s axis than at the top of the troposphere. How significant is this difference? Can we neglect it?

E54. Suppose that air at 30° latitude has no eastwest velocity relative to the Earth’s surface. If that air moves equatorward while preserving its angular momentum, which direction would it move relative to the Earth’s surface? Why? Does it agree with real winds in the general circulation? Elaborate.

E55. Picture a circular hot tub of 2 m diameter with a drain in the middle. Water is initially 1.2 m deep, and you made rotate one revolution each 10 s. Next, you pull the plug, allowing the water depth to stretch to 2.4 m as it flows down the drain. Calculate the new angular velocity of the water, neglecting frictional drag. Show your steps.

E56. In eq. (11.20), why is there a negative sign on the last term? Hint: How does the rotation direction implied by the last term without a negative sign compare to the rotation direction of the first term?

E57. In the Thunderstorm chapters, you will learn that the winds in a portion of the tornado can be irrotational. This is surprising, because the winds are traveling so quickly around a very tight vortex. Explain what wind field is needed to gave irrotational winds (i.e., no relative vorticity) in air that is rotating around the tornado. Hint: Into the wall of a tornado, imagine dropping a neutrally-buoyant small paddle wheel the size of a flower. As this flower is translated around the perimeter of the tornado funnel, what must the local wind shear be at the flower to cause it to not spin relative to the ground? Redraw Fig. 11.43 to show what you propose.

E58. Eq. (11.25) gives names for the different terms that can contribute toward vorticity. For simplicity, assume ∆z is constant (i.e., assume no stretching). On a copy of Fig. 11.44, write these names at appropriate locations to identify the dominant factors affecting the vorticity max and min centers.

E59. If you were standing at the equator, you would be rotating with the Earth about its axis. However, you would have zero vorticity about your vertical axis. Explain how that is possible.

E60. Eq. (11.26) looks like it has the absolute vorticity in the numerator, yet that is an equation for a form of potential vorticity. What other aspects of that equation make it like a potential vorticity?

E61. Compare the expression of horizontal circulation C with that for vertical circulation CC.

E62. Relate Kelvin’s circulation theorem to the conservation of potential vorticity. Hint: Consider a constant Volume = A·∆z .

E63. The jet stream sketched in Fig. 11.49 separates cold polar air near the pole from warmer air near the equator. What prevents the cold air from extending further away from the poles toward the equator?

E64. If the Coriolis force didn’t vary with latitude, could there be Rossby waves? Discuss.

E65. Are baroclinic or barotropic Rossby waves faster relative to Earth’s surface at midlatitudes? Why?

E66. Compare how many Rossby waves would exist around the Earth under barotropic vs. baroclinic conditions. Assume an isothermal troposphere at 50°N.

E67. Once a Rossby wave is triggered, what mechanisms do you think could cause it to diminish (i.e., to reduce the waviness, and leave straight zonal flow).

E68. In Fig. 11.50 at point (4) in the jet stream, why doesn’t the air just continue turning clockwise around toward points (2) and (3), instead of starting to turn the other way?

E69. Pretend you are a newspaper reporter writing for a general audience. Write a short article describing how baroclinic Rossby waves work, and why they differ from barotropic waves.

E70. What conditions are needed so that Rossby waves have zero phase speed relative to the ground? Can such conditions occur in the real atmosphere?

E71. Will Rossby waves move faster or slower with respect to the Earth’s surface if the tropospheric static stability increases? Why?

E72. For a baroclinic wave that is meandering north and south, consider the northern-most point as the wave crest. Plot the variation of this crest longitude vs. altitude (i.e., x vs. z). Hint: consider eq. (11.40).

E73. Use tropopause-level Rossby-wave troughaxes and ridge-axes as landmarks. Relative to those landmarks, where east or west is: (a) vertical velocity the greatest; (b) potential-temperature deviation the greatest; and (c) vertical displacement the greatest?

E74. In Figs. 11.51 and 11.53 in the jet stream, there is just as much air going northward as there is air going southward across any latitude line, as required by mass conservation. If there is no net mass transport, how can there be heat or momentum transport?

E75. For the Southern Hemisphere: (a) would a direct circulation cell have positive or negative CC? (b) for each term of eq. (11.51), what are their signs?

E76. Compare definitions of circulation from this chapter with the previous chapter, and speculate on the relevance of the static stability and Earth’s rotation in one or both of those definitions.

E77. Consider a cyclonic air circulation over an ocean in your hemisphere. Knowing the relationship between ocean currents and surface winds, would you anticipate that the near-surface wind-driven ocean currents are diverging away from the center of the cyclone, or converging toward the center? Explain, and use drawings. Note: Due to mass conservations, horizontally diverging ocean surface waters cause upwelling of nutrient-rich water toward the surface, which can support ocean plants and animals, while downwelling does the opposite.

11.15.4. Synthesize

S1. Describe the equilibrium general circulation for a non-rotating Earth.

S2. Circulations are said to spin-down as they lose energy. Describe general-circulation spin-down if Earth suddenly stopped spinning on its axis.

S3. Describe the equilibrium general circulation for an Earth that spins three times faster than now.

S4. Describe the spin-up (increasing energy) as the general circulation evolves on an initially non-rotating Earth that suddenly started spinning.

S5. Describe the equilibrium general circulation on an Earth with no differential radiative heating.

S6. Describe the equilibrium general circulation on an Earth with cold equator and hot poles.

S7. Suppose that the sun caused radiative cooling of Earth, while IR radiation from space caused warming of Earth. How would the weather and climate be different, if at all?

S8. Describe the equilibrium general circulation for an Earth with polar ice caps that extend to 30° latitude.

S9. About 250 million years ago, all of the continents had moved together to become one big continent called Pangaea , before further plate tectonic movement caused the continents to drift apart. Pangaea spanned roughly 120° of longitude (1/3 of Earth’s circumference) and extended roughly from pole to pole. Also, at that time, the Earth was spinning faster, with the solar day being only about 23 of our present-day hours long. Assuming no other changes to insolation, etc, how would the global circulation have differed compared to the current circulation?

S10. If the Earth was dry and no clouds could form, how would the global circulation differ, if at all? Would the tropopause height be different? Why?

S11. Describe the equilibrium general circulation for an Earth with tropopause that is 5 km high.

S12. Describe the equilibrium general circulation for an Earth where potential vorticity isn’t conserved.

S13. Describe the equilibrium general circulation for an Earth having a zonal wind speed halfway between the phase speeds of short and long barotropic Rossby waves.

S14. Describe the equilibrium general circulation for an Earth having long barotropic Rossby waves that had slower intrinsic phase speed than short waves.

S15. Describe the nature of baroclinic Rossby waves for an Earth with statically unstable troposphere.

S16. Describe the equilibrium general circulation for an Earth where Rossby waves had no north-south net transport of heat, momentum, or moisture.

S17. Describe the equilibrium general circulation for an Earth where no heat was transported meridionally by ocean currents.

S18. Describe the equilibrium ocean currents for an Earth with no drag between atmosphere and ocean.

S19. Suppose there was an isolated small continent that was hot relative to the surrounding cooler ocean. Sketch a vertical cross section in the atmosphere across that continent, and use thickness concepts to draw the isobaric surfaces. Next, draw a planview map of heights of one of the mid-troposphere isobaric surfaces, and use thermal-wind effects to sketch wind vectors on this same map. Discuss how this approach does or doesn’t explain some aspects of monsoon circulations.

S20. If the Rossby wave of Fig. 11.50 was displaced so that it is centered on the equator (i.e., point (1) starts at the equator), would it still oscillate as shown in that figure, or would the trough of the wave (which is now in the S. Hem.) behave differently? Discuss.

S21. If the Earth were shaped like a cylinder with its axis of rotation aligned with the axis of the real Earth, could Rossby waves exist? How would the global circulation be different, if at all?

S22. In the subtropics, low altitude winds are from the east, but high altitude winds are from the west. In mid-latitudes, winds at all altitudes are from the west. Why are the winds in these latitude bands different?

S23. What if the Earth did not rotate? How would the Ekman spiral in the ocean be different, if at all?

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Exercises: Calculus (OpenStax)

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These are homework exercises to accompany OpenStax's "Calculus" Textmap.

• 1.E: Functions and Graphs (Exercises) These are homework exercises to accompany Chapter 1 of OpenStax's "Calculus" Textmap.
• 2.E: Limits (Exercises) These are homework exercises to accompany Chapter 2 of OpenStax's "Calculus" Textmap.
• 3.E: Derivatives (Exercises) These are homework exercises to accompany Chapter 3 of OpenStax's "Calculus" Textmap.
• 4.E: Applications of Derivatives (Exercises) These are homework exercises to accompany Chapter 4 of OpenStax's "Calculus" Textmap.
• 5.E: Integration (Exercises) These are homework exercises to accompany Chapter 5 of OpenStax's "Calculus" Textmap.
• 6.E: Applications of Integration (Exercises) These are homework exercises to accompany Chapter 6 of OpenStax's "Calculus" Textmap.
• 7.E: Techniques of Integration (Exercises) These are homework exercises to accompany Chapter 7 of OpenStax's "Calculus" Textmap.
• 8.E: Differential Equations (Exercises) These are homework exercises to accompany Chapter 8 of OpenStax's "Calculus" Textmap.
• 9.E: Sequences and Series (Exercises) These are homework exercises to accompany Chapter 9 of OpenStax's "Calculus" Textmap.
• 10.E: Power Series (Exercises) These are homework exercises to accompany Chapter 10 of OpenStax's "Calculus" Textmap.
• 11.E: Parametric Equations and Polar Coordinates (Exercises) These are homework exercises to accompany Chapter 11 of OpenStax's "Calculus" Textmap.
• 12.E: Vectors in Space (Exercises) These are homework exercises to accompany Chapter 12 of OpenStax's "Calculus" Textmap.
• 13.E: Vector-Valued Functions (Exercises) These are homework exercises to accompany Chapter 13 of OpenStax's "Calculus" Textmap.
• 14.E: Differentiation of Functions of Several Variables (Exercise) These are homework exercises to accompany Chapter 14 of OpenStax's "Calculus" Textmap.
• 15.E: Multiple Integration (Exercises) These are homework exercises to accompany Chapter 15 of OpenStax's "Calculus" Textmap.
• 16.E: Vector Calculus (Exercises) These are homework exercises to accompany Chapter 16 of OpenStax's "Calculus" Textmap.
• 17.E: Second-Order Differential Equations (Exercises) These are homework exercises to accompany Chapter 17 of OpenStax's "Calculus" Textmap.

Thumbnail: The logarithmic spiral of the Nautilus shell is a classical image used to depict the growth and change related to calculus. (GNU Free Documentation License, Version 1.3 and CC- SA-BY 3.0; Wikipedia).

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• A2 listening

Using colours to do homework

Listen to the presentation about using colours to organise homework and do the exercises to practise and improve your listening skills.

Instructions

Do the preparation exercise before you listen. Then do the other exercises to check your understanding.

Preparation

Girl: My presentation is about how you can use colour coding to organise your homework.

To start you need a few things from the stationery shop. This photo shows the things I use. They aren't expensive. They are all cheap. I've got coloured pens and pencils, sticky notes, page markers, glue and folders.   

First, I choose a different colour for each school subject.  The colour I choose has to be easy to remember so I make sure it means something to me. Maths is green because my ruler is green. PE is yellow because my trainers are yellow. 

Here is a photo of my folders. I use the cheapest kind and I add a coloured sticky note to the top and to the front. I keep all my notes inside the different folders. 

This is a photo of some more sticky notes. I wrote them in the library when I was studying. The blue notes are for history. My history teacher has got a blue car! The black notes are for geography. One day I want to visit the Black Sea.

This photo shows the pages I need to read for homework. I use two coloured page markers to mark where it starts and ends. Those blue ones mark the pages I need to read for history. 

Finally, this last photo shows my wall calendar. This green star shows I have a maths test on Friday. This pink circle shows I've got French homework for Monday. It's pink because 'pink' is 'rose' in French … and the rose is my favourite flower.

Has anyone got any questions?

Check your understanding: true or false

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Which colours would you choose for each school subject? Why?

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Couples Therapy: Homework Exercises For Communication And Bonding

A common part of couples therapy for many is partaking in exercises outside of sessions, which are often known as “homework” exercises. Below, we’ve compiled some easy and helpful homework exercises that might aid you in your journey to strengthen your relationship, including gratitude lists, relationship check-ins, journaling, and more. These homework exercises can be tailored to specific romantic relationship goals, so feel free to get creative with how you use them. It can also be a good idea to complete these exercises under the guidance of a licensed mental health professional, which you can do in person or online.

Improve communication and strengthen your bond

Couples therapy is not just for couples experiencing challenges; anyone can benefit from improving relationship skills, bettering communication, and strengthening their bond with their partner. Researchers have looked into the impact of communication on relationships and found evidence that the better a couple communicates with each other, the more long-lasting and fulfilling their relationship is likely to be. 

What to expect in couples therapy

Couples therapy can go beyond the therapist’s office. Professional relationship therapists often recommend homework to their clients, such as the exercises included in this list. Relationship counseling is often the most effective when both members of the couple are willing to put in the work, both inside and outside of the therapist’s office. 

When you first attend couples therapy, the therapist will likely get to know you as a couple and then may want to talk to you individually. After determining your goals as a couple and as individuals, the therapist can support you in reaching those goals with evidence-based therapeutic interventions and relationship-building exercises. 

Depending on the therapist’s approach to counseling, they may use a variety of techniques, such as behavioral experiments, cognitive behavioral therapy, dialectical behavior therapy, psychotherapy, and homework. 

Best couples therapy homework exercises

Below are a few of the best couples therapy homework exercises recommended by couples therapists. You can use these couples therapy homework exercises at home with your partner, but they may be more impactful when combined with talk therapy from a licensed professional. A therapist can guide you through couples therapy exercises with tips for how to get the most out of the experience. 

Letter writing

If you go to couples counseling, you might practice letter writing as a homework assignment. Writing a letter to your partner can have many benefits, such as making it easier to express things that are hard to say out loud. By writing the letter, you may also discover underlying feelings, beliefs, or thoughts that can shift your perspective on a particular issue or subject. 

A great writing prompt for couples therapy that you can try at home is writing a letter to your partner describing all their best qualities and what you love about them. Then, you can have them write the same letter from their perspective, describing what they love about you and your relationship. This couples therapy exercise can help you better understand your partner’s views and recognize their best qualities. 

Gratitude lists

Making gratitude lists can be an ongoing homework exercise for couples to reflect on the positive things in their relationship and better appreciate each other. A gratitude list normally involves writing everything you are grateful for, or, in this case, what you are grateful for in your relationship. This exercise can be all about recognizing what the other person does that makes you happy and showing appreciation for them. 

For two weeks or more, write down a few things that made you happy or went well that day. When you look back on your list of positive moments, it may reveal patterns in the relationship. Talking with your partner about the list and noticing the patterns together can help you determine what is working in your relationship and how you can create joyful memories together. 

Studies show that displaying gratitude can have powerful benefits for mental health and well-being, such as reducing symptoms of anxiety and depression. Giving thanks has been found to make people happier overall, including in their relationships. 

One study on the benefits of gratitude for couples found that mutually expressing gratitude not only tended to make couples feel happier, but also made it easier to express what they wanted to change in their relationships. Positive encouragement from being shown gratitude could also help couples engage in more relationship “maintenance,” such as spending time together, checking in with each other, and being more responsive to each other’s needs. 

Scrapbooking memories

A fun and romantic couples therapy activity to try is making a scrapbook out of your memories together. Instead of a scrapbook, you could create a picture book with handmade drawings, collages, or online cut-outs. This can be an opportunity to assemble a cohesive memory book for you to reflect on your relationship together. 

If you have mementos, like romantic letters from the beginning of the relationship, or sentimental items, such as your first concert tickets together, you can put them in your memory book. You can also print out photos from your favorite memories together. Create the narrative of your love story in your scrapbook, then label the images with context about the memories and how you each feel about them. 

Icebreakers 

When you are first getting started with couples therapy, doing some fun and easy exercises like asking each other “icebreaker” questions may be beneficial. You may be surprised to find that there are things you do not know about your partner, even if you have been in a long-term relationship. These icebreaker questions are generally meant to be light-hearted and get couples comfortable before they delve into more challenging communication exercises. 

• What is your favorite childhood memory?
• Is there a funny story from your past you can share with me? 
• Would you ever want to be famous?
• What is your favorite love song?
• Do you know any random or useless facts?
• What was the first album or CD you purchased?
• If you had to eat one food for the rest of your life, what would it be?
• If you were a candy, what kind would you be?
• What is your favorite thing to do when you are home alone?

Relationship journaling

Studies have shown that journaling can be a beneficial therapeutic device for tapping into your inner feelings, thoughts, and beliefs. Journaling together as a couple can be a homework exercise that bonds you closer through shared communication. You may choose to journal weekly or daily. 

For journaling to be most effective in a therapy setting, the couple should be honest with themselves and their partners about their feelings. Recording your feelings, thoughts, experiences, and goals in a journal can help you better understand what is going on in your partner’s inner world. Reflecting on journal entries can make patterns in the relationship more transparent, showing you what is working versus what you may need to adjust. 

The journal can be used to reflect on positive memories together and as a safe way to express frustrations about the relationship or things that you wish were different. The journal entries can also be reviewed with your therapist during couples therapy sessions later on, helping you create a plan for how to best support each other in reaching your relationship goals. 

Relationship check-in

Around once a week, try to set aside 30 minutes to an hour to discuss your relationship and check in with each other about your feelings. You may also want to record your check-ins in your relationship journal or with couples therapy worksheets so you can reflect on them later. There are couples therapy toolkits that you can download for free online, or your therapist may provide resources. 

Checking in with each other can be an important step in maintaining healthy relationships, ensuring that you are both on the same page communication-wise and not letting anything slip through the cracks.

Benefits of online therapy

These homework exercises for building bonds and improving communication may be the most impactful when combined with guidance from a licensed therapist. You can find highly qualified couples therapists online with therapy platforms like BetterHelp. Couples with busy schedules or travel limitations may have an easier time accessing online couples therapy than traditional therapy at an office. 

Effectiveness of online therapy

One 2022 study examined the effectiveness of online and in-person couples therapy and found that internet-based therapeutic interventions could be just as effective as traditional sessions. However, online sessions typically offered the benefit of being more accessible and appealing to couples who may not otherwise attend. The data collected by the researchers in this study showed overwhelmingly positive results for the majority of participants. 

• Navigating Sympathy Vs. Empathy In Interactions Medically reviewed by Andrea Brant , LMHC
• De-Escalation Techniques To Defuse Conflicts in Relationships Medically reviewed by Julie Dodson , MA
• Relationships and Relations

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Lesson 1: Lines, Ellipses and Boxes

Lines: homework.

Hate to read? No problem. We can read the text to you .

This feature is available completely free . While we will be keeping an eye on how feasible it is to eat the costs associated, we hope to keep it that way.

Just click "Listen with Drawabox"!

Don't forget!

Do not grind . Complete the recommended amount of each exercise to the best of your ability and move on. You'll have ample time to keep practicing and improving your skills when doing these exercises as warmups later.

Do not rush . Give yourself the time you need to plan your lines out, to prepare appropriately, and to demonstrate your current best. Every mark is independently important. Once the ghosting method is introduced in the Ghosted Lines exercise, use it consistently for all your structural marks .

Read all of the instructions carefully , multiple times if necessary. While I've tried to organize this content in as digestible a manner as I can, there is a lot of information here and there is no way you'd absorb all of it at once.

Take breaks! One day you're going to be a beast who can draw for hours without breaking a sweat, but right now, you need to be patient with yourself and take it all one step at a time.

Homework and exercises

The homework assignment for this section is as follows:

2 filled pages of the Superimposed Lines exercise

1 filled page of the Ghosted Lines exercise

2 filled pages of the Ghosted Planes exercise

Each exercise in the list above links off to more detailed instructions on how they're done.

NOTE : These three exercises constitute just one section of this lesson. You should hold onto your homework until you're done all three sections (lines, ellipses, boxes) , and only submit for feedback once they're all done . You may feel hesitant or uncertain about whether or not you're doing things correctly - that's normal, but it's best you push past the urge to second-guess yourself. Focus on reading the instructions carefully, complete the work, and submit once all of it is complete. This will give others a solid body of work on which to base their feedback, giving you a more useful analysis of what you're doing well and what you may not understand.

All the assigned work for this section should be done in ink, using fineliners/felt tip pens as described here . In a pinch, I will accept work done in ballpoint, but only if the situation is dire. This is an exception only for this lesson as students get started.

Of course, if you're not planning on making use of the official critique program , then this is a recommendation rather than a hard requirement.

Drawabox-Tested Fineliners (Pack of 10, $17.50 USD)

Let's be real here for a second: fineliners can get pricey. It varies from brand to brand, store to store, and country to country, but good fineliners like the Staedtler Pigment Liner (my personal brand favourite) can cost an arm and a leg. I remember finding them being sold individually at a Michael's for $4-$5 each . That's highway robbery right there.

Now, we're not a big company ourselves or anything, but we have been in a position to periodically import large batches of pens that we've sourced ourselves - using the wholesale route to keep costs down, and then to split the savings between getting pens to you for cheaper, and setting some aside to one day produce our own.

These pens are each hand-tested (on a little card we include in the package) to avoid sending out any duds (another problem with pens sold in stores). We also checked out a handful of different options before settling on this supplier - mainly looking for pens that were as close to the Staedtler Pigment Liner. If I'm being honest, I think these might even perform a little better, at least for our use case in this course.

We've also tested their longevity. We've found that if we're reasonably gentle with them, we can get through all of Lesson 1, and halfway through the box challenge. We actually had ScyllaStew test them while recording realtime videos of her working through the lesson work, which you can check out here , along with a variety of reviews of other brands.

Now, I will say this - we're only really in a position to make this an attractive offer for those in the continental United States (where we can offer shipping for free). We do ship internationally, but between the shipping prices and shipping times, it's probably not the best offer you can find - though this may depend. We also straight up can't ship to the UK, thanks to some fairly new restrictions they've put into place relating to their Brexit transition. I know that's a bummer - I'm Canadian myself - but hopefully one day we can expand things more meaningfully to the rest of the world.

Getting Your Work Critiqued

Having your work reviewed by others is critical, as those who are just starting out aren't in a position to properly judge their own work, and won't be for quite some time. Don't be afraid to show your struggles - it's by analyzing your mistakes that we can help you grow. Perfect homework is not what we're looking for; we just need it to be complete .

There are currently two places you can get your work critiqued by the community - Reddit and our Discord Chat Server .

Both of these are completely free .

Private Patreon Critiques

If you are interested in receiving extra help, I critique the work of those who support Drawabox on Patreon .

All of these private critiques are done through reddit, in specific threads where students post their work as a comment, including a link to their work (often hosted on Imgur , though most image hosts are okay).

My requirements are more strict than the free community critiques:

• You must complete the lessons in order, in their entirety, starting from lesson 1
• All work for the lesson must be completed - that means all exercises in the lesson, not just those in a given section
• You may only move onto the next lesson once the previous has been marked complete
• The work must be done in the tools recommended in the lesson

The minimum pledge for this lesson is $5.00/month . The orange button above will take you to the reddit thread for this lesson, you can post a link to your work there and I'll be notified. Once I catch the submission, I'll add it to this backlog spreadsheet .

Pledges are collected at the beginning of the following month, but you may start submitting your work immediately. If you're a new patron, I'll be reaching out to your shortly to collect your reddit username.

Part One: The Basics

An overview of basic skills - both technical and conceptual - with exercises that you will incorporate into your regular warmups for a long time to come. no matter how skilled or experienced you are, start at lesson 0..

Challenges and Drills

A series of drills that fit into the lessons at various times. these should not all be completed after lesson 2, but rather will be listed as recommended next steps or prerequisites as you follow the numbered lessons in order..

Part Two: Constructional Drawing

An exploration of how complex objects can be broken down into their fundamental components, then rebuilt from simple forms. we look at this concept of constructional drawing by applying it to many different topics - the focus is not on learning how to draw that specific subject matter, but rather to tackle construction from different perspectives..

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26 Must-Try Couples Therapy Exercises And Activities

Discover the best couples therapy exercises and activities in this article. It is written for therapists and counselors but will also benefit couples who want to improve their relationship with some tools they can even use at home.

The powerful exercises will help to improve communication and listening skills while also helping to develop and (re)build trust.

The exercises include the know-how from different treatment approaches such as cognitive-behavioral therapy ( CBT ), Positive Psychology, and Mindfulness-based interventions. All these different approaches work wonderfully together and complement each other.

We included exercises for trust-building, deepening the connection, resolving roadblocks, promoting awareness, and improving communication. Some of them can be used during therapy sessions while others work great as homework in couples therapy.

26 Couples Therapy Exercises and Activities

1.) the icebreaker.

Icebreakers can be a great opportunity to te an interesting conversation going and to learn something new about each other. It’s a great exercise for the early stage of any couples therapy or relationship coaching.

Some icebreaker questions are:

• What is a funny story you’ve never told me about?
• What is a childhood or your anecdote you could tell me?
• What did you want to become when you were a child?
• What is an embarrassing moment of your life you’d like to share with me?

Powerful Couples Therapy Exercises For Trust

2.) let’s be honest.

The rules of this exercise are easy. Both partners should answer each other’s questions honestly. This will enhance the connection between each other. You can vary between general and easy to answer questions and end up with philosophical and thought-provoking questions:

• What is your favorite memory of dating me?
• What is your favorite thing that I do for you?
• What’s something you’re glad you’ll never have to do again?
• Which memory comes up when you think about your childhood?
• If you woke up tomorrow with no fear, what would you do first?
• What is one behavior that you never tolerate?
• If you could change anything about the way you were raised, what would it be?
• What about me made you fall in love?

3.) Try the Trust Fall

The trust fall is an exercise in which one person stands straight, closes their eyes, and lets him- or herself fall without trying to stop it, relying on the partner to catch them. As the name says it’s a trust-building exercise that needs some courage at first.

4.) Share your favorite songs

Each partner is asked to share three of their favorite songs. They should also try to explain the meaning of the songs. Listen to the songs together.

• What does it remind you about?
• Which feelings come up while listening?
• In which mood are you usually listening to it?

Music is very personal and this exercise is a great way to open up and connect with the partner and also express some vulnerability with each other. Maybe the couple even has „their“ song. In this case, both can describe the feelings and emotions that come up while listening.

5.)  What do you know about me?

Make a small challenge and find out what the couple knows about each other. After answering one question it’s the other partner’s turn. Some example questions:

• What is the one thing that makes me feel alive?
• What makes me smile?
• What scares me?
• How would my dream holiday look like?

Click the image to read more

6.)  The favorite book exercise

Ask the couple to swap their favorite books. They should tell each other what they like about this book in particular. How did it influence their life?

Reading the partner’s favorite book can be an opportunity to get a look into the partner’s mind and understand each other better. Discussing the book and the impact it has on one is a great way to deepen the connection of the couple. This is a great homework exercise. Discuss the results together in the next session.

Best Homework For Couples Therapy

7.)  the relationship assessment.

The Relationship Assessment is a couples therapy exercise for the early stage. Each partner is asked to answer some basic questions about the relationship. It’s a questionnaire that helps explore the challenges and problems.

It gives you some fundamental background information about the couple. You’ll find out how long the clients know each other, get information about previous relationships or marriages. You’ll also get information about children, the family background, and also stress-factors that may have caused the relationship problem.

This questionnaire should be part of the inventory of any couples therapist or consultant. You can create your own or get the one that’s included here in the couples therapy toolkit.

8.)  Identify Relationship Problems

This is another great exercise for the early stage of any relationship coaching or couples therapy. The exercise allows you to identify specific areas to work on with the couple. It’s a set of questions that each partner should answer individually.

You will find out that each partner might identify different problems in their relationship. It’s a homework assignment before or after the first session.

Note the major problems each partner identifies in this questionnaire and specify with them what needs changing.

Possible areas of relationship problems are: Financial, Child-rearing, Communication, Decision-making, Jobs, Controlling each other…

The full exercise is included here

9.) Identify Relationship Goals

Couples therapy is not only about problems, but also about goals. It’s important to find common goals within a relationship. Something both partners are ready to work for. Keep in mind that a goal should always be SMART.

SMART goal means:

• Specific (Is your goal too generic? Specify it!
• Measurable (How can we measure the outcome?)
• Attainable (Is our goal attainable?)
• Realistic (Is our goal realistic?)
• Time-Bound (We want to achieve our goal until…)

The goals or priorities can be different for everyone. Help your clients create and shape a vision for their ideal relationship. The Toolkit includes a ready-to-use worksheet for your sessions. Ask clients to create their goals separately and then try to find a common goal together in one of the first sessions.

10.) The Problem-Solving Blueprint

After the relationship problems have been identified it’s time to solve them one by one. The first step is to connect the individual problem with real-life situations. This will increase the understanding of the origin and the problem itself. Once this is done it’s time to attack the problem and find strategic ways to solve it.

This exercise prompts the couple to come up with creative solutions. The problem-solving blueprint is best used after the exercise where your clients identified the biggest problems that need solving.

It’s also a great tool that comes in handy whenever new problems come up during the coaching/therapy. Assign the tool to each client individually and discuss their answers together.

Each partner defines the problem, describes it in a real-life situation, and is prompted to come up with a creative solution to that problem. The results can be discussed together with the partner and the therapist. The full exercise is included here .

11.) The Pre-Session Check-In – Prepare for each Couples Therapy Session

This is a vital exercise for any marriage or couples therapy. Each partner should sit down individually the day before a session. They should write down what went well since the last session, which change they saw, and what they want to talk about in the next session. It’s a quick progress report that allows each therapist to make their session preparation a matter of a few minutes.

The clients get prompted to focus on the upcoming session to get the most out of it. CleverMemo allows you to assign these kinds of exercises and questionnaires with two single clicks s an action item. You pick a due date, an optional reminder and clients can fill everything out in the stream they share with their therapist.

12.) Therapy Session Gold Nuggets Exercise

This is the perfect addition to the pre-session check-in exercise. Prompt your clients to write down their key insights of each session and share them with you. This should be done individually.

The notes are super helpful as clients reflect on their session while memory is still fresh. They become aware of what they’ve learned, and you get invaluable insights and feedback about what was most valuable to them. Assign this exercise as an action item within CleverMemo. This allows clients to share their answers right in their private stream. Over time you both have a running record about the entire couple therapy with each partner.

• Possible questions are:
• What did you learn in this session?
• The most valuable insight was…
• What do you want to accomplish until our next session?

The complete exercise is part of the C ouples Therapy Toolkit

13.) The Relationship Journal

Keeping a regular relationship journal (daily/weekly) is the perfect exercise to get to know the different perspectives of each partner.

It takes two for a successful relationship. If both parties start journaling about their thoughts, feelings, experiences, mistakes, successes, and wishes, a lot of invaluable insights will be uncovered.

It’s also a great way to call out and keep track of things and habits they don’t like about each other.

The therapist could discuss the journal entries individually with each partner and afterward try to solve and work on them together.

The CleverMemo automation allows you to assign the journal entry as a homework item. Just define how often (e.g. weekly) an entry should be done and the system will send reminders and nudge your clients not to forget their daily or weekly entry.

Rereading past entries is a great way to reflect and uncover recurring patterns, habits, and thoughts. Two journaling templates are included here .

14.) Don’t Overlook Your Qualities And Strengths! – Couples Therapy Exercise

Too often we focus on the bad things and what doesn’t work. This exercise prompts each partner to take a closer look at the strengths. Both their own and their strengths as a couple – as a team Awareness and understanding one’s strengths can be a huge confidence booster.

The couple should make this exercise individually. Sometimes we are sure that we possess certain strengths but our partner may not notice them or take them for granted. It’s also possible that something we consider our strong side (e.g. “I’m a very organized person”) is seen completely different by our partner without us even knowing it (e.g. He/She is a control freak“).

Two great questions to start are:

• Which three big strengths do I think my partner would say I possess?
• What are the strengths we should develop together as a couple?
• The complete exercise is part of the Couples Therapy Toolkit.

15.) The CleverMemo PIT-STOP (R) – Quickly de-escalate any argument with your partner

Even the best couples fight sometimes — that’s just what happens when two people who care about each other spend a lot of time together. But unfortunately, in some cases, arguments can escalate quickly, turning a little disagreement into a big issue.

The CleverMemo PIT-Stop exercise will help your clients to de-escalate any argument or upcoming fight. It’s a simple technique that helps them to step back and become aware of the situation and their feelings. Once the emotions cooled down it’s time to address the topic calmly.

Each time an argument comes up the couple should say some keyword like Pause, Stop, or PIT-Stop and then leave the situation. Each partner takes a seat and writes down their thoughts and feelings. You’ll find the entire exercise including all the questions for clients here .

Effective Couples Therapy Exercises For Communication

Communication and the ability to listen to each other are vital skills for any relationship to be successful. There are several exercises to assess communication issues:

16.) Let’s Improve our Communication

Good communication is an essential part of a healthy relationship. Every relationship has its ups and downs, we all have bad days, but a healthy way of communicating with our partner makes it easier to deal with conflicts and building a stronger relationship.

We cannot read our partner’s mind. That’s why is crucial to tell our significant other how we are feeling, what we want and need and what we are feeling.

Every person has different communication ways and needs of communication. That’s why it’s so important that the couple becomes aware of their current communication patterns. How would they rate their current communication? Are they able to talk about everything with their partner?

This is the first step to improve communication. The whole worksheet is part of the Couples Therapy Toolkit.

17.) The Miracle Question

The miracle question is a great thought experiment in coaching and counseling. The question has its origin in the solution-focused therapy and its name is credited to Steve de Shazer and Insoo Kim Berg. The focus is on the future, on the goal the client wants to achieve.

This question helps our couple to become aware of their own dreams and desires and learn about their partner’s dreams and desires. It can be very helpful in understanding what both they and their significant other needs to be happy with the relationship.

Ask them to answer the following miracle question:

Imagine while sleeping tonight a miracle occurred: All your current problems disappeared. What would you notice that would tell you life suddenly gotten better? How would life look like?

Tip: Couples Therapy Questions

The miracle question is just one example that shows how great the impact of the right questions can be in couples therapy. Questions can be a great resource for any couples therapist, and relationship counselor, or coach. We created a collection that will help to identify problematic areas within the relationship.

But even when you’re not a therapist, you can use some of them as an icebreaker exercise to get communication with your spouse going. Check out the list of couples therapy questions for your next session here.

18.) Listening Without Interruption

This famous couples therapy exercise focuses on both verbal and nonverbal communication.

Set a timer for 3 minutes. One partner has the chance to speak about whatever they are thinking or feeling without being interrupted. The other partner is not allowed to say anything but could use nonverbal methods to show empathy and understanding.

After three minutes both can discuss their experience, feelings, and observations. Then it’s time to switch roles so that each partner can improve their listening skills.

19.) Repeat it – Exercise

This is a variation of the „Listening without interruption“ exercise.

One is asked to tell a short story (3-5 minutes) while the partner is just listening. Once the story is over the partner is asked to reflect on what they just heard. It’s great training to enhance listening skills.

Some additional Homework Exercises For Couples Therapy

20.) send me a letter.

Both partners are asked to write a letter to each other. In this letter, they can express their frustration, feelings, or desires. For many people, it’s easier to express their emotions and feelings in written form instead of telling it to another person’s face. Each partner is then asked to write a response to their partner’s letter.

Ask your clients to share their letters with you in their CleverMemo stream. You’ll gain invaluable insights that will be useful for the upcoming therapy sessions. Discuss the letters together with them.

21.) Becoming the Best Partner I can be

This exercise will help each partner to find out what they can do to improve their relationship skills and do their part in becoming the best partner they can be.

First, we must recognize our responsibility and not get caught up blaming it all on our partner, even when it appears our partner is the one with the problem.

Let’s take a look at ourselves and what we can do to become the best partner we can be. You’ll find the exercise here.

22.) Get Your Needs Met In Your Relationship

A happy relationship thrives on our understanding of our partner’s needs. Recognizing and communicating our own needs is also very important. If both partners don’t care about or ignore each other’s needs, the relationship will fail sooner or later.

The relationship will only have a future if the mutual and individual needs of both partners are met. Common needs in a relationship are the feeling of security, appreciation, shared experiences of love, tenderness, and affection.

Each partner should ask themselves „What do I need?“ and „What does my partner need?“ and both partners should make it a habit to clearly communicate their needs. It needs some training in the beginning but it can become a routine after some time. The worksheet is part of the Couples Therapy Toolkit.

23.) Explore New Things Together

Prompt the couple to find something new they could learn or try together. This could be a skill, a hobby, or an adventure. It’s ideal if both have never done it before so that they share the experience of trying it the first time together. This could be some sport or going to dance class for example.

24.) Let’s Review Our Life Together

This is a great homework exercise for couples. Prompt them to have a glass of wine or cup of tea and review their life together. They could take a look at their first pictures as a couple and discuss all the things they’ve experienced together throughout their relationship. They can also think of things they still would like to do together. You can discuss the results in the next session.

25.)  The Gratitude List

A great couples therapy exercise is the Gratitude List or even a journal. It helps each partner to restructure how they think about their partner and to become aware of all the small positive details that made them once fall in love with each other.

Ask each partner to write down at least five things they appreciate/are grateful for about their partner. This could be followed by three things they could do to make their partner feel more loved and appreciated in the relationship. If the couple is ready for it you could take this exercise a step further and let them keep a daily gratitude journal over 2-4 weeks.

This will help them to focus on the good in their relationship and become aware of the daily little positive things they notice about their partner. A template for this journal is included here.

26.)  The Weekly Relationship Check-In

This couples therapy exercise is valuable for every relationship. It improves the communication between the partners and allows each of them to have their speak. Ask the couple to schedule 30-60 minutes per week where they talk about their latest experiences, their wishes, what they want and need from each other, and how they could improve their relationship.

There are not a lot of rules. But the listening partner agrees not to interrupt and take things personally. Both should take this time as a chance to talk honestly to each other without the fear of being judged or that the partner might overreact.

Ask your clients to share the experiences and key insights of this exercise in their CleverMemo stream with you.

Wrapping Up Couples Therapy Exercises And Activities

These were 25 must-try couples therapy and counseling exercises you can use with your clients. Practicing communication, trust, and increasing empathy and awareness for each other are undoubtedly helpful for any relationship or marriage.

If you’re looking to support your couples therapy sessions with a professional software tool you can start a free CleverMemo trial here. And if you want to improve your couples therapy with some ready-to-use worksheets and questionnaires this Toolkit is for you: Check it out

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Bringing It Together: Homework

A certain small town in the United states has a population of 27,873 people. Their ages are as follows:

• Construct a histogram of the age distribution for this small town. The bars will not be the same width for this example. Why not? What impact does this have on the reliability of the graph?
• What percentage of the community is under age 35?
• Which box plot most resembles the information above?

Javier and Ercilia are supervisors at a shopping mall. Each was given the task of estimating the mean distance that shoppers live from the mall. They each randomly surveyed 100 shoppers. The samples yielded the following information.

• How can you determine which survey was correct ?
• Explain what the difference in the results of the surveys implies about the data.

Use the following information to answer the next three exercises : We are interested in the number of years students in a particular elementary statistics class have lived in California. The information in the following table is from the entire section.

What is the IQR ?

What is the mode?

Is this a sample or the entire population?

• entire population

Twenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follows:

• Find the sample mean x ¯ x ¯ .
• Find the approximate sample standard deviation, s .

Forty randomly selected students were asked the number of pairs of sneakers they owned. Let X = the number of pairs of sneakers owned. The results are as follows:

• Find the sample mean x – x –
• Find the sample standard deviation, s
• Construct a histogram of the data.
• Complete the columns of the chart.
• Find the first quartile.
• Find the median.
• Find the third quartile.
• Construct a box plot of the data.
• What percent of the students owned at least five pairs?
• Find the 40 th percentile.
• Find the 90 th percentile.
• Construct a line graph of the data
• Construct a stemplot of the data

Following are the published weights (in pounds) of all of the team members of the San Francisco 49ers from a previous year.

177; 205; 210; 210; 232; 205; 185; 185; 178; 210; 206; 212; 184; 174; 185; 242; 188; 212; 215; 247; 241; 223; 220; 260; 245; 259; 278; 270; 280; 295; 275; 285; 290; 272; 273; 280; 285; 286; 200; 215; 185; 230; 250; 241; 190; 260; 250; 302; 265; 290; 276; 228; 265

• Organize the data from smallest to largest value.
• The middle 50% of the weights are from _______ to _______.
• If our population were all professional football players, would the above data be a sample of weights or the population of weights? Why?
• the population mean, μ .
• the population standard deviation, σ .
• the weight that is two standard deviations below the mean.
• When Steve Young, quarterback, played football, he weighed 205 pounds. How many standard deviations above or below the mean was he?
• That same year, the mean weight for the Dallas Cowboys was 240.08 pounds with a standard deviation of 44.38 pounds. Emmit Smith weighed in at 209 pounds. With respect to his team, who was lighter, Smith or Young? How did you determine your answer?

One hundred teachers attended a seminar on mathematical problem solving. The attitudes of a representative sample of 12 of the teachers were measured before and after the seminar. A positive number for change in attitude indicates that a teacher's attitude toward math became more positive. The 12 change scores are as follows:

3 ; 8 ; –1 ; 2 ; 0 ; 5 ; –3 ; 1 ; –1 ; 6 ; 5 ; –2

• What is the mean change score?
• What is the standard deviation for this population?
• What is the median change score?
• Find the change score that is 2.2 standard deviations below the mean.

Refer to Figure 2.51 determine which of the following are true and which are false. Explain your solution to each part in complete sentences.

• The medians for all three graphs are the same.
• We cannot determine if any of the means for the three graphs is different.
• The standard deviation for graph b is larger than the standard deviation for graph a.
• We cannot determine if any of the third quartiles for the three graphs is different.

In a recent issue of the IEEE Spectrum , 84 engineering conferences were announced. Four conferences lasted two days. Thirty-six lasted three days. Eighteen lasted four days. Nineteen lasted five days. Four lasted six days. One lasted seven days. One lasted eight days. One lasted nine days. Let X = the length (in days) of an engineering conference.

• Organize the data in a chart.
• Find the median, the first quartile, and the third quartile.
• Find the 65 th percentile.
• Find the 10 th percentile.
• The middle 50% of the conferences last from _______ days to _______ days.
• Calculate the sample mean of days of engineering conferences.
• Calculate the sample standard deviation of days of engineering conferences.
• Find the mode.
• If you were planning an engineering conference, which would you choose as the length of the conference: mean; median; or mode? Explain why you made that choice.
• Give two reasons why you think that three to five days seem to be popular lengths of engineering conferences.

A survey of enrollment at 35 community colleges across the United States yielded the following figures:

6414; 1550; 2109; 9350; 21828; 4300; 5944; 5722; 2825; 2044; 5481; 5200; 5853; 2750; 10012; 6357; 27000; 9414; 7681; 3200; 17500; 9200; 7380; 18314; 6557; 13713; 17768; 7493; 2771; 2861; 1263; 7285; 28165; 5080; 11622

• Organize the data into a chart with five intervals of equal width. Label the two columns "Enrollment" and "Frequency."
• If you were to build a new community college, which piece of information would be more valuable: the mode or the mean?
• Calculate the sample mean.
• Calculate the sample standard deviation.
• A school with an enrollment of 8000 would be how many standard deviations away from the mean?

Use the following information to answer the next two exercises. X = the number of days per week that 100 clients use a particular exercise facility.

The 80 th percentile is _____

The number that is 1.5 standard deviations BELOW the mean is approximately _____

• Cannot be determined

Suppose that a publisher conducted a survey asking adult consumers the number of fiction paperback books they had purchased in the previous month. The results are summarized in the Table 2.84 .

• Are there any outliers in the data? Use an appropriate numerical test involving the IQR to identify outliers, if any, and clearly state your conclusion.
• If a data value is identified as an outlier, what should be done about it?
• Are any data values further than two standard deviations away from the mean? In some situations, statisticians may use this criteria to identify data values that are unusual, compared to the other data values. (Note that this criteria is most appropriate to use for data that is mound-shaped and symmetric, rather than for skewed data.)
• Do parts a and c of this problem give the same answer?
• Examine the shape of the data. Which part, a or c, of this question gives a more appropriate result for this data?
• Based on the shape of the data which is the most appropriate measure of center for this data: mean, median or mode?

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Access for free at https://openstax.org/books/introductory-statistics-2e/pages/1-introduction

• Authors: Barbara Illowsky, Susan Dean
• Publisher/website: OpenStax
• Book title: Introductory Statistics 2e
• Publication date: Dec 13, 2023
• Location: Houston, Texas
• Book URL: https://openstax.org/books/introductory-statistics-2e/pages/1-introduction
• Section URL: https://openstax.org/books/introductory-statistics-2e/pages/2-bringing-it-together-homework

© Dec 6, 2023 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

Home Workouts & Exercises

Search our free database of exercises and workouts that you can do at home. Home Workouts provides concise how-to guides and muscle targeting diagrams on bodyweight, free-weight, yoga and stretching exercises.

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23 Post Traumatic Growth Worksheets for Therapy (+PDF)

Post Traumatic Growth, or PTG, explains how trauma survivors can not only heal from their trauma, but can actually learn from the experience to become more resilient individuals.

In the mid-1990s, psychologists Richard Tedeschi and Lawrence Calhoun (Tedeschi & Calhoun, 1996) discovered that the severe psychological struggle that follows major life crises can result in positive growth and deepening resilience afterward.

While our other PTG article defines Post-Traumatic Growth with detail on the concept itself and the science behind it, this article provides you with practical tools to apply PTG with your clients or students.

Before you continue, we thought you might like to download our three Resilience Exercises for free . These engaging, science-based exercises will help you cope with difficult circumstances and give you the tools to improve the resilience of your clients, students, or employees.

This Article Contains:

A look at trauma therapy techniques, post traumatic growth worksheet, 6 ptsd worksheets (pdf), 3 common therapy techniques for trauma, 16 pdf trauma worksheets, activities for trauma therapy, positivepsychology.com resources, a take-home message.

There are many trauma therapy techniques mentioned in this article. In this section, we will explore how some of these techniques can be applied to promote post-traumatic growth (PTG) using the model developed by Stephanie D. Nelson, a Behavioral Science Officer from the United States Army.

In 2011, Nelson developed a posttraumatic growth path (PTGP) for veterans suffering from post-traumatic stress disorder ( PTSD ; Nelson, 2011). This pathway can also work with other types of trauma survivors.

The program comprises four stages for those struggling with PTSD symptoms (Nelson, 2011):

Evidence shows the techniques applied during each stage are beneficial for relieving specific PTSD symptoms in all types of trauma survivors and promoting post-traumatic growth (Ogilvie & Carson, 2021).

1. Deal – Writing a Trauma Narrative

This stage consists of writing a trauma narrative by focusing on the facts surrounding the incident(s), including the who, what, where, and when. Next, the client describes the thoughts and feelings that arose during the experience to create a comprehensive narrative.

Finally, the client is asked to write a paragraph reflecting on how they feel now, what they have learned, and if they have grown from the experience. Trauma survivors should complete this exercise with a therapist or counselor for support with any distressing feelings and sensations that may arise such as flashbacks, anxiety, or panic.

Once the trauma narrative is completed, the client proceeds to step 2.

2. Feel – Imaginal Exposure

The next step involves experiencing the feelings aroused by reading the trauma narrative aloud using imaginal exposure.

Exposure therapies work by exposing then desensitizing clients to any uncomfortable, distressing, and frightening feelings associated with the original trauma (Van Der Kolk, 2014).

Imaginal exposure entails revisiting the experience in the mind’s eye using the vivid sensory capacity of the imagination. Imaginary exposure to traumatic experiences using a trauma narrative, helps clients fully process their feelings with the support of a counselor or therapist.

This technique reconnects the client to their original emotional responses to the trauma which otherwise can become displaced onto other associated stimuli called ‘triggers’. Often, trauma survivors avoid emotional triggers which can lead to a narrowing of life experience and a lower quality of life.

For example, physical contact with their partner or spouse may trigger a rape survivor who withdraw or even freeze upon physical contact. This can destroy a survivor’s capacity for intimate relationships. Imaginal exposure allows a client to process any repressed feelings safely, and overcome avoidance.

3. Heal – Channeling PTG

Stage three helps the client reintegrate their feelings and thoughts about the original trauma to facilitate opportunities for learning and growth. The healing stage involves three phases.

• Freedom of choice During this phase, the therapist explains that while the client did not choose their traumatic experience, they can choose how to go forward. The narrative therapy technique of “rewriting the ending” can help the client create their own path.
• Finding meaning The client is encouraged to find meaning in their experience in whatever way is appropriate and workable for them.
• The hero archetype Finally, the therapist guides the client through the transformative journey of the Hero archetype by re-telling their story in the context of the client’s spiritual and cultural values to make the experience more meaningful. The client may also benefit from hearing stories where the hero experiences a significant trauma and becomes a much stronger person as a result.

Once these three techniques have been explored, the therapist can teach the client PTG channeling which involves redirecting their emotional energy away from avoiding triggers into productive, goal-oriented behavior. The therapist may assign the client homework exercises to help shift them from survival toward post-traumatic growth.

4. Seal – The mind as a filing cabinet

The last step of the post-traumatic growth path involves reorganizing the traumatic memory using the “mind as a filing cabinet” metaphor. This likens the memory of the traumatic experience to disorganized information scattered throughout the filing system of the mind.

Rather than the files being neatly ordered, numerous folders contain fragments of information that are confusing and disorientating.

The ‘sealing’ step reorganizes memories as files and stores them away safely. Files can be consulted in the future, but are no longer anything more than one of the many files that are stored in the cabinet of the mind.

The client may need to repeat this process of reorganizing further memories over the course of therapy.

For a moving true-life account of how traumatic childhood experiences can lead to post-traumatic growth and a rounded, fulfilling life, check out this TEDx talk by Martha Londagin below.

Here at PositivePsychology.com, we have several free worksheets that help clients deal with trauma.

However, we selected one as the ultimate post traumatic growth worksheet.

The worksheet start by identifying what is distressful, and causes avoidance.

Avoidance is a strategy trauma survivors often use to eliminate triggers and other associations with the original traumatic event. The problem with avoidance is that it constrains life by restricting options and prevents learning and growth.

The consequences of avoidance are an intensification of fear and restrictions that undermine quality of life .

It is possible to overcome avoidance through gradual exposure until desensitized to the triggering stimuli. Although this process is uncomfortable, it results in an increased sense of safety, widens options, and leads to a more fulfilling life (Collier, 2016).

The post-traumatic growth worksheet then assists with selecting and implementing healthier coping mechanisms than avoidance.

You can access the Conquering Avoidant Tendencies worksheet via the link.

The worksheets include identifying triggers, self-regulating emotions, grounding, decatastrophizing, and taking steps towards gratitude for the things they still enjoy and that support them as they heal.

1. What are your unique triggers?

Identifying triggers is an essential coping skill that can help a client manage their symptoms during their recovery. If a client is aware of their triggers this also helps in overcoming avoidance (Van Der Kolk, 2014).

Look at our What Are Your Unique Triggers? worksheet for guidance.

2. Letter of self-compassion

Cultivating self-compassion is crucial when recovering from a traumatic experience (Collier, 2016). All too often we expect way too much of ourselves and don’t give ourselves enough time and space to heal. Try our Letter of Self-compassion worksheet and read it aloud whenever the inner critic looms.

3. Skills for self-regulating emotions

An ability to self-regulate our emotions is an essential life skill in any context but this can be especially challenging after a traumatic experience when our emotions can become unpredictable or even numb (Van Der Kolk, 2014).

Try our Skills for Self-Regulating Emotions worksheet to help clients self-soothe.

4. Catastrophizing and decatastrophizing

Catastrophizing entails imagining the worst-case scenario every time we face a problem. It is rooted in a limbic brain response designed to protect us from danger, but following trauma, it can be a symptom of hypervigilance (Van Der Kolk, 2014).

Try our Decatastrophizing worksheet for practical support.

5. Countdown to calmness

Grounding ourselves is essential when feeling disconnected from our body or environment, or after catastrophizing (Van Der Kolk, 2014).

Try our Countdown to Calmness worksheet which uses radical acceptance to ground you by focusing on your five senses.

6. It could be worse

Despair and anger are natural responses to a traumatic experience that can rob our lives of meaning (Collier, 2016).

Download 3 Free Resilience Exercises (PDF)

These detailed, science-based exercises will equip you or your clients to recover from personal challenges and turn setbacks into opportunities for growth.

Download 3 Free Resilience Tools Pack (PDF)

By filling out your name and email address below.

Although there are various therapies that can be used for trauma therapy, including EMDR , the following are commonly known therapy types used.

Narrative Therapy

Narrative therapy was developed in the 1980s by Michael White and David Epston (White & Epston, 1990). We explained above how writing a trauma narrative can be used to process and integrate traumatic experiences.

White and Epston believed that separating a person from their problematic behavior was crucial for therapeutic success (White, 2011). Narrative therapy achieves this by helping clients externalize their experience in writing.

White and Epston (1990) formulated their model using three key principles:

• Narrative therapy is respectful.
• Narrative therapy is non-judgmental.
• Narrative therapy views the client as the expert on their problems.

Narrative therapy equips clients with story-telling skills to help separate their sense of personal identity from their trauma. When the client stops seeing their trauma as an integral part of their identity, resolving to learn and grow from the experience becomes easier (Van Der Kolk, 2014).

Art Therapy

Art therapy is a therapeutic practice that uses visual arts techniques to facilitate the therapeutic process and can be especially helpful given that many aspects of traumatic experiences are difficult to express in words (Malchiodi, 2020).

A client doesn’t need any artistic skills to take part in this type of therapy. Rather, the art therapist encourages the client to tap into their creative process to explore and express emotions and develop greater self-awareness. This can help with processing buried conflicts and unresolved trauma.

For a more detailed account of this approach to trauma therapy, we recommend these art therapy , and expressive arts therapies articles.

Play Therapy

Play therapy is typically used to facilitate psychotherapy with children but can also be used with adults. Play therapy requires movement which can help address unresolved trauma that is difficult to express in words, especially for children (Allen & Hoskowitz, 2017).

Play therapy incorporates many techniques such as sand and water play, role play, and the use of representational toys like dolls, trucks, and guns to create play that expresses the client’s traumatic experience. This helps the client externalize their trauma similar to narrative therapy and art therapy, making the experience easier to process (Allen & Hoskowitz, 2017).

We have grouped them into 5 themes for your convenience.

1. Strengths

Identifying a client’s strengths and previous experiences of overcoming difficulties helps with recovery from a traumatic experience. These two worksheets help clients identify their character strengths and recognize their capacity for post-traumatic growth.

• Exploring Character Strengths
• Exploring Past Resilience

2. Exposure

Exposure is an evidence-based approach to overcoming triggers and avoidance. These three worksheets can help guide clients through different types of exposure.

• For physiological symptoms of trauma try our Interoceptive Exposure worksheet,
• For traumatic memories try our Imagery Based Exposure worksheet
• For feared objects and situations try our Graded Exposure worksheet.

Fear and anxiety are common responses to trauma which can lead to dysfunctional thinking. These four worksheets are designed to help clients cope with the anxiety that often arises during and after trauma, and support them in moving on to post-traumatic growth.

• Challenging Catastrophic Thinking Worksheet
• Replacing ‘What if’ Statements
• Dysfunctional Thought Record
• FLARE for Anxiety and Fear

4. Grounding

Feeling far away or unreal is common following a traumatic experience. This is because of the dissociation and depersonalization that can occur as the body struggles to process sensory overload.

These three worksheets are designed to ground clients in the present moment using breathwork and radical acceptance.

• Yogic Breathing
• Anchor Breathing
• Focus on the Present for Radical Acceptance

Finally, these four worksheets have been designed using evidence-based interventions that promote post-traumatic growth.

Eye Movement Desensitization and Reprocessing (EMDR) involves coupling negative cognition with a chosen target image, selecting a positive replacement cognition, then reprocessing traumatic memories into more adaptive thoughts.

Download our EMDR Worksheet to find out more.

Meanwhile, our Imaginal Exposure worksheet uses the Subjective Units of Distress Scale (SUDS) to quantify the disturbance a client feels when revisiting their traumatic experience during therapy. It is especially useful for those who misuse substances to self-soothe.

Your clients can also try this Goal Planning and Achievement Tracker worksheet to monitor their progress during their post-traumatic growth journey.

Finally, our Growing Stronger From Trauma worksheet helps clients identify what they’ve learned from a traumatic experience, and appreciate the strengths they have developed as a result. This exercise helps clients cultivate a more balanced perspective on previous trauma and identify ways to manage future challenges.

The following activities aim at improving the reintegration of the mind, heart, and body connection that is often fragmented by a traumatic experience.

1. Psychoeducation

Psychoeducation is an important intervention to help trauma survivors understand they are experiencing a normal response to an abnormal experience. (Whitworth, 2016).

Our article on psychoeducation interventions explains more.

2. Self-soothing

Equipping a client with self-soothing skills will help support their recovery between sessions (Dreisoerner et al., 2021).

Look at our article 24 Best Self-Soothing Techniques and Strategies for Adults for more resources.

3. Expressive arts

Expressive arts activities can help to process blocked emotional responses to trauma through painting, drawing, clay modeling, photography, music, and movement (Malchiodi, 2020).

Check out our article Expressive Arts Therapy: 15 Creative Activities and Techniques for more resources.

4. Mindfulness

Mindful movement can support grounding when clients feel scattered or fragmented (Teut et al., 2013). Take a look at our articles on Mindful Yoga and Mindful Walking for further guidance.

5. Nature therapy

Ecotherapy interventions are deeply grounding for trauma survivors (Atkins & Snyder, 2017). Activities include forest bathing (Mao et al., 2012), walking in nature, or just gazing at the ocean (Cracknell, 2019).

17 Tools To Build Resilience and Coping Skills

Empower others with the skills to manage and learn from inevitable life challenges using these 17 Resilience & Coping Exercises [PDF] , so you can increase their ability to thrive.

Created by Experts. 100% Science-based.

Besides all the resources we’ve included above, consider our 6-module, science-based Realizing Resilience Masterclass© . It includes all the resources you’ll need to deliver high-quality resilience training and more.

We have other useful related articles with linked resources including:

• 7+ Trauma-Focused Cognitive-Behavioral Therapy Worksheets . Trauma-focused CBT comes highly recommended by the APA as a trauma treatment with a firm evidence base.
• What is Post-Traumatic Growth? (+ Inventory & Scale) examines the science behind PGT in detail.
• PTSD Treatment: How to Support Clients Dealing With Trauma includes psychoeducation tips and resources for working with children and groups.
• Military Counseling & Helping Veterans Deal With Trauma offers more specialized guidance on working with this client group after they have served in an active combat zone.

If you’re looking for more science-based ways to help others overcome adversity, this collection contains 17 Resilience & Coping Exercises . Use them to help others recover from personal challenges and turn setbacks into opportunities for growth.

We hope you find the resources in this article useful. Nobody wants to suffer, but we will inevitably face adverse experiences, whether it’s through loss and grief, sudden illness or injury, a natural calamity, or witnessing violence and extreme suffering in others.

If you struggle with trauma and its aftermath, remember that you have overcome obstacles in the past, and that you can draw on those experiences to cultivate the skills you need to process your experience, and become a wiser, more compassionate, and more resilient person as a result.

Finally, if you would like further inspiration about the potential for growth after trauma check out this short and powerful TED Talk by trauma survivor Charles Hunt. You won’t regret it!

We hope you enjoyed reading this article. Don’t forget to download our three Resilience Exercises for free .

• Allen, B. & Hoskowitz, N. A. (2017). Structured trauma-focused CBT and unstructured play/experiential techniques in the treatment of sexually abused children: A field study with practicing clinicians. Child Maltreatment 22(2) , 112-120.
• Atkins, S., & Snyder, M. (2017). Nature-based expressive arts therapy: Integrating the expressive arts and ecotherapy . Jessica Kingsley Publishers.
• Collier, L. (2016). Growth after trauma. Monitor on Psychology, 47(10).
• Cracknell, D. (2019). By the sea: The therapeutic benefits of being in, on, and by the water . Aster.
• Dreisoerner, A., Junker, N. M., Schlotz, W., Heimrich, J., Bloemeke, S., Ditzen, B., & van Dick, R. (2021). Self-soothing touch and being hugged reduce cortisol responses to stress: A randomized controlled trial on stress, physical touch, and social identity. Comprehensive Psychoneuroendocrinology, 8.
• Malchiodi, C. A. (2020). Trauma and expressive arts therapy: Brain, body, and imagination in the healing process. Guilford Press.
• Mao, G. X., Lan, X. G., Cao, Y. B., Chen, Z. M., He, Z. H., Lv, Y. D., Wang, Y. Z., Hu, X. L., Wang, G. F., & Yan, J. (2012). Effects of short-term forest bathing on human health in a broad-leaved evergreen forest in Zhejiang Province, China. Biomedical Environmental Science. 25(3) , 317-24.
• Nelson, S. D. (2011). The posttraumatic growth path: An emerging model for prevention and treatment of trauma-related behavioral health conditions. Journal of Psychotherapy Integration 21 , 1-42.
• Ogilvie, L. & Carson, J. (2021) Trauma, stages of change and post-traumatic growth in addiction: A new synthesis. Journal of Substance Use , 27 (2), 122-127.
• Tedeschi, R. G. & Calhoun L. G. (1996). The Posttraumatic Growth Inventory: measuring the positive legacy of trauma. Journal of Traumatic Stress . 9(3), 455-71.
• Teut, M., Roesner, E. J., Ortiz, M., Reese, F., Binting, S., Roll, S., … Brinkhaus, B. (2013). Mindful walking in psychologically distressed individuals: A randomized controlled trial. Evidence-Based Complementary and Alternative Medicine , 1–7.
• Van Der Kolk, B. (2014). The body keeps the score . Penguin.
• Whitworth, J. D. (2016). The role of psychoeducation in trauma recovery: Recommendations for content and delivery. Journal of Evidence-Informed Social Work , 13(5), 442-51.
• White, M. & Epston, D. (1990). Narrative means to therapeutic ends . W. W. Norton & Company.
• White, M. (2011). Narrative practice: Continuing the conversations (D. Denborough, Ed.), W.W. Norton.

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A parent of a Marine that just had a tragic experience, and as a father would like to help in his recovery from PTSD from war ….

I’m a solution-focused narrative therapy and your PTG approach so resonates with me. Appreciate your work and resources and worksheets.

Thank you for the information!

Great information!

Great article. Interesting worksheets. Is there any link to these worksheets to download in pdf. Also looking for the ACTUAL PTG-24 tool link.

Hi Eulinda,

Glad you liked the article! If you click the hyperlinks in-text where the worksheet name is mentioned, they’ll take you to the PDF download. Also, I’m not finding a tool with this name in our Toolkit. Could you elaborate on what specifically the tool is about and perhaps I can help find what you’re looking for.

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Thanks to share this wonderful articles.

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Where can I find my homework? How can I see my exercises?

There are two types of Talaera homework:

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