Evaporation

This tutorial follows on from the evaporation lecture. The first exercises ask you to reason about what controls evaporation and how we tell potential from actual evaporation. The middle exercises work through a vapour pressure deficit calculation and a comparison of the main ways evaporation is measured and estimated, from a single lysimeter up to continental satellite products. The final exercise is a full numerical worked example of the Thornthwaite method, so that you have estimated potential evapotranspiration by hand at least once.

Work through the questions in order and write your reasoning out in full. For the numerical parts, keep your units consistent and state any assumption you make.

Potential and actual evaporation

You are given three months of daily climate data (temperature, humidity, radiation and wind speed) for a small catchment. Using what you know from the lecture, answer the following.

1. Describe how you would estimate potential evaporation (E_{pt}) from these data, and name the type of equation you would use.
2. State the key assumptions built into that estimate.
3. Explain how E_{pt} relates to actual evaporation (E_t), and describe how you would test whether E_t \approx E_{pt} during the wet season.

Vapour pressure deficit

At midday a weather station records the following.

1. Calculate the actual vapour pressure e_a and the vapour pressure deficit (VPD).
2. Explain in one or two sentences what this VPD tells you about the potential for evaporation at this moment.
3. What are plants likely to do in response to a VPD of this size, and how does that feed back on actual evaporation?

Evaporation from bare and vegetated soil

A lysimeter study runs two neighbouring plots through a dry summer: one is bare soil, the other is vegetated.

1. Can you determine which plot will lose more water over the full summer from the information given? Explain the competing controls.
2. Describe how soil moisture limits actual evaporation in each plot as the summer dries out.
3. Explain the roles of capillary rise and transpiration in the vegetated plot.

Comparing ways of measuring and estimating evaporation

No gauge catches evaporated vapour in the way that a rain gauge catches water. Each evaporation method instead observes a turbulent flux, a water balance, or variables that constrain an estimate. Evaluate the strengths and limitations of each of the following.

1. Evaporation pans
2. Weighing lysimeters
3. Catchment water balance
4. Eddy covariance
5. Satellite remote sensing (for example GLEAM globally, or CMRSET over Australia)

For each method, comment on its spatial support (plot, flux footprint, landscape, or continent), the type of surface it represents, and its main source of uncertainty.

For satellite remote sensing, distinguish the measured signal from the final evaporation estimate. Explain what thermal infrared, optical, and microwave sensors observe, and state how each observation can constrain an evaporation model. Then distinguish GLEAM, CMRSET, and the AWRA-L land-surface model.

Finish by explaining why Australia’s Bureau of Meteorology reports modelled actual evapotranspiration rather than relying on the pan network alone. Describe how a hydrologist can use flux towers and catchment water balances to test a gridded evaporation product.

The Thornthwaite method for estimating potential evapotranspiration

Direct measurement with a lysimeter gives the best actual evapotranspiration a hydrologist can hope for, but the instruments are expensive and hard to maintain, so they are rare. In data-sparse regions we fall back on empirical models. The Thornthwaite method is one of the simplest: it needs only mean monthly air temperature and the site latitude, which is why it remains in wide use despite its known shortcomings. It estimates monthly potential evapotranspiration as

where E_{pt} is the monthly potential evapotranspiration (cm/month), T_a is the mean monthly air temperature (°C), I is the annual heat index and a is an empirical exponent.

The calculation has three parts. First, sum a monthly heat index over every month warmer than 0 °C to obtain the annual heat index,

Second, evaluate the exponent as a cubic function of that heat index,

Third, multiply each month’s raw E_{pt} by a latitude-dependent day-length factor, which corrects the nominal 30-day, 12-hour month for the real number of daylight hours. The factors are tabulated below.

Applying the method: Saskatoon, 1961

Estimate the total potential evapotranspiration for the growing season at Saskatoon, Canada (latitude about 52 °N), for the period 16 May to 24 September 1961. The mean monthly temperatures that contribute to the annual heat index were as follows. The omitted months, November to March, had mean temperatures at or below 0 °C and therefore contribute zero.

Work through the following.

1. Calculate the annual heat index I, using every month warmer than 0 °C.
2. Determine the exponent a from the cubic above.
3. Compute the unadjusted monthly E_{pt} for May through September.
4. Apply the day-length correction. Saskatoon is at 52 °N, so use the nearest tabulated latitude (50 °N).
5. Sum the corrected values to find the total E_{pt} for 16 May to 24 September. Remember that May and September are only partly inside this window, so weight them by the fraction of the month that falls within it.

Reflection

The lecture noted that Thornthwaite tends to underestimate potential evapotranspiration in hot, arid regions. Explain briefly why a temperature-only model would struggle across the Australian interior, where pan evaporation reaches 3,000 to 3,600 mm per year, and name one estimation method from the lecture that would handle those conditions better.