Overview and Basic Definitions

Evaporation is the process where liquid water undergoes a phase change to water vapor and disappears into the atmosphere. Sublimation is a similar process involving the solid phase, ice or snow, that vaporize and become airborne. Transpiration is a biologically-mediated process where liquid water is taken up by plants and returned to the atmosphere as vapor via the stomata on leaves. The combined consequence of all these processes is commonly called evapotranspiration, abbreviated ET.

Because the product of ET is gaseous water molecules, it is hard to collect meaningful samples, and this is especially so for natural systems. To illustrate this, consider what you would do if your boss asked you to collect a representative sample of ET from a large watershed! Clearly no analogous sampling method such as filling a water bottle with spring water will suffice here. In fact, the most reliable way to to quantify ET or its constituent processes is to measure the change in the volume or mass of the solid or liquid reservoir of interest over time, and to calculate ET as the difference (loss). Thus, ET and related processes are best quantified by water balance methods.

Physical Process

Evaporation, which is most easily conceptualized as the transfer of water molecules from the liquid surface to the atmosphere, is actually a very complex process involving many different microscpoic mechanisms including kinetic processes and molecular diffusion in both liquid and gaseous media. Evaporation is also a two way process, as water molecules both leave and re-enter the liquid water surface, but the loss rate is faster than the return rate.

The rate of evaporation depends on many physical conditions, including the temperature of the air and the water, which may differ, and also the wind speed, the intensity of solar irradiation, and the vapor pressure of the water. Several of these effects can be combined, with the most imporatant factor being the quantity (1-h), where h is the relative humidity of the air, defined in the PRECIPITATION chapter. Several other terms are included as empitrical proportionalities, and no accurate, fundamental equation has ever been devised to describe this complex overall process. A useful equation for evaporation rate E is:

E=Psat(1-h)*(a+bv)                              EQ 1

where Psat is the vapor pressure of saturated air at the temperature of the water, v is the wind speed, and a and b are constants.

Measurements and Data  
Evaporation Measurements
Given the complexity of natural systems and the incomplete development of a theoretical description, evaporation rates are best quantified by field measurements. This is normally accomplished with the aid of an evaporation pan. The characteristics of the standard “Class A Land Pan” used in the USA are well established: the pan is 4 feet in diameter, and the water depth is maintained at 10 inches; many additional details about the configuration, field setup and operating conditions are provided by the NWS.  Precise measurements of water levels are made at regular intervals, most commonly daily, with careful account of all water additions by direct rainfall into the pan, or by intentional additions made to maintain the depth close to 10 inches. Accurate measurements during winter months cannot be made if freezing occurs.  

Long term evaporation data are available for several hundred sites. Typical results in temperate areas define an approximately symmetrical curve over a calendar year, with very low rates during winter and high rates during summer.  For many areas the curve is approximately “bell shaped”, somewhat similar to the well-known Gaussian curve of statistics. 

Measurement of Transpiration and ET  

Measurements of transpiration can be made with a potted plant where the soil is covered by wax.  Repeat measurements of the mass of the entire assembly quantify the loss of water, which necessarily has passed through the leaves.  A similar method is used to determine ET, using a “lysimeter” which is also a large box with soil plus plants.  A wax covering is not used, since evaporation from the soil is of interest.  Additions of water by rainfall or application is monitored, and the entire assembly is periodically weighed. Good data are few, but for temperate areas the ET has a “bell-shaped” annual curve that is similar to that for evaporation, although the amplitude is lower (Fig. 1). 

Water Balance Method  

The magnitude of ET can be quantified by consideration of the additions and losses of water to a given area.  In this approach, ET is not determined by direct measurement, but by difference of terms in flux equations.  

Planetary ET    

On a planetary scale, Earth’s inventory of water is a constant, with no appreciable additions or losses over time intervals of interest to hydrologists.  Mass balance requires that:

P = ET                                        EQ 2

where P is the integrated global rainfall in the interval of interest. A simple interpretation of this equation is that “what goes up, must come down.” Note that P and ET in equation are water fluxes, not “amounts”.  This is an important point, as precipitation is normally reported and considered as “inches” or “centimeters” of rainfall.  In fact, we are really discussing the quantity of rain delivered to the land in a stated interval of time.  The real quantity being discussed is a volumetric flux, that is, the volume of rain delivered per unit area per unit time. In metric units, this becomes m3/m2-s, or m/s, which has the units of velocity. 

Global  ET   

As discussed in Chapter 2, global scale variations in precipitation and climate primarily depend on latitude because of the Hadley cell and parallel atmospheric unicells.  Figure 3.x shows how ET, P and humidity vary with latitude.  Even though P and ET must be equal on a planetary scale, at any latitude these quantities generally differ.  The only large region where ET >P is in the trade wind belt, where the Hadley cell is downwelling. Fundamentally, this zone is the “mother” of Earth’s hydrologic cycle. Near the equatorial and poles, P substantially exceeds E.  These differences are balanced by latitudinal fluxes of atmospheric water. 

Continental Scale

On the scale of large land masses, runoff (R) must be included in the flux equation, which becomes:

P =  ET + R                                                            EQ 3

Consider those terms for the lower 48 states of the USA. For this 800 M km2 region, the average precipitation is 75 cm/y, whereas the surface runoff from the combined rivers of the region is about 22 cm/y.  Smaller terms including subsurface runoff, or the flow of groundwater to the sea, plus consumptive use are estimated to be 3 cm/y. The difference of 50 cm/y must be ET.  This incredible result is not atypical.  More than 2/3 of all precipitation delivered to Earth’s large land masses is destined to return to the atmosphere.  Here again, units are important.  The flow of rivers is usually considered as discharge (m3/s). Converting such measurements to appropriate flux units (m/s) requires both time conversion, an incorporation of the watershed area from which that flow is derived. 

Watershed Scale 

Very useful estimates of ET can be made on the watershed scale.  On short time intervals (e.g., monthly) changes in storage can be important, so the flux equation becomes:

P = ET + R   +/-  S                                 EQ 4

where S represents changes in storage, which mostly represents changes in the amount of soil water and groundwater.  If irrigation is important, or if water is brought into or transferred out of the basin by humans, terms for additions or withdrawals are needed. If precipitation and streamflow data are available for a given basin, Equation 3.x can be used to estimate ET plus storage.  Because the time lag between precipitation delivery and peak discharge can be several days, this is best done on a monthly scale.  Figure 2a  shows the quantity (P-R)/P plotted vs month for several small to moderate watersheds whose flow is gaged and that have a proximal weather station.  This curve exhibits the following differences with the pan an lysimeter data discussed above, namely 1) significant ET (+/-S) occurs during winter months, with the amount being nearly half as large as during warmer seasons; 2) the peak ET (+/-S) occurs in late summer or early fall, later in the year, and 3) the curve is strongly skewed rather than symmetrical. Many factors contribute to these differences, but an important one is that the area of an evaporation pan is constant, but the effective area of a natural watershed changes dramatically over the year, due to the leaf area of plants; this effective area remains large even during fall when trees are dormant. This area is a major control on the transfer of water to the atmosphere.

Over an annual cycle the amount of water stored in many basins is relatively constant.  In such cases equation 4 can be used with good accuracy. 

Lakes and Reservoirs   

Water balance is very important for lakes and reservoirs. The flux equation becomes:

dV/dt = (P – E)*A + I – O                                      EQ 5

where V is the lake volume, t is time, P is direct precipitation on the lake surface, E is evaporation from the lake surface,  A is the lake area, I is the total inflow to the lake, particularly from inflowing streams, and O is outflow from the lake. The inflow and outflow can also include contributions or losses due to ground water flows, which may be difficult to estimate.  Care must be exercised so that all terms have consistent units.

Simplifications are possible for certain cases.  For example, for a terminal lake the surface outflow is zero, so all inflowing water must either evaporate or be lost to the groundwater system.  In all cases the term dV/dt quantifies changes in storage. At steady state, or over long time intervals, dV/dt approaches zero.

As a rule of thumb, evaporation from a reservoir surface is about 70% of the water loss from a nearby evaporation pan; this factor is known as the “pan coefficient”.  Reasons for this difference probably include an overall higher temperature of water in the pan, especially during summer, and an increase in the humidity of the air above the lake surface at some distance from the shore.  

Use of Geochemical Data to Identify and Quantify ET

Concentration Effects   

Evaporation has obvious effects on water chemistry.  The major effect is one of increased concentration, because as the water molecules disappear into the air, but practically all salts and particulates remain behind, as do many organic compounds. 

Because both precipitation and evaporated water are dilute, the mass balance equation for a lake or sub watershed is:

dC/dt = I*Ci -O*Co                                     EQ 6

where C, Ci and Co are the average concentrations of any dissolved constituent of interest  in the lake and in the inflow and outflow, respectively. Again, the inflow and outflow terms may contain contributions from both surface and groundwater, and if groundwater is important, both the flux magnitudes and their concentrations may be difficult to quantify. 

Several useful simplifications are appropriate for special circumstances.  If the lake is well mixed, a useful simplification is that the average lake concentration is equal to that of the total outflow. In addition, at steady state, or on a long time interval, dC/dt is zero or small, so that

I*Ci=O*Co                              EQ 7

This equation simply states that the chemical “load” of a constituent that enters the water body must equal to the load that leaves.  Finally, for a terminal lake, it is clear that the water concentration iss unbounded, which in a real system means that the dissolved minerals of interest (e.g., halite) must attain saturation.  These equations may be combined with equations above.