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 microscopic 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 empirical 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

Evapotranspiration Measurement

Efforts to begin to understand ET mostly for agricultural purposes date back to the 19th century, leading to the use of pan evaporation as a measure of the potential crop water requirements. Understood though was that plants lose water vapor as evapotranspiration slower than an open pan evaporating in direct sunlight. Accordingly, early research focused on trying to quantify this difference in evaporation with measurements. These include soil moisture as part of water mass balance methods that incorporate precipitation and infiltration. This evolved into the development of a reference ETo based on a single crop type, which in this case today is a short grass. All other plant ET measurements can then be compared to ETo as a ratio known as the crop coefficient or Kc, where

and ETc is the evapotranspiration of the specific crop. Lookup tables of Kc values have been generated over the years and have been widely used worldwide since the United Nation’s implemented this approach in their agricultural development programs in the 1970s. This method is sufficient for well-watered crops and has measurement uncertainties comparable to uncertainties in water diversion or groundwater pumping measurements, making it a practical tool.

Somewhat in parallel, theoretical arguments developed for computing ET based on first-principal physics and complemented by field measurements. Initially developed by Penman in 1948 (Penman, 1948) and later modified by Monteith, the widely cited Penman-Monteith equation emerged for this purpose. This relationship is a non-empirical multi-variant equation that calculates ET following the relationship

where Δ is the rate of change in saturated vapor pressure, Rn is net radiation, G the soil heat flux, Ρ the density of air, cc specific heat of moist air, γ the psychrometric constant, rs the canopy surface resistance to vapor transfer, and ra the aerodynamic resistance between the crop and a reference height where meteorological measurements are acquired. VPD is the vapor pressure deficit measured at the reference level. The equation attempts to reflect how fast vapor will move from differences in the heat between soil and the reference level and is buffered by the nature of the crop shape as defined by the resistance terms. The resistance is a highly uncertain term for any given crop, so this equation has mostly been accepted in computing ETo values only. From a farming perspective the complexity of the equations appears to make it impractical, which essentially what has been occurring. However, because the Penman-Monteith equation is a model that captures surface energy change, the observational focus since has been on field measurements of solar radiation, temperature, air moisture, and wind velocities, all of which today are easily made with off-the-shelf meteorological products. This has further evolved into networks of measurements in different regions of the US. Additional development emerging from this available data type is the eddy correlation technique that computes vapor flux based on measurements alone. This has largely replaced the use of the Bowen ratio, which computed flux based on sensible and latent heat terms.

Many of the field measurements traditionally employed for calculating ET are limited in scale and tend to reflect local effects. For soil moisture for instance, soil and root heterogeneities make dubious extrapolation of a single measurement spot over a field scale. Furthermore, field data collected at limited times during the day and not capturing diurnal variability creates additional uncertainty and limits extrapolation over time. These uncertainties today are being addressed by use of airborne and satellite based measurements with coverages from a single field to large regions. These methods employ indirect measures of heat and moisture using either laser based systems or multi-wavelength spectroscopic detection. Deconvolution algorithms are employed to derive ET, but again uncertainties can be high where baseline conditions are poorly constrained.

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 are 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 ±ΔS 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 4 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 (±ΔS) occurs during winter months, with the amount being nearly half as large as during warmer seasons; 2) the peak ET (±ΔS) 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 is 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.

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