There are many sources of data for pan evaporation rates. The source could be the monthly evaporation normals for a site where data is collected with an evaporation pan. More often the data are presented within the context of a regional analysis utilizing multiple measure sites, for example Roderick and Farquhar (2004).
Within the United States the National Weather Service has estimated average evaporation as shown in Figure 25.
Figure 25.Calculated evaporation climatology in millimeters for the month of January using data from 1971 to 2000.
The measured pan evaporation rates overestimate evapotranspiration. The usual practice is to multiple the pan evaporation rate by a reduction ratio in order to approximate the evapotranspiration. The ratio typically ranges from 0.5 to 0.85 with the specific value depending on how the evaporation pan is sited and the atmospheric conditions. The ratio is larger when the relative humidity is higher. The ratio decreases as the windspeed increases. Typical values taken from the United Nations Food and Agriculture Organization (FAO, 1998) are shown in Table 14 and Table 15. The values are for a Class A evaporation pan and depend on the how the pan is located relative to vegetation, as shown in Figure 26.
Figure 26.Two cases of evaporation pan siting and their environment.
Table 14.Pan coefficients for Class A pan sited on grass with a grass fetch but measuring transpiration over bare ground, and different levels of mean relative humidity (RH) and windspeed.
RH (%) --> Low (< 40) Medium (40-70) High (> 70) Windspeed
(m/s)
Fetch Length (m)
Light 1 0.55 0.65 0.75
< 2 10 0.65 0.75 0.85
100 0.70 0.80 0.85
1,000 0.75 0.85 0.85
Moderate 1 0.50 0.60 0.65
2-5 10 .06 0.70 0.75
100 0.65 0.75 0.80
1,000 0.70 0.80 0.80
Strong 1 0.45 0.50 0.60
5-8 10 0.55 0.60 0.65
100 0.60 0.65 0.70
1,000 0.65 0.70 0.75
Very strong 1 0.40 0.45 0.50
> 8 10 0.45 0.55 0.60
100 0.50 0.60 0.65
1,000 0.55 0.60 0.65
Table 15.Pan coefficients for Class A pan sited on bare ground with a bare ground fetch but measuring transpiration over grass, and different levels of mean relative humidity (RH) and windspeed.
RH (%) --> Low (< 40) Medium (40-70) High (> 70) Windspeed
(m/s)
Fetch Length (m)
Light 1 0.70 0.80 0.85
< 2 10 0.60 0.70 0.80
100 0.55 0.65 0.75
1,000 0.50 0.60 0.70
Moderate 1 0.65 0.75 0.80
2-5 10 0.55 0.65 0.70
100 0.50 0.60 0.65
1,000 0.45 0.55 0.60
Strong 1 0.60 0.65 0.70
5-8 10 0.50 0.55 0.65
100 0.45 0.50 0.60
1,000 0.40 0.45 0.55
Very strong 1 0.50 0.60 0.65
> 8 10 0.45 0.50 0.55
100 0.40 0.45 0.50
1,000 0.35 0.40 0.45
The monthly average method is designed to work with data collected using evaporation pans. Pans are a simple but effective technique for estimating evaporation. There is a long history of using them and data is widely available throughout the United States and other regions.
Basic Concepts and Equations
Evaporation pans are measurement instruments. A standard pan is 121 centimeters in diameter and 24 centimeters deep, though variations exist. It is set on a wooden platform close to the ground as shown in Figure 24. It is common to measure the windspeed adjacent to the evaporation pan, as well as the minimum and maximum water temperature each day. Water is added to the pan. Care must be taken to keep the water surface at least 5 centimeters below the top of the pan so that wind does not blow waves over the edge.
Usually the pan will be refilled daily to keep the water level from falling more than 7.5 centimeters below the top. If the pan is allowed to empty too much, the temperature of the water may increase and cause
overestimation of the evaporation rate.
Figure 24.Example installation of a Class A evaporation pan.
Measurements are often performed in two separate ways. First, the pan may be marked with calibrated graduations. The graduations represent depth and measure the volume in the evaporation pan. The water surface is noted against the graduations to determine the water level each day. The difference on two sequential days is the amount of evaporation that occurred, measured as an equivalent depth. Second, the volume of water added to the pan each day can be measured; with the pan always being filled to the same level. Given the volume of water added and the area of the pan, the equivalent depth can be calculated. An average of the two depths may be taken as the estimate of the evaporation for each day.
Data collected with evaporation pans is usually reported in monthly averages. Averages must be determined for a long period of time in order to eliminate yearly variations. The United Nations World Meteorological Organization (ref needed) recommends a minimum record length of 30 years. It has been found that for long- term simulations greater than 15 years, using pan evaporation data compares favorably with more
sophisticated models of evaporation (ref needed).
Estimating Parameters
There are many sources of data for pan evaporation rates. The source could be the monthly evaporation normals for a site where data is collected with an evaporation pan. More often the data are presented within the context of a regional analysis utilizing multiple measure sites, for example Roderick and Farquhar (2004).
Within the United States the National Weather Service has estimated average evaporation as shown in Figure 25.
Figure 25.Calculated evaporation climatology in millimeters for the month of January using data from 1971 to 2000.
The measured pan evaporation rates overestimate evapotranspiration. The usual practice is to multiple the pan evaporation rate by a reduction ratio in order to approximate the evapotranspiration. The ratio typically ranges from 0.5 to 0.85 with the specific value depending on how the evaporation pan is sited and the atmospheric conditions. The ratio is larger when the relative humidity is higher. The ratio decreases as the windspeed increases. Typical values taken from the United Nations Food and Agriculture Organization (FAO, 1998) are shown in Table 14 and Table 15. The values are for a Class A evaporation pan and depend on the how the pan is located relative to vegetation, as shown in Figure 26.
Figure 26.Two cases of evaporation pan siting and their environment.
Table 14.Pan coefficients for Class A pan sited on grass with a grass fetch but measuring transpiration over bare ground, and different levels of mean relative humidity (RH) and windspeed.
Daily and monthly average pan evaporation rates for CONUS can be visualized here: https://
www.cpc.ncep.noaa.gov/products/Soilmst_Monitoring/US/Evap/Evap_clim.shtml
RH (%) --> Low (< 40) Medium (40-70) High (> 70) Windspeed
(m/s)
Fetch Length (m)
Light 1 0.55 0.65 0.75
< 2 10 0.65 0.75 0.85
100 0.70 0.80 0.85
1,000 0.75 0.85 0.85
Moderate 1 0.50 0.60 0.65
2-5 10 .06 0.70 0.75
100 0.65 0.75 0.80
1,000 0.70 0.80 0.80
Strong 1 0.45 0.50 0.60
5-8 10 0.55 0.60 0.65
100 0.60 0.65 0.70
1,000 0.65 0.70 0.75
Very strong 1 0.40 0.45 0.50
> 8 10 0.45 0.55 0.60
100 0.50 0.60 0.65
1,000 0.55 0.60 0.65
Table 15.Pan coefficients for Class A pan sited on bare ground with a bare ground fetch but measuring transpiration over grass, and different levels of mean relative humidity (RH) and windspeed.
RH (%) --> Low (< 40) Medium (40-70) High (> 70) Windspeed
(m/s)
Fetch Length (m)
Light 1 0.70 0.80 0.85
< 2 10 0.60 0.70 0.80
100 0.55 0.65 0.75
1,000 0.50 0.60 0.70
Moderate 1 0.65 0.75 0.80
2-5 10 0.55 0.65 0.70
100 0.50 0.60 0.65
1,000 0.45 0.55 0.60
Strong 1 0.60 0.65 0.70
5-8 10 0.50 0.55 0.65
100 0.45 0.50 0.60
1,000 0.40 0.45 0.55
Very strong 1 0.50 0.60 0.65
> 8 10 0.45 0.50 0.55
100 0.40 0.45 0.50
1,000 0.35 0.40 0.45
Hamon Method
Basic Concepts and Equations
The Hamon method (Hamon, 1963) 24is one of two temperature-based evapotranspiration methods included in HEC-HMS. These method use an empirical relationship between temperature and net radiation. In this method, potential evapotranspiration is proportional to saturated water vapor concentration, at the mean daily air temperature, adjusted for daytime hours. Since transpiration occurs during the day, the daytime hour adjustment accounts for plant response, duration of turbulence, and net radiation. For simulation time steps less than one day, potential evapotranspiration is redistributed for each time step based on a sinusoidal distribution between sunrise and sunset.
Average potential evapotranspiration ETo is computed as (Hamon, 1963):
16)
where c is a coefficient, N is the number of daylight hours, and Pt is the saturated water vapor density at the daily mean temperature.
The number of daylight hours N is computed as (Allen et al., 1998):
17)
where is the sunset hour angle.
Annual variation in daylight hours (Allen et al., 1998)
The sunset hour angle is computed as (Allen et al., 1998):
18)
where is the latitude and is the solar declination.
The saturation vapor pressure es at the mean daily temperature T is computed as (Allen et al., 1998):
25 https://www.hec.usace.army.mil/confluence/hmsdocs/hmsguides/meteorologic-models-for-historical-precipitation/gridded- precipitation-method
26 https://www.hec.usace.army.mil/confluence/hmsdocs/hmsguides/hec-hms-example-applications/advanced-applications-of-hec-hms- final-project
19)
The saturation vapor density Pt is computed as (Wiederhold, 1997):
20)
Required Parameters
The only parameter required to utilize this method within HEC-HMS is the coefficient [in/g/m3 or mm/g/m3].
In addition, air temperature must be specified as a meteorologic boundary condition.
A Note on Parameter Estimation
While HEC-HMS provides a default coefficient value of 0.0065 in/g/m3 (0.1651 mm/g/m3), this value must be calibrated and validated. In addition, air temperature must be provided as a meteorologic boundary condition.
Hargreaves Method
Basic Concepts and Equations
The Hargreaves method (Hargreaves and Samani, 1985) is one of two temperature-based evapotranspiration methods included in HEC-HMS. The method is based on an empirical relationship where reference
evapotranspiration was regressed with solar radiation and air temperature data. The regression was based on eight years of precision lysimeter observations for a grass reference crop in Davis, CA. The method has been validated for sites around the world (Hargreaves and Allen, 2003). The method is capable of capturing diurnal variation in potential evapotranspiration for simulation time steps less than 24 hours.
Potential evapotranspiration ETo is computed as (Hargreaves and Samani, 1985):
21)
where K is a coefficient, RS is solar radiation, and T is mean daily temperature.
A tutorial using the Gridded Hamon method in an event simulation can be found here: Gridded Precipitation Method25.
A tutorial using the Gridded Hamon method in an continuous simulation can be found here:
Advanced Applications of HEC-HMS Final Project26.
Hargreaves and Samani (1982) developed an equation for determining solar radiation from extraterrestrial radiation and the measured temperature range. Extraterrestrial radiation is the amount of solar energy that would be on a horizontal plane on the earth's surface if the earth was not surrounded by an atmosphere:
22)
where KRS is a coefficient, Ra is extraterrestrial radiation, and Tmax and Tmin are the daily maximum and minimum air temperature, respectively.
When the Hargreaves Evapotranspiration Method is used in combination with the Hargreaves Shortwave Radiation Method, the computed Hargreaves evapotranspiration form is equivalent to Hargreaves and Allen (2003) Eq. 8:
23)
Required Parameters
The only parameter required to utilize this method within HEC-HMS is the coefficient [deg C-1]. In addition, air temperature must be specified as a meteorologic boundary condition.
A Note on Parameter Estimation
While HEC-HMS provides a default coefficient value of 0.0135 deg C-1, this value must be calibrated and validated.
Priestley Taylor Method
Basic Concepts and Equations
Priestley and Taylor (1972)27 developed a simplified energy balance approach to modeling
evapotranspiration. Data from multiple sites, each with saturated surface or open water conditions and without advection, were used to develop a widely applicable formula for the relationship between sensible and latent heat fluxes. For partially saturated land surfaces, the reference evapotranspiration is related to the saturated evaportranspiration rate by a coefficient:
where is the dryness coefficient, R is the net incoming radiation, G is the heat flux into the ground (R - G = LE + H) where H is sensible heat and LE is latent heat, is the slope of the saturation vapour pressure curve, and is the psychrometric constant.
Required Parameters
The only parameter required to utilize this method within HEC-HMS is the dryness coefficient. In addition, air temperature and net radiation must be specified as a meteorologic boundary condition. Net radiation should be computed, entered in the program as a radiation time-series gage, and selected as the shortwave
radiation method.
28 https://royalsocietypublishing.org/doi/10.1098/rspa.1948.0037
29 https://repository.rothamsted.ac.uk/item/8v5v7/evaporation-and-environment
A Note on Parameter Estimation
While HEC-HMS provides a default coefficient value of 1.26, this value must be calibrated and validated. The default value corresponds to a saturated surface, or wet conditions. Specifically, lower values of the dryness coefficient should be used in humid regions while higher values should be used in arid regions.
Penman Monteith Method
Basic Concepts and Equations
HEC-HMS implements the Penman-Monteith method as derived by the United Nations Food and Agriculture Organization (FAO) (Allen et al., 1998 (see page 118)). The Penman Monteith was adopted as the standard for reference evapotranspiration by the FAO. The reference evapotranspiration provides a standard to which evapotranspiration in different seasons or regions and of other crops can be compared.
Evapotranspiration can be derived using an energy balance or mass transfer method. Evaporation of water requires energy, either in the form of sensible heat or radiant energy. The rate of evapotranspiration is governed by the energy exchange at the vegetation surface and is limited by the amount of available energy.
Therefore, the rate of evapotranspiration can be derived from a surface energy balance. Evapotranspiration can also be derived by balancing the incoming and outgoing water fluxes to the soil, or root zone. The mass transfer method is better suited for estimating ET over long time periods (on the order of weeks or more).
The Penman Monteith method combines energy balance and mass transfer methods (Penman, 194828; Monteith, 196529). The evapotranspiration rate is represented by the latent heat flux:
24)
where Rn is the net radiation at the crop surface, G is the soil heat flux , is the mean air density at constant pressure, cp is the specific heat of air, es is the saturation vapour pressure, ea is the actual vapour pressure, es - ea is the vapour pressure deficit, is the slope of the saturation vapour pressure temperature relationship, and is the psychrometric constant, and rs and ra are the (bulk) surface and aerodynamic resistances, respectively.
The bulk surface resistance accounts for the resistance of vapour flow through the transpiring crop
(stomata, leaves) and evaporating soil surface. The aerodynamic resistance describes the upward resistance from vegetation resulting from the friction from air flowing over vegetated surfaces.
While a large number of empirical evapotranspiration methods have been developed worldwide, some have been calibrated locally leading to limited global validity. The FAO Penman Monteith method uses the concept of a reference surface, removing the need to define parameters for each crop and stage of growth.
Evapotranspiration rates of different crops are related to the evapotranspiration rate from the reference surface through the use of crop coefficients. A hypothetical grass reference was selected to avoid the need for local calibration. According to FAO (Allen et al., 1998):
The reference surface closely resembles an extensive surface of green grass of uniform height, actively growing, completely shading the ground and with adequate water. The requirements that the grass surface should be extensive and uniform result from the assumption that all fluxes are one-dimensional upwards.
•
•
•
•
•
•
•
•
•
The reference crop is defined as a hypothetical crop with a height of 0.12 m, a surface resistance of 70 s/m, and an albedo of 0.23. The FAO's simplified equation for reference evapotranspiration is (Allen et al., 1998):
25)
where ETo is the reference evapotranspiration, Rn is the net radiation at the crop surface, G is the soil heat flux density, T is the mean daily air temperature at 2 m height, u2 is the wind speed at 2 m height, es is the saturation vapour pressure, ea is the actual vapour pressure, es - ea is the vapour pressure deficit, is the slope of the saturation vapour pressure curve, and is the psychrometric constant.
Required Parameters
The parameterization is entirely dependent on the atmospheric conditions: solar radiation, air temperature, humidity, and wind speed measurements. Weather measurements should be made at 2 m above the ground surface (or converted to that height).
Applicability and Limitations of Evapotranspiration Models
The following table contains a list of various advantages and disadvantages regarding the aforementioned evapotranspiration methods available for use within HEC-HMS. However, these are only guidelines and should be supplemented by knowledge of, and experience with, the methods and the watershed in question.
Method Advantages Disadvantages
Hamon Simple, parsimonious method.
Mean air temperature is the only required meteorologic input.
Based on an empirical relationship between air temperature and net radiation.
Hargreaves Simple, parsimonious method.
Mean air temperature is the only required meteorologic input.
Based on an empirical relationship between air temperature and net radiation.
Priestley Taylor
Penman
Monteith Energy balance with mass transfer method.
Widely used and documented through United Nations Food and Agricultural Organization (FAO).
Method is less parsimonious than simpler ET methods; it requires many more meteorologic boundary
conditions.
•
•
•
•
Method Advantages Disadvantages
Monthly
Average Simple, parsimonious method.
Pan evaporation data is widely available.
Differences in the water and cropped surface can produce significant differences in the water loss from an open water surface and the crop.
Empirical coefficients used to relate evapotranspiration to pan evaporation.
Evaporation and Transpiration References
Allen, R. G., Pereira, L. S., Raes, D., & Smith, M. (1998). Crop Evapotranspiration: Guidelines for Computing Crop Water Requirements. FAO Irrigation and Drainage Paper No. 56. Rome: United Nations Food and Agriculture Organization.
Hamon, W. R. (1963). Estimating Potential Evapotranspiration. American Society of Civil Engineers Transactions, 128, 324-338.
Hargreaves, G. H., & Allen, R. G. (2003). History and Evaluation of Hargreaves Evapotranspiration Equation.
Journal of Irrigation and Drainage Engineering, 129(1), 53-63.
Hargreaves, G. H., & Samani, Z. A. (1985). Reference Crop Evapotranspiration from Temperature. Applied Engineering in Agriculture, 1(2), 96-99.
Monteith, J. L. (1965). Evaporation and the Environment. Symposia of the Society for Experimental Biology, 205-234.
Penman, H. L. (1948). Natural evaporation from open water, bare soil and grass. Proceedings of the Royal Society of London, 193, 120-145.
Priestley, C. H., & Taylor, R. J. (1972). On the Assessment of Surface Heat Flux and Evaporation Using Large- Scale Parameters. Monthly Weather Review, 100(2), 81-92.
Roderick, M. L., & Farquhar, G. D. (2004). Changes in Australian pan evaporation from 1970 to 2002.
International Journal of Climatology, 24(9), 1077-1090.
Wiederhold, P. R. (1997). Water vapor measurement: methods and instrumentation. New York: Marcel Dekker.
Canopy, Surface, Infiltration, and Runoff Volume
HEC-HMS computes runoff volume by computing the volume of water that is intercepted, infiltrated, stored, evaporated, or transpired and subtracting it from the precipitation. Interception (canopy) and surface storage are intended to represent the storage of water by trees or grass, local depressions in the ground surface, cracks and crevices in parking lots or roofs, or a surface area where water is not free to move as overland flow. Infiltration represents the movement of water to areas beneath the land surface. Interception, infiltration, storage, evaporation, and transpiration collectively are referred to in the program and
documentation as losses. This chapter describes the various canopy, surface, and infiltration (loss) models as well as how to use them to compute runoff volumes.
Losses and Runoff Volume Basic Concepts
Determining the portion of precipitation that becomes runoff volume is a complicated matter. Precipitation may first fall on a vegetation canopy that intercepts a portion of the precipitation. Surface depressions capture some of the precipitation reaching the ground and allow it to infiltrate. Water that does not infiltrate
generally moves over the ground surface to become runoff volume. Once water is in the soil it can move vertically and a portion that infiltrated may return to the atmosphere through evapotranspiration. The weight of consideration given to each of these components depends on the purposes of the hydrologic study.
Studies using event simulation methods tend to focus on the initial condition at the beginning of the storm and the portion of the storm volume that becomes runoff. Studies using continuous simulation methods usually focus on infiltration and evapotranspiration in order to estimate monthly or annual runoff volumes.