# ERS 482/682 Small Watershed Hydrology

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ERS 482/682 Small Watershed Hydrology
Evapotranspiration ERS 482/682 Small Watershed Hydrology ERS 482/682 (Fall 2002)

water becoming water vapor consumptive use by plants
Definition Total evaporation from all water, soil, snow, ice, vegetation, and other surfaces plus transpiration water becoming water vapor consumptive use by plants ERS 482/682 (Fall 2002)

Processes Evaporation of precipitation intercepted by plant surfaces
Evaporation of moisture from plants through transpiration Evaporation of moisture from soil (ground) surface ERS 482/682 (Fall 2002)

How significant is evapotranspiration?
Can be as much as 90% of precipitation Affected by changes in Vegetation Weather   ET   streamflow air temperature  ET   streamflow ERS 482/682 (Fall 2002)

Evaporation Fick’s Law:
A diffusing substance moves from where its concentration is larger to where its concentration is smaller at a rate that is proportional to the spatial gradient of concentration Figure 8.2 (Chapra 1997) ERS 482/682 (Fall 2002)

Evaporation Fick’s Law: A diffusing substance moves from where its concentration is larger to where its concentration is smaller at a rate that is proportional to the spatial gradient of concentration gradient (change) in concentration indicates movement from regions of higher concentration to regions of lower concentration will have units of substance *[L T-1] where Fz(X) = rate of transfer of substance X in z direction DX = diffusivity of substance X C(X) = concentration of X [L2 T-1]  units depend on substance ERS 482/682 (Fall 2002)

Evaporation where E = evaporation rate
Fick’s Law: A diffusing substance moves from where its concentration is larger to where its concentration is smaller at a rate that is proportional to the spatial gradient of concentration where E = evaporation rate KE = efficiency of vertical transport of water vapor va = wind speed es = vapor pressure of evaporating surface ea = vapor pressure of overlying air [L T-1] [L T-1 M-1] [L T-1] [M L-1 T-2] [M L-1 T-2] ERS 482/682 (Fall 2002)

water temperature at surface
Vapor pressure, e Partial pressure of water vapor saturation vapor pressure, e*: maximum vapor pressure relative humidity ea = Waea* water vapor water es = es* water temperature at surface ERS 482/682 (Fall 2002)

Latent heat exchange, LE
Occurs whenever there is a vapor pressure difference between water and air [E L-2 T-1] where w = water density v = latent heat of vaporization 1000 kg m-3 surface water temperature (°C) [MJ kg-1] ERS 482/682 (Fall 2002)

Sensible heat exchange, H
Occurs whenever there is a temperature difference between water and air where B = Bowen ratio Depends on air pressure  constant at a particular site ERS 482/682 (Fall 2002)

All expressed in units of [E L-2 T-1] except Q [E L-2]
Energy balance Equation 7-15 where Q = change in heat storage per unit area over time t K = shortwave (solar) radiation input L = longwave radiation H = turbulent exchange of sensible heat with atmosphere LE = turbulent exchange of latent heat with atmosphere Aw = heat input due to water inflows and outflows G = conductive exchange of sensible heat with ground All expressed in units of [E L-2 T-1] except Q [E L-2] ERS 482/682 (Fall 2002)

Classification of ET processes
Surface type: Open water Bare soil Leaf/canopy type Crop type Land region Water availability Unlimited vs. limited Stored energy use, Q Water-advected energy, Aw often assumed negligible ERS 482/682 (Fall 2002)

Free-water evaporation
“Potential evaporation” Evaporation that would occur from an open-water surface in the absence of advection and changes in heat storage Depends only on climate/meteorology Evaporation: net loss of water from a surface resulting from a change in the state of water from liquid to vapor and the net transfer of this vapor to the atmosphere ERS 482/682 (Fall 2002)

Free-water evaporation
“Potential evaporation” Penman equation Standard hydrological method recall: ERS 482/682 (Fall 2002)

Free-water evaporation
“Potential evaporation” Penman equation Standard hydrological method psychrometric constant ERS 482/682 (Fall 2002)

Free-water evaporation
“Potential evaporation” Penman equation Standard hydrological method dimensionless Table 4-6 Dunne & Leopold (1978) ERS 482/682 (Fall 2002)

Free-water evaporation
“Potential evaporation” Pan-evaporation Direct measurement method where W = precipitation during time t V1 = storage at beginning of period t V2 = storage at end of period t 12 in. Class-A evaporation pan Diameter = 1.22 m Height = .254 m ERS 482/682 (Fall 2002)

Free-water evaporation
“Potential evaporation” Pan-evaporation Direct measurement method 0.7 average for US Efw = (PC)Epan See Morel-Seytoux (1990) for pan coefficients No adjustments necessary for annual values ERS 482/682 (Fall 2002)

Bare-soil evaporation
Stages Atmosphere-controlled stage (wet soil surface) Evaporation rate  free-water evaporation rate Soil-controlled stage (dry soil surface) Evaporation rate << free-water evaporation rate ERS 482/682 (Fall 2002)

Transpiration Transpiration: evaporation of water from the vascular system of plants into the atmosphere Figure 6.1 (Manning 1987) ERS 482/682 (Fall 2002)

Transpiration Dry soils Saline soils
Figure 6.2 (Manning 1987) Dry soils soil capillary pressure > osmotic pressure Saline soils water concentrationsoil < water concentrationplant ERS 482/682 (Fall 2002)

Transpiration Leaf/canopy conductance Depends on Cleaf
Number of stomata/unit area Size of stomatal openings Density of vegetation Cleaf LAI: fraction of area covered with leaves shelter factor Penman-Monteith model (Equation 7-56) ERS 482/682 (Fall 2002)

Transpiration Figure 3.4 (Brooks et al. 1991) ERS 482/682 (Fall 2002)

Potential evapotranspiration (PET)
Rate at which evapotranspiration would occur from a large area completely and uniformly covered with growing vegetation with unlimited access to soil water and without advection or heat-storage effects ERS 482/682 (Fall 2002)

Potential evapotranspiration (PET)
Thornthwaite method where Et = potential evapotranspiration Ta = mean monthly air temperature I = annual heat index a = I – I I3 [cm mo-1] [°C] ERS 482/682 (Fall 2002)

Potential evapotranspiration (PET)
Thornthwaite method Figures 5-4 and 5-5 (Dunne & Leopold 1978) Index must be adjusted for # days/mo and length of day ERS 482/682 (Fall 2002)

Potential evapotranspiration (PET)
Blaney-Criddle formula where Et = potential evapotranspiration Ta = average air temperature k = empirical crop factor d = monthly fraction of annual hours of daylight [cm mo-1] [°C] ERS 482/682 (Fall 2002)

Potential evapotranspiration (PET)
Notes Wind speed has little or no effect Local transport of heat can be significant Taller and widely spaced vegetation tend to have greater heat transfer ERS 482/682 (Fall 2002)

Measuring evapotranspiration
Cannot be measured directly Transpiration Lysimeters Figure 6.3 (Manning 1987) ERS 482/682 (Fall 2002)

Measuring evapotranspiration
Cannot be measured directly Transpiration Lysimeters Tent method Evaporation Evaporation pans Water budget: ET + G = P – Q Paired watershed studies Figure 3.5 (Brooks et al. 1991) ERS 482/682 (Fall 2002)