Lecture 10 - 1 ERS 482/682 (Fall 2002) Evapotranspiration ERS 482/682 Small Watershed Hydrology.

ERS 482/682 (Fall 2002) Lecture 10 - 1

Evapotranspiration

ERS 482/682Small Watershed Hydrology

ERS 482/682 (Fall 2002) Lecture 10 - 2

Definition

Total evaporation from all water, soil, snow, ice, vegetation, and other

surfaces plus transpiration

water becoming water vaporwater becoming water vapor

consumptive use by consumptive use by plantsplants

ERS 482/682 (Fall 2002) Lecture 10 - 3

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) Lecture 10 - 4

How significant is evapotranspiration?

• Can be as much as 90% of precipitation• Affected by changes in

– Vegetation– Weather

ETET streamflowstreamflow

air temperature air temperature ETET streamflowstreamflow

ERS 482/682 (Fall 2002) Lecture 10 - 5

Fick’s Law:A diffusing substance moves from where

its concentration is larger to where itsconcentration is smaller at a ratethat is proportional to the spatial

gradient of concentration

Evaporation

Figure 8.2 (Chapra 1997)

ERS 482/682 (Fall 2002) Lecture 10 - 6




Evaporation

dz

XdCDXF Xz )(

where Fz(X) = rate of transfer of substance X in z direction DX = diffusivity of substance X C(X) = concentration of X

[L[L22 T T-1-1]]

units depend on substanceunits depend on substance

will have units ofwill have units ofsubstance *[L Tsubstance *[L T-1-1]]

indicates movementindicates movementfrom regions of higherfrom regions of higher

concentration to regionsconcentration to regionsof lower concentrationof lower concentration

gradient (change) ingradient (change) inconcentrationconcentration

ERS 482/682 (Fall 2002) Lecture 10 - 7




Evaporation

asaE eevKE 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[L T-1-1]]

[L T[L T-1-1 M M-1-1]]

[L T[L T-1-1]][M L[M L-1-1 T T-2-2]]

[M L[M L-1-1 T T-2-2]]

ERS 482/682 (Fall 2002) Lecture 10 - 8

Vapor pressure, e

Partial pressure of water vapor

saturation vapor pressure, e*: maximum vapor pressure

waterwater vapor

eess = e = ess**

3.237

3.17exp611.0*

s

ss T

Te water temperaturewater temperature

at surface at surface

eeaa = W = Waaeeaa**

3.237

3.17exp611.0*

a

aa T

Terelative humidityrelative humidity

ERS 482/682 (Fall 2002) Lecture 10 - 9

Latent heat exchange, LE

• Occurs whenever there is a vapor pressure difference between water and air

ELE vwwhere w = water density v = latent heat of vaporization

Tv31036.250.2

[E L[E L-2-2 T T-1-1]]

[MJ kg[MJ kg-1-1]]

1000 kg m1000 kg m-3-3

surface water temperature (surface water temperature (°C)°C)

ERS 482/682 (Fall 2002) Lecture 10 - 10

Sensible heat exchange, H

• Occurs whenever there is a temperature difference between water and air

LEBHLEH

B

where B = Bowen ratio

Depends on air pressure constant at a particular site

ERS 482/682 (Fall 2002) Lecture 10 - 11

Energy balanceEquation 7-15

All expressed in units of [E LAll expressed in units of [E L-2-2 T T-1-1]]except except Q Q [E L[E L-2-2]]

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

LEAHGLKtQ

w

ERS 482/682 (Fall 2002) Lecture 10 - 12

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 negligibleoften assumed negligible

ERS 482/682 (Fall 2002) Lecture 10 - 13

Free-water 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

“Potential evaporation”

Evaporation: net loss of water from a surface resulting from achange in the state of water from liquid to vapor and the net

transfer of this vapor to the atmosphere

ERS 482/682 (Fall 2002) Lecture 10 - 14


• Penman equation– Standard hydrological method

LEAHGLKtQ

w 0 0 0

vw

HLKE

ELE vwrecall:


ERS 482/682 (Fall 2002) Lecture 10 - 15



as

as

TT

ee

**

v

a Pc

622.0psychrometric constantpsychrometric constant

1-K kPa 066.0

EH

Evw

HLKE


ERS 482/682 (Fall 2002) Lecture 10 - 16



EH

E1

EH

E

dimensionless

Table 4-6 Dunne & Leopold (1978)


ERS 482/682 (Fall 2002) Lecture 10 - 17


• Pan-evaporation– Direct measurement method

12 VVWEpan where W = precipitation during time t V1 = storage at beginning of period t V2 = storage at end of period t

Class-A evaporation panDiameter = 1.22 m

Height = .254 m


12 in.

ERS 482/682 (Fall 2002) Lecture 10 - 18


• Pan-evaporation– Direct measurement method

12 VVWEpan

Efw = (PC)Epan

See Morel-Seytoux (1990) for pan coefficientsNo adjustments necessary for annual values


0.7 average for US

ERS 482/682 (Fall 2002) Lecture 10 - 19

Bare-soil evaporation

• Stages– Atmosphere-controlled stage (wet soil wet soil

surface)surface)• Evaporation rate free-water evaporation rate

– Soil-controlled stage (dry soil surfacedry soil surface)• Evaporation rate << free-water evaporation rate

ERS 482/682 (Fall 2002) Lecture 10 - 20

Transpiration

Transpiration: evaporation of water from the

vascular system of plants into the atmosphere

Figure 6.1 (Manning 1987)

ERS 482/682 (Fall 2002) Lecture 10 - 21

Transpiration

• Dry soilssoil capillary pressure > osmotic pressure

• Saline soilswater concentrationsoil < water concentrationplant


ERS 482/682 (Fall 2002) Lecture 10 - 22

Transpiration

• Leaf/canopy conductance– Depends on

• Number of stomata/unit area• Size of stomatal openings• Density of vegetation

Cleaf

LAI: fraction of area covered with leaves

leafcan CLAIfC s

shelter factorshelter factor

Penman-Monteith model (Equation 7-56)

ERS 482/682 (Fall 2002) Lecture 10 - 23

Transpiration

Figure 3.4 (Brooks et al. 1991)

ERS 482/682 (Fall 2002) Lecture 10 - 24

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) Lecture 10 - 25


• Thornthwaite methoda

at I

TE

10

6.1

where Et = potential evapotranspiration Ta = mean monthly air temperature I = annual heat index a = 0.49 + 0.0179I – 0.000077I2 + 0.000000675I3

[cm mo[cm mo-1-1]]

[°C][°C]5.1

12

1 5

i

aiT

ERS 482/682 (Fall 2002) Lecture 10 - 26


• Thornthwaite method

Figures 5-4 and 5-5 (Dunne & Leopold 1978)

Index must be adjusted for Index must be adjusted for # days/mo and length of # days/mo and length of

dayday

ERS 482/682 (Fall 2002) Lecture 10 - 27


• Blaney-Criddle formula

kdTTE aat 8.17095.1142.0

where Et = potential evapotranspiration Ta = average air temperature k = empirical crop factor d = monthly fraction of annual hours of daylight

[cm mo[cm mo-1-1]][°C][°C]

ERS 482/682 (Fall 2002) Lecture 10 - 28


• 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) Lecture 10 - 29

Measuring evapotranspiration

• Cannot be measured directly• Transpiration

– Lysimeters


ERS 482/682 (Fall 2002) Lecture 10 - 30

Measuring evapotranspiration

• Cannot be measured directly• Transpiration

– Lysimeters

Figure 3.5 (Brooks et al. 1991)

– Tent method• Evaporation

– Evaporation pans

• Water budget: ET + G = P – – Q

• Paired watershed studies

Lecture 10 - 1 ERS 482/682 (Fall 2002) Evapotranspiration ERS 482/682 Small Watershed Hydrology.

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