Estimating ETType of method used will be determined by:

1. Type of surface (e.g. open water vs. leaf)2. Availability of water for evaporation3. 4. 5. Amount of air-advected energy

Free-water and lake evaporation- start with simplest situation, evaporation from an open water body- generally not possible to generate evaporation equations for a lake using meteorological data alone because Aw and )Q/)t vary significantly from lake to lake-annual values exceptions in lakes with residence time < 1 year

- theoretical concept of free-water evaporation (FWE) developed: assumes no advection or changes in heat storage- depends only on overlying climate

actual lake evaporation can be calculated from FWE for particular lakes..

Water Balance Approach

E = W + SWin + GWin - SWout - GWout - ΔV

W isSW is surface waterGW is ground waterΔV is lake storage change during the period of consideration

- in theory simple, in practice not easy..

Energy-Balance Approach

or, by inserting the Bowen ratio

The energy balance approach has many of the same detractions as the water-balance approach, but with the energy balance, at least we can:a)

b) use regional climatic data to estimate some of the radiation components..

EK L G H A Q tW

w v

/

EK L G A Q t

BW

w v

/

( ) 1

Shortwave Radiation

K=Kin(1-a)

Kin is incoming SW radiation, and a is the albedo of the surfaceKin is the amount of SW radiation hitting the ground. It is conceptually thought of as:

Λ =J = day of yearβ =α = aspectC = fraction of sky covered by cloudsF = fraction of sky covered by forest canopy

Kin can be measured directly using pyranometers, or an empirical relation can be used:

Kin = [0.355+0.68(1-C)]Kcs

albedo can also be directly measured, or a constant assumed depending on the surface type. For water, a typically ranges between 0.05 to 0.10, but with low solar angles can be very high (up to 0.6)..

K K J f f C f Fin cs ( , ) ( , , ) ( ) ( ) 1 2 3

Long-Wave Radiation

Net long-wave rad is equal to the LW flux coming in from the atmosphere, minus the amount reflected from the surface and the amount radiated from the surface

where:εw =εat = effective emmisivity of the atmosphereσ = the Stefan-Boltzman constant (1.17x10-7 cal/cm2/day/K4)temperatures are in Celciusεat is a function of humidity and cloud cover and can be estimated as:

ea is

L T Tw a t a w s ( . ) ( . )2 73 15 273 154 4

a t ae C ( . . )( . ).0 53 0 065 1 0 40 5

Conduction to the Ground

In the case of lakes can be considered negligible

Water-Advected Energy

cww is average precipitation rateSW and GW are surface and groundwater inflows and outflows (in volume per time per unit area)temperatures are in celcius..

A c wT SW T SW T

GW T GW Tw w w a in sw in ou t sw ou t

in gw in ou t gw ou t

[ ( ) ( )

( ) ( ) ]

Change in Stored energy

V is lake volumeT is average lake (reservoir) temperaturesubscripts 1 and 2 are values at start and end of time periodAL =

Bowen RatioUse of the Bowen ratio has the main advantage that it eliminates the need for measuring wind speed

Summary of Energy Balance Approach- suffers some of the same problems as water balance approach- better suited to longer (7 days +) time periods to get a maximum accuracy of ±5%..

Qc

AV T V Tw w

LL L

( )2 2 1 1

Pan-Evaporation Approach

- simple concept...set a “bathtub” out an measure the water loss

E=W-(V2-V1)

W =V= storage loss measured to high precision

Pans generally over-estimate real evaporation and coefficients are applied for correction so that daily free-water evaporation (mm/day) can be calculated as:

αpan =P = atmospheric pressure (mb)vpan is mean wind speed 15 cm above the pan (km/day)Tspan is water surface temperature (EC)± is plus when Tspan > Ta and minus when Tspan < Ta

"αpan is a factor to account for energy exchange at the edge of the pan (see equation 7-40 in text)

Corrections to the evaporative loss are only needed for calculating short-term (e.g. daily) values since the errors cancel out over the long term (e.g. annually)..

E E P v T Tfw pan pan pan span a 0 7 0 00064 0 37 0 002550 88

. [ . ( . . ) ].

pan span span panT T v 0 34 0 011 7 3 5 10 17 8 0 01357 3 0 36. . ( . )( . ) . .

Moving to the more complex...ET

When we consider ET,

Transpiration and Interception Loss

- Transpiration is evaporation from the vascular system of plants into the atmosphere- transpiration is a physical process (not metabolic) driven by water content gradients- interception loss is that precip that is caught by the canopy and evaporated directly to the atmosphere..

Potential ET

Potential Evaporation (PET) is the rate of ET that occurs under the prevailing solar inputs and atmospheric properties, if the surface is fully wet. Actual ET is the amount really removed.

PET is a theoretical concept that defines the “drying power” of the climate or local meteorological conditions, but actual ET is affected by:1. 2. Maximum leaf conductance3. 4. presence or absence of intercepted water

1. Temperature-based: e.g. Hammond2. Radiation-based: use net rad, air temp and pressure. E.g. Priestltley and Taylor3. Combination4. Pan: uses pan evap as a proxy for short veg ET

“Direct” Measurement of ET

Water-balance approaches

Lysimeters

-Artificially enclosed volumes of soil that have a representative vegetative cover, outflows and inflows of water can be measured, and changes in storage can be measured by weighing-accurate for low-lying vegetation, but very difficult for large (e.g. forest vegetation)

Soil moisture Balance- Total ET is monitored by precise measurement of rainfall and soil water content throughout the root zone-- can be useful for larger vegetation an is more natural than lysimeters, however obtaining accurate soil moisture profiles is difficult..

Land-Area Water Balance

- Problems in accurate assessment of components and ensuring storage change is negligable-error associated with storage change is minimal when mostly soil water involved

-Review Dingman’s evaporatranspiration chapter’s section on Turbulent Transfer Methods..