Evapotranspiration Estimates from Remote Sensing for Irrigation Water Management - Satellite-based Applications on Climate Change - page 195

where ET r is the estimated instantaneous rate (interpolated from hourly data)
(mm h 1 ) for the standardized 0.5 m tall alfalfa reference at the time of the
image. Generally, only one or two weather stations are required to estimate ET r
for a Landsat image that measures 180

180 km, as discussed below. ET r F is the
same as the well-known crop coefficient K c when used with an alfalfa reference
basis and is used to extrapolate ET from the image time to 24-h or longer periods.
One should generally expect ET r F values to range from 0 to about 1.0 (Wright
1982 ; Jensen et al. 1990 ). At a completely dry pixel, ET ¼ 0.

A pixel in a well-established field of alfalfa or corn can occasionally have an ET
slightly greater than ET r and, therefore an ET r F > 1, perhaps up to 1.1 if it has been
recently wetted by irrigation or precipitation. However, ET r generally represents an
upper bound on ET for large expanses of well-watered vegetation. In calculation of
ET r F , each pixel retains a unique value for ET inst that is derived from a common
value for ET r, which is derived from the representative weather station data.
Daily values of 24-h evapotranspiration ( ET 24 ) are generally much more useful
than the instantaneous ET that is derived from the satellite image. In the METRIC
process, ET 24 is estimated by assuming that the instantaneous ET r F computed at
image time is the same as the average ET r F over the 24-h average. The consistency
of ET r F over a day has been demonstrated by various studies, including Romero
( 2004 ), Colaizzi et al. ( 2006 ) and Allen et al. ( 2007a ).
The assumption of constant ET r F during a day has been shown to be valid for
agricultural crops that have been developed to maximize photosynthesis and thus
stomatal conductance. The advantage of using ET r F is that it accounts for the
increase in ET 24 that can occur under advective conditions, impacts of which are
represented well by the Penman-Monteith equation.
The ET 24 (mm/day) is computed for each image pixel as

0 and therefore ET r F ¼

ET 24 ¼ EðÞR n24 ð Þ

(13.7)

or

ET 24 ¼ C rad ET r F ð Þ ET r24 ð Þ (13.8)

where ET r F (or EF ) is assumed equal to the ET r F (or EF ) determined at the satellite
overpass time, ET r24 is the cumulative 24-h ET r for the day of the image, and C rad is
a correction term used in sloping terrain to correct for variation in 24-h vs. instan-
taneous energy availability.
After ET and ET r F have been determined using the energy balance and the
application of the single d T function, then, when interpolating between satellite
images, a full grid for ET r is used for the extrapolation over time to account for
both spatial and temporal variation in ET r .The ET r grid is generally made on a 3- or
5-km base using as many quality-controlled weather stations located within and in the
vicinity of the study area as are available. Depending on data availability and the
density of the weather stations, various gridding methods can be used, including
kriging, inverse distance, and splining.