Evapotranspiration Estimates from Remote Sensing for Irrigation Water Management - Satellite-based Applications on Climate Change - page 194

approximate the ET of the cold-pixel calibration condition because METRIC does
not require the specific crop type for computation by pixel, thus eliminating the
need for relatively costly crop classification exercises.
The calibration of the sensible heat process equations to ET r corrects the surface
energy balance for lingering systematic computational biases associated with
empirical functions used to estimate some components and uncertainties in other
estimates, as summarized by Allen et al. ( 2005 ). Included are atmospheric correc-
tion, albedo calculation, net radiation calculation, surface temperature from the
satellite thermal band, air temperature gradient function used in sensible heat flux
calculation, aerodynamic resistance including stability functions, soil heat flux
function, and wind speed field. This list of biases plagues essentially all surface
energy balance computations that use satellite imagery as the primary spatial
information resource. Most polar orbiting satellites orbit about 700 km above the
earth's surface, yet the transport of vapor and sensible heat from land surfaces is
strongly impacted by aerodynamic processes including wind speed, turbulence, and
buoyancy, all of which are essentially invisible to satellites. In addition, precise
quantification of albedo, net radiation, and soil heat flux is uncertain and potentially
biased. Therefore, even though best efforts are made to estimate each of these
parameters as accurately and as unbiased as possible, some biases do occur, and
calibration to ET r helps to compensate for this by introducing a bias correction into
the calculation of H . The result is that biases inherent to R n , G , and subcomponents
of H are largely canceled by the subtraction of a bias-canceling estimate for H . The
result is an ET map with values ranging between near zero and near ET r , for images
having a range of bare or nearly bare soil and full vegetation cover.

13.4.4 Calculation of Evapotranspiration

ET at the instant of the satellite image is calculated for each pixel by dividing LE
from Eq. 13.1 by latent heat of vaporization:

600 LE
λρ w

ET inst ¼ 3 ; (13.5)

where ET inst is instantaneous ET (mm h 1 ), 3,600 converts from seconds to hours,
ρ w is the density of water [~1,000 kg m 3 ], and

is the latent heat of vaporization
(J kg 1 ) representing the heat absorbed when a kilogram of water evaporates. The
reference ET fraction ( ET r F ) is calculated as the ratio of the computed instanta-
neous ET ( ET inst ) from each pixel to the reference ET ( ET r ) computed from weather
data:

λ

ET inst
ET r

ET r F ¼ (13.6)