Environmental Engineering Reference
In-Depth Information
ρ
air
is air density (kg m
3
),
C
p
is specific heat of air at constant pressure
(J kg
1
K
1
), and
r
ah,1,2
is aerodynamic resistance (s m
1
) between two near-
surface heights
z
1
and
z
2
(generally 0.1 and 2 m above the zero-plane displacement
height) computed as a function of estimated aerodynamic roughness of the particu-
lar pixel. In METRIC, the
r
ah,1,2
calculation uses wind speed extrapolated from
some blending height above the ground surface (typically 100-200 m) and an
iterative stability correction scheme based on the Monin-Obhukov functions
(Allen et al.
1996
). The d
T
parameter (
K
) represents the near-surface temperature
difference between
z
1
and
z
2
.d
T
is used in Eq.
13.2
because of the difficulty in
estimating surface temperature (
T
s
) accurately from satellites due to uncertainty in
atmospheric attenuation or contamination, radiometric calibration of the sensor,
and unknown values for air temperature,
T
a
, above any particular surface in an
image, where
T
a
can vary by more than 5
C between cold and dry conditions.
Equation
13.2
is relatively unique to SEBAL and METRIC and contrasts with
classical approaches where
H
is estimated using
T
s
and T
a
—factors with a great
deal of uncertainty that can cause large error in the estimate for
H
. Elevating d
T
above the surface eliminates the need to estimate roughness length for sensible heat
transfer,
z
oh
, the partitioning of
LE
between
E
and
T
, and the degree of vegetation
clumping. It is the blended d
T
that Bastiaanssen et al. (
1998
) found to be linearly
related to radiometric surface temperature,
T
s
.
d
T
is approximated as a relatively simple linear function of
T
s
as pioneered by
Bastiaanssen (
1995
):
where
d
T ¼ a þ bT
s datum
(13.3)
where
a
and
b
are empirically determined constants for a given satellite image and
T
s datum
is surface temperature adjusted to a common elevation datum for each
image pixel using a digital elevation model and customized lapse rate. The near-
surface temperature gradient over the two calibration pixels (cold pixel and hot
pixel) is computed using the inverse of Eq.
13.2
:
Hr
ah
ρ
air
C
p
d
T ¼
(13.4)
where
r
ah
is computed for the roughness and stability conditions of the cold and hot
pixels.
13.4.3 Calibration via Reference Evapotranspiration
METRIC uses the standardized ASCE Penman-Monteith equation for the alfalfa
reference
ET
r
(ASCE - EWRI
2005
) to calibrate the energy balance functions.
ET
r
is typically 20-30% greater than grass reference ET (
ET
o
).
ET
r
is used to
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