where ρ air is air density (kg m
À3 ), C p is specific heat of air at constant pressure
(J kg
À1 K
À1 ), and r ah,1,2 is aerodynamic resistance (s m
À1 ) between two nearsurface 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 particular 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 dT parameter (K) represents the near-surface temperature
difference between z 1 and z 2 . dT 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 dT
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 dT that Bastiaanssen et al. (1998) found to be linearly
related to radiometric surface temperature, T s .
dT is approximated as a relatively simple linear function of T s as pioneered by
Bastiaanssen (1995):
dT ¼ a þ b T 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 nearsurface temperature gradient over the two calibration pixels (cold pixel and hot
pixel) is computed using the inverse of Eq. 13.2:
dT ¼
H r ah
ρ air C p
(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
13 Evapotranspiration Estimates from Remote Sensing. . .
201
À3 ), C p is specific heat of air at constant pressure
(J kg
À1 K
À1 ), and r ah,1,2 is aerodynamic resistance (s m
À1 ) between two nearsurface 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 particular 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 dT parameter (K) represents the near-surface temperature
difference between z 1 and z 2 . dT 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 dT
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 dT that Bastiaanssen et al. (1998) found to be linearly
related to radiometric surface temperature, T s .
dT is approximated as a relatively simple linear function of T s as pioneered by
Bastiaanssen (1995):
dT ¼ a þ b T 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 nearsurface temperature gradient over the two calibration pixels (cold pixel and hot
pixel) is computed using the inverse of Eq. 13.2:
dT ¼
H r ah
ρ air C p
(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
13 Evapotranspiration Estimates from Remote Sensing. . .
201