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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
To model sensible heat flux on a large scale using remote 
sensing data, the similarity formulation based on the Monin- 
Obukhov similarity (MOS) theory has been the most widely 
used approach (Brutsaert,1982,1999; Su,et al.,2000). This 
approach has been proved to be successful to calculate regional 
average surface sensible heat fluxes (Lhomme et al.,1994; 
Bastiaassen, 1995; Wang et al., 1995; Ma et al., 1997,1999; Su 
et al., 2000). Based on this approach, combining Eqs 11, 12 and 
13, the regional sensible heat flux H can be derived from the 
following equation: 
2 
pC pK Up (7, E 7410) 
Zp 
zd 7 
nés Ta grep qne p 
0m 0m 
H = 
  
(14) 
where Zi is the bulk atmosphere boundary layer (ABL) 
height, 4, and T vh are wind speed and air temperature at 
the ABL height respectively. In this study, these variables over 
the Longxi Loess plateau area are determined with the aid of 
field measurements. Lan is the effective aerodynamic 
roughness length derived by relating the effective stress to the 
surface characteristics (Wieringa, 1992; Ma et al.,2002). 
2.1.4 The Latent Heat flux AE 
The latent heat flux between surface and atmosphere can be 
expressed as: 
pC le pif] 
y. 
AE (15) 
Residual approach based on surface energy balance Eq. (1) is 
widely used to calculate surface latent heat flux. Specifically, 
after computing the sensible heat flux (H) with Eq.(14), the net 
radiation (R,) with Eq.(2) and soil heat flux ( 7, ) with Eq.( 9), 
the latent heat flux can be derived as the residual of the energy 
budget theorem from Eq (1) as 
JE=R -G,-H (16) 
2.2 Calculation of instantaneous evaporative fraction 
Based the surface energy balance system model (SEBS) 
discussed above, the evaporative fraction A using 
NOAA/AVHRR data of Oct.1“, 2002 (6:26AM) can be given 
below after the net radiation À , sensible heat flux H , latent 
n? 
heat AE and soil heat flux G are derived: 
PT 
R -G, AE«H 
where H = 0, À = | (water surface) , AE =0, A = 0 (dry 
land surface). 
  
A= (17) 
The calculated evaporative fraction is shown in Fig.2. Higher 
values (0.6-0.9) occur in the Liupan Mountains, Qinling 
Mountains. Tibet Plateau, Qilianshan Mountains and several 
reservoirs where more water is available for evaporation. A 
large area of low evaporative fraction, ranging between 0 and 
0.25 (dark areas in Fig. 2), is found in Yellow River Valley, 
Zhuli River basin and the northern desert area, suggesting that a 
major portion of the study area is characterized by lack of water 
for evaporation. 
2.3 Calculation of daily evaporation 
The above-calculated evaporative fraction A is instantaneous 
value (6:26AM) and it can be extrapolated to daily À : 
  
8.64 x 10” At Gay) T 
AS f 
day 1. pi 
where Ey is the actual daily evaporation (mm d'). An 
the daily evaporative fraction, Ant (instantaneous 
evaporative fraction) has a constant relationship with the daily 
A 
dep: R and Gd are the daily net radiation flux and soil 
heat flux respectively, PP, the density of water (Kgm?) 
p. 1000kg / m^ , À the latent heat of vaporization 
(Kg) and can be calculated as : 
À =[2.501 —0.00237 # T, )]x10* (19) 
; : & 0 ; . 
where 7 is mean air temperature ( C. ). The daily soil heat 
flux Ga should be close to zero because of the fact that 
daytime downward flux is approximately equal to the nighttime 
upward flux. The daily ET thus depends on the daily net 
radiation flux as following: 
  
— 64x10! A, x R,, 
* day = ; (20) 
| A: p, 
Ru = (1 TÉ r)Ki, + Las (21) 
where Ki is daily incoming global radiation and Los is 
daily net long wave radiation. 
The calculated daily ET generally matches the instantaneous 
evaporative fraction in Fig.2. Low ET ranging between 0 and 
1.0 mm/d (black areas in Fig.3) is found in the Zuli basin, 
Yellow River valley and northern desert. The ET in the Qilian 
Mountains, Tibet Plateau, Liupan Mountains and Qinling 
Mountains are evidently higher than in those low-elevation 
valleys and basins and also increases with increasing elevation 
in these high-elevation mountains and plateau (Fig.3). This 
spatial distribution patterns suggest that both increased 
precipitation and better vegetation coverage in the mountains 
contribute to the elevated ET. 
3. DATA PROCESSING 
In order to use SEBS model to calculate evapotranspiration, 
several land surface biophysical parameters, such as albedo, 
land surface temperature, emissivity, and NDVI, have to be 
determined from remote sensing data (NOAA/AVHRR). The 
calculation of both the surface bi-directional reflectance and 
vegetation index (NDVI) are based on AVHRR channels 1 and 
2 (Valiente et al., 1995). The algorithm for deriving surface 
temperature is based on a theoretical split-window algorithm of 
Coll and Caselles (1997). Emissivity is calculated using the 
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