## Estimates of sensible heat fluxes using the developed dualsource model

The dual-source model developed in our study is used to estimate the sensible heat flux density. The model is tested first on the field measurements in IMGRASS site (Fig.7): the mean RMSD was 27.1 Wm"2. The measurements of directional brightness surface temperature and sensible heat flux density were not exactly simultaneous. Moreover, a series of observations of directional radiometric surface temperature at three view angles and four azimuth angles required a few minutes, while the measurements of sensible heat flux density were averaged over the thirty minutes centered at each hour and half-hour. This may contribute to the observed scatter (Fig. 7).

However, we may conclude that the sensible heat flux density calculated by our dual-source model agree reasonably well with the observed values, particularly after taking into account that 30 Wm'2 is the order of magnitude of the accuracy of eddy correlation systems like the one used during the IMGRASS experiment.

The ATSR-1 and -2 aboard the ERS-1 and -2 provide the opportunity to derive and for estimating heat flux density using our dual-source model at regional scale.

The calculations at the regional scale are done first for the HEIFE area using Tv and Ts derived from ATSR-1 image and the meteorological observations at blending height (Table 6). Fig.8 gives the histograms of the sensible heat flux density obtained in this way. At the satellite overpass time, sensible heat fluxes measured in the field were 46.6 Wm"2. The estimated mean values of H for 9 pixels close to the site was 52.5 Wm"2 with a standard deviation 4.2 Wm"2. The agreement between measured H and modeled H seems fairly good although we have used the atmospheric sounding 3 hours earlier than satellite overpass time to obtain blending height information. Table 6 also gives the modeled sensible heat flux using RAMS (Regional Atmospheric Modeling System) (Yan et al 1999) in the HEIFE area with 4km x 4km grid resolution. The value of H modeled by RAMS in Table 6 was taken from the model grid of RAMS where Zhang-Ye site is located. It appears that the RAMS H-values were significantly larger than the value observed (relative errors larger than 60%) and the value obtained with our dual-source model.

Sensible heat flux density was also estimated for the IMGRASS case using Tv and Ts retrieved pixel by pixel from ATSR-2. Atmospheric variables were estimated by assuming the lowest level of sounding as the reference height. The relative error between H modeled and H observed is smaller than 15%(see Table 6).

Fig. 8 gives the histograms of modeled sensible heat fluxes for both the HEIFE and IMGRASS areas. The modus is 60 Wm'2 for HEIFE, a reasonable value in comparison with the field measurements. The limited range of H-values indicates that the land surface is relatively homogeneous. On the contrary, in the IMGRASS area, the values of H vary in a wide range with two peaks (one is around the other one is around which is the consequence of the sparse grass cover and more heterogeneous surfaces.

Site |
time |
Dual-source |
RAMS |
Observation | |||

Mean(Wm'2) (3x3 pixels) |
oH(Wm'J) (3x3 pixels) |
RE |
model (Wm-1) |
RE |
(Wm2) | ||

IMGRASS |
Uh, 14/06/1998 |
174.6 |
30.1 |
8% |
- |
190,0 | |

HEIFE |
llh,19/08/1991 |
52.S |
4.2 |
13% |
- |
46.6 | |

10h,l 4/08/1991 |
- |
- |
- |
120.0 |
62% |
74.0 | |

lOh,15/08/1991 |
- |
- |
- |
160.0 |
64% |
97.6 |

mean: mean value of H modeled in 3x3 pixels closest to the site; oH: standard deviation of modeled H in 3x3 pixels closest to the site; RE: relative error between the value of modeled H and observed H.

mean: mean value of H modeled in 3x3 pixels closest to the site; oH: standard deviation of modeled H in 3x3 pixels closest to the site; RE: relative error between the value of modeled H and observed H.

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