3. Data
This study used multi-temporal SPOT images to estimate the atmospheric aerosol optical depth. The data set includes 6 SPOT imageries acquired between April to August, 1998 covering Chung-Li area. The geometric information of the data set is shown in Table 1. meanwhile, the sun photometer data were collected at the same time. The aerosol depths derived from sun photometer data were used to verify the accuracy of the method proposed in this study ( Table 2).

Date	Loc	View Angle		Solar Angle
	al time	Zenith	Azimuth	Zenith	Azimuth
1998/04/24	02:23	-29	193	24	117
1998/05/11	02:27	-23	193	20	107
1998/06/27	02:24	-30	193	21	89
1998/07/02	02:28	-24	193	20	90
1998/07/30	02:59	31	193	15	110
1998/08/21	02:36	-9	193	22	119

Table 1.The geometric information of SPOT images used in this study

Date	1020nm	870nm	670nm	440nm
1998/04/24	0.133	0.157	0.249	0.470
1998/05/11	0.272	0.326	0.499	0.860
1998/06/27	0.125	0.141	0.215	0.418
1998/07/02	0.088	0.092	0.151	0.296
1998/07/30	0.159	0.175	0.259	0.478
1998/08/21	0.050	0.038	0.059	0.105

Table 2. Aerosol optical depth collected by sun photometer.
4. Result and Analysis
The singular structure function pattern are depicted in the Figure 2(a) . as mentioned previously, these poor structure functions are mainly caused by satellite observation geometry and complex land cover distribution. Therese patterns would induce further errors in the optical depth estimation. When multi-directional structure function is employed as illustrated in Fig 2(b), the improvement is evident.



Figure 2(a) The varieties of the structure function with different distances of SPOT XS1 Channel .(b) same as (a), except for multi-directional structure function.
Further analysis showed the some abnormal patterns still existed in our approach. Therefore, the " optimal number " decision was added to determine the proper distance value, d and made sure that the abnormal structure function patterns can be removed.

The final result is summarized in Table 3. obviously, the accuracy of multi-directional method is better than the single-directional method, except on may 11 ( party cloudy ). The error is reduced from 33% to 9%. The result reveals improvement in accuracy derived from multi-directional method and the optimal number decision .

Date	Sunphotometer measurements	Single-directional		Multi-directional
		Retrieved	Error (%)	Retrieved	Error (%)
1998/04/24	0.339	0.386	14	0.348	3
1998/05/11	0.647	0.394	39	0.374	43
1998/06/27	0.299	0.347	16	0.311	4
1998/07/02	0.209	0.277	33	0.228	9
1998/07/30	0.315	0.356	13	0.345	9
1998/08/21*	0.078	-------	-----	------	------

Table 3. The comparison between the estimated optical depths estimated by the single & multi direction structure function methods .( *: reference date )
5. Conclusions
The results strongly suggest that including multi-direction and optimal number in structure function method will greatly improve the accuracy of derived aerosol optical depth. In the further study, the relationship of test area size and distance values are necessary to be investigate in detail. In order to verify the accuracy of optical depth estimation, the accuracy and method of deriving optical depth from sun photometer observation is also an important task.

Acknowledgements
This work has been supported by grant form the National Science Council, China Taipei under NSC86-2612-E-008-007.

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