3. Data used in this analysis
The data for this analysis was measured with the ratio-spectrometer of Field Spec FR (Analytical Spectral Devices Inc.) or MSR7000 ( Opto Research Corp.). Both radio-spectrometers gives reflectance values every 1 nm with a spectral resolution of 3nm. In this analysis, we averaged every 10 data points to simulate 10 nm resolution data. The spectral region used for this analysis was restricted to where the atmospheric transmittance is higher than 80%. In all, 121 bands with 10 nm width were selected as shown in Figure 1. the number of samples for this analysis was 595.

Figure 1 Selected 121 band indicated by vertical lines and three un-normalized universal reflectance patterns of vegetation, water and soil.



Figure 2 three normalized universal patterns of vegetation, water and soil for 121 band.
Figure 2, shows the normalized universal spectrum patterns of water, vegetation and soil, respectively. The samples for the universal spectrum patterns are the sea at Kata port, Wakayama in Japan, ten overlapped green leaves of Quecus glauca and dry desert sand near Dunhaung in China, respectively.

4.Results and Discussions
The results of the pattern Decomposition Method for some typical samples with [2] channels are shown in Figure 3. All samples have small remainders. The average relative errors defined by equation (3) for all samples is about 1.3%. The c2 defined by equation (4) is 0.002. The square root of 0.002 is 0.045 (4.5%) and is the fitting error per degree of freedom. The continuous spectral response patterns could be decomposed using only three universal patterns with 4.5% error per degree of freedom.

Figure 3 Pattern decomposition coefficients and remainder for typical samples



Figure 4 Frequency distribution of relatives errors.
Next, we studied the relationship between the band number and the c². For this study, several data sets with different numbers of bands were selected from the data with 121 bands. We picked up one band from every 2 bands and made two data sets from the data with 121 bands. 75 data sets were prepared in total. We also have made a simulated TM data set that has 6 bands.

Figure 4 shows the correction between the c_n-3² and the band number n. The c_n-3² is decreased according to increase the band number n and converges to constant value of 0.002 for n larger than 15. The square root of 0.002 is 0.045 (45%) and is the finding error per degree of freedom. Therefore, in the PDM, the spectral reflectance can be fitted within the error of 4.5% at all measured points using only the three universal patterns. It is concluded as a general rule that land cover objects could be decomposed by three universal spectral patterns.