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Oceangraphy
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Optimum selection method of initial guess values for maximum likelihood estimation of Sea Surface Temperature and Precipitable Water
Where S x is the variance-covariance matrix of x, S y is the variance matrix of the noise of the sensor or crrors due to sensor function in channel 3 and 4 of MOS-1VTIR[2]
- Optimum selection method of initial guess values
Figure 1 shows the flow chart to select the optimum initial guess values. At first, ten reasonable atmospheric groups selected around Japan. The mean values of air temperature and perceptible water. Obtained from the radio sounding near or in the each area are adopted as initial guess values. Figure 2 shows the examples of vertical distribution of air temperature and perceptible water. Corresponding to atmospheric group, reasonable sea surface temperature values are selected from the mean sea surface temperature in August (summer) and February (winter) . From these data, initial guess value of brightness temperature T°B is calculated by using computer code LOWTRAN7 [3]
On the other hands, in order to retrieve several cloudless sea category. MOS-1/VTRchannel 3 and arc classfied by means of cluster analysis (Figure 3) , and TB which is spatial mean value of
brightness temperature TB is calculated for each category
After that, the distance between T°B and  is calculated, and T°B which has the minimum distance from is adopted as initial guess value for that category. Thus, initial guess values of air temperature, perceptible water and sea surface temperature are also decided. Based on these initial guess values, sea surface temperature and perceptible water for each category are simultaneously estimated as the maximum likelihood data and the variance of spatial distribution of sea surface temperature is approximated based on that of channel 3 brightness temperature for each category.
Results of estimation
Figure 4 and show the results of estimation of sea surface temperature and perceptible water respectively. The average RMS error between the observed values [4] and those estimated is also shown in Table. 1. The average RMS error for sea surface temperature is 1.13 [K] and correlation coefficient is 0.99. According to this result, sea surface temperature can satisfactorily be estimated by the method developed in this research. It should be pointed out that the RMS error of perceptible water in the Table 1 is computed under the assumption that perceptible water over the respective study area is nearly equal to that of the nearly radio sounding station. A little large error of 0.62 (cm) may be due to the above reason since the true perceptible water over the area may be a little different from that of nearly radio sounding station.
Table Results of estimation of sea surface temperature (SST)and precipitable water (PW)
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Corr.
Coef. |
Bias
error |
RMS
error |
SST
PW |
0.99
0.95 |
-0.40(K)
0.27(cm) |
1.13(k)
0.62(cm) |
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