Neural networks are known for their capability in handling nonlinear mapping problems (Chen et al. 1999; Liou et al. 1999b, 1999c). Hence, they are suitable to characterize the f function for the problems of our interest. One major feature using neural networks is that f does not have to be explicit. Instead, f is simply defined through a training process using a representative data set. The EPLBP neural network is used to handle nonlinear mappings from microwave emissions to the parameter of interest, SM. It encourages different individual networks to get improved in an ensemble to learn different parts or aspects of a training data. The errors associated with each individual networks are negatively correlated through an adjustable penalty parameter ? (0 = ? = 1) This negative correlation learning is a simple extension to the standard back propagation algorithm of the Rumelhart et al. (1986). Weight updating of all the individual networks is performed simultaneously with equal penalty parameter. Since the correlation is quite often decreased with increasing distance from the individual network of concern, a distance dependent penalty parameter is expected to simulate the neurons more appropriately than a constant penalty parameter.
The EPLBP algorithm is developed not only to correlate the errors associated with individual network via adjustable penalty parameters, but also to allow the penalty parameter to be distance dependent, that is, the limit of the distance in which neural networks are correlated is tunable. In addition, the value of the penalty parameter within that specific distance of concern is variable with distance from the center of a concerned region. The details for the EPLBP algorithm have been reported by Liu et al. (2001).
Analysis of the Results
A. Observation Modes
The viewing characteristics of AMSR and SMOS provide the basis to define the observation modes. Since there are many observation modes, we will not show all of the results. A more completed summary on the results will be presented in Liou et al. (2001). Results from four observing modes are presented.
- One integrated 2 AMSR channels observation mode: The observations at both 6.9 and 10.7 GHz channels of the AMSR are used simultaneously to become an integrated 2 AMSR frequency observation mode.
- One 1D SMOS observation mode: L-band observation at 30 degrees is studied. This observing mode is defined as a 1D L-band mode.
- One 2D SMOS observation mode: L-band observations at 20 and 30 degrees are utilized as inputs of the retrieval algorithm. This observation mode is defined as a 2D L-band mode.
- One integrated AMSR and
1D SMOS observation mode: The observation at
AMSR's 6.9 GHz is combined with the observation
from the 1D L-band mode at 30 degrees to become
an integrated AMSR and SMOS observation mode.
B. Comparison of Observation Modes
Based on the above four observational modes, the sensitivity of microwave brightness to SM can be examined by comparing the retrieved SM with the corresponding reference. Note that Gaussian-distributed noises with standard deviation of 2 K are imposed upon the input nodes of the neural network to simulate instrument noises for all observation modes of concern.
Figure 1 shows the retrieved SM from the 2 AMSR frequency observation mode versus the corresponding reference. The correlation between the retrieved SM and the reference with the corresponding root mean squared error (RMSE) in volumetric SM content are also shown in the figure. Overall, the retrieved SM falls onto or near the 1:1 line. The correlation is 81.3 % with RMSE less than 1.76%. The corresponding correlation is near 1 when no noise is imposed upon the input node.
Fig. 1 Retrieved SM from the integrated 2 AMSR frequency mode versus the reference.
Figure 2 shows the retrieved SM for the 1D L-band observation mode at 30 degrees versus the corresponding reference. The retrieved SM is improved significantly compared to that derived from the 2 AMSR frequency observation mode. Figure 3 presents the retrieved SM from the L-band 2D observation mode at 20 and 30 (20-30) degrees versus the corresponding reference. It is observable that the retrieved SM is further improved compared to that from the previous two cases. The correlations between the retrieved SM and the reference is 1 with RMSE as low as 0.025%. A comparison between Figures 2 and 3 clearly demonstrates the advantage of a 2D mode over a 1D mode since the RMSE is reduced significantly.
Fig. 2 Retrieved SM for the 1D L-band mode at 30 degree versus the reference.
