# Spatial Downscaling of Soil Moisture Based on Fusion Methods in Complex Terrains
## 3 Methodology
The initial population size was 100, the roulette method was used for the gene selection, the learning rate was set to 0.05, and the target accuracy was a mean square error (MSE) of 0.001 m\({}^{3}\)/m\({}^{3}\). Genetic algorithms consist of three important parameters:  
Figure 2: Flowchart of the fusion procedure in this study. chromosome structure, gene coding, and fitness function. In this study, the chromosome structure included the weight and threshold of each layer and the number of neurons in the hidden layer. Real number coding was used for gene coding because its data are the weights and thresholds themselves, which are suitable for continuous data. Arithmetic crossover was chosen because it is well-suited for real encoding. The nonuniform mutation method was selected after comparing it to multiple widely used methods. The crossover probability and mutation probability were adjusted based on the fitness value of individuals. The reciprocal of the sum of squared errors was used as the fitness function according to the problem addressed in this study. The population evolved for 4000 generations according to the fitness function curves of the genetic algorithm. However, maximum fitness was reached and stayed stable after 262 generations. Considering the network accuracy and efficiency, the 262 nd-generation parameters were used as the optimal initial weight, threshold, and number of hidden layer neurons. The fitness of this model was 0.27, the R\({}^{2}\) of the validation set was 0.76, and the average absolute error was 0.03 m\({}^{3}\)/m\({}^{3}\). The CNN was implemented using Python3.6 GPU Keras 2.4.3. According to the model complexity theory [58], the neural network's best fitting was obtained when the errors of both the training set and validation set were very low. Through drawing the 1500-epoch training curves, the best fitting was at the 570 th epoch. The validation set reached the minimum mean absolute error (MAE) (0.0355 m\({}^{3}\)/m\({}^{3}\)), and the MAE (0.0349 m\({}^{3}\)/m\({}^{3}\)) of the training set was also very low. In the optimal model, four groups of convolutional layers were designed to learn higher-level features, and each group included two one-dimensional convolutional layers, a maximum pooling layer, and a dropout layer. Adam and MSE were used as the optimization function and loss function, respectively. RF was modeled using RandomForestRegressor from Python's Sklearn package. A grid search and 20-fold cross-validation were used for hyperparameter tuning. The optimal model parameters were obtained according to the MSE. The 1 km test set was imported into the three models for prediction, and the 1 km downscaled results were obtained, which are hereafter referred to as \"GABP\", \"CNN\", and \"RF\", respectively. SMAP SM and in situ SM were used to compare the three results from the statistical, temporal, and spatial distributions. In the fusion step, the in situ SM and high-resolution SM (HRSM) data were pre-processed by eliminating systematic errors and spatiotemporal matching. The error was expanded from the point scale to the fine-grid scale by geospatial interpolation. The downscaled results and in situ information fusion were realized by a geographic analysis, which is a nonparametric data fusion method based on error. It is often used to calibrate satellite data from ground-measured data and usually includes a geographical difference analysis (GDA) and geographical ratio analysis (GRA) [59]. The neighboring in situ stations were used to correct the background field by determining the weight of the in situ points at the interpolation point to estimate the error field. Finally, the fusion field is the sum or product of the error and the background fields. Equations (1) and (2) describe the fusion process based on the addition and multiplication errors, respectively.