## 3 Estimation Methods and Techniques
### Machine Learning Approaches  
The machine learning approach for estimating rainfall in Indonesia has been applied to several different case studies. With backpropagation, the multi-layer perceptron (MLP) algorithm was used to estimate rainfall at locations lacking direct rainfall observation data. The input data consisted of radar data validated with automatic rainfall observation data collected around a single polarization radar observation. The results improved the rainfall detection accuracy by 79% and reduced the error value in rainfall estimation [115], as shown in Figure 8. The MLP algorithm, with its ability to handle non-linear patterns, can model the relationship between the complexity of weather data and observed rainfall. Non-linear activation functions in the MLP algorithm, such as ReLU (rectified linear unit) or sigmoid, allowing the model to learn non-linear relationships between input and output features [116, 117]. However, the MLP algorithm has a risk of overfitting because the model tends to memorize training data patterns without regularization [118]. The model's performance decreases on new data. In addition, the MLP algorithm has an architecture with many layers and many neurons [117]. Training this model requires intensive mathematical operations, including matrix multiplication, vector operations, and non-linear activation for each neuron in each layer. The requirement for large computing resources [119, 120] will be a problem if implemented on a large scale in Indonesia. Figure 8: Conceptual diagram of the MLP algorithm for rainfall estimation using single-polarization radar (**a**) and the estimation results compared with the radar equation (**b**) (modified from [115]). Figure 7: An illustration of the (**a**) TMM, (**b**) PMM, and (**c**) WPMM techniques (modified from [24]). Another study compared the decision tree, random forest, adaptive boosting, and gradient boosting machine learning algorithms. All four algorithms optimized rainfall estimation using rain gauge, radar, and satellite data, with the gradient boosting algorithm outperforming the other three [121]. A similar study compared tree-based algorithms for rainfall estimation in different regions using radar measurements [122, 123]. Regions with local [123] and equatorial [122] rainfall patterns have high and even rainfall throughout the year. The difference between the wet and dry seasons is not very clear [124]. Rainfall estimation using the adaptive boosting algorithm shows the worst results in these regions. Heterogeneous and fluctuating data training can increase weather radar uncertainty. When adaptive boosting encounters difficult data points to estimate correctly, this algorithm gives high weight to these points with the aim of increasing model performance. Mathematically, adaptive boosting gives high weight to incorrect data, which means that its performance decreases if there is excessive noise [125]. The relationship between radar reflectivity and rainfall can be categorized as complex data due to various physical and atmospheric factors that influence each other [30]. Decision trees with complex datasets are complicated tree structures with many nodes representing specific features and patterns from the training data [126]. For example, in cases of inconsistent or irrelevant rainfall fluctuations, the decision tree separates the data based on these fluctuations. This can cause the decision tree to be too specific to the training data [127]. As a result, the model will overfit due to being unable to generalize well on new test data, which causes poor rainfall estimation results. Using random forests and gradient boosting can produce better rainfall estimates. Random forest has the ability to handle noise in data because it uses many decision trees independently [128]. By considering multiple features and random subsets of the training data, random forests tend to be more tolerant of noise [129] because they can reduce overfitting on each individual decision tree [130].