## 4 Model Development  
In this study, machine learning methods and the capabilities of the SHAP method were utilized to develop a new drought index by combining individual indices into a CDI. The data used for calculating single indices within the study area were obtained from remote sensing systems and subsequently underwent normalization processes for the calculation of each index. The normalized images were cropped to cover the study area. The input data utilized to obtain the CDI were rescaled to have a temporal resolution of monthly and a spatial resolution of \(1\times 1\) km. This was achieved by averaging the daily data on a monthly basis. The bilinear algorithm was applied for spatial rescaling, transforming all cropped images to a target resolution of \(1\times 1\) km, and they were subsequently masked to include crop areas based on crop land information obtained from GLAD. After the masking process, spatial averages were taken for each month from October to June, considering the district boundaries within the study area. Thus, a single value representing each month was obtained for each district. Using these values, the weights of the CDI equation were calculated using three different methods. Of these, PCA and empirical methods do not require a target variable, but for the SHAP method, crop yield values measured in each district were used as the target variable. To provide inputs for the SHAP algorithm, prediction models were created using the XGBoost method. The inputs of the XGBoost model were TCI, VCI, SMCI, PCI, GPP, and NDWI values, while the target variable was the detrended crop yield values. Since the GPP input has been available since 2000, the period between 2001 and 2020 was selected for modeling. During the ML model creation phase, all possible scenarios for the six inputs (63 different combinations) were tested. During the modeling phase, a random splitting strategy was embraced, with 75% of the data were used for training and 25% for testing. The districts selected for the test set were Aksehir, Altinkin, Altinhsar, Beysehir, Bor, Camardi, Cihanbeyli, Ilgin, Karapinar, and Selcuklu. In the next step, the calculation of mean SHAP values was carried out using the results of the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**CDI and SPEI** & **Class** & **scPDSI** & **Class** \\ \hline \(\leq-2\) & Extreme Drought & \(\leq-4\) & Extreme Drought \\ \(-1.5\) to \(-1.99\) & Severe Drought & \(-3\) to \(-3.99\) & Severe Drought \\ \(-1\) to \(-1.49\) & Moderate Drought & \(-2\) to \(-2.99\) & Moderate Drought \\ \(-0.5\) to \(-0.99\) & Mild Drought & \(-1\) to \(-1.99\) & Mild Drought \\ \(-0.49\) to \(-0.49\) & Near Normal & \(-0.5\) to \(-0.99\) & Incipient Drought \\ \(0.5\)–\(0.99\) & Slightly Wet & \(0.49\) to \(-0.49\) & Near Normal \\ \(1\)–\(1.49\) & Moderately Wet & \(0.5\)–\(0.99\) & Incipient Wet \\ \(1.5\)–\(1.99\) & Severely Wet & \(1\)–\(1.99\) & Slightly Wet \\ \(\geq 2\) & Extremely Wet & \(2\)–\(2.99\) & Moderately Wet \\  & & \(3\)–\(3.99\) & Very Wet \\  & & \(\geq 4\) & Extremely Wet \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Classification thresholds for CDI, SPEI, and scPDSI. model with high prediction accuracy. Using the SHAP feature importance values obtained, the weights of the CDI equation were determined, thereby obtaining accurate weights using a method that calculates the marginal contributions of all variables in a nonlinear manner. The correlation between the CDI equations obtained by three different methods and crop yield was examined to measure the success of the new index in representing agricultural drought. Additionally, a comparative analysis with SPEI and scPDSI values, which are also used in agricultural drought studies in the literature, was conducted. Furthermore, the similarities and differences between CDI, SPEI, and scPDSI were examined. The analysis steps are shared in Figure 2.  
Figure 2: Study flowchart. The hyperparameters of the XGBoost algorithm used in the study were optimized using the grid search method.