## 1 Introduction
[50] optimized the CDI equation weights through trial and error by assigning different weights to the TCI, SMCI, and PCI indices. This trial-and-error method requires evaluating the CDI values against a target. [PERSON] et al. [51] used seven different weighting scenarios in a trial-and-error approach, with the PDSI, \(Z\)-index, and SPI as target variables to determine the optimal scenario. In studies conducted without a target variable, researchers often utilize methods such as principal component analysis (PCA) [52; 53], entropy [54; 55], and analytic hierarchy process (AHP) [56; 57]. In CDI calculations, PCA captures the common variance of the single indices and creates principal components for analysis, assigning weights to each single index. These weights are determined by each input's contribution to the principal components, with higher variance components receiving more weight. CDIs based on PCA assume linearity among random variables, which can lead to information loss post-analysis [58]. This linearity assumption can be problematic in drought studies involving complex hydrological and meteorological systems with nonlinear characteristics [59]. AHP methods, on the other hand, rely on expert opinions to weigh criteria. Some disadvantages of this method include high computational requirements even for small problems, a subjective nature that can depend on emotional judgments, and increased time and effort required for additional pairwise comparisons [60]. A review of the CDI literature reveals that very few studies have used machine learning (ML) methods to calculate the weights of the equation. Of those that have employed ML, [PERSON] et al. [61] used the random forest (RF) method to determine the weights of CDI inputs. However, metrics used in the RF model, such as Gini impurity and permutation importance, can be biased, especially for features with high cardinality (many categories). This can inflate the importance of certain features, thereby leading to an inaccurate assessment of their true contribution to the model [62]. Recently, methods have been developed to explain nonlinear relationships and work alongside ML techniques to evaluate the power of inputs in predicting the output, taking into account their intricate relationships. One of the most frequently used methods that can adapt to almost any type of ML model is the SHapley Additive exPlanations (SHAP) method. SHAP uses Shapley values from game theory, which are used to fairly deter mine each player's (in this case, the features in the model) contribution to a game (the model's prediction). A feature's contribution to the model is calculated as the average of its marginal contribution across all possible combinations. While random forest's feature importance ranks the general contributions across the entire model, it does not provide local (individual prediction level) explanations. In contrast, SHAP provides individual explanations for each prediction, allowing for a more detailed and fair understanding of the model's decisions [63]. The study aims to answer the following questions:  
1. Does adding NDWI and GPP values improve CDI calculations? 2. How successful is the developed CDI in detecting agricultural drought? 3. What are the relationships between CDI, formed by different combinations of single drought index indicators, and crop yield? 4. What is the nonlinear behavior of each input on the output? To find answers to the questions listed above, this study aims to define a new CDI that will reflect winter wheat yield values. In addition to the commonly used TCI, PCI, VCI, and SMCI, the NDWI and GPP are included to calculate CDI values. To demonstrate the effectiveness of including the CDI, the correlation coefficients between CDI and winter wheat yield are calculated. This is intended to more accurately detect agricultural drought events.