## 1 Introduction
Combined drought indices (CDIs) are formed by merging several single drought indices to highlight the multidimensional characteristics and multifaceted effects of drought [31], and, therefore, may be of particular use for characterizing key drought impacts that single and multivariate models may miss. With the advancement of technology, there has been a significant increase in the number of parameters measured at Earth's surface. These measurements can be made by both ground-based stations and remote sensing systems. In contrast to ground-based measurements, remote sensing products (attempt to) provide continuous measurements in both time and space, despite varying spatial, temporal, and spectral resolutions. The data obtained from remote sensing systems, such as land surface temperature, precipitation, soil moisture, and vegetation reflectance characteristics, have introduced numerous drought indices into the literature. Some of the most commonly used indices include the Temperature Condition Index (TCI) [32], the Vegetation Condition Index (VCI) [32], the Normalized Difference Water Index (NDWI) [33], and the Soil Moisture Condition Index (SMCI) [34], all of which measure different physical phenomena. CDIs, derived from the combination of these and/or other indices, play a critical role in the detection of agricultural drought events [35]. One of the earliest examples of such combined indices is the Vegetation Health Index (VHI), which combines the TCI and VCI [36]. [PERSON] et al. [37] conducted a study in India using TCI, VCI, PCI, and SMCI values to calculate CDI values and found significant positive relationships between CDI values and crop yield. [PERSON] et al. [38] used TCI, PCI, Soil Water Index, and VCI inputs to calculate CDI for their drought analysis in Iran and reported that the resulting CDI values better represented the 2008 and 2014 droughts than SPI. In a study conducted in Niger, [PERSON] et al. [35] constructed a CDI index usingNormalized Rainfall Efficiency Index, PCI, TCI, and smoothed vegetation index values. They reported that the index had a high correlation with VHI and PDSI, thus providing important information for agricultural drought monitoring. [PERSON] et al. [30] proposed a new CDI index using PCI, TCI, and Evapotranspiration Condition Index values as inputs. They found that the new index had a higher correlation with SPI-1, a one-month SPI, than the individual indices. In addition, the proposed index showed a negative correlation with drought affected/disaster area and net primary productivity. In reviewing the literature on CDI studies, there are a limited number of studies using gross primary productivity (GPP) and NDWI despite opportunities for integrating carbon and other water-based metrics into drought indices. In [PERSON] et al. [39], GPP was not used as an input, but, rather, to validate the derived CDI. NDWI is sensitive to the water content of the vegetation canopy [40], and numerous studies have shown that NDWI is effective in monitoring agricultural drought [41; 42]; for example, [PERSON] et al. [43] found that NDWI was more responsive than NDVI to crop responses to drought. Similarly, in another study, [PERSON] et al. [44] found that NDWI was more sensitive to agricultural drought than NDVI in semiarid regions. The GPP, as a critical component of terrestrial ecosystem productivity and surface carbon cycling, represents photosynthesis at the ecosystem level [45]. Recent studies have highlighted the importance of the relationship between drought and GPP [46; 47; 48]. The study by [PERSON] et al. [49] found that changes in GPP should also be considered when examining the causes of regional meteorological and agricultural droughts. Most methods for creating a CDI derive a linear equation, with the optimal calculation of the equation's coefficients being one of the main challenges. To address this issue, [PERSON] [36] calculated the Vegetation Health Index by taking the arithmetic mean of TCI and VCI, giving equal importance to both inputs. In their study, [PERSON] et al.