Autoencoder-based composite drought indices

Depending on the type, drought events are described using different indices, such as meteorological, agricultural, and hydrological. The use of different indices often causes confusion for making water-related management decisions. One simple summarized index which can describe the different aspects of drought is desired. Several methods have therefore been proposed, especially with the linear combination method which does not adequately describe drought characteristics. Meanwhile, autoencoders, nonlinear transformation in dimensional reduction, have been applied in the deep learning literature. The objective of this study, therefore, was to derive autoencoder-based composite drought indices (ACDIs). First, a basic autoencoder was directly applied as ACDI, illustrating a negative relation with the observed drought indices which was further multiplied by a negative. Also, the hyperbolic tangent function was adopted instead of the sigmoid transfer function due to its higher sensitivity to drought conditions. For better expression of drought indices, positive and unity constraints were applied for weights, denoted as ACDI-C. Further simplification was made as sACDI by excluding the decoding module since it was not necessary. All applied weights of different sites over a country can be unified into one weight, and the same weights were made for all the sites, called as sACDI1. In the context of model evaluation, a comprehensive analysis was undertaken employing metrics as root mean squared error (RMSE), mean absolute error (MAE), and correlation coefficients. The collective findings underscore the superior performance of both the sACDI and sACDI1 models over their counterparts. Notably, these simplified models manifestly diminished RMSE and MAE values, indicating their enhanced predictive capabilities. Of particular note, sACDI1 exhibited a discernibly lower MAE in comparison to alternative models. Further alarm performance metrics was conducted including the false alarm ratio, probability of detection, and accuracy (ACC). The investigations revealed superiority of the simplified models in terms of alarm ACC, especially in the case of SRSI(A). The developed ACDI can comprehensively summarize multiple drought aspects and provide summarized information about drought conditions.