Signature kernel ridge regression time series model: A novel approach for hydrological drought modeling using multi-station meteorological drought information

Abstract

In the context of growing environmental challenges and the need for sustainable water resource management, hydrological drought prediction has gained prominence as a critical issue. Existing artificial intelligence and time series-based models for hydrological drought indices have traditionally been established using streamflow data. This study gives a significant progress in hydrological drought modeling through the introduction of the Signature Kernel Ridge Regression (SKRR) time series model. Instead of directly using rainfall and runoff data to develop a rainfall-runoff (RR) model, the Standardized Precipitation Evapotranspiration Index (SPEI) values in neighbor meteorological stations serve as inputs for estimating the Streamflow Drought Index (SDI) in target hydrometric stations, considering the 3-, 6-, and 12-month moving average time windows. The objective of this study is to enhance hydrological drought modeling by integrating soft computing techniques that effectively handle multivariate and irregular time series. The efficacy of the SKRR is compared with the well-established Generalized Regression Neural Network (GRNN), Random Forest (RF), and Auto Regressive Integrated Moving Average model with eXogenous input (ARIMAX). The findings indicate that SKRR is capable of precisely estimating SDI in three hydrometric stations using meteorological drought information from 14 stations, outperforming the GRNN, RF and ARIMAX models. The enhanced performance of the SKRR time series model stems from the utilization of a new and effective signature kernel which can be utilized for the study of irregularly sampled, multivariate time series in addition to be applicable to time series of different temporal spans while being a positive-definite kernel, facilitating usage in the Hilbert space. The novel drought based-RR model established by SKRR utilized various external stations' meteorological drought indices to compute the hydrological drought indices in target stations not only enhances the modeling capability but also progress our understanding of drought dynamics by showcasing the power of soft computing in handling environmental