Regional drought forecasting in data-scarce regions through a novel cluster-based liquid neural network

The Global Drought Monitor (GDM) provides real-time information about drought to enhance drought forecasting; however, applying complex machine learning algorithms across large spatial domains is computationally challenging. This study presents a novel approach for one-month-ahead regional drought forecasting using GDM data. The new approach first uses k-means to cluster GDM grid points into homogeneous regions based on their geographic coordinates (latitude, longitude, and elevation) and temporal variation of the Standardized Precipitation-Evapotranspiration Index (SPEI) series. Then, a cluster representative SPEI series (SPEI_cr) is generated for each cluster, and is targeted for modeling and forecasting using the state-of-the-art liquid neural network (LNN) technique. To achieve the best forecasting accuracy, the univariate and multivariate LNN models are configured by the most effective lags of SPEI_cr and exogenous inputs chosen among the GDM-SPEI series that show the minimum Euclidean distance to each cluster centroid in both the geographic and feature spaces. Based on the superior performance of the multivariate LNN, the SPEI_cr forecasts are ultimately extended across all GDM points in the corresponding homogenous region to map future regional drought patterns. The new approach was demonstrated through a case study conducted for the Lake Urmia Basin (LUB), which suffers from both frequent prolonged meteorological droughts and scarce long-term ground truth data. The results showed that a rigorous spatially adaptive drought forecasting map can be delineated across LUB via the proposed model. Notably, the LUB was clustered into five drought-hemogenic clusters where multivariate LNN models showed, on average, more than 100% and 40% performance improvement in terms of Nash-Sutcliffe efficiency over the univariate LNN and Seasonal Auto Regressive Integrated Moving Average benchmarks, respectively. This corresponded to an average root mean squared error of 0.25 for the multivariate models, whereas the benchmark errors remained higher, at approximately 0.54 and 0.72, respectively.