S-Transformer: a new deep learning model enhanced by sequential transformer encoders for drought forecasting

Abstract Droughts are prolonged periods of rainfall deficit, the frequency of which has increased due to global warming, causing severe impacts on water resources, agriculture, ecosystems, and food security. Given their significance, accurate monitoring and forecasting of droughts are crucial for effective water resource management. This paper introduces sequential-based transformers (S-Transformer), a novel deep-learning approach, aimed to apply for meteorological droughts prediction using their historical events. The core of the S-transformer algorithm is the orderly computing of an output by utilizing the sequence of inputs. Training of the S-transformer involves forward and backward passes through the network to adjust the weights and biases, using gradient descent optimization. This process uses fixed-size dynamic windows to minimize the difference between the observed and forecasted outputs. To demonstrate the effectiveness and performance of the new model, two case studies were presented based on the observed standardized precipitation index in Isparta and Burdur cities, Türkiye. In addition, the S-Transformer efficiency was compared with those of three benchmark models including a classic multilayer perceptron, a deep learning long-short-term memory, and a deep classic transformer model. The promising results of the proposed model proved its superiority over its counterparts in terms of different performance metrics. In Isparta and Burdur cities, the S-Transformer achieved the root mean squared values of 0.096 and 0.098 on the testing set, respectively.