پیش‌بینی شاخص خشکسالی با استفاده از مدل همکارانه‌ی LSTM (مطالعه موردی: شمال استان اصفهان )

Introduction
Drought is a natural phenomenon that significantly impacts human life and ecosystems. Lack of rainfall can cause various problems, including damage to crops and a shortage of drinking water for local communities. These effects can lead to devastating economic and social disasters, such as famine, forced migration away from drought-affected areas, and conflicts over remaining resources. Predicting drought indices, such as the Standardized Precipitation Index (SPI), is crucial for assessing this phenomenon in water resource management. The SPI is a tool for evaluating and measuring the intensity and duration of drought, allowing for drought analysis on both short-term and long-term time scales, and providing accurate information on drought severity to water resource managers and policymakers.
 
However, predicting the SPI can be challenging due to the complex interactions of influencing factors. While deep learning models, especially Long Short-Term Memory (LSTM) networks, have shown promise in predicting SPI, they also have key limitations. First, the LSTM model has parameters that need fine-tuning. Second, selecting the best input combination for the LSTM model is complex and challenging. The inputs required for drought prediction are usually associated with various time lags. Choosing the best input combination from a large number of inputs is important and affects the performance of the LSTM model. The third challenge is that the LSTM model lacks connections that directly transfer information from the model's memory to its computation gates, which can lead to the loss of important information.
Materials and Methods
This study investigates the challenges and aims to improve the performance of the Long Short-Term Memory (LSTM) model in predicting the drought index (SPI) at 3, 6, and 9-month time scales (SPI-3, SPI-6, and SPI-9) in the northern part of Isfahan Province by presenting a novel "Collaborative LSTM" model and developing a binary genetic algorithm. Various large-scale climate indices were utilized as input data for the prediction models. To optimize model performance, a binary genetic algorithm was employed to select the optimal input scenario and fine-tune the model parameters.
In the first step, the input data, including time series, were divided into training and test datasets. Eighty percent of the input data were selected for training, and twenty percent were selected for testing to minimize prediction error. The algorithm then selected the best input parameters from large-scale climate signals with different delays. Each chromosome comprised two parts: the first part contained the model inputs, and the second part contained the initial parameter values. Binary chromosomes were encoded based on 0 and 1 values, indicating the absence or presence of a factor in the modeling process, respectively. Each binary value in the second part determined how the initial value of a particular parameter was chosen.
A new version of the LSTM model was then built with three additional weighted connections compared to the original LSTM model. The Collaborative LSTM incorporates three novel weight connections that facilitate the flow of crucial information from the memory cell to the input, forget, and output gates, enhancing information retention and improving prediction accuracy. The performance of the Collaborative LSTM was compared against traditional LSTM, Multilayer Perceptron (MLP), Radial Basis Function Neural Network (RBFNN), and Multiple Linear Regression (MLR) models. Multiple error metrics were used to assess model accuracy. The modeling process involved a multi-step approach:
Optimal input scenario selection using the binary genetic algorithm, Model parameter optimization using the genetic algorithm, and Development and evaluation of the Collaborative LSTM model for SPI prediction.
 
Results
The results demonstrated the effectiveness of the binary genetic algorithm in optimizing both input selection and model parameters. The Collaborative LSTM consistently outperformed other models, achieving a 2.1-6.1% improvement in Willmott Index (WI) for SPI-3, 1.1-5.1% for SPI-6, and 1.1-2.2% for SPI-9. Statistical analysis revealed that the predicted SPI values from the Collaborative LSTM closely resembled the observed SPI data. The superior performance of the Collaborative LSTM can be attributed to its enhanced information flow architecture, enabling more effective utilization of past information stored in the memory cell. Boxplots further visualized the improved accuracy of the Collaborative LSTM in predicting SPI values across different scenarios.
 
Conclusion
The findings of this study demonstrate the potential of the Collaborative LSTM model as a reliable tool for accurate drought index forecasting. By addressing the limitations of traditional LSTMs and incorporating optimized input selection and parameter tuning, this novel approach offers significant advancements in drought prediction capabilities.