Evaluation of Combined Models Wavelet-ARIMA-ANN and Wavelet-ARIMA-LSTM Using SRGI Index Simulation in Enhancing Drought Monitoring

Extended Abstract

Introduction

Drought monitoring entails the simulation of indices which are categorized into single and combined types. Historically, simulations have predominantly relied on single indices, including Standardized Precipitation Index (SPI), Standardized Runoff Index (SRI), resulting in limited research on drought simulation using combined indices (i.e. MSPI and SPTI), particularly in conjunction with combined models. Over the years, several single models have been developed for simulating individual drought indices. For instance, the Autoregressive Integrated Moving Average (ARIMA) model has been applied to simulate drought indices like Standardized Precipitation Index (SPI) and Standard Index of Annual Precipitation (SIAP). Additionally, models such as Artificial Neural Network (ANN) and Long Short Term Memory (LSTM) have been used for simulating indices like SPI, DI, SIAP, and SHDI. Recent studies suggest that combined models outperform single models. Wavelet ARIMA ANN (W-2A) and Wavelet ANFIS combined models to simulate the single drought index SPEI. Other researchers have developed combined models such as ARIMA-LSTM, Wavelet-ARIMA-LSTM, Wavelet-ARIMA-ANN and LSTM-CM to simulate single drought indices SPI, DI, SIAP. Despite the progress in developing drought simulation models, including single models and particularly combined models, their application has primarily focused on individual indices. Historically, simulations have predominantly relied on single indices, resulting in limited research on drought simulation using combined indices, particularly in conjunction with combined models. This study has combined the strengths of the Wavelet transformation, Autoregressive Integrated Moving Average (ARIMA), Artificial Neural Network (ANN) and Long Short Term Memory (LSTM) to test new methods of hybrid models for their ability to drought simulations based on the new combined index SRGI, employing the combined models W-AL and W-2A.



Materials and Methods

Drought simulated in the Alashtar sub-basin between 48, 15 east longitude and 33, 54 north latitudes, covering an area of 811 square kilometers from 1991 to 2020, utilizing individual indices such as SPI, SRI, SGI, and the combined index SRGI. The study area encompasses the Karkheh River basin. Both single models (ARIMA, LSTM, ANN) and combined models (W-AL and W-2A) were employed for this purpose. Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and Mean Error (ME) were used to evaluate the performance of the models. Also, relative frequency and error distribution charts were used to evaluate and compare the results of the models.

Individual indices were calculated based on fitting the best cumulative probability function to monthly precipitation, monthly discharge, and monthly water table data, respectively for indices SPI, SRI, and SGI, and then inversely transforming to a N (0,1). The SRGI index is a combination of two drought indices, SGI and SRI (Feng et al., 2020). For this purpose, the copula function is used to obtain the best joint probability distribution function governing precipitation and water table data. The selection of the best copula function was done through the Kolmogorov-Smirnov K-S test at a significant level of 5%. In the current research, four copula functions of Frank, Clayton, Gamble and Joe were used.

The process of building the combined models includes the analysis of the time series of the studied drought index, using DWT and decompose into two series named approximate and partial. Then, the approximate and detail series modeled by ARIMA and ANN respectively, in W-2A model and ARIMA and LSTM, respectively, in W-AL model.



Results and Discussion

The results demonstrate that the combined models W-AL and W-2A exhibit higher accuracy across all indices, both individual and combined, compared to single models ARIMA, LSTM, and ANN. The RMSE ranges for the combined models were 0.44 to 0.71, while for single models, they ranged from 0.47 to 1.54. Specifically, model W-

AL displayed superior accuracy across all individual indices, with RMSEs of 0.44, 0.62, and 0.59, in contrast to model W-2A, which yielded RMSEs of 0.49, 0.71, and 0.63. However, W-AL's performance lagged behind W-2A for the combined SRGI index, with respective RMSEs of 0.64 and 0.61. Thus, the simpler model yielded more acceptable results in simulating the composite index.



Conclusion

Among all the combined and individual models, the combined models perform better in simulating drought, based on all indices, compared to the individual models. Therefore, it can be said that combined models are more suitable for simulating and monitoring drought compared to individual models. However, the performance of the two combined models, W-2A and W-AL, in simulating the combined SRGI index is different. The performance of the simpler W-2A model is better than the more complex W-AL model, with RMSE values of 0.61 and 0.64, respectively. Therefore, in combined indices, despite the complexity of their computational process, there is not necessarily a need to use a more complex combined model. Overall, the use of combined models is recommended for monitoring various types of indices, especially drought based on combined indices such as SRGI. The major objectives of this study are: (1) to use hybrid models Wavelet-ARIMA-LSTM (W-AL) and Wavelet-ARIMA-ANN (W-2A) methods to predict monthly drought. (2) To analyze drought characteristics in Alashtar basin based on the new combined drought index, SRGI. It is expected that the research results will help to provide decision support which in turn will help in planning adaptative measures to reduce drought impacts and provide decision support for disaster prevention.