Advanced Approaches for Imputing Missing Rainfall Data in Time Series: Dynamic Adaptive Wavelet-Based Compressed Sensing

Abstract Discrete wavelet (DW) analysis is commonly employed to decompose raw observed data into stochastic and deterministic components, aiming to improve model accuracy. Nonetheless, the DW technique is recognized for its significant limitations, often leading to inaccurate predictions of daily rainfall. In this study, a dynamic adaptive wavelet algorithm is introduced to decompose the raw observed data into components, aiming to address the drawbacks associated with DW analysis. The ultimate goal is to enable the estimation of daily rainfall with enhanced accuracy and precision in missing value imputation. The decomposed stochastic and deterministic components derived from the maximum overlap discrete wavelet (MODW) and DW techniques are incorporated as inputs in compressed sensing (CS) framework. This procedure facilitates the creation of novel methodologies MODW-based compressed sensing (MODW-CS) and DW-based compressed sensing (DW-CS) for daily rainfall prediction. These methodologies are deployed across scenarios utilizing 50%, 70%, and 90% of the available data. Twenty-two years of validated daily rainfall data were collected from five stations situated within the Euphrates-Tigris Basin. The novel methodologies were assessed against the CS model, with root-mean squared error (RMSE), mean absolute error (MAE), and coefficient of efficiency (CE) being taken into account. Findings revealed that both the MODW-CS and DW-CS models outperformed the CS model, with enhanced prediction accuracy observed through the utilization of decomposed signals. However, the MODW-CS model exhibited superior performance compared with the DW-CS model for all scenarios. This suggests that the MODW algorithm possesses a dynamic adaptive structure enabling it to capture the natural structure of observed data more effectively than DW analysis. The findings of this study have significant implications across various domains, including hydrology, agriculture, flood control, drought management, and weather forecasting. Accurate predictions of missing data points in time series are essential for better understanding and forecasting rainfall event behavior.