On the reliability of a novel MODWT-based hybrid ARIMA-artificial intelligence approach to forecast daily Snow Depth (Case study: The western part of the Rocky Mountains in the U.S.A)

In this study, a novel algorithm is presented to combine different wavelet transform (WT) approaches comprising discrete wavelet transform (DWT), maximal overlap discrete wavelet transform (MODWT), and multiresolution-based MODWT (MODWT-MRA) along with autoregressive integrated moving average (ARIMA), and artificial intelligence (AI) models for one-day-ahead forecasting of the snow depth (SD) in the North Fork Jocko snow telemetry (SNOTEL) station located in the city of Missoula, Montana State of the United States. The performance of the proposed wavelet-based hybrid models was compared with the standalone AI models. Owing to considering both linear and nonlinear features, hybrid ARIMA-artificial intelligence (AI) models were found to provide more accurate results than the standalone ARIMA and AI models. Moreover, the capability of the wavelet technique to decompose an original signal into the separated sub-signals in different time scales enhanced the overall performance of the whole models. The results confirmed the priority of wavelet-based models over standalone ones. Among wavelet-based models, the MODWT-MRA coupled with ARIMA and Adaptive neuro-fuzzy inference system (ANFIS) abbreviated in this paper as MODWT-MRA-ARIMA-ANFIS with the correlation coefficient (R2) = 0.9998, root mean square error (RMSE) = 1.66 cm, mean absolute error (MAE) = 1.04 cm, Nash-Sutcliffe efficiency (NSE) = 0.9998 during the testing period. This confirmed that the novel wavelet-based model is a promising technique to provide beneficial information over snow-covered regions that merit future studies. •Forecasting of SD by hybrid of ARIMA model, three AI models and three DWTs•Illustrating of the best method for estimation of SD (MODWT-MRA-ARIMA-ANFIS model)•Using of TOPSIS method for ranking of different models•Illustration of superiority of ANFIS over ANN and GEP in hybrid with ARIMA and DWTs