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.

在这项研究中，提出了一种新的算法来结合不同的小波变换 (WT) 方法，包括离散小波变换 (DWT)、最大重叠离散小波变换 (MODWT) 和基于多分辨率的 MODWT (MODWT-MRA) 以及自回归集成移动位于美国蒙大拿州米苏拉市的 North Fork Jocko 雪地遥测 (SNOTEL) 站雪深 (SD) 一天前预报的平均值 (ARIMA) 和人工智能 (AI) 模型. 将所提出的基于小波的混合模型的性能与独立的 AI 模型进行了比较。由于同时考虑了线性和非线性特征，发现混合 ARIMA-人工智能 (AI) 模型比独立的 ARIMA 和 AI 模型提供更准确的结果。而且，小波技术将原始信号分解为不同时间尺度的分离子信号的能力增强了整个模型的整体性能。结果证实了基于小波的模型优于独立模型。在基于小波的模型中，MODWT-MRA 耦合 ARIMA 和自适应神经模糊推理系统（ANFIS）在本文中缩写为 MODWT-MRA-ARIMA-ANFIS，相关系数为（R ² ) = 0.9998，均方根误差 ( RMSE ) = 1.66 cm，平均绝对误差 (MAE) = 1.04 cm，测试期间Nash-Sutcliffe 效率 ( NSE ) = 0.9998。这证实了新的基于小波的模型是一种很有前途的技术，可以在积雪覆盖的地区提供有益的信息，值得未来研究。