Deterministic Analysis and Uncertainty Analysis of Ensemble Forecasting Model Based on Variational Mode Decomposition for Estimation of Monthly Groundwater Level

Abstract

Precise multi-time scales prediction of groundwater level is essential for water resources planning and management. However, credible and reliable predicting results are hard to achieve even to extensively applied artificial intelligence (AI) models considering the uncontrollable error, indefinite inputs and unneglectable uncertainty during the modelling process. The AI model ensembled with the data pretreatment technique, the input selection method, or uncertainty analysis has been successfully used to tackle this issue, whereas studies about the comprehensive deterministic and uncertainty analysis of hybrid models in groundwater level forecast are rarely reported. In this study, a novel hybrid predictive model combining the variational mode decomposition (VMD) data pretreatment technique, Boruta input selection method, bootstrap based uncertainty analysis, and the extreme learning machine (ELM) model named VBELM was developed for 1-, 2- and 3-month ahead groundwater level prediction in a typical arid oasis area of northwestern China. The historical observed monthly groundwater level, precipitation and temperature data were used as inputs to train and test the model. Specifically, the VMD was used to decompose all the input-outputs into a set of intrinsic mode functions (IMFs), the Boruta method was applied to determine input variables, and the ELM was employed to forecast the value of each IMF. In order to ascertain the efficiency of the proposed VBELM model, the performance of the coupled model (VELM) hybridizing VMD with ELM algorithm and the single ELM model were estimated in comparison. The results indicate that the VBELM performed best, while the single ELM model performed the worst among the three models. Furthermore, the VBELM model presented lower uncertainty than the VELM model with more observed groundwater level values falling inside the confidence interval. In summary, the VBELM model demonstrated an excellent performance for both certainty and uncertainty analyses, and can serve as an effective tool for multi-scale groundwater level forecasting.

Assessment of Groundwater Quality and Pollution in the Songnen Plain of Jilin Province, Northeast China

“…Groundwater recharge mainly depends on meteoric precipitation and surface water. In the past few decades, agricultural, domestic, and industrial effluent discharges have also become a source of groundwater recharge [41][42][43][44].…”

Hydrological peaks evaluation at Chitral and Tarbela stations, Pakistan, using combined Bayesian regularized neural network and signal difference average based variational mode decomposition method: A case study

“…VMD decomposes the original signal, f(t) (streamflow in our case), into k IMFs components, defined as: U k (t) ¼ B k (t) cos (w ϕk (t)), where B k (t) and w k (t) are the instantaneous amplitude and phase, respectively (Wu et al 2021). VMD was first introduced by Dragomiretskiy & Zosso (2013) based on the Wiener filtering, Hilbert transform, and frequency shifting theories (Wu et al 2021) as follows: Firstly, VMD computes the analytical signal of U k (t) to obtain the one-sided frequency spectrum by employing Hilbert transform. Secondly, the spectrum of each U k (t) is shifted to the baseband by mixing with an exponential tuned to the respective estimated central frequency.…”

“…Data pre-processing techniques have been coupled with different ML methods for accuracy enhancement of the models (Zuo et al 2020;Wu et al 2021). Wavelet transforms, empirical and ensemble empirical mode decomposition techniques are commonly used for decomposition of actual time series data into sub-series (Wu et al 2021).…”

“…Data pre-processing techniques have been coupled with different ML methods for accuracy enhancement of the models (Zuo et al 2020;Wu et al 2021). Wavelet transforms, empirical and ensemble empirical mode decomposition techniques are commonly used for decomposition of actual time series data into sub-series (Wu et al 2021). Among recently available data decomposition techniques, variational mode decomposition (VMD) proposed by Dragomiretskiy & Zosso (2013) with solid mathematical foundation has been utilized successfully to enhance the robustness of the models in various fields including hydrology (Isham et al 2018;Wang et al 2021).…”

“…Furthermore, different approaches have been reported for selection of k in literature such as: the traditional empirical mode decomposition (EMD) method (Wu et al 2021) or by observing the existence of central-frequency distortion of the previous IMF component (Zuo et al 2020). Whereas, determination of k, based on the similarity concept between actual and ensemble decomposed IMFs is applied in this paper known as SDA.…”