The development of dissolved oxygen forecast model using hybrid machine learning algorithm with hydro-meteorological variables

Abstract

Dissolved oxygen (DO) forecasting is essential for aquatic managers responsible for maintaining ecosystem health and the management of water bodies affected by water quality parameters. This paper aims to forecast dissolved oxygen (DO) concentration using a multivariate adaptive regression spline (MARS) hybrid model coupled with maximum overlap discrete wavelet transformation (MODWT) as a feature decomposition approach for Surma River water using a set of water quality hydro-meteorological variables. The proposed hybrid model is compared with numerous machine learning methods, namely Bayesian ridge regression (BNR), k-nearest neighbourhood (KNN), kernel ridge regression (KRR), random forest (RF), and support vector regression (SVR). The investigational results show that the proposed model of MODWT-MARS has a better prediction than the comparing benchmark models and individual standalone counter parts. The result shows that the hybrid algorithms (i.e. MODWT-MARS) outperformed the other models (r = 0.981, WI = 0.990, RMAE = 2.47%, and MAE = 0.089). This hybrid method may serve to forecast water quality variables with fewer predictor variables.

Keywords: Bangladesh; Dissolved oxygen; Forecasting; Hybrid model; MARS; MODWT; Surma River.

Fig. 1

The study region showing the Keane Bridge station of Surma River, Sylhet, Bangladesh

Fig. 2

The study's workflow details the steps in the model designing phase and the proposed hybrid CEEMDAN-MARS predictive models. Note: IMF = Intrinsic Mode Function, CCF = Cross-Correlation Functions, PACF = partial autocorrelation function, CEEMDAN = complete ensemble empirical mode decomposition with adaptive noise and DO = Dissolved Oxygen (mg/l)

Fig. 3

Time series of the a maximum overlap discrete wavelet coefficient (MODWC) of Dissolved Oxygen using MODWT, and intrinsic mode functions (IMFs) and the residual components after decomposing the DO in the training period using b CEEMDAN and c EEMD. The time series of the actual DO is plotted at the top of the figure

Fig. 4

Partial autocorrelation function (PACF) plot of the DO time series exploring the antecedent behaviour in terms of the lag of daily DO. The blue line in the figures indicates the ± 95% confidence level

Fig. 5

An analysis of the statistically significant cross-correlation function plots of a actual variables vs DO, b IMF1 of all variables vs IMF1 of DO, c IMF2 of all variables vs IMF2 of DO, d IMF3 of all variables vs IMF3 of DO, e IMF4 of all variables vs IMF4 of DO, f) residuals of all variables vs residuals of DO

Fig. 5

An analysis of the statistically significant cross-correlation function plots of a actual variables vs DO, b IMF1 of all variables vs IMF1 of DO, c IMF2 of all variables vs IMF2 of DO, d IMF3 of all variables vs IMF3 of DO, e IMF4 of all variables vs IMF4 of DO, f) residuals of all variables vs residuals of DO

Fig. 6

Box plots of hybrid models (MODWT-MARS) and their respective standalone counterparts (i.e. MARS, BNR, KRR, KNN, RNN, and SVR) in forecasting DO compare to the observed DO of Surma River

Fig. 7

Empirical cumulative distribution function (CDF) of forecasted error |FE| of DO generated by the proposed MODWT-MARS and comparing models

Fig. 8

Comparison of the forecasting skill of proposed models in terms of RRMSE (%) and MAPE (%) in the testing period

Fig. 9

Tylor diagram representing correlation coefficient and the standard deviation difference for proposed hybrid models vs benchmark models

Fig. 10

Scatter plot of forecasted vs observed DO, using a Bayesian ridge regression (BNR) and b multiple adaptive regression splines model using MODWT and CEEMDAN decomposition. A least square regression line and coefficient of determination (R²) with a linear fit equation are shown in each sub-panel

Fig. 11

Comparison between forecasted DO and observed DO during model testing using MODWT-MARS and Standalone MARS model

Fig. 12

Effect of a EMD, b EEMD, c CEEMDAN, d MODWT, and e DWT of the performance of six models based on r, LM, and APB