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. 2022 Apr 23;22(9):3241.
doi: 10.3390/s22093241.

A Hybrid Water Balance Machine Learning Model to Estimate Inter-Annual Rainfall-Runoff

Amir Aieb  1 , Antonio Liotta  2 , Ismahen Kadri  3 , Khodir Madani  1   4
Affiliations

A Hybrid Water Balance Machine Learning Model to Estimate Inter-Annual Rainfall-Runoff

Amir Aieb et al. Sensors (Basel). .

Abstract

Watershed climatic diversity poses a hard problem when it comes to finding suitable models to estimate inter-annual rainfall runoff (IARR). In this work, a hybrid model (dubbed MR-CART) is proposed, based on a combination of MR (multiple regression) and CART (classification and regression tree) machine-learning methods, applied to an IARR predicted data series obtained from a set of non-parametric and empirical water balance models in five climatic floors of northern Algeria between 1960 and 2020. A comparative analysis showed that the Yang, Sharif, and Zhang's models were reliable for estimating input data of the hybrid model in all climatic classes. In addition, Schreiber's model was more efficient in very humid, humid, and semi-humid areas. A set of performance and distribution statistical tests were applied to the estimated IARR data series to show the reliability and dynamicity of each model in all study areas. The results showed that our hybrid model provided the best performance and data distribution, where the R2Adj and p-values obtained in each case were between (0.793, 0.989), and (0.773, 0.939), respectively. The MR model showed good data distribution compared to the CART method, where p-values obtained by signtest and WSR test were (0.773, 0.705), and (0.326, 0.335), respectively.

Keywords: climate floor; decision tree; machine learning; modeling; multiple regression; rainfall runoff; water balance models; watershed.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
Map of northern Algeria area showing weather stations in different climate floors.
Figure 2
Figure 2
Boxplots of real and predicted IARR data series obtained by Zhang’s model in five climatic regions in northern Algeria for ‘w’ between 0.5 and 2.5.
Figure 3
Figure 3
Boxplots of real and predicted IARR data series obtained by Yang’s model in five climatic regions in northern Algeria for ‘n’ between 0.5 and 3.5.
Figure 4
Figure 4
Box-plots of real and predicted IARR data series obtained by a set of non-parametric and empirical water balance models in five climatic regions of northern Algeria.
Figure 5
Figure 5
Graphs of (a) standardized coefficients, (b) regression, and (c) standardized residuals obtained by MR machine learning for IARR estimation in five climatic areas in northern Algeria. Predicted data (Pred), very humid (VH), humid (H). semi-humid (SH), Mediterranean (ME), semi-dry (SD).
Figure 6
Figure 6
Graphs of non-linear regression between the A-Index data series and predicted IARR, which were obtained by the set of water balance models used in the northern Algeria region. Adjusted coefficient of determination (R2Adj).
Figure 7
Figure 7
Graphs of (a) standardized coefficients, (b) regression, and (c) standardized residuals obtained by MR-CART’s hybrid model to estimate IARR in five climatic areas in northern. Predicted data (Pred), very humid (VH), humid (H), semi-humid (SH), Mediterranean (ME), semi-dry (SD).
Figure 8
Figure 8
Flowchart summarizing steps design of MR-CART proposed model of IARR. Very humid (VH), humid (H), semi-humid (SH), Mediterranean (ME), semi-dry (SD), inter-annual rainfall (IAR), inter-annual potential evapotranspiration (IAEo), inter-annual actual evapotranspiration (IAEa).
Figure 9
Figure 9
Graphs of (a) scattergrams and (b) radars showing data distribution and performance of proposed models in Algeria’s northern area. Coefficient of determination (R2), adjusted coefficient of determination (R2Adj), mean absolute error (MAE), root mean square error (RMSE).
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