The Taylor charts check the performance of estimated and actual values based on the standard deviation and Pearson Correlation Coefficient (Qin & Xiao 2018), which are contained simultaneously in assessing the respective models (Taylor 2001; Ghorbani et al. 2018). The standard deviation and CC between the actual and predicted datasets for the models are present in the Taylor diagram, and it also can be seen overall consistency between observed and estimated values when the CC value is approaching up to 1, as pointed in Figure 6. This can be considered for the MARS model with CCtraining phase = 0.94, CCtesting phase = 0.93, FFNN-BP model with CCtraining phase = 0.91, CCtesting phase = 0.92, and DTR model with CCtraining phase = 0.93, CCtesting phase = 0.91. The large number of correlation coefficients indicate that there is a strong relationship. The Taylor plot also shows that these models are optimal with the highest accuracy (Taylor 2001). In other words, if the standard deviation of the predicted value of the higher standard deviation of the observed value, it will lead to an over estimation and vice versa (Abba et al. 2020). Furthermore, the GCV indicator of MARS brings about equilibrium between flexibility and generalization ability of the function of MARS model (Deo et al. 2016).
Table 2

Accuracy parameters for physico-chemical components prediction

ParameterDTR
FFNN-BP
MARS
TestingTrainingTestingTrainingTestingTraining
MAE (mg/l) 0.25 0.25 0.50 0.46 0.21 0.14
RMSE (mg/l) 0.34 0.33 0.99 0.90 0.41 0.24
Bias (mg/l) −0.09 −0.19 −0.12 0.01 −0.04 0.00
SI (mg/l) 3.23 3.10 1.53 1.19 0.21 0.26
0.91 0.93 0.92 0.91 0.93 0.94
NSE 0.89 0.94 0.91 0.90 0.95 0.95
GCV (mg/l)     0.14 0.14
ParameterDTR
FFNN-BP
MARS
TestingTrainingTestingTrainingTestingTraining
MAE (mg/l) 0.25 0.25 0.50 0.46 0.21 0.14
RMSE (mg/l) 0.34 0.33 0.99 0.90 0.41 0.24
Bias (mg/l) −0.09 −0.19 −0.12 0.01 −0.04 0.00
SI (mg/l) 3.23 3.10 1.53 1.19 0.21 0.26
0.91 0.93 0.92 0.91 0.93 0.94
NSE 0.89 0.94 0.91 0.90 0.95 0.95
GCV (mg/l)     0.14 0.14
Figure 4

Physico-chemical properties prediction with (a) MARS model, (b) FFNN-BP model, and (c) DTR model (Unit: mg/l).

Figure 4

Physico-chemical properties prediction with (a) MARS model, (b) FFNN-BP model, and (c) DTR model (Unit: mg/l).

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Figure 5

The best performance indicators for CaCO3 prediction (a) MARS training model, (b) FFNN-BP training model, (c) DRT training model.

Figure 5

The best performance indicators for CaCO3 prediction (a) MARS training model, (b) FFNN-BP training model, (c) DRT training model.

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Figure 6

The best performance indicators for CaCO3 prediction for Training, and Testing.

Figure 6

The best performance indicators for CaCO3 prediction for Training, and Testing.

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