**4. Results and discussions**

#### **4.1 Performance evaluation of MARS model in predicting relative humidity**

The performance evaluation statistics of the MARS model for the prediction of relative humidity at Khunjerab, Naltar, and Ziarat are presented in **Tables 3**–**5**, respectively. The MARS model performed excellent for the prediction of relative humidity at all meteorological stations both during training and testing processes especially, it provided the best predictions for the 6th scenario (S6) of input data combination which is highlighted in bold. The RMSE, MAE, and R<sup>2</sup> values during the training (5.58%, 4.51%, 0.852) and testing (5.98%, 5.43%, 0.808) stages for Khunjerab meteorological station are displayed in **Table 3**. The MARS model performed better during training as compared to testing at Khunjerab. However, the MARS model did not perform well for the S1, S2, and S3 scenarios. Our study results were found better than the study conducted by [1]. They described that GEP and ANNs models can predict relative humidity reliably at two Californian stations (RMSE= 10.7%, MAE= 7.6% and R<sup>2</sup> = 0.73) during training; and (RMSE= 10.1%, MAE= 7.5% and R<sup>2</sup> = 0.714) during testing stage in the case of GEP model. However, ANN model produced better results as compared to GEP such as (RMSE= 7.8%, MAE= 3.6% and R<sup>2</sup> = 0.826) during training, and (RMSE= 8.2%, MAE= 4.1% and R2 = 0.751) during testing stage.


*Prediction of Relative Humidity in a High Elevated Basin of Western Karakoram by Using… DOI: http://dx.doi.org/10.5772/intechopen.98226*

#### **Table 3.**

*The statistical evaluation of the MARS model at Khunjerab.*


#### **Table 4.**

*The statistical evaluation of the MARS model at Naltar.*

Similarly, the MARS model provided the best prediction of relative humidity for the S6 input data scenario at Naltar both during training and testing stages as shown in **Table 4**. The RMSE, MAE and R2 values for the best input parameter combination were 5.63%, 4.53%, and 0.826 respectively, during training whereas 6.58%, 5.08%, and 0.806, were during testing (**Table 4**). The MARS model did not perform well for S1, S2, and S3 input combinations. However, a study conducted by [5] observed that the XGBoost model provided the best prediction of relative humidity (MAE= 2.29%) as compared to SARIMA (MAE= 2.97%) and HW additive (MAE= 2.74%).


#### **Table 5.**

*The statistical evaluation of the MARS model at Ziarat.*

However, the MARS model performed the best (RMSE= 5.86, MAE= 4.97%, R2 = 0.815) for prediction of relative humidity at Ziarat for the S6 input combination during the testing stage as shown in **Table 5**. The MARS model also performed fairly well during training stage (RMSE= 5.26%, MAE= 4.59%, R<sup>2</sup> = 0.833) for S6 input combination. The MARS model provided a poor prediction of relative humidity for S1, S2, and S3 input scenarios (**Table 5**). Overall, the MARS model performed fairly well at Khunjerab (R2 = 0.852) and showed slightly low performance at Naltar (R2 =0.826) for the S6 input combination during the training stage (**Tables 3**–**5**).

The MARS model performance was also evaluated by drawing scatter plots. The scatter plots had been drawn between observed and predicted relative humidity from 2007 to 2009 on daily data as displayed in **Figure 3**. Scatter plots also displayed that the MARS model outperformed for prediction of relative humidity at

#### **Figure 3.**

*Scatter plots between observed and predicted relative humidity by using MARS model at (a) Khunjerab; (b) Naltar and (c) Ziarat.*

all meteorological stations, especially, at Ziarat with R2 = 0.815 for the S6 input combination during the testing stage (**Figure 3**).
