## 6 Error Analysis and Model Reliability
### Unreliable Predictions from Out-of-Bound Feature Values  
As already discussed in Section 3, XGBost models do not have the ability to extrapolate, which means if a feature value is not within the range of the training set, the effect of the feature may not be accurately accounted for by XGBost. Data scaling is applied during pre-processing to counter this problem, as previously described in Section 5. The method has proved highly effective, but does not fully eliminate the presence of out-of-bound feature values in the validation set. Especially when a high-importance feature has an out-of-bound value, the model prediction is more likely to be less accurate than average.  
This error source can be best visualized by plotting feature value with respect to its SHAP value. Consistent with the convention in Figure 8, Figure 10a plots the scaled feature values vs. the corresponding SHAP values of the most important feature, \(T_{\text{dSW}}\), in a dew point prediction model. The model is trained on data from 18 January 2023 to 23 March 2023 and validated on the 24 March 2023 to 31 March 2023 period for site Archerfield Airport. All points are coloured by pointwise absolute error. Similar to the exemplar model explained in Section 5, the SHAP value of \(T_{\text{dSW}}\) is approximately linearly correlated to its feature value. In the validation set, the samples whose feature values are within the range of the training set (around \(-2.0\)\({}^{\circ}\)C to \(2.5\)\({}^{\circ}\)C) largely overlap with the samples in the training set. However, for validation samples with out-of-bound feature values (highlighted by red square region), the SHAP values no longer increase with the feature values, which means the effect of these feature values is likely to be underestimated by the model. Correspondingly, these points are coloured dark green, indicating much higher error than the rest of the samples. Thisresults in the high-error predictions in the time series plotted in Figure 10b, in which the high error points within the red square in Figure 10a are highlighted in red. The figure shows that a sudden drop in dew point occurred on 30 March 2023 (due to a sudden change in the weather pattern) to very low values that were not experienced in the entire training period. As a result, the trained model significantly overestimates the dew point temperature (as did IMPROVER).  
Based on the analysis above, we include in MSB an automatic detection of potentially unreliable predictions by examining if the value of the most important feature of any validation point is outside the range of the training set. Figure 11 plots the RMSE and critical error rate of recognized unreliable points as compared to the metrics on all data points for each site. Only predictions with lead day 0 are considered. The results show that for almost all sites, the unreliable subset has a higher error than global. For some sites, the RMSE of the unreliable subset can be twice as high as average (site Curtin, dew point temperature).  
Figure 11: Statistics of RMSE and critical error rate of all predictions and unreliable predictions due to out-of-bound feature values. (**a**) Temperature; (**b**) dew point temperature. Lead day: 0.  
Figure 10: Example of inaccurate outputs from XGBoost due to out-of-bound feature values, (**a**) feature values vs. corresponding SHAP values for data samples in training set and validation set, coloured by absolute error of the prediction. Circles: training set; squares: validation set; (**b**) time series of XGBoost predictions in the validation period and site observations. Inaccurate predictions due to out-of-bound feature values are highlighted in red.  
It should be noted that the appearance of this type of error is very rare. Statistically, only 0.5% of all forecasts are affected by this error. However, this error analysis does highlight the importance of data scaling, without which more out-of-range feature values would appear in the validation set.