# Contextual Background Estimation for Explainable AI in Temperature Prediction
## 3 Results
### Evaluation of Background Estimation Method  
The predictions for 15 July 2021 at 01:00:00 (IMGW) and 15 July 2014 at 01:00:00 (Jena) were explained using the Background Estimation Method. In this case, only one example \(y_{b}\) was chosen, set to 0 \({}^{\circ}\)C for both IMGW and Jena. The margin \(m\) was set to 0.1 \({}^{\circ}\)C. The XAI method was applied using Algorithm 1. During the calculation, the matrix **E** was generated, containing percentage explanations for each feature and background. Each Shapley value was then transformed into the percentage of the explanation for the difference between the prediction and the background target. The mean values and standard deviations for each feature and dataset are presented in Tables 2-4. A detailed analysis of the percentage of explanation distributions for four stations is presented in Figures 8 and 9. The utility index calculated via mean and standard deviation is presented in Figure 10.  
A detailed analysis of the percentage of explanation distributions for four stations is presented. Not all the features are included in Figures 8 and 9; only the features with a mean percentage of explanation equal to or greater than 2% are shown. Several significant observations can be made. The station in Figure 8 on the right is an example of a relatively stable explanation across the given set of backgrounds, resulting in the prediction \(y_{b}\). The Shapley values for each feature do not fluctuate significantly across the different backgrounds in the entire dataset. This is reflected in the thick and high histograms. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Feature Name** & **Mean [\%]** & **Std [\%]** \\ \hline
**p** & 0.40 & 0.52 \\
**T** & 5.60 & 0.06 \\
**Tpot** & 40.24 & 0.40 \\
**Tdew** & 3.04 & 0.07 \\
**rh** & 5.00 & 0.06 \\
**VPmax** & 3.43 & 0.05 \\
**VPact** & 1.67 & 0.06 \\
**VPdef** & 0.00 & 0.00 \\
**sh** & 4.94 & 0.11 \\
**H2 OC** & 7.83 & 0.07 \\
**rho** & 10.44 & 0.19 \\
**wv** & 0.00 & 0.00 \\
**max. wv** & 1.23 & 0.33 \\
**wd** & 0.69 & 0.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Distribution of explanation description of Jena dataset. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Feature Name**} & \multicolumn{6}{c}{**Dataset Name**} \\ \cline{2-10}  & **IMGW 351180455** & **IMGW 352200375** & **IMGW 353170235** & **IMGW 349190650** & **IMGW 351190469** \\ \cline{2-10}  & **Mean** & **Std [\%]** & **Mean** & **Std [\%]** & **Mean** & **Std [\%]** & **Mean** & **Std [\%]** & **Mean** \\  & [\%] & & [\%] & & [\%] & & [\%] & & [\%] & [\%] & [\%] \\ \hline Air temperature & 31.81 & 0.63 & 26.27 & 0.50 & 25.98 & 0.76 & 36.61 & 0.84 & 41.46 & 0.71 \\ Wind direction & 0.61 & 0.13 & 0.26 & 0.27 & 1.14 & 0.10 & 0.26 & 0.31 & 3.15 & 0.56 \\ Wind speed & 0.73 & 0.38 & 0.37 & 0.39 & 1.50 & 0.31 & 6.57 & 0.78 & 1.46 & 0.58 \\ Wind gust & 0.14 & 0.32 & 0.15 & 0.16 & 0.14 & 0.07 & 0.58 & 0.40 & 0.12 & 0.14 \\ Steam pressure & 45.29 & 0.71 & 32.20 & 1.39 & 36.52 & 0.90 & 57.06 & 3.77 & 25.17 & 0.74 \\ Relative humidity & 28.66 & 0.53 & 17.36 & 1.12 & 22.75 & 0.23 & 27.67 & 0.57 & 8.62 & 1.29 \\ Pressure at station level & 13.44 & 1.35 & 34.82 & 2.33 & 26.55 & 1.11 & 75.39 & 2.51 & 20.44 & 2.99 \\ Precipitation over 6 h & 0.27 & 0.09 & 0.24 & 0.20 & 0.75 & 0.13 & 0.09 & 0.09 & 0.30 & 0.21 \\ Sunshine duration & 0.47 & 0.50 & 0.39 & 0.50 & 2.08 & 0.80 & 1.95 & 1.06 & 4.03 & 1.27 \\ Max wind gust over 12 h & 0.39 & 0.12 & 0.77 & 0.38 & 0.15 & 0.06 & 4.04 & 0.54 & 0.25 & 0.12 \\ Min temperature over 12 h & 0.02 & 0.03 & 0.16 & 0.19 & 0.25 & 0.09 & 0.21 & 0.18 & 0.50 & 0.28 \\ Max temperature over 12 h & 0.24 & 0.07 & 0.22 & 0.08 & 0.58 & 0.14 & 1.01 In the same figure, on the left side, there are also histograms that are thick and high; however, some of them appear within the same feature. In other words, the presented percentages consist of two or more separate distributions.