## 3 Results
### Evaluation Criterion and Temporal Sampling  
Next we compare a selection of the presented methods in more detail. The selection was mainly based on the performance of the methods summarized in Figures 3 and 4, where GradBoost, LinReg (day-time) and SVM were among the best performing methods. With RandFor and Ridge (day-time) we also obtained very good results for the predicted 10-months average emission value, but results were almost identical to GradBoost and LinReg (day-time), while the latter were faster. Thus, we selected only GradBoost and LinReg (day-time) for the detailed investigation. As a forth method we considered ANN in the detailed investigation since this method is a frequently used modern machine learning technique in the context of emission modeling in contemporary literature [20; 42; 43; 44; 45]. The comparison of the mentioned four methods in terms of train, test and extrapolation error confirmed the ranking of these methods found before (see Figures 5 and 6). GradBoost and LinReg (day-time) achieved in general the lowest error values. SVM performed slightly worse in terms of the test and extrapolation error, particularly in scenarios with three and four measurement periods. The train error was comparable amongst GradBoost and SVM, but larger with LinReg (day-time). ANN resulted in the largest errors amongst the four methods. In general, the results for the test error deviated more among the methods than for the train and extrapolation error. For larger training sets the different types of errors were more similar than for smaller training sets. The box plots for the same selection of methods indicate that the variability of the projected values in general decreased if larger training datasets were used, while the trend with regard to the average value was less pronounced (see Figure 6). However, in many cases, in scenarios with 7 and 14 days the average value was closer to the actual 10-month average than in scenarios with only 1 day. Furthermore, GradBoost exhibited clearly the least outliers among all realizations. Therefore, GradBoost was selected to further evaluate the effect of sampling frequency and duration on the model predictions on the basis of different accuracy measures. Figure 7 indicates that scenarios resulting in very accurate average emission values did not necessarily result in low extrapolation errors. Among the scenarios with reasonably low MAE and at the same time small deviation between the projected and the measured average emission value were the scenarios 20, 21, 23, 24, 26 and 27. All of those were scenarios with 6 time 7 days (in case of scenarios 20, 23 and 26) or 14 days (in the other cases). Moreover, the mentioned scenarios had a strong focus on transition periods in the training datasets. Figure 4: Predictions of methane emissions averaged over the 10 month measuring period with two regression methods and only the sine and cosine transformed day-time as input features. The mean over the predictions based on 30 random realizations of each of the 27 scenarios (as depicted in Figure 1) is marked in blue. The associated one-sigma intervals are indicated by the light blue dashed lines. The red horizontal lines highlight the mean observed emission (\(\bar{E}_{n}\) = 11.6 g h\({}^{-1}\) LU\({}^{-1}\)). Figure 5: Mean absolute errors [g h\({}^{-1}\) LU\({}^{-1}\)] for four distinct regression methods (where LinReg used only the sine and cosine transformed day-time feature and the other three methods used all features). In each case, the error was determined on three different datasets: The data that were used for learning (train error depicted in orange), the data that were used for model testing in the cross-validation (test error depicted in red) and the data that were not used in the cross-validation (extrapolation error depicted in blue). All error values were averaged over 30 realizations of data selection, which fulfill the scenario constraints. Please note that the \(y\)-axes in the subplots have different scaling.