# Micro-Location Temperature Prediction Leveraging Deep Learning Approaches
## 3 Proposed Method Maximus
The MSE metric is defined as follows:  
\[MSE=\frac{1}{N}\sum_{i=1}^{N}(y_{i}-x_{i})^{2}, \tag{3}\]  
where the meaning of the variables \(y_{i}\) and \(x_{i}\) are the same as in the case of Equation (2). Also here, the lower the MSE, the closer to the actual values and the better the model's accuracy. In general, the MSE measure indicates more sensibility to observations that deviate more from the means. The intention of the learning phase was to improve the air temperature forecasts for the next 12 h for a given micro-location predicted by the ICON-D2 reference model, by using the optimal prediction model enriched with real meteorological ICON-D2 weather data, as provided by the mobile weather station. The prediction is presented as the flow diagram in Figure 7. where the example considers the \(N\) feature values that enter as inputs into the Maximus prediction model, and thus defines the topology of the LSTM network. The selected set of features is extracted from two different sources: (1) the mobile weather station, and (2) the ICON-D2 higher-resolution dataset. Let us assume the mobile weather station is given that consists of five sensors. The features acquired from these sensors (i.e., air temperature, air pressure, relative humidity, wind speed, and rainfall intensity) are denoted as 'Feat_1' to 'Feat_5', as can be seen from the legend in the figure. Actually, the first five inputs to the LSTM network are taken from the mobile weather station by merging the \(T-1\) past feature values with the current values, while the remaining \(N-5\) features enter from the RNWP model ICON-D2 to the Maximus prediction model unchanged. The result of the Maximus prediction model is the predicted time-series of air temperatures for the next \(T\) hours. Finally, the time-series predicted by the Maximus is compared with the time-series for the next \(T\) hours as predicted by the ICON-D2 reference model according to the statistical measure MAE, in order to determine the deviance between both. Let us emphasize that the MAE cannot be treated in the same way as in modeling case, because now the following holds: The higher the MAE value, the more powerful the Maximus prediction at the specific micro-location. On the other hand, if the value of MAE is zero, it seems, there is no need for using the special prediction model for micro-locations. However, this problem can also be viewed from another perspective: In the case that the prediction models could have integrated physics indicators (i.e., the common indicators included in all weather prediction models), together with micro-physics indicators of a particular micro-location (e.g., turbulence caused by local wind; influence of relief, like altitude, atmospheric overheating, etc. ), such models reflect the characteristics of the micro-location as a whole (i.e., ensure that MAE \(\
eq 0\)) and therefore could be tested on a regional level together with the specific micro-physics indicators. Moreover, if we could change the micro-physics indicators of the model by ourselves, such models could predict air temperature for the specific micro-location more accurately. Unfortunately, this development is connected also with additional resources and, therefore, remains a future direction in this moment. Thus, the reference data were aggregated from the ICON-D2 dataset, starting at a specific start time during the next 12 h. Interestingly, there is a little discrepancy between the sampling times of weather data entered in the ICON-D2 dataset, where the weather data are predicted on an hourly basis but refreshed in three hour intervals, and either the CERRA dataset or mobile weather station, where these data are sampled on an hourly basis. The meteorological station data from our autonomous professional weather station are very important, as they contribute hugely to the prediction of the air temperature. Indeed, there are only a limited number of features that are able to serve as an input to the LSTM network.