# Forecasting Daily Temperatures with Different Time Interval Data Using Deep Neural Networks
## 4 Data
### Experimental Setup
To measure the accuracy of the models, we used mean absolute error (MAE) because it intuitively shows the differences between the actual and predicted temperatures. The mathematical loss function is shown in (11):  
\[MAE=\frac{1}{n}\sum\
olimits_{i=1}^{n}\left|y_{i}-\hat{y}_{i}\right| \tag{11}\]  
where \(n\) is the number of instances, \(y_{i}\) is the target value of \(i\)-th instance, and \(\hat{y}_{i}\) is its predicted value. We conducted additional experiments by combining the proposed method with recent approaches including multimodal learning, multitask learning, and input variables from other regions. First, we employed satellite images as additional inputs to the numerical meteorological data of the target region for forecasting temperature to apply multimodal learning to the proposed method. In this experiment, we added convolution layers that processes satellite images, and then concatenated it with the output of the convolution layer that processed the numerical weather data to perform forecasting temperature. The CNN model for multimodal learning has two sets of convolutional layers for two types of inputs, numerical weather data, and satellite images. The convolutional layers for satellite images consist of seven layers with \(2\ \times\ 2\) convolution filters with stride 2 and those for the numerical weather data are the same with the convolutional layers used for ordinary forecasting. After both types of inputs are processed into intermediate output values by the corresponding convolutional layers, these intermediate outputs are flattened and concatenated. Then, this concatenated vector is transmitted to the fully connected layers, whose structure is the same with the CNN models in Tables 4-6, to predict the target temperature. The satellite image data was taken from 12-h period observations over three years from 2015 to 2017 [44]. Therefore, the numerical weather data was also used for the corresponding period. In addition, the number of satellite images used for prediction coincides with the length of the numerical inputs. For example, six consecutive satellite images are employed for forecasting temperatures for the models that use three-day numerical inputs. We divided the entire three years of data into batches of two years of data, six months of data, and another six months of data in sequential order [3; 36; 43]. We then used these three batches as training, validation, and test data, respectively. Second, we studied if global variables such as input variables from other regions can improve the temperature forecasting performance. We used the numerical meteorological variables collected from the stations other than the target region for these experiments. For instance, when forecasting the temperatures in Seoul, the input variables of Daegwallyeong and Seongsan are input together with the data of Seoul. For this experiment, we used three convolution layers of the same structure of the CNN model and passed the convolution by receiving input data from Seoul, Daegwallyeong and Seongsan areas, respectively. After that, we concatenate it into a fully connected layer with the same structure as the above experiment and then forecast the temperature in a specific area. Third, temperatures in each region may be closely related to those in each other. Therefore, we verified the effect of shared information between the temperature forecasting tasks using deep multitask learning that learns related tasks simultaneously. We used input variables from all three regions as in the case for global variables. Using the input variables, four multitask learning models were constructed as follows: (1) a model forecasting average temperatures in three regions, (2) a model forecasting minimum temperatures in three regions, (3) a model forecasting maximum temperatures in three regions, (4) a model forecasting the average, minimum, and maximum temperatures in all three regions.