# A Model Output Deep Learning Method for Grid Temperature Forecasts in Tianjin Area
## 2 Data and Organization
### Model Data  
Many countries and regions have their own global numerical weather prediction centers, including ECMWF (European Centre for Medium-Range Weather Forecasts), GFS (United States Global Forecast System), or RHMC (Russian Hydrological and Meteorological Center). Among these centers, ECMWF is an independent intergovernmental organization with the world's largest archive of numerical weather prediction data. Because of the noticeable correction effect on the deterministic forecast of extreme weather, it has become a vital reference product for short- and medium-term weather forecasting [38].  
The forecast data that are used in this paper are The International Grand Global Ensemble (TIGGE) dataset, which is the global ensemble forecast data from ECMWF. The model data provided by TIGGE includes wind speed, temperature, precipitation, humidity, and other basic physical quantities and basic weather phenomenon elements that explain the state of the atmosphere, which we call weather elements. During weather consultation, meteorologists will select some, but not all, weather elements for weather consultation based on meteorological principles and their own local forecasting experience. Based on the experience of weather forecasters, this paper selects 21 kinds of weather elements with a correlation with temperature. In the correlation analysis in Section 3, further screening of these weather elements will be carried out.  
As part of the experimental data \(D_{0}\), the model forecast data is recorded as \(X_{0}\). \(X_{0}\) used in the experiment is the combination of three-hourly forecast data initialized at 0000 UTC up to a lead time of 72 h and six-hourly forecast data up to lead time of 240 h from January 2016 to November 2018 provided by Tianjin Bureau of Meteorology. Each day provides a forecast sample from January 2016 to November 2018. Thus, there are 1065 samples recorded as S in a specific space on a certain day, i.e., \(S=1,2,\cdots,1065\). For the numerical forecast in the above time range with a resolution of 0.125\({}^{\circ}\), the grid shape covering the Tianjin area (38.5\({}^{\circ}\)-40.25\({}^{\circ}\) N, 116.25\({}^{\circ}\)-118.5\({}^{\circ}\) E) is 16 \(\times\) 12. Because grid points at the grid boundary need to be considered, this paper uses grid data with a shape of \(18\times 14\). Each point on the grid can be represented by (\(m\), \(n\)), where \(m=1,2,\cdots,14\) and \(n=1,2,\cdots,18\). As part of the experimental data \(D_{0}\), the model forecast data are recorded as \(X_{0}\). Each sample contains 21 weather elements \((2T,2D,\cdots,VIS)\) and we use \(C\) to represent some element, i.e., \(C\in(2T,2D,\cdots,VIS)\), which will be introduced in detail later. Each sample has 53 time steps (or called forecast lead time) and can be divided into two groups according to the time steps, which is the 3-h interval sample of the first 72 h and the 6-h interval sample of 72-240 h (\(t=0\), 3,..., 69, 72, 78,..., 234, 240). Each point on the grid can be represented by (\(m\), \(n\)), where \(m=1,2,\cdots,14\) and \(n=1,2,\cdots,18\). Therefore, the five-dimensional (5D) tensor \(X_{0}\) of size \(14\times 18\times 53\times 21\times 1065\) can be written as  
\[X_{0}=\left\{x_{m,n,S,I,C}\right\}, \tag{1}\]  
where \(x_{m,n,S,I,C}\) is the value of forecast sample \(S\) with the weather element \(C\) in grid point (\(m,n\)) whose forecast lead time is \(t\).  
Figure 1 shows an element in \(X_{0}\). Three of 21 different weather elements (\(C\)) with fixed parameters are drawn using four different color tables. Each weather element is composed of three heat maps, representing three different time parameters (\(t\)). The length of the time dimension is 53, and each time parameter corresponds to a two-dimensional matrix of \(14\times 18\) (\(m,n\)) in space. The figure shows the value of weather elements in the form of heat maps through nearest neighbor interpolation.