# Improving the Gross Primary Production Estimate by Merging and Downscaling Based on Deep Learning
## 2 Materials and Methods
### Deep Learning Network
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model Name** & **Institution** & **Variant Label** & **Resolution (Longitude \(\times\) Latitude)** \\ \hline ACCESS-ESM1-5 & CSIRO, Australia & r1i1p1f1 & 1.875\({}^{\circ}\)\(\times\) 1.25\({}^{\circ}\) \\ BCC-CSM2-MR & BCC, China & r1i1p1f1 & 1.125\({}^{\circ}\)\(\times\) 1.125\({}^{\circ}\) \\ CAS-ESM2-0 & CAS, China & r1i1p1f1 & 1.4062\({}^{\circ}\)\(\times\) 1.4062\({}^{\circ}\) \\ CESM2 & NCAR, USA & r1i1p1f1 & 1.25\({}^{\circ}\)\(\times\) 0.9424\({}^{\circ}\) \\ CESM2-WACCM & NCAR, USA & r1i1p1f1 & 1.25\({}^{\circ}\)\(\times\) 0.9424\({}^{\circ}\) \\ CMCC-CM2-SR5 & CMCC, Italy & r1i1p1f1 & 1.25\({}^{\circ}\)\(\times\) 0.9424\({}^{\circ}\) \\ CMCC-ESM2 & CMCC, Italy & r1i1p1f1 & 1.25\({}^{\circ}\)\(\times\) 0.9424\({}^{\circ}\) \\ CNRM-CM6-1 & CNRM, France & r1i1p1f2 & 1.4\({}^{\circ}\)\(\times\) 1.4\({}^{\circ}\) \\ CNRM-CM6-1-HR & CNRM, France & r1i1p1f2 & 1.4\({}^{\circ}\)\(\times\) 1.4\({}^{\circ}\) \\ CNRM-ESM2-1 & CNRM, France & r1i1p1f1 & 0.5\({}^{\circ}\)\(\times\) 0.5\({}^{\circ}\) \\ CanESM5-CanOE & CCCMA, Canada & r1i1p2f1 & 2.8125\({}^{\circ}\)\(\times\) 2.8125\({}^{\circ}\) \\ CanESM5 & CCCMA, Canada & r1i1p1f1 & 2.8125\({}^{\circ}\)\(\times\) 2.8125\({}^{\circ}\) \\ EC-Earth3-Veg-LR & EC-Earth-Consortium, EU & r1i1p1f1 & 0.7031\({}^{\circ}\)\(\times\) 0.7031\({}^{\circ}\) \\ EC-Earth3-Veg & EC-Earth-Consortium, EU & r1i1p1f1 & 0.7031\({}^{\circ}\)\(\times\) 0.7031\({}^{\circ}\) \\ GISS-E2-1-G & NASA, USA & r1i1p1f2 & 2.5\({}^{\circ}\)\(\times\) 2\({}^{\circ}\) \\ GISS-E2-1-H & NASA, USA & r1i1p1f2 & 2.5\({}^{\circ}\)\(\times\) 2\({}^{\circ}\) \\ INM-CM4-8 & INM, Russia & r1i1p1f1 & 2\({}^{\circ}\)\(\times\) 1.5\({}^{\circ}\) \\ INM-CM5-0 & INM, Russia & r1i1p1f1 & 2\({}^{\circ}\)\(\times\) 1.5\({}^{\circ}\) \\ IPSL-CM6A-LR & IPSL, France & r1i1p1f1 & 2.5\({}^{\circ}\)\(\times\) 1.2676\({}^{\circ}\) \\ MIROC-ES2L & MIROC, Japan & r1i1p1f2 & 2.8125\({}^{\circ}\)\(\times\) 2.8125\({}^{\circ}\) \\ MPI-ESMI-2-zHR & MPI-M, Germany & r1i1p1f1 & 0.9375\({}^{\circ}\)\(\times\) 0.9375\({}^{\circ}\) \\ MPI-ESM1-2-LR & MPI-M, Germany & r1i1p1f1 & 1.875\({}^{\circ}\)\(\times\) 1.875\({}^{\circ}\) \\ UKESM1-0-LL & MOHC, UK & r1i1p1f2 & 1.875\({}^{\circ}\)\(\times\) 1.25\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Detailed information on 23 models used in this study. Therefore, to reduce the problem, a convolutional layer is added after each deconvolution layer to compensate for upsampling. Specifically, this part's input to the model is low-resolution CMIP6 GPP. The second part of the model is upsampling, which is mainly used for downscaling. It consists of one upper sampling layer using bilinear interpolation and two convolution layers with the same feature depth as the input channel. As in the first part, the last two convolution layers were added to eliminate the checkerboard effect. The third part is data merging, which consists of three input datasets, including upsampling output, auxiliary data, and unsampled CMIP6 GPP. The three datasets calculated by the two convolution layers are joined to obtain high-resolution data. Among them, auxiliary data are used to help improve the results, which remained constant throughout different months over the training and testing periods. The loss function can be calculated according to the following formula:  
\[L(\theta)=\frac{1}{N}\sum_{i=1}^{N}||f(X_{i},\theta)-Y_{i}||^{2}, \tag{1}\]  
Among them, \(\theta\) is the network parameter that needs to be optimized. \(f(X_{i},\theta)\) represents the learned function. In addition, \(n\) is the total number of training samples. \(X\) and \(Y\) represent the input data and the target at position \(i\).