## 3 Methodology
### Random Forest and Ridge Regression Ensemble Algorithm (RFRR)
#### 3.4.4 Continuous All-Weather TIR Land Surface Temperature  
The ensemble algorithm of Random Forest and Ridge Regression (RFRR) has a strong ability to fit complex nonlinear relationships, making it an ideal choice for developing a continuous all-weather TIR LST generation model. The fundamental premise for constructing such a model is that the nonlinear relationship between LST and other environmental variables remains consistent under both clear and cloudy conditions. Based on this premise, this study utilizes the RFRR algorithm to establish a nonlinear relationship model between FY-3C VIRR LST and six environmental variables (Downscaled PMW LST, NVI, LC, longitude and latitude, slope, and DEM) under clear conditions. Subsequently, the RFRR model established under clear conditions is applied to all-weather conditions to generate spatially continuous LST products, referred to as RFRR LST (RFRR-LST). Finally, RFRR-LST is used to fill the cloudy pixels of FY-3C VIRR LST, generating an all-weather LST product, called the Filled FY-3C VIRR LST (FM-LST).  
To present the proposed all-weather LST generation method in a more structured manner, it is divided into three main steps:  
1. **Selection of Input Variables for the RFRR Model:**  
Surface temperature is influenced by numerous environmental variables. In this study, the input variables for the RFRR model include Dow_LST, NDVI, LC, DEM, slope, and climate. Dow_LST refers to the microwave data that has been filled using SSA and downscaled. The NDVI has been normalized and smoothed using the S-G filter. It is  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**NO.** & **Parameter** & **Setting Value** \\ \hline
1 & alpha & 1.0 \\
2 & tol & \(1\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Table of hyperparameters for ridge regression used in stacking.  
important to note that different land cover types exhibit distinct surface temperature characteristics. For instance, the surface temperature of bare soil is higher than that of vegetation during the day, but lower at night. Therefore, this study selects NDVI and LC as input variables.  
China's climate exhibits significant latitudinal and land-sea heterogeneity, leading to variations in surface temperature driven by different climate types. Additionally, surface temperature is also influenced by DEM and slope. As a result, longitude and latitude, DEM, and slope data are chosen as input variables for the RFRR model.  
Establishment of the RFRR Model for Generating Continuous All-Weather TIR Land Surface Temperature:  
Leveraging the powerful nonlinear fitting capability of the RFRR algorithm, this study proposes a continuous all-weather LST generation method, which includes two key steps. First, using monthly time-series datasets, an RFRR model is trained and established to represent the relationship between FY-3C VIRR LST and six environmental variables (Downscaled PMW LST, NDVI, LC, longitude and latitude, slope, and DEM) under clear conditions. During model training, the dataset is split into training and testing sets in an 80:20 ratio. The training dataset is used to train the RFRR model, while the testing dataset is used to prevent overfitting. Next, the RFRR model established under clear conditions is applied to all-weather conditions. By inputting the six environmental variables for date T into the trained RFRR model, a high-resolution and spatially continuous LST for date T is generated, referred to as RFRR-LST.