# Vegetation Health in China Is Severely Compromised by Drought, Wet and Heat Stress Events
## 2 Materials and Methods
### Methods
#### 2.3.1 Construction of the Vegetation Health Assessment System
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline
**Data Type** & **Spatial Resolution** & **Temporal Resolution** & **Source** \\ \hline ET, SM & 0.25\({}^{\circ}\) & Yearly & [[https://www.gleam.eu/](https://www.gleam.eu/)]([https://www.gleam.eu/](https://www.gleam.eu/)) (accessed on 17 March 2024) \\ \hline Slope, DEM & 1 km & Yearly & [[https://www.gscloud.cn/](https://www.gscloud.cn/)]([https://www.gscloud.cn/](https://www.gscloud.cn/)) (accessed on 18 March 2024) \\ \hline PM2.5 & 1 km & Monthly & [[https://data.tpdc.ac.cn/](https://data.tpdc.ac.cn/)]([https://data.tpdc.ac.cn/](https://data.tpdc.ac.cn/)) (accessed on 18 March 2024) \\ \hline PDSI & 1 km & Monthly & [[https://crudata.uea.ac.uk/cru/data/drought/](https://crudata.uea.ac.uk/cru/data/drought/)]([https://crudata.uea.ac.uk/cru/data/drought/](https://crudata.uea.ac.uk/cru/data/drought/))\#global (accessed on 18 March 2024) \\ \hline Nighttime Light & 500 m & Yearly & [[http://nnu.geodata.cn/data/datadetails.html?](http://nnu.geodata.cn/data/datadetails.html?)]([http://nnu.geodata.cn/data/datadetails.html?](http://nnu.geodata.cn/data/datadetails.html?)) & \\  & & & & \\  & & & & \\  & & & & \\  & & & & \\  & & & & \\ \hline Soil properties & 1 km & Yearly & [[https://data.tpdc.ac.cn/zh-hans/data/8](https://data.tpdc.ac.cn/zh-hans/data/8) ba0a731-5 bbb-4e2f-8b95-8b29 cc3c0f3a]([https://data.tpdc.ac.cn/zh-hans/data/8](https://data.tpdc.ac.cn/zh-hans/data/8) ba0a731-5 bbb-4e2f-8b95-8b29 cc3c0f3a) (accessed on 20 March 2024) \\ \hline GDP, Tertiary industry added value & 1 km & Yearly & [[https://github.com/thestarlab/ChinaGDP](https://github.com/thestarlab/ChinaGDP)]([https://github.com/thestarlab/ChinaGDP](https://github.com/thestarlab/ChinaGDP)) (accessed on 25 March 2024) \\ \hline Population density & 1 km & Yearly & [[https://landscan.ornl.gov](https://landscan.ornl.gov)]([https://landscan.ornl.gov](https://landscan.ornl.gov)) (accessed on 25 March 2024) \\ \hline NDVI & 1 km & Yearly & [[https://www.geodata.cn/main/](https://www.geodata.cn/main/)]([https://www.geodata.cn/main/](https://www.geodata.cn/main/))\#/face_science_detail? & \\  & & & & \\  & & & & \\ LAI & 0.05\({}^{\circ}\) & Yearly & [[https://doi.org/10.3974/geodb.2023.10.03.V1](https://doi.org/10.3974/geodb.2023.10.03.V1)]([https://doi.org/10.3974/geodb.2023.10.03.V1](https://doi.org/10.3974/geodb.2023.10.03.V1)) (accessed on 30 March 2024) \\ \hline SIF & 0.05\({}^{\circ}\) & 4 day & [[https://cstr.cn/18406.11.Ecolo.tpdc.271751](https://cstr.cn/18406.11.Ecolo.tpdc.271751)]([https://cstr.cn/18406.11.Ecolo.tpdc.271751](https://cstr.cn/18406.11.Ecolo.tpdc.271751)) (accessed on 3 April 2024) \\ \hline NPP & 500 m & Yearly & [[https://lpdaac.usgs.gov/product_search/?view=](https://lpdaac.usgs.gov/product_search/?view=)]([https://lpdaac.usgs.gov/product_search/?view=](https://lpdaac.usgs.gov/product_search/?view=)) listhttl://lpdaac.usgs.gov/product_search/?view=list (accessed on 3 April 2024) \\ \hline
1:1,000,000 vegetation types in China & 1 km & [[https://www.plantplus.cn](https://www.plantplus.cn)]([https://www.plantplus.cn](https://www.plantplus.cn)) (accessed on 5 April 2024) \\ \hline \end{tabular}
\end{table} 
Table 1: _Cont._the ranking of various schemes by calculating their similarity to the ideal solution and the negative ideal solution [31]. Here, we interpret vegetation health solely based on the composite score. Assuming there are \(n\) evaluation objects and \(m\) attributes, the original decision matrix \(X\) can be represented as  
\[X=\left[ \begin{array}{cccc}x_{11}&x_{12}&\cdots&x_{1m}\\ x_{21}&x_{22}&\cdots&x_{2m}\\ \vdots&\vdots&\ddots&\vdots\\ x_{n1}&x_{n2}&\cdots&x_{nm}\\ \end{array} \right] \tag{2}\]  
The standardized matrix \(R\), \(R\) with elements \(r_{ij}\), is calculated as follows:  
\[r_{ij}=\frac{x_{ij}}{\sqrt{\sum_{k=1}^{m}x_{kj}^{2}}} \tag{3}\]  
where \(x_{ij}\) represents the value of the \(i^{th}\) evaluation object with respect to the \(j^{th}\) attribute.