# Quantifying Climate Change and Ecological Responses within the Yangtze River Basin, China
## Materials and Methods
### Methodology  
To facilitate assessment of climate trends in the region, it is necessary to interpolate temperature and precipitation data to produce spatially continuous data. Spatial interpolation methods such as the Thiessen polygon [36], radial basis functions (RBF) [37], Kriging interpolation [38] and inverse distance weighting (IDW) [39] can be interpolated. Kriging is an estimation of optimal, linear and unbiased interpolation of spatial distribution data, which is divided into ordinary kriging and co-kriging, etc. Compared to other methods, co-kriging [40] not only takes the spatial correlation of the known data points but the elevation factor as well. Therefore, we used this method for the spatial interpolation of the atmospheric and rainfall data by choosing the elevation of each meteorological station as the covariable and implementing repeated exploratory spatial data analysis, cross validation, error analysis, and parameter modification, to get the better spatial distribution map of them over the YRB. Regression and correlation are the most commonly used analytical methods [41]. We used linear regression analysis to analyze the trends of the meteorological factors and ecological indicators at two scales: for the whole basin and for the grid unit [42]. The rate of change of the climatic parameters (e.g., temperature and precipitation) and the ecological indicators (e.g., NDVI, EVI, LAI, GPP, NPP) were calculated using Equation (1) [43],  
\[S=\frac{n\times\sum\limits_{i=1}^{n}{(Ti\times Ei)-(\sum\limits_{i=1}^{n}{Ti} )(\sum\limits_{i=1}^{n}{Ei})}}{n\times\sum\limits_{i=1}^{n}{Ti^{2}-(\sum \limits_{i=1}^{n}{Ti})}} \tag{1}\]  
Here, \(S\) is the slope of the trend line of the climatic factors and the ecological indicators; \(T_{i}\) is the time label; \(n\) is the number of years, and \(E_{i}\) is the value of the climatic factor or ecological indicator for the \(i\) year. \(S\) describes the trend in the climatic factors or the ecological indicators. If \(S>0\), the variation of the dependent variable exhibits an increasing trend, whereas if \(S<0\), the variation of the dependent variable exhibits a decreasing trend. The linear variation trend of climatic factors and ecological factors was calculated by least squares linear fitting using the time series data for each pixel. A program was implemented using MATLAB to calculate the slope and the significance of the regression of air temperature/precipitation and NDVI/EVI/LAI/GPP/NPP for each pixel. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Data Category** & **Data Description** & **Interval** & **Source** \\ \hline \multirow{3}{*}{Climate data} & Daily mean temperature & 1961–2013 & \multirow{3}{*}{China Meteorological Data Service Center (CMDC)} \\  & Daily precipitation & 1961–2013 & \multirow{3}{*}{([[http://data.cma.cn/](http://data.cma.cn/)]([http://data.cma.cn/](http://data.cma.cn/)))} \\ \hline \multirow{6}{*}{Ecological indicator} & Normalized Difference Vegetation Index/Enhanced Vegetation Index (NDVI/EVI) & 2001–2013 & \multirow{3}{*}{Moderate Resolution Imaging Spectroradiometer (MODIS)} \\  & (NDVI/EVI) & & 13A1 product \\ \cline{1-1} \cline{2-4}  & Leaf Area Index (LAI) & 1982–2011 & \multirow{3}{*}{Advanced Very High-Resolution Radiometer (AVHRR) at Boston University (BU) generated the Leaf Area Index (LAI) datasets ([[http://sites.bu.edu/cliveg/datacodes](http://sites.bu.edu/cliveg/datacodes)]([http://sites.bu.edu/cliveg/datacodes](http://sites.bu.edu/cliveg/datacodes)))} \\ \cline{1-1} \cline{2-4}  & Gross Primary Production/Net Primary Production (GPP/NPP) & 2000–2010 & \multirow{3}{*}{MODIS 17A3 product ([[http://ladsweb.nascom.nasa.gov/data/search.html](http://ladsweb.nascom.nasa.gov/data/search.html)]([http://ladsweb.nascom.nasa.gov/data/search.html](http://ladsweb.nascom.nasa.gov/data/search.html)))} \\ \cline{1-1} \cline{2-4}  & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Description of the multi-source data used in this study.