## Materials and Methods
### LPJ Model  
The LPJ model has been developed as a DGVM of intermediate complexity with a broad range of potential applications to global problems. The LPJ model can be used to simulate the potential vegetation distribution and estimate the inter-annual variation of NPP [16]. The vegetation structure and composition are described by ten plant functional types (PFTs), which are distinguished according to their phenology, physiology and physiognomy. Monthly gross production for an average PFT individual is summed over a year, and after subtraction of plant respiration expenditures, the remainder is allocated to plant tissues.  
The LPJ model is a well-developed model and has been widely used to determine global and regional NPP; therefore, in this study, the LPJ model was used to simulate the NPP in the Yangtze River basin. The LPJ was run from 1961 to 1980 with a pseudo-daily time step, preceded by a 1000-year spin-up period that brought the carbon pools and vegetation cover in equilibrium with climate. The LPJ model used in our article has been intensively validated against observed NPP values by using a data set of forest NPP obtained from forest inventory in China between 1989 and 1993 from plot sites to 0.5\({}^{\circ}\) latitude \(\times\) 0.5\({}^{\circ}\) longitude grid cells [27].  
The LPJ DGVM was employed in this article due to its broad application in modelling both terrestrial carbon cycles and hydrological cycles [28; 29]. The model, which originates from the BIOME model family [30], simulates the vegetation patterns and functions for any time if climate data are available for the specified time [31]. The model was run on a grid-cell basis with input of soil texture, monthly temperature, precipitation, cloud, humidity days and annual atmospheric CO\({}_{2}\) concentration, and the output data includes the vegetation NPP, biomass, leaf area index (LAI), evapotranspiration and so on.  
In the LPJ model, the NPP is calculated by subtracting maintenance and growth respiration from GPP (Gross Primary Production), which is computed by coupling the photosynthesis and water balance schemes. Additional details about this approach can be found in several studies [32; 33]. The formula is as follows:  
\[\text{NPP}=0.75\times(\text{GPP}-\text{R}_{\text{m}}) \tag{1}\]  
where GPP is the total primary productivity, \(\text{R}_{\text{m}}\) is the amount of carbon required for a plant to maintain its own required respiration, and 0.75 is the ratio of NPP in the remainder, considering 0.25 to be the growth respiration coefficient.  
Simple linear regression was used in this paper for long-term linear trend test. The simple linear regression method is a parametric test method, which consists of two steps, fitting a linear simple regression equation with the time \(t\) as independent variable and the vegetational variable (i.e., NPP or NDVI in our article) as dependent variable; testing significance of the slope of the regression equation by the \(t\)-test. The 95% confidence interval was used as a threshold to classify the significance of positive and negative [34; 35].  
A geographic information system was used to process and spatially interpolate meteorological data and NPP data, from which raster images are derived. Correlation analysis was applied to statistically analyse the relationship among the variables. The closer the \(r\) value is to 1, the higher the linear correlation among the variables; the smaller the absolute value of the correlation coefficient, the lower the linear correlation among the variables. A correlation coefficient of 0 indicates that there is no linear correlation between the variables. In this study, correlation analysis was used to study the correlation among temperature, precipitation with forest NPP and NDVI. The correlation coefficient (CC) was used to assess the linearity of the correlated datasets. T-test was used to perform the significance test of the slope [34].