# Impacts of Heat and Drought on Gross Primary Productivity in China
## 4 Results and Analysis
### Impact of Drought on GPP  
A 2D joint distribution of the annual GPP anomaly and drought index (SPI/SPEI) sequences was constructed utilizing the 2D copula function pixel by pixel, and then the ENAG probability was calculated under different drought levels for each pixel.  
The ENAG probability in each vegetation region decreased with decreasing SPI drought levels (Figure 4a,c,e,g). Under extreme drought conditions, the ENAG probability reached 87.1%, and pixels with a probability greater than 60% accounted for 7.3% of the entire study area, mainly located in the temperate grassland region (R2), the subtropical evergreen broad-leaved forest region (R4), and the warm temperate deciduous broad-leaved forest region (R6). Under severe drought conditions, the areas with high ENAG probabilities were significantly reduced and mainly occurred in small portions of the temperate grassland region (R2) and the warm temperate deciduous broad-leaved forest region (R6). When a moderate drought occurred, all pixels in the study area had an ENAG probability below 40%, and when a mild drought occurred, the ENAG probability was less than 20% in all regions.  
The spatial distributions of pixels representing the ENAG probabilities calculated from the SPEI (Figure 4b,d,f,h) were similar to those calculated from the SPI. Under SPEI-derived extreme drought conditions, the number of pixels with an ENAG probability occurrence greater than 80% was reduced. Pixels with high ENAG occurrence probabilities (>60%) only occurred in a few portions of the temperate grassland region (R2), the warm temperate deciduous broad-leaved forest region (R6), and the temperateiferous and deciduous forest mixed forest region (R7); the highest occurrence probability was 83.4%. Under severe drought conditions, the highest ENAG probability was 65.2%. There was no obvious difference between the SPI and SPEI results when moderate or mild drought events occurred, but the ENAG probabilities calculated in terms of the SPI were generally higher than those calculated in terms of the SPEI.  
As the drought level increased, the drought impact gradually increased in each vegetation region, and the higher the drought level was, the more evidently the ENAG probabilities increased (Figure 5). According to the total average probabilities of ENAG under different drought levels, the impacts of SPI-derived drought on GPP in different vegetation regions were determined in order from highest to lowest as follows: the temperate grassland region (R2, 68.22%) > the warm temperate deciduous broad-leaved forest region (R6, 65.56%) > the subtropical evergreen broad-leaved forest region (R4, 49.04%) > the tropical monsoon forest and rainforest region (R5, 48.13%) > the temperateiferous and deciduous forest mixed forest region (R7, 44.87%) > the cold temperateiferous forest region (R8, 43.20%) > the alpine vegetation region on the Qinghai-Tibet Plateau (R3, 24.99%) > the temperate desert region (R1, 23.47%). The impacts of SPEI-derived drought were determined in order from highest to lowest as follows: the warm temperate deciduous broad-leaved forest region (R6, 59.68%) > the temperate grassland region (R2, 51.71%) > the subtropical evergreen broad-leaved forest region (R4, 47.27%) > the tropical monsoon forest and rainforest region (R5, 46.00%) > the temperateiferous and deciduous forest mixed forest region (R7, 43.03%) > the cold temperateiferous forest region (R8, 42.28%) > the alpine vegetation region on the Qinghai-Tibet Plateau (R3, 21.16%) > the temperate desert region (R1, 20.78%).  
Figure 4: Spatial distribution of the probabilities of ENAG under different drought levels. (**a,c,e,g**) represent extreme, severe, moderate, and mild droughts classified in terms of the SPI, respectively; (**b,d,f,h**) represent extreme, severe, moderate, and mild drought classified in terms of the SPIEI, respectively. (Note: The copula function cannot be built in the pixels where the GPP data are missing or the GPP value is constant in all years. Those pixels were removed and are shown as white).