# Spatiotemporal Evolution and Impact Mechanisms of Gross Primary Productivity in Tropics
## 4 Results
### Impact of Climatic Factors on GPP  
In order to spatially analyze the effects of temperature and precipitation on GPP, the correlation between vegetation GPP and temperature and precipitation in the tropics was calculated image by image and expressed as the magnitude of partial correlation coefficients and complex correlation coefficients (Figure 6). A positive partial correlation coefficient indicates that when temperature (or precipitation) increases in the region, GPP also increases, reflecting a positive correlation. Conversely, a negative partial correlation coefficient indicates that temperature (or precipitation) in the region is negatively correlated with GPP. The complex correlation coefficient indicates the combined effect of temperature and precipitation on the GPP of vegetation in the region. A positive complex correlation coefficient indicates a positive correlation between climate and GPP, whereas a negative complex correlation coefficient indicates a negative correlation between climate and GPP. The closer the absolute value of the correlation coefficient is to 0, the smaller the effect of climate change on GPP in the region; conversely, the closer the absolute value is to 1, the larger the effect of climate change on GPP in the region.  
The results indicate that the coefficient of partial correlation between vegetation _GPP_ and precipitation exhibits fluctuations within the range of \(-0.89\) to \(0.91\), with a mean value of \(0.21\), indicating an overall positive correlation (Figure 6a). The regions exhibiting a high positive bias correlation between vegetation _GPP_ and precipitation in the tropics were primarily concentrated in South America and central Africa, along with the southern archipelago of Asia. Conversely, the regions displaying a high negative bias correlation were predominantly situated in eastern South America, southern and eastern Africa, the Indian Peninsula, and Oceania.  
Figure 5: Trend chart of the annual mean GPP of vegetation in the tropical zone from 2001 to 2020.  
A review of the bias correlation coefficient of temperature and _GPP_ (Figure 6b) reveals a fluctuation range of \(-0.98\)-\(0.92\), with an average value of \(-0.011\), indicating an overall negative correlation. The regions exhibiting a high positive correlation between vegetation _GPP_ and air temperature in the tropics are primarily located in the eastern and western regions of South America and the coast of Africa. Conversely, the northwestern region of South America, the central region of Africa, and the southern region of Asia exhibit a high negative correlation.  
A plot of the complex correlation coefficients between climate and _GPP_ (Figure 6c) reveals that regions with strong positive correlations between climate factors and _GPP_ are mainly located in South America and central Africa, the southeastern islands of Asia, and central Oceania. This indicates that the _GPP_ in these regions increases significantly when the temperature increases. The regions with strong negative correlations are located in the northern and southern parts of South America, the coastal areas of Africa, and the Indian Peninsula. These regions exhibit stronger negative correlations, suggesting that GPP in these regions decreases significantly when temperatures increase and precipitation increases. A comparison of the three images in Figure 6 reveals that the degree of similarity between Figure 6a,c is greater than that between Figure 6b,c. This indicates that the biased correlation between vegetation GPP and precipitation is stronger than that between temperature and precipitation. In other words, the influence of precipitation on _GPP_ is greater than that of temperature.  
Figure 6: Plot of partial correlation and complex correlation coefficients between vegetation GPP and climate (precipitation and temperature) factors in the tropical zone from 2001 to 2020.