Uncertainty of Partial Dependence Relationship between Climate and Vegetation Growth Calculated by Machine Learning Models

As more machine learning and deep learning models are applied in studying the quantitative relationship between the climate and terrestrial vegetation growth, the uncertainty of these advanced models requires clarification. Partial dependence plots (PDPs) are one of the most widely used methods to estimate the marginal effect of independent variables on the predicted outcome of a machine learning model, and it is regarded as the main basis for conclusions in relevant research. As more controversies regarding the reliability of the results of the PDPs emerge, the uncertainty of the PDPs remains unclear. In this paper, we experiment with real, remote sensing data to systematically analyze the uncertainty of partial dependence relationships between four climate variables (temperature, rainfall, radiation, and windspeed) and vegetation growth, with one conventional linear model and six machine learning models. We tested the uncertainty of the PDP curves across different machine learning models from three aspects: variation, whole linear trends, and the trait of change points. Results show that the PDP of the dominant climate factor (mean air temperature) and vegetation growth parameter (indicated by the normalized difference vegetation index, NDVI) has the smallest relative variation and the whole linear trend of the PDP was comparatively stable across the different models. The mean relative variation of change points across the partial dependence curves of the non-dominant climate factors (i.e., radiation, windspeed, and rainfall) and vegetation growth ranged from 8.96% to 23.8%, respectively, which was much higher than those of the dominant climate factor and vegetation growth. Lastly, the model used for creating the PDP, rather than the relative importance of these climate factors, determines the fluctuation of the PDP output of these climate variables and vegetation growth. These findings have significant implications for using remote sensing data and machine learning models to investigate the quantitative relationships between the climate and terrestrial vegetation.