Clarifying the response of wetland changes to climate change can improve the scientific conservation and utilization capabilities of wetland ecosystems, which is vital for their sustainable development. In this study, the spatial distribution and area changes of the different types of wetlands in the Yellow-River-Source National Park (YRSNP) were obtained using the object-based classification method for the years 2000, 2010, and 2020. The relationship between wetland change and climate factors was investigated by combining grey relation analysis and correlation analysis. The response of wetland change to different climatic factors was consequently clarified. The results showed that the river wetlands and lake wetlands increased significantly from the year 2000 to 2010 (4.04% and 4.21%, respectively). However, the total wetland area demonstrated a decreasing trend (7.08%), primarily due to the significant decrease in the marsh wetlands (6.81%). The total wetland area demonstrated a slightly increasing trend from the year 2010 to 2020 (0.14%), in which river wetlands and lake wetlands increased by 3.25% and 2.09%, respectively, while the marsh wetlands demonstrated a tendency to be stable. From the year 2000 to 2010, 75.53% of precipitation and 27.68% of temperature demonstrated a significant increase and an obvious warm–humid climate trend. However, from the year 2010 to 2020, the trend of increasing precipitation weakened, the temperature decreased slightly, and the warm–humid climate trend was not significant. From the year 2000 to 2020, the YRSNP river wetlands and lake wetlands were significantly and positively correlated with temperature and precipitation, while the marsh wetlands were most affected by climate warming, especially the warm-season temperatures. The spatial–temporal difference was not obvious in the correlation coefficient between marsh wetlands area change and the precipitation and temperature. The results of the study can provide a theoretical basis and technical support for the conservation of wetland ecosystems in the Three-River-Source National Park.
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