Abstract
Traditional linear correlation analysis may not fully capture the true relationship between these variables. Therefore, multi-scale running correlation analysis, such as time-dependent intrinsic correlation (TDIC) and continuous wavelet transform based on Hilbert-Huang transform (HHT), provides valuable insights into local correlations and the evolving relationship between nutrients and environmental factors over time. In this study, we investigated seven environmental factors and four water quality nutrient indicators in deep lakes on the Yungui Plateau in southwestern China. The results revealed that there may be strong correlations between environmental factors and nutrient levels during certain periods, while opposite trends may emerge at other times. These variations in correlation could be attributed to uncertain physical processes, spatial heterogeneity, or the impact of different climatic factors on local hydrological processes. Wavelet analysis indicated that changes in environmental factors lag behind those in nutrient levels, particularly on a cycle of about 12 months. This suggests that changes in environmental factors align with natural patterns after the water body has been polluted. These conclusions underscore the complexity and dynamic nature of the relationship between environmental factors and nutrient levels in water bodies, highlighting the importance of employing advanced analysis techniques to capture this complexity.