Time-Domain Correlation Quantitative Analysis Method of Regional Rainfall-Landslide Displacement Responses Based on a Time-Domain Correlation Model

Landslide deformation is the most intuitive and effective characterization of the evolution of landslides and reveals their inherent risk. Considering the inadequacy of existing deformation monitoring data in the early warning of landslide hazards, resulting in insufficient disaster response times, this paper proposes a time-domain correlation model. Based on a regional rainfall-landslide deformation response analysis method, a time-domain correlation measure between regional rainfall and landslide deformation and a calculation method based on impulse response functions are proposed for prevalent rainfall-induced landslide areas, and the correlation with the rainfall-triggered landslide deformation mechanism is quantitatively modeled. Furthermore, using rainfall monitoring data to optimize the indicator system for landslide deformation monitoring and early warning significantly improves the preliminary warning based on landslide deformation. The feasibility of the method proposed in this paper is verified by analyzing the historical monitoring data of rainfall and landslide deformation at 15 typical locations in 5 landslide hidden hazard areas in Fengjie County, Chongqing city. (1) The correlation models for the XP landslide and XSP landslide involve a 5-day lagged correlation under a 56-day cycle and a 18-21-day lagged correlation under a 49-52-day cycle, which means that the deformation in the above areas can be modeled cyclically according to monitoring data, and early landslide warnings can be provided in advance with a lag time. (2) The correlation models for the TMS landslide and OT landslide show consistent correlations under a 48-50-day cycle and a 58-day cycle, which means that the deformation in the above areas can be predicted based on rainfall accumulation, and real-time warnings of future landslide deformation and displacement can be obtained. (3) The HJWC landslide presents a disorderly correlation pattern, which means that a preliminary landslide deformation warning cannot be provided based on rainfall alone; other monitoring data need to be supplemented and analyzed.

A skewed perspective of the Indian rainfall–El Niño–Southern Oscillation (ENSO) relationship

Wavelet coherence is a method that is commonly used in hydrology to extract scale-dependent, nonstationary relationships between time series. However, we show that the method cannot always determine why the time-domain correlation between two time series changes in time. We show that, even for stationary coherence, the time-domain correlation between two time series weakens if at least one of the time series has changing skewness. To overcome this drawback, a nonlinear coherence method is proposed to quantify the cross-correlation between nonlinear modes embedded in the time series. It is shown that nonlinear coherence and auto-bicoherence spectra can provide additional insight into changing time-domain correlations. The new method is applied to the El Niño–Southern Oscillation (ENSO) and all-India rainfall (AIR), which is intricately linked to hydrological processes across the Indian subcontinent. The nonlinear coherence analysis showed that the skewness of AIR is weakly correlated with that of two ENSO time series after the 1970s, indicating that increases in ENSO skewness after the 1970s at least partially contributed to the weakening ENSO–AIR relationship in recent decades. The implication of this result is that the intensity of skewed El Niño events is likely to overestimate India's drought severity, which was the case in the 1997 monsoon season, a time point when the nonlinear wavelet coherence between AIR and ENSO reached its lowest value in the 1871–2016 period. We determined that the association between the weakening ENSO–AIR relationship and ENSO nonlinearity could reflect the contribution of different nonlinear ENSO modes to ENSO diversity.