Intrinsic Cross-Correlation Analysis of Hydro-Meteorological Data in the Loess Plateau, China.

Xiaowei Wei,Xinghui Gong,Tong Zhi,Xingchen Wei,Chiheng Dang,Hongbo Zhang

doi:10.3390/ijerph17072410

Abstract

The purpose of this study is to illustrate intrinsic correlations and their temporal evolution between hydro-meteorological elements by building three-element-composed system, including precipitation (P), runoff (R), air temperature (T), evaporation (pan evaporation, E), and sunshine duration (SD) in the Wuding River Basin (WRB) in Loess Plateau, China, and to provide regional experience to correlational research of global hydro-meteorological data. In analysis, detrended partial cross-correlation analysis (DPCCA) and temporal evolution of detrended partial-cross-correlation analysis (TDPCCA) were employed to demonstrate the intrinsic correlation, and detrended cross-correlation analysis (DCCA) coefficient was used as comparative method to serve for performance tests of DPCCA. In addition, a novel way was proposed to estimate the contribution of a variable to the change of correlation between other two variables, namely impact assessment of correlation change (IACC). The analysis results in the WRB indicated that (1) DPCCA can analyze the intrinsic correlations between two hydro-meteorological elements by removing potential influences of the relevant third one in a complex system, providing insights on interaction mechanisms among elements under changing environment; (2) the interaction among P, R, and E was most strong in all three-element-composed systems. In elements, there was an intrinsic and stable correlation between P and R, as well as E and T, not depending on time scales, while there were significant correlations on local time scales between other elements, i.e., P-E, R-E, P-T, P-SD, and E-SD, showing the correlation changed with time-scales; (3) TDPCCA drew and highlighted the intrinsic correlations at different time-scales and its dynamics characteristic between any two elements in the P-R-E system. The results of TDPCCA in the P-R-E system also demonstrate the nonstationary correlation and may give some experience for improving the data quality. When establishing a hydrological model, it is suitable to only use P, R, and E time series with significant intrinsic correlation for calibrating model. The IACC results showed that taking pan evaporation as the representation of climate change (barring P), the impacts of climate change on the non-stationary correlation of P and R was estimated quantitatively, illustrating the contribution of climate to the correlation variation was 30.9%, and that of underlying surface and direct human impact accounted for 69.1%.

Highlights

Complex hydro-meteorological systems contain various interactions among hydro-meteorological elements [1,2]
With the emerging of non-stationary problems, correlation analysis between non-stationary variables has been paid much attention, and scholars worldwide have consecutively put forward the detrended cross-correlation analysis (DCCA) cross-correlation coefficient [16,17], detrended partial cross-correlation analysis (DPCCA) [18], temporal evolution of detrended cross-correlation analysis (TDCCA) correlation coefficient, and temporal evolution of detrended partial-cross-correlation analysis (TDPCCA) [19], which have been applied in the fields of meteorology and hydrology [17,19,20]
It is worth noting that impact assessment of correlation change (IACC)-1 model illustrates the temporal evolution of impact of one factor to the change of investigative correlation on certain time scale, while IACC-2 model demonstrate the average impact of that over the whole time span

Summary

Introduction

Complex hydro-meteorological systems contain various interactions among hydro-meteorological elements [1,2]. Many indexes of correlation have been proposed and applied in the fields of finance, biology, meteorology, and hydrology [10,11,12,13,14], such as commonly Person correlation coefficient [10,11], Kendall’s tau coefficient [12], Spearman’s rho coefficient [13], Gini’s gamma coefficient [14], and so on. Therein, Person correlation coefficient can only reflect the degree of linear correlation between variables, and Kendall’s tau coefficient, Spearman’s rho coefficient, and Gini’s gamma coefficient are able to reflect the nonlinear correlation between variables, but insufficient to describe dependence structure and characteristics [12,13,14,15]. With the emerging of non-stationary problems, correlation analysis between non-stationary variables has been paid much attention, and scholars worldwide have consecutively put forward the detrended cross-correlation analysis (DCCA) cross-correlation coefficient [16,17], detrended partial cross-correlation analysis (DPCCA) [18], temporal evolution of detrended cross-correlation analysis (TDCCA) correlation coefficient, and temporal evolution of detrended partial-cross-correlation analysis (TDPCCA) [19], which have been applied in the fields of meteorology and hydrology [17,19,20]

Objectives

Methods

Results

Discussion

Conclusion