Table 2 Cointegration relationships between the time series of decomposed approximate coefficients for four flood indices and five forcing variables from 950 to 2000 CE

From: Anthropogenic transition in flood regimes: insights from a millennium of the Yangtze River records

Time series (Y)

Cointegration relations with forcing variables (regression function)

R2

Standardized coefficients for variables in regression

Global mean temperature (T)

Precipitation regime (P)

Population (Po)

Forest cover (Fc)

Polder area (Pa)

Annual flood sum

Y = 2.834T−0.025 P + 1.273*10−8Po + 0.009Fc +9.247*10−6Pa−39.554

0.771 (***)

0.273 (***)

−0.026

0.771 (***)

0.089

0.109 (*)

Annual flooded basin

Y = 5.142T−0.040 P + 2.450*10−8Po + 0.046Fc +2.250*10−5Pa−73.723

0.778 (***)

0.296 (***)

−0.026

0.886 (***)

0.288 (***)

0.158 (***)

Overall flood intensity

Y = 0.503 T + 0.003 P + 2.339*10−10Po−0.020Fc −2.256*10−6Pa–5.573

0.719 (***)

0.208 (***)

0.012

0.061

−0.891 (***)

−0.114 (*)

100-year flood density

Y = 35.370T−0.224P−1.739*10−9Po−1.391Fc−391.352

0.839 (***)

0.246 (***)

−0.017

−0.008

−1.009 (***)

−0.123 (**)

  1. The Johansen cointegration test confirmed the presence of multicointegration at p = 0.05 level, yielding relationships with high correlation coefficients (R2 > 0.71). The standardized coefficients in the regression indicate the contributions of the forcing variables to the flood series, with higher absolute values representing greater contributions. The results demonstrate that anthropogenic factors (population growth, changes in forest cover, and polder expansion) have had a more significant impact on flood trends than climatic factors (temperature and precipitation).
  2. (***), (**), and (*) denote the test significance at the level of p < 0.001, <0.01, and <0.05, respectively.
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