Moving correlation coefficient-based method for jump points detection in hydroclimate time series

Abstract

The jump points detection is critical to the understanding of hydrologic variability, especially in investigating the anthropogenic effects. Conventional methods are mainly statistical and cannot directly reflect the jump change degrees. This article proposes a moving correlation coefficient-based detection (MCCD) method for the detection of jump points (JPs) in hydroclimate data. The correlation coefficient (CC) between the potential jump component and the original data is calculated, and the CC series is realized by moving from the starting to the ending points of the original time series. Bigger CC value reflects higher jump degree; the position with the biggest absolute CC value is the JP that is the most expected. Its significance is evaluated by comparing its value with the CC threshold value at the relevant significance level. Monte-Carlo experimental results verify the MCCD method’s higher efficiency compared with four commonly used conventional methods. It is especially noteworthy that the results indicate its stable efficiency, even when encountering the influences of some unfavorable factors. By applying the MCCD method to the Lancang River Basin, the JP of runoff in 2004 is detected at the Yunjinghong station in the lower reach. It is mainly attributed to the construction and operation of some major water hydropower projects, while the stable variations of areal precipitation and actual evapotranspiration, as well as the stable land-cover conditions, contribute little to the abrupt decrease in runoff. The MCCD method can be an effective alternative for the detection of JPs in hydroclimate data.

Appendices

Appendix 1: Groups of parameters used in statistical experiments

Group	$n$	$EX$	$Cv$	$Cs$	$q$	$a$
1	50, 100, 150, 200, 250, 300, 350, 400, 450, 500	500	0.5	2.0	300	0.5
2	200	100, 300, 500, 700, 900	0.5	2.0	300	0.5
3	200	500	0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9	2.0	300	0.5
4	200	500	0.5	1.0, 1.5, 2.0, 2.5, 3.0	300	0.5
5	200	500	0.5	2.0	100, 150, 200, 250, 300, 350, 400, 450, 500	0.5
6	200	500	0.5	2.0	300	0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9

Appendix 2: Mathematical expressions of the four jump point detection methods used in the statistical experiments

Method	Category	Mathematical expression	Core statistics	Indicator for jump point
Pettitt	Non-parametric	$U_{t,N} = U_{t - 1,N} + \sum\limits_{i = 1}^{N} {\text{sgn} (x_{t} - x_{i} )} ,\quad t = 2,3, \ldots ,N$ $K_{t,N} = \hbox{max} \left| {U_{t,N} } \right|,\quad (1 \le t \le N)$	$K_{t,N}$	$p \le 0.05$
M–K	Non-parametric	$UF_{k} = \frac{{s_{k} - \overline{{s_{k} }} }}{{\sqrt {\text{var} (s_{k} )} }},\quad s_{k} = \sum\limits_{i = 1}^{k} {\sum\limits_{j}^{i - 1} {a_{i,j} (k = 2,3, \ldots ,n),\quad a_{i,j} = \left\{ {\begin{array}{*{20}l} {1,} \hfill & {x_{i} > x_{j} } \hfill \\ {0,} \hfill & {x_{i} \le x_{j} } \hfill \\ \end{array} } \right.} }$	$s_{k}$	$\left\{ {\begin{array}{*{20}c} {\left| {UB_{k} } \right| < U_{\alpha /2} } \\ {\left| {UF_{k} } \right| < U_{\alpha /2} } \\ {UB_{k} = UF_{k} } \\ \end{array} } \right.$
B–F	Parametric	$F = \sum\limits_{i = 1}^{m} {n_{i} (\overline{{x_{1} }} - \bar{x})^{2} } /\sum\limits_{i = 1}^{m} {(1 - n_{i} /N)S_{i}^{2} }$	$F$	$F > F_{\alpha }$
Bayesian	Parametric	$P(H|E) = \frac{P(E|H)P(H)}{P(E)}$	–	Max posterior probability