Applications: Modelling trends in groundwater levels by segmented regression with constraints

Abstract

This paper provides a statistically unified method for modelling trends in groundwater levels for a national project that aims to predict areas at risk from salinity in 2020. It was necessary to characterize the trends in groundwater levels in thousands of boreholes that have been monitored by Agriculture Western Australia throughout the south-west of Western Australia over the last 10 years. The approach investigated in the present paper uses segmented regression with constraints when the number of change points is unknown. For each segment defined by change points, the trend can be described by a linear trend possibly superimposed on a periodic response. Four different types of change point are defined by constraints on the model parameters to cope with different patterns of change in groundwater levels. For a set of candidate change points provided by the user, a modified Akaike information criterion is used for model selection. Model parameters can be estimated by multiple linear regression. Some typical examples are presented to demonstrate the performance of the approach.

Water quality trend and change-point analyses using integration of locally weighted polynomial regression and segmented regression

“…Segmented regression with segments separated by breakpoints (i.e., change-points) is useful for quantifying abrupt changes in water quality over time (Shao andCampbell 2002, Kazemnejad et al 2014). The least squares method is applied separately to each segment; each regression line is optimized to minimize the sum of squares of the differences (SSD).…”

“…SegReg has also been widely used in trend and change-point analyses in many research fields (Mathews and Hamilton 2005;Wu and Chang 2012;Kazemnejad et al 2014), including hydrology (Shao and Campbell 2002). For water quality trend and change-point analyses, graphical methodsare limited as they do not produce the regression functions necessary to determine significance levels and change-point detection, while SegReg is limited by statistically compromised data issues common in water quality time series records.…”

“…An important advantage of the integrated LWPR-SegReg approach is the ability of LWPR to extract long-term trend information from water quality time series (Cleveland 1979;Bodo 1989;Stow et al 2015) and subsequently providing an appropriate dataset for SegReg analysis. Another notable advantage is the ability of SegReg to quantitatively detect change-points and trends with statistical rigor (Shao and Campbell 2002;Kazemnejad et al 2014). Furthermore, this approach is easily performed in R packages, and all results can be graphed to provide an effective visualization of the time series dynamics.…”

“…Nowadays, segmented regression (SegReg) has been widely used in trend and change-point analyses in research fields including medicine (Kazemnejad et al 2014), hydrology (Shao and Campbell 2002), economics (Wu and Chang 2012), society (Mathews and Hamilton 2005), etc. In comparison with graphical methods, major advantages of SegReg are that the regression function is defined by a mathematical formula to describe the relationship, the significance levels of the trend can be determined statistically (Kazemnejad et al 2014), and the change-point can be quantitatively defined (Taljaard et al 2014).…”

Separation of the impacts of climate change and human activity on runoff variations

“…Recognition of abrupt-change points has attracted considerable attention globally and a number of methods can be applied to determine the abrupt-change points of a time series (Yamamoto and Sanga 1986, Wei 1999, Hubert 2000, Shao and Campbell 2002, Kehagias and Fortin 2006, Zheng et al 2007, Gedikli et al 2008, Gedikli et al 2010a, 2010b, Abrate et al 2013.…”