Using variograms to detect and attribute hydrological change

Abstract. There have been many published studies aiming to identify temporal changes in river flow time series, most of which use monotonic trend tests such as the Mann–Kendall test. Although robust to both the distribution of the data and incomplete records, these tests have important limitations and provide no information as to whether a change in variability mirrors a change in magnitude. This study develops a new method for detecting periods of change in a river flow time series, using temporally shifting variograms (TSVs) based on applying variograms to moving windows in a time series and comparing these to the long-term average variogram, which characterises the temporal dependence structure in the river flow time series. Variogram properties in each moving window can also be related to potential meteorological drivers. The method is applied to 91 UK catchments which were chosen to have minimal anthropogenic influences and good quality data between 1980 and 2012 inclusive. Each of the four variogram parameters (range, sill and two measures of semi-variance) characterise different aspects of the river flow regime, and have a different relationship with the precipitation characteristics. Three variogram parameters (the sill and the two measures of semi-variance) are related to variability (either day-to-day or over the time series) and have the largest correlations with indicators describing the magnitude and variability of precipitation. The fourth (the range) is dependent on the relationship between the river flow on successive days and is most correlated with the length of wet and dry periods. Two prominent periods of change were identified: 1995–2001 and 2004–2012. The first period of change is attributed to an increase in the magnitude of rainfall whilst the second period is attributed to an increase in variability of the rainfall. The study demonstrates that variograms have considerable potential for application in the detection and attribution of temporal variability and change in hydrological systems.