Alternative methods to determine the δ2H-δ18O relationship: An application to different water types

Abstract

The Ordinary Least Squares (OLS) regression is the most common method for fitting the δ2H-δ18O relationship. Recently, various studies compared the OLS regression with the Reduced Major Axis (RMA) and Major Axis (MA) regression for precipitation data. However, no studies have investigated so far the differences among the OLS, RMA, and MA regressions for water types prone to evaporation, mixing, and redistribution processes. In this work, we quantified the differences in terms of slopes and intercepts computed by the OLS, RMA, and MA methods for rainfall, snow and ice, stream, spring, groundwater, and soil water, and investigated whether the magnitude of such differences is significant and dependent on the water type, the datasets statistics, geographical or climatic characteristics of the study catchments. Our results show that the differences between the regression methods were largest for the isotopic data of some springs and some stream waters. Conversely, for rainfall, snow, ice, and melt waters datasets, all the differences were small and, particularly, smaller than their standard deviation. Slopes and intercepts computed using the different regression methods were statistically different for stream water (up to 70.4%, n = 54), followed by groundwater, springs, and soil water. The results of this study indicate that a thorough analysis of the δ2H-δ18O relationship in isotope hydrology studies is recommended, as well as considering the measurement errors for both δ2H and δ18O, and the presence of outliers. In case of small measurement errors and no significant differences between the slopes computed through the three methods, we suggest the application of the widely used OLS regression. Conversely, if the computed slopes are significantly different, we recommend investigating the possible reasons for such discrepancies and prefer the RMA over the MA approach, as the latter tends to be more sensitive to data with high leverage (i.e., data points with extreme δ18O values).