Comparison between total least squares and ordinary least squares for linear relationship of stable water isotopes

Abstract

A linear relationship between two stable water isotopes, oxygen and hydrogen, has been used to understand the water cycle as a basic tool. A slope and intercept from the linear relationship indicates what kind of physical processes occur during movement of water. Traditionally, ordinary least squares (OLS) method has been utilized for the linear relationship, but total least squares (TLS) method provides more accurate slope and intercept theoretically because isotopic compositions of both oxygen and hydrogen have uncertainties. In this work, OLS and TLS were compared with isotopic compositions of snow and snowmelt collected from the King Sejong Station, Antarctica and isotopic compositions of water vapor observed by Lee et al. (2013) in the western part of Korea. The slopes from the linear relationship of isotopic compositions of snow and snowmelt at the King Sejong Station were estimated to be 7.00 (OLS) and 7.16(TLS) and the slopes of stable water vapor isotopes were 7.75(OLS) and 7.87(TLS). There was a melting process in the snow near the King Sejong Station and the water vapor was directly transported from the ocean to the study area based on the slope calculations. There is no significant difference in two slopes to interpret the physical processes. However, it is necessary to evaluate the slope differences from the two methods for studies for example, groundwater recharge processes, using the absolute slope values. © 2017 Korean Society of Economic and Environmental Geology. All rights reserved.