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|Title: ||Alternative least squares methods for determining the meteoric water line, demonstrated using GNIP data|
|Authors: ||Crawford, J|
|Issue Date: ||1-Nov-2014|
|Citation: ||Crawford, J., Hughes, C. E., & Lykoudis, S. (2014). Alternative least squares methods for determining the meteoric water line, demonstrated using GNIP data. Journal of Hydrology, 519, 2331-2340. doi: http://dx.doi.org/10.1016/j.jhydrol.2014.10.033|
|Abstract: ||The relationship between δ2H and δ18O in precipitation at a site, known as the local meteoric water line (LMWL), is normally defined using an ordinary least squares regression (OLSR). However, it has been argued that this form of minimisation is more appropriate when a predictive model is being developed (and there are no measurement errors associated with the independent variable) and that orthogonal regression, also known as major axis regression (MA), or reduced major axis regression (RMA) may be better suited when a relationship is being sought between two variables which are related by underlying physical processes.
The slope of the LMWLs for the GNIP data is examined using the three linear regressions, and the corresponding precipitation weighted regressions. The MA and RMA regressions generally produced larger slopes, with the largest differences for oceanic islands and coastal sites. The difference between the various methods was the least for continental sites. In all considered cases, both for the standard and precipitation weighted regressions, the slope produced by RMA was in between those determined by OLSR and MA, with OLSR producing the smaller slope. Further, the results of both RMA and precipitation weighted RMA were less sensitive to the removal of outliers and values with high leverage statistic.
The results indicate that when a good linear relationship exists between δ2H and δ18O, all considered regressions result in a close fit. When the values are distributed within circles or ellipses on the δ18O–δ2H bivariate plot, as would appear in coastal and oceanic sites from first stage rainout, care needs to be taken as to which regression is utilised. However, in some of these cases, it appears the precipitation weighted MA (and in some cases MA) produces large slopes. In these cases the average Root Mean Sum of Squared Error (rmSSEav) value of the fit can be used as a guide of the suitability of the MA and PWMA for each site. Where the slope of the PWRMA was significantly different to the slope of the OLSR regression (22% of sites; dominated by coastal, island and Mediterranean locations), we believe PWRMA is more suitable.© 2014 Elsevier B.V.|
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