Stable isotope ratios of H and O are widely used to identify the source of water, e.g., in aquifers, river runoff, soils, plant xylem, and plant-based beverages. In situations where the sampled water is partially evaporated, its isotope values will have evolved along an evaporation line (EL) in δ2H/δ18O space, and back-correction along the EL to its intersection with a meteoric water line (MWL) has been used to estimate the source water's isotope ratios. Here, we review the theory underlying isotopic estimation of source water for evaporated samples (iSWE). We note potential for bias from a commonly used regression-based approach for EL slope estimation and suggest that a model-based approach may be preferable if assumptions of the regression approach are not valid. We then introduce a mathematical framework that eliminates the need to explicitly estimate the EL-MWL intersection, simplifying iSWE analysis and facilitating more rigorous uncertainty estimation. We apply this approach to data from the US EPA's 2007 National Lakes Assessment. We find that data for most lakes are consistent with a water source similar to annual runoff, estimated from monthly precipitation and evaporation within the lake basin. Strong evidence for both summer- and winter-biased sources exists, however, with winter bias pervasive in most snow-prone regions. The new analytical framework should improve the rigor of iSWE in ecohydrology and related sciences, and our initial results from US lakes suggest that previous interpretations of lakes as unbiased isotope integrators may only be valid in certain climate regimes.
Keywords: Bayesian methods; Ecohydrology; Evaporation; Stable isotopes; Water source.