Abstract
Abstract. The terrestrial water cycle partitions precipitation between its two ultimate fates: “green water” that is evaporated or transpired back to the atmosphere, and “blue water” that is discharged to stream channels. Measuring this partitioning is difficult, particularly on seasonal timescales. End-member mixing analysis has been widely used to quantify streamflow as a mixture of isotopically distinct sources, but knowing where streamwater comes from is not the same as knowing where precipitation goes, and this latter question is the one we seek to answer. Here we introduce “end-member splitting analysis”, which uses isotopic tracers and water flux measurements to quantify how isotopically distinct inputs (such as summer vs. winter precipitation) are partitioned into different ultimate outputs (such as evapotranspiration and summer vs. winter streamflow). End-member splitting analysis has modest data requirements and can potentially be applied in many different catchment settings. We illustrate this data-driven, model-independent approach with publicly available biweekly isotope time series from Hubbard Brook Watershed 3. A marked seasonal shift in isotopic composition allows us to distinguish rainy-season (April–November) and snowy-season (December–March) precipitation and to trace their respective fates. End-member splitting shows that about one-sixth (18±2 %) of rainy-season precipitation is discharged during the snowy season, but this accounts for over half (60±9 %) of snowy-season streamflow. By contrast, most (55± 13 %) snowy-season precipitation becomes streamflow during the rainy season, where it accounts for 38±9 % of rainy-season streamflow. Our analysis thus shows that significant fractions of each season's streamflow originated as the other season's precipitation, implying significant inter-seasonal water storage within the catchment as both groundwater and snowpack. End-member splitting can also quantify how much of each season's precipitation is eventually evapotranspired. At Watershed 3, we find that only about half (44±8 %) of rainy-season precipitation evapotranspires, but almost all (85±15 %) evapotranspiration originates as rainy-season precipitation, implying that there is relatively little inter-seasonal water storage supplying evapotranspiration. We show how results from this new technique can be combined with young water fractions (calculated from seasonal isotope cycles in precipitation and streamflow) and new water fractions (calculated from correlations between precipitation and streamflow isotope fluctuations) to infer how precipitation is partitioned on multiple timescales. This proof-of-concept study demonstrates that end-member mixing and splitting yield different, but complementary, insights into catchment-scale partitioning of precipitation into blue water and green water. It could thus help in gauging the vulnerability of both water resources and terrestrial ecosystems to changes in seasonal precipitation.
Highlights
End-member mixing analysis has been widely used in isotope hydrograph separation, as well as in other applications that seek to interpret environmental flows as mixtures of chemically or isotopically distinct end-member sources
Whereas end-member mixing has been widely explored in hydrology, the potential for new insights from end-member splitting has been less widely appreciated
Much less of snowy-season precipitation (18 ± 18 %) is eventually evapotranspired, the remainder is split between summer and winter streamflow in nearly the same 2 : 1 ratio (55 ± 13 % and 27 ± 6 %, respectively) as the rainy-season precipitation is partitioned
Summary
End-member mixing analysis has been widely used in isotope hydrograph separation, as well as in other applications that seek to interpret environmental flows as mixtures of chemically or isotopically distinct end-member sources The simplest form of end-member mixing analysis uses a single conservative tracer to estimate the fractions of two sources in a mixture (see Fig. 1) It is derived from the mass balances for the water and tracer, qA→M + qB→M = QM (1). Whereas end-member mixing only requires measurements of the volume-weighted tracer composition in the mixture and all of its potential sources, end-member splitting requires measurements of the water fluxes in the endmembers and mixture(s). Both end-member mixing and endmember splitting analyses should always be accompanied by uncertainty estimates (quantified via, for example, Gaussian error propagation), to avoid over-interpretation of highly uncertain results. Endmember splitting can be generalized straightforwardly to any number of mixtures, even using only one tracer if each mixture combines only two end-members; in the general case, the number of (not-too-correlated) tracers in each mixture must equal at least the number of end-members minus one
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