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Hydrologic Mixing Models

Hydrologic Mixing Models. Ken Hill Andrew McFadden. Mixing Method. -25 ‰ < snow < -20 ‰ -15 ‰ < groundwater < -18‰ Streamflow should be a mixture of these components. The quantity from each component is predicted by the mixing model. 2-Component Mixing Model. Mass Balance Equations

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Hydrologic Mixing Models

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  1. Hydrologic Mixing Models Ken Hill Andrew McFadden

  2. Mixing Method • -25‰ < snow < -20‰ • -15‰ < groundwater < -18‰ • Streamflow should be a mixture of these components. The quantity from each component is predicted by the mixing model.

  3. 2-Component Mixing Model • Mass Balance Equations • Qp + Qe = QT • QpCp + QeCe = QTCT • Qe/QT = fe = (CT-Cp) / (Ce – Cp)

  4. MIXING MODEL: 3 COMPONENTS Simultaneous Equations Solutions • Two Conservative Tracers • Mass Balance Equations for Water and Tracers Q - Discharge C - Tracer Concentration Subscripts - Components identification Superscripts – Tracer identification

  5. MIXING MODEL: 3 COMPONENTS(Using Discharge Fractions) Simultaneous Equations Solutions • Two Conservative Tracers • Mass Balance Equations for Water and Tracers f - Discharge Fraction C - Tracer Concentration Subscripts - # Components Superscripts - # Tracers

  6. Simultaneous Equations MIXING MODEL: Generalization Using Matrices • One tracer for 2 components and two tracers for 3 components • N tracers for N+1 components? -- Yes • However, solutions would be too difficult for more than 3 components • So, matrix operation is necessary Where Solutions • Note: • Cx-1 is the inverse matrix of Cx • This procedure can be generalized to N tracers for N+1 components

  7. Chemical Tracers Isotopic Tracers Unreactive Tracers Reactive Tracers Event Water Pre-event Water Concentration changes as they react with geologic substrate. Examples: Na+, Ca2+, NO3- Do not react with geologic substrate. Examples: Cl- Examples: Snowmelt, Precipitation Event Example: Water residing in the basin prior to the event Used to delineate flowpaths Used to delineate source waters

  8. Assumptions • Tracers are conservative • Components have significantly different isotopic composition • Isotopic content of each component is temporally constant or its variation is known • Isotopic content of each component is spatially constant • Unmeasured components are not significant

  9. Counterpoint (Burns, 2002) • Stormflow-hydrology separation based on isotopes: the thrill is gone- what’s next? • Mixing models based on assumptions and if not all assumptions are met how valid are the results? • There is a high degree of uncertainty • What if there are more than two components contributing to steam isotope composition? • Results for small forested catchments were confirmed numerous times while catchments in other climate zones are untested • Suggests mixing models just another tool • When coupled with other hydrologic models, mixing models will continue to contribute to hydrology in the future

  10. Determination of hydrologic pathways during snowmelt for alpine/subalpine basins, Rocky Mountain National Park, ColoradoSueker et al., 2000 Water Resources Research.

  11. Overview • Atmospheric deposition of nitrogen and acid pulse from snowmelt. • Alpine systems • Poorly developed soils • Short flowpaths • Steep • Buffered by: • Displaced subsurface water • Reactive pathways

  12. Methods • 6 catchments in RMNP 1994 water year. • Field methods • Hydrograph Separation Models • Unreacted vs. Reacted (tracer = sodium) • Pre-event vs. Event (tracer = δ18O) • Three component mixing model used with both tracers

  13. Results • Unreacted/Event/ Meltwater contributions greatest from May-July. • Boulder Brook has a high reacted/pre-event component • 2-Component mixing model is violated when δ18Ostream > δ18Ope • Rain is not a highly significant contributor to streamflow for most months.

  14. Discussion • Streamflow Mechanisms • 1) Infiltration and displacement of “old” water. • 2) As infiltration capacity is exceeded, Hortonian overland flow occurs. • Correlation Analysis • Steep slopes, unvegetated area, and young debris means more event/unreactive contribution • Basin area is not correlated with flowpaths

  15. Model Assumptions • Constant isotopic composition of event water • Components are not collinear • Constant isotopic composition of reacted/ pre-event/subsurface component.

  16. Concentration-Discharge Relation • Available pool of exchange cations decreases as snowmelt progresses.

  17. Why is Boulder Brook different? • Low Gradient • Extensive surficial debris • Most water is pre-event/reacted/subsurface, even during snowmelt

  18. Conclusion • Overall, although subsurface contributions were likely underestimated the mixing model method was useful in comparing stream sources in multiple basins • All basins studied except for Boulder Brook where proven to be sensitive to acid deposition • These basin’s were shown to be especially sensitive at higher elevations, and during the summer • Old debris contributed to pre-event water and was shown to increase residence time which in turn increased the Na concentrations • Event water was common in steeper sloped basins • At the onset of snowmelt, water in the subsurface is forced into the stream and is replaced by meltwater

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