Hydrologic Mixing Models Ken Hill Andrew McFadden

Mixing Method -25 ‰ < snow < -20 ‰ -25 ‰ < snow < -20 ‰ -15 ‰ < groundwater < -18‰ -15 ‰ < groundwater < -18‰ Streamflow should be a mixture of these components. The quantity from each component is predicted by the mixing model. 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 –Q p + Q e = Q T –Q p C p + Q e C e = Q T C T –Q e /Q T = f e = (C T -C p ) / (C e – C p )

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

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

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 Simultaneous Equations Where Solutions Note: C x -1 is the inverse matrix of C x This procedure can be generalized to N tracers for N+1 components

Chemical Tracers Reactive Tracers Unreactive Tracers Do not react with geologic substrate. Examples: Cl - Concentration changes as they react with geologic substrate. Examples: Na+, Ca 2+, NO 3 - Used to delineate flowpaths Event Water Pre-event Water Used to delineate source waters Examples: Snowmelt, Precipitation Event Example: Water residing in the basin prior to the event Isotopic Tracers

Assumptions 1. Tracers are conservative 2. Components have significantly different isotopic composition 3. Isotopic content of each component is temporally constant or its variation is known 4. Isotopic content of each component is spatially constant 5. Unmeasured components are not significant

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

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

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

Methods 6 catchments in RMNP 1994 water year. 6 catchments in RMNP 1994 water year. Field methods Field methods Hydrograph Separation Models Hydrograph Separation Models Unreacted vs. Reacted (tracer = sodium) Unreacted vs. Reacted (tracer = sodium) Pre-event vs. Event (tracer = δ 18 O) Pre-event vs. Event (tracer = δ 18 O) Three component mixing model used with both tracers Three component mixing model used with both tracers

Results Unreacted/Event/ Meltwater contributions greatest from May-July. Unreacted/Event/ Meltwater contributions greatest from May-July. Boulder Brook has a high reacted/pre-event component Boulder Brook has a high reacted/pre-event component 2-Component mixing model is violated when δ 18 O stream > δ 18 O pe 2-Component mixing model is violated when δ 18 O stream > δ 18 O pe Rain is not a highly significant contributor to streamflow for most months. Rain is not a highly significant contributor to streamflow for most months.

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

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

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

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

Conclusion Overall, although subsurface contributions were likely underestimated the mixing model method was useful in comparing stream sources in multiple basins 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 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 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 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 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 At the onset of snowmelt, water in the subsurface is forced into the stream and is replaced by meltwater