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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

Ken Hill

• -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.

• Mass Balance Equations

• Qp + Qe = QT

• QpCp + QeCe = QTCT

• Qe/QT = fe = (CT-Cp) / (Ce – Cp)

Simultaneous Equations

Solutions

• Two Conservative Tracers

• Mass Balance Equations for Water and Tracers

Q - Discharge

C - Tracer Concentration

Subscripts - Components identification

Superscripts – Tracer identification

Simultaneous Equations

Solutions

• Two Conservative Tracers

• Mass Balance Equations for Water and Tracers

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

Where

Solutions

• Note:

• Cx-1 is the inverse matrix of Cx

• This procedure can be generalized to N tracers for N+1 components

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

• 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

• 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

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

Overview alpine/subalpine basins, Rocky Mountain National Park, Colorado

• Atmospheric deposition of nitrogen and acid pulse from snowmelt.

• Alpine systems

• Poorly developed soils

• Short flowpaths

• Steep

• Buffered by:

• Displaced subsurface water

• Reactive pathways

Methods alpine/subalpine basins, Rocky Mountain National Park, Colorado

• 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

Results alpine/subalpine basins, Rocky Mountain National Park, Colorado

• 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.

Discussion alpine/subalpine basins, Rocky Mountain National Park, Colorado

• 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

Model Assumptions alpine/subalpine basins, Rocky Mountain National Park, Colorado

• Constant isotopic composition of event water

• Components are not collinear

• Constant isotopic composition of reacted/ pre-event/subsurface component.

Concentration-Discharge Relation alpine/subalpine basins, Rocky Mountain National Park, Colorado

• Available pool of exchange cations decreases as snowmelt progresses.

Why is Boulder Brook different? alpine/subalpine basins, Rocky Mountain National Park, Colorado

• Extensive surficial debris

• Most water is pre-event/reacted/subsurface, even during snowmelt

Conclusion alpine/subalpine basins, Rocky Mountain National Park, Colorado

• 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