Hydrologic mixing models
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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 l.jpg

Hydrologic Mixing Models

Ken Hill

Andrew McFadden


Mixing method l.jpg
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.


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2-Component Mixing Model

  • Mass Balance Equations

    • Qp + Qe = QT

    • QpCp + QeCe = QTCT

    • Qe/QT = fe = (CT-Cp) / (Ce – Cp)


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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


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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


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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


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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


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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


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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


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


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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


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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


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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.


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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


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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.


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

  • Available pool of exchange cations decreases as snowmelt progresses.


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

  • Low Gradient

  • Extensive surficial debris

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


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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


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