1Chemical HydrographSeparation
2STEP 1 -MIXINGDIAGRAMS•Generate all plots for all pair-wise combinations of tracers;• The simple rule to identify conserv...
3Assumptions• Only 2 components in Streamflow• Mixing is complete• Tracer signal is distinct for eachcomponent• No evapora...
4MIXINGMODEL: 3COMPONENTS(UsingSpecificDischarge)tt QCQCQCQC 2323222121 =++• TwoConservativeTracers• Mass BalanceEquations...
5MIXINGMODEL: 3COMPONENTS(UsingDischargeFractions)• TwoConservativeTracers• Mass BalanceEquations forWater and1321 =++ fff...
6MIXING MODEL:GeneralizationUsing Matrices• One tracer for 2 componentsand two tracers for 3components• N tracers for N+1 ...
Cook and Herczeg, 2000, Environmental Tracers in Subsurface Hydrology
Stable isotopes are efficient tools for identifyingthe history of water…NO3δ15N = 20‰δ13C = -27‰Microsoft® ClipArt
Power POint SLides to accompany integration assignment.
Power POint SLides to accompany integration assignment.
Power POint SLides to accompany integration assignment.
Power POint SLides to accompany integration assignment.
Power POint SLides to accompany integration assignment.
Power POint SLides to accompany integration assignment.
Power POint SLides to accompany integration assignment.
Power POint SLides to accompany integration assignment.
Power POint SLides to accompany integration assignment.
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Power POint SLides to accompany integration assignment.

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PPT slides useful for introducing assignment to students.

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Power POint SLides to accompany integration assignment.

  1. 1. 1Chemical HydrographSeparation
  2. 2. 2STEP 1 -MIXINGDIAGRAMS•Generate all plots for all pair-wise combinations of tracers;• The simple rule to identify conservative tracers is to see if streamflow samplescan be bound by a polygon formed by potential end-members or scatter around aline defined by two end-members;• Be aware of outliers and curvature which may indicate chemical reactions!03060901201501800 20 40 60 80 100Tracer 1Tracer2StreamflowEnd-member 1End-member 2End-member 3
  3. 3. 3Assumptions• Only 2 components in Streamflow• Mixing is complete• Tracer signal is distinct for eachcomponent• No evaporation or exchange with theatmosphere• Concentrations of the tracer are constantover time or changes are known
  4. 4. 4MIXINGMODEL: 3COMPONENTS(UsingSpecificDischarge)tt QCQCQCQC 2323222121 =++• TwoConservativeTracers• Mass BalanceEquations forWater andtQQQQ =++ 321tt QCQCQCQC 1313212111 =++tttQCCCCCCCCCCCCCCCCQ))(())(())(())((2321131223221311232131223221311−−−−−−−−−−=11312131113121312 QCCCCQCCCCQ tt−−−−−=213 QQQQ t −−=Simultaneous EquationsSolutionsQ - DischargeC - Tracer ConcentrationSubscripts - # ComponentsSuperscripts - # Tracers
  5. 5. 5MIXINGMODEL: 3COMPONENTS(UsingDischargeFractions)• TwoConservativeTracers• Mass BalanceEquations forWater and1321 =++ fff1313212111 tCfCfCfC =++2323222121 tCfCfCfC =++))(())(())(())((2321131223221311232131223221311CCCCCCCCCCCCCCCCf tt−−−−−−−−−−=11312131113121312 fCCCCCCCCf t−−−−−=213 1 fff −−=Simultaneous EquationsSolutionsf - Discharge FractionC - Tracer ConcentrationSubscripts - # ComponentsSuperscripts - # Tracers
  6. 6. 6MIXING MODEL:GeneralizationUsing Matrices• One tracer for 2 componentsand two tracers for 3components• N tracers for N+1 components?-- Yes• However, solutions would betoo difficult for more than 3components• So, matrix operation isnecessary1321 =++ fff1313212111 tCfCfCfC =++2323222121 tCfCfCfC =++Simultaneous EquationsWheretxx CfC =txx CCf 1−=232221131211111CCCCCCCx =321ffffx =211tttCCC =SolutionsNote:• Cx-1is the inverse matrix of Cx• This procedure can be generalized toN tracers for N+1 components
  7. 7. Cook and Herczeg, 2000, Environmental Tracers in Subsurface Hydrology
  8. 8. Stable isotopes are efficient tools for identifyingthe history of water…NO3δ15N = 20‰δ13C = -27‰Microsoft® ClipArt

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