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.

PPT slides useful for introducing assignment to students.

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Power POint SLides to accompany integration assignment. Presentation Transcript

  • 1. 1Chemical HydrographSeparation
  • 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. 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. 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. 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. 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. Cook and Herczeg, 2000, Environmental Tracers in Subsurface Hydrology
  • 8. Stable isotopes are efficient tools for identifyingthe history of water…NO3δ15N = 20‰δ13C = -27‰Microsoft® ClipArt