Power POint SLides to accompany integration assignment.
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
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
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
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