Chemical Hydrograph Separation

STEP 1 - MIXING DIAGRAMS Generate all plots for all pair-wise combinations of tracers; The simple rule to identify conservative tracers is to see if streamflow samples can be bound by a polygon formed by potential end-members or scatter around a line defined by two end-members; Be aware of outliers and curvature which may indicate chemical reactions!

Assumptions Only 2 components in Streamflow Mixing is complete Tracer signal is distinct for each component No evaporation or exchange with the atmosphere Concentrations of the tracer are constant over time or changes are known

MIXING MODEL: 3 COMPONENTS(Using Specific Discharge) Simultaneous Equations Solutions Two Conservative Tracers Mass Balance Equations for Water and Tracers Q - Discharge C - Tracer Concentration Subscripts - # Components Superscripts - # Tracers

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

MIXING MODEL: Generalization Using Matrices 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

Cook and Herczeg, 2000, Environmental Tracers in Subsurface Hydrology

Stable isotopes are efficient tools for identifying the history of water… Microsoft® ClipArt d13C = -27‰ NO3 d15N = 20‰