1. Chemical Hydrograph Separation

2. 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!

3. 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

4. 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

5. 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

6. 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

8. Cook and Herczeg, 2000, Environmental Tracers in Subsurface Hydrology

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