This document discusses chemical hydrograph separation techniques to identify sources of water using conservative tracers. It provides the following key points: 1. Mixing diagrams are used to identify conservative tracers by seeing if streamflow samples fall along a line between two end-members. Curvature may indicate chemical reactions. 2. Mixing models assume two components, complete mixing, distinct tracer signals for each component, and no other processes altering tracer concentrations. 3. Mixing models for three components use mass balance equations to solve for discharge and tracer concentrations of each component simultaneously. This can be generalized to more components using matrix operations.

1. 1
Chemical Hydrograph
Separation

2. 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!
0
30
60
90
120
150
180
0 20 40 60 80 100
Tracer 1
Tracer2
Streamflow
End-member 1
End-member 2
End-member 3

3. 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. 4
MIXING
MODEL: 3
COMPONENT
S(Using
Specific
Discharge)
tt QCQCQCQC 2
3
2
32
2
21
2
1 =++
• Two
Conservative
Tracers
• Mass Balance
Equations for
Water and
tQQQQ =++ 321
tt QCQCQCQC 1
3
1
32
1
21
1
1 =++
t
tt
Q
CCCCCCCC
CCCCCCCC
Q
))(())((
))(())((
2
3
2
1
1
3
1
2
2
3
2
2
1
3
1
1
2
3
21
3
1
2
2
3
2
2
1
3
1
1
−−−−−
−−−−−
=
11
3
1
2
1
3
1
1
1
3
1
2
1
3
1
2 Q
CC
CC
Q
CC
CC
Q t
t
−
−
−
−
−
=
213 QQQQ t −−=
Simultaneous Equations
Solutions
Q - Discharge
C - Tracer Concentration
Subscripts - # Components
Superscripts - # Tracers

5. 5
MIXING
MODEL: 3
COMPONENT
S(Using
Discharge
Fractions)
• Two
Conservative
Tracers
• Mass Balance
Equations for
Water and
1321 =++ fff
1
3
1
32
1
21
1
1 tCfCfCfC =++
2
3
2
32
2
21
2
1 tCfCfCfC =++
))(())((
))(())((
2
3
2
1
1
3
1
2
2
3
2
2
1
3
1
1
2
3
21
3
1
2
2
3
2
2
1
3
1
1
CCCCCCCC
CCCCCCCC
f tt
−−−−−
−−−−−
=
11
3
1
2
1
3
1
1
1
3
1
2
1
3
1
2 f
CC
CC
CC
CC
f t
−
−
−
−
−
=
213 1 fff −−=
Simultaneous Equations
Solutions
f - Discharge Fraction
C - Tracer Concentration
Subscripts - # Components
Superscripts - # Tracers

6. 6
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
1321 =++ fff
1
3
1
32
1
21
1
1 tCfCfCfC =++
2
3
2
32
2
21
2
1 tCfCfCfC =++
Simultaneous Equations
Where
txx CfC =
txx CCf 1−
=
2
3
2
2
2
1
1
3
1
2
1
1
111
CCC
CCCCx =
3
2
1
f
f
f
fx =
2
1
1
t
tt
C
CC =
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…
NO3
δ15
N = 20‰
δ13
C = -27‰
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