Using isotopes to identify source waters: mixing models
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Transcript of Using isotopes to identify source waters: mixing models
Mark Williams, CU-Boulder
Using isotopes to identify source waters: mixing
models
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135 165 195 225 255 285
Calendar Day (1996)
Q (10
3 m3 day
-1)
New Water
Old Water
MWL (18O-D) graph can tell us:
Sources of groundwater recharge: Average annual precipitation Summer rain Winter rain/snow Very old water, eg “Pleistocene age”
Recharge flowpaths Piston flow Exponential flow
Problem: Regional groundwater vs South Platte river water as recharge to
wells
New well users near the South Platte River do not have water rights to Colorado River water
Sued because downstream water users with senior water rights say that the wells are pumping their water
What can the state engineer do?What can a consultant do for their client (on
either side of the debate)Isotopes to the rescue!
2-component mixing models
We can go from these simple examples to a general equation that works for almost all systems
We assume our “sample” (well-water, streamflow, etc) is a mixture of two sources
We can “unmix” the sample to calculate the contribution of each source
Either as a mass of water or percentage
2 Component hydrograph separation
Source 2(Groundwater)
Source 1(River water)
Well
? %
? %
Tracer = 18O
Groundwater
River water
Mixing line that connects the two end-members:a) sample must plot between the two end-membersb) sample must plot on or near the mixing line.
Well 1
Well 2X
MIXING MODEL: 2
COMPONENTS
• One Conservative Tracer
• Mass Balance Equations for Water and Tracer
Groundwater
River water
Let’s put in some actual tracer concentrations.
Well -20‰
-15‰
-10‰
Calculate the fraction contribution of groundwater and river water to our well
Groundwater (g); River water (r), Well (w)Percent river water contribution to the well is:
Cw – Cg/ Cr – Cg
Sampling only for the tracer concentration (c) allows us to calculate the fraction contribution of each end-member to our mixture
We need only three samples! No water flow measurements
2-component mixing model: calculation
Cw – CgCr – Cg
= percent contribution of river water
-15 – (-20) = +5-10 – (-20) = +10
= 50%
2-component mixing model: assumptions
Only 2 components in mixture (groundwater well in this example)
Mixing is completeTracer signal is distinct for each componentNo evaporation or exchange with the
atmosphereConcentrations of the tracer are constant
over time or changes are known
Case Study:Hydrograph separation
in a seasonally snow-covered catchment
Liu et al., 2004
Green Lake 4 catchment, Colorado Rockies
2 Component hydrograph separation
“Old” Water(Groundwater)
“New” Water(Snowmelt)
Streamflow
? %
? %
Tracer = 18O
Temporal Hydrograph Separation
Solve two simultaneous mass-balance equations for Qold and Qnew
1. Qstream = Qold + Qnew
2. CstreamQstream =ColdQold+CnewQnew
Yields the proportion of “old” or “new” water for each time step in our hydrograph for which we have tracer values
GL4 Dataset
-25
-20
-15
-10
-5
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120 140 160 180 200 220 240 260 280 300 320 340 360
Calendar Day
Delta
18O (%o)
Soil Water
Stream Water
Snowmelt
Event formula (D10-B10)/(D10-C10)
Pre-event formula (B10-C10)/(D10-C10)
Day Stream Event Preevent127 -15.89 -21.19 -15.02144 -17.58 -21.19 -15.02151 -17.96 -21.19 -15.02158 -17.49 -21.19 -15.02165 -17.47 -21.19 -15.02172 -17.19 -21.19 -15.02179 -17.23 -21.19 -15.02186 -17.31 -21.19 -15.02193 -17.7 -21.19 -15.02200 -17.67 -21.19 -15.02207 -17.55 -21.19 -15.02214 -17.33 -21.19 -15.02221 -17.28 -21.19 -15.02228 -16.96 -21.19 -15.02235 -16.76 -21.19 -15.02242 -16.53 -21.19 -15.02254 -16.17 -21.19 -15.02291 -15.02 -21.19 -15.02
Fe Fp0.141005 0.8589950.414911 0.5850890.476499 0.5235010.400324 0.5996760.397083 0.6029170.351702 0.6482980.358185 0.6418150.371151 0.6288490.43436 0.56564
0.429498 0.5705020.410049 0.5899510.374392 0.6256080.366288 0.6337120.314425 0.6855750.28201 0.71799
0.244733 0.7552670.186386 0.813614
Data Hydrographfractions
Green Lake 4 hydrograph separation
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135 155 175 195 215 235 255 275 295
Calendar Day
Discharge (1000m
3 )
Event
Preevent
Life is often complicated: 18O not distinct
(a) Martinelli
-25
-20
-15
-10
-5
100 150 200 250 300
18O (‰)
Stream Flow
Snowmelt
Soil Water
(b) Martinelli
0
10
20
30
40
50
125 155 185 215 245 275
Calendar Day (1996)
Q (10
2 m3 day
-1)
Fractionation in Percolating Meltwater
‰
‰
Difference between maximum 18O values and Minimum 18O values about 4 ‰
Snow surface
Ground
VARIATION OF 18O IN SNOWMELT
-22
-20
-18
-16
(‰)O
OriginalDate-StretchedbyMonteCarlo
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100 125 150 175 200 225 250 275 300
Calendar Day (1996)
Snowmelt (mm)
• 18O gets enriched by 4%o in snowmelt from beginning to the end of snowmelt at a lysimeter;
• Snowmelt regime controls temporal variation of 18O in snowmelt due to isotopic fractionation b/w snow and ice;
• Given f is total fraction of snow that have melted in a snowpack, 18O values are highly correlated with f (R2 = 0.9, n = 15, p < 0.001);
• Snowmelt regime is different at a point from a real catchment;
• So, we developed a Monte Carlo procedure to stretch the dates of 18O in snowmelt measured at a point to a catchment scale using the streamflow 18O values.
Summary/Review
Isotopes can quantify the contribution of different source waters to wells, etc.
2-component separation assumes that the sample lies on a line between 2 end-members
Assumptions in hydrograph separations Not always met
Can extend to 3 or more end-membersSimple diagnostic tool that should be
consider as one of your first field measurements