using isotopes to identify source waters: mixing models

Mark Williams, CU-Boulder

Using isotopes to identify source waters: mixing

models

0

10

20

30

40

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

0

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

0

10

20

30

40

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

0

50

100

150

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