Source waters, flowpaths, and solute flux in

mountain catchments

Mark Williams

Watershed Hydrology

Mountain-BlockMountain-BlockRecharge (MBR)Recharge (MBR)

Stream InfiltrationStream Infiltration

Mountain-Front Recharge

(MFR)

+

SNOWMELT

HYDROLOGIC UNKNOWNS Flowpaths Residence time Circulation depth Reservoir sizes Groundwater fluxes Fractured rock environment increases

difficulty of understanding mountain plumbing

Add snowmeltrunoff

Permafrost

APPLICATION IN GREEN LAKES VALLEY: LTER RESEARCH SITE

Sample Collection• Stream water - weekly grab samples• Snowmelt - snow lysimeter• Soil water - zero tension lysimeter• Talus water – biweekly to monthly

Sample Analysis• Delta 18O and major solutes

Green Lake 4

Source Waters

Mixing Models in Catchment Hydrology

MIXING MODEL: 2

COMPONENTS

• One Conservative Tracer

• Mass Balance Equations for Water and Tracer

ASSUMPTIONS FOR MIXING MODELASSUMPTIONS FOR MIXING MODEL

• Tracers are conservative (no chemical reactions);• All components have significantly different

concentrations for at least one tracer; • Tracer concentrations in all components are

temporally constant or their variations are known;• Tracer concentrations in all components are

spatially constant or treated as different components;

• Unmeasured components have same tracer concentrations or don’t contribute significantly.

(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 (

102 m

3 day

-1)

1818O IN SNOW AND O IN SNOW AND STREAMFLOWSTREAMFLOW

• 18O fractionation of 4%o in snowmelt;

• Cannot use 18O values measured at snow lysimeter directly to the catchment.

•Failed assumption

Fractionation in SnowpackFractionation in Snowpack

‰

‰

Difference between maximum 18O values and Minimum 18O values about 4 ‰

Snow surface

Ground

Isotopic FractionationIsotopic Fractionation

• Fractionation occurs as melt from surface percolates towards bottom of snowpack

• Isotopic exchange between ice and percolating liquid water

• 18Osolid > 18Oliquid > 18Ovapour

• Molecules of surface meltwater are not the same as the ones at the base of the snowpack

ACCOUNTING FOR ACCOUNTING FOR 1818O IN MELTWATERO IN MELTWATER

-22

-20

-18

-16

18 O

(‰

)

Original

Date-Stretched by Monte Carlo

0

50

100

150

100 125 150 175 200 225 250 275 300

Calendar Day (1996)

Snow

mel

t (m

m)

18O values are highly correlated with amount of melt (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.

NEW WATER FROM VARIOUS MODELSNEW WATER FROM VARIOUS MODELS

(a) Martinelli

-500-400-300-200-100

0100200300400

M1 M2 M3 M4

Fra

ctio

ns

(%) (a) Green Lake 4

01020304050607080

M1 M2 M3 M4

Fra

ctio

ns

(%)

M1 - Original time-series of snowpack 18O

M2 - Date-stretched time-series of snowpack 18O

M3 - Original time-series of snowmelt lysimeter 18O

M4 - Date-stretched time-series of snowmelt lysimeter 18O

NEW WATER AND OLD WATEROld Water = 64%

0

10

20

30

40

135 165 195 225 255 285

Calendar Day (1996)

Q (

103 m

3 day

-1)

New Water

Old Water

Not Teflon basins!

HYDROLOGIC FLOWPATHS

MIXING MODEL: 3

COMPONENTS

• Two Conservative Tracers

• Mass Balance Equations for Water and Tracers

tQQQQ 321

ttQCQCQCQC 13

132

121

11

tt QCQCQCQC 23

232

221

21

ttt QCCCCCCCC

CCCCCCCCQ

))(())((

))(())((23

21

13

12

23

22

13

11

23

213

12

23

22

13

1

1

113

12

13

11

13

12

13

1

2 QCC

CCQ

CC

CCQ t

t

213 QQQQ t

Simultaneous Equations

Solutions

Q - Discharge

C - Tracer Concentration

Subscripts - # Components

Superscripts - # Tracers

MIXING MODEL: 3

COMPONENTS(Using Discharge

Fractions)

• Two Conservative Tracers

• Mass Balance Equations for Water and Tracers

1321 fff

13

132

121

11 tCfCfCfC

23

232

221

21 tCfCfCfC

))(())((

))(())((23

21

13

12

23

22

13

11

23

213

12

23

22

13

1

1 CCCCCCCC

CCCCCCCCf tt

113

12

13

11

13

12

13

1

2 fCC

CC

CC

CCf t

213 1 fff

Simultaneous Equations

Solutions

f - Discharge Fraction

C - Tracer Concentration

Subscripts - # Components

Superscripts - # Tracers

MIXING DIAGRAM: PAIRED TRACERSMIXING DIAGRAM: PAIRED TRACERS

0

10

20

30

40

50

60

-24 -20 -16 -12 -8

18O(‰)

Si (m m

ol L

-1)

Stream FlowIndex SnowpitSnowmeltTalus EN1-LTalus EN1-MTalus EN1-UTalus EN2-LTalus EN2-UTalus EN4-VTalus EN4-LTalus EN4-USoil WaterBase Flow

FLOWPATHS: 2-TRACER 3-FLOWPATHS: 2-TRACER 3-COMPONENT MIXING MODELCOMPONENT MIXING MODEL

0

10

20

30

40

50

60

135 165 195 225 255 285

Calendar Day (1996)

Q (

103 m

3 day

-1)

0

40

80

120

160

200

240

280

320

Per

cen

tage

(%

)

Surface FlowTalus WaterBaseflow

FLOWPATHS: 2-TRACERFLOWPATHS: 2-TRACER 3-COMPONENT MIXING3-COMPONENT MIXING

• Did we choose the right end-members?• Did we choose the right tracers?• Is there any way to quantitatively

evaluate our results?

END-MEMBER MIXINGANALYSIS (EMMA)

• Uses more tracers than components• Decides number of end-members• Quantitatively select end-members• Quantitatively evaluate results of the

mixing model

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 fff1

3132

121

11 tCfCfCfC

23

232

221

21 tCfCfCfC

Simultaneous Equations

Where

txx CfC

1 xtx CCf

23

22

21

13

12

11

111

CCC

CCCCx

3

2

1

f

f

f

f x 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

This slide is from Hooper, 2001

EMMA PROCEDURES• Identification of Conservative Tracers - Bivariate solute-solute plots to screen data;

• PCA Performance - Derive eigenvalues and eigenvectors;

• Orthogonal Projection - Use eigenvectors to project chemistry of streamflow and end-members;

• Screen End-Members - Calculate Euclidean distance of end-members between their original values and S-space projections;

• Hydrograph Separation - Use orthogonal projections and generalized equations for mixing model to get solutions!

• Validation of Mixing Model - Predict streamflow chemistry using results of hydrograph separation and original end-member concentrations.

STEP 1 - MIXING

DIAGRAMS

• Look familiar?

• This is the same diagram used for geometrical definition of mixing model (components changed to end-members);

• 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

Tra

cer

2

Streamflow

End-member 1

End-member 2

End-member 3

STEP 2 - PCA PERFORMANCE

• For most cases, if not all, we should use correlation matrix rather than covariance matrix of conservative solutes in streamflow to derive eigenvalues and eigenvectors;

• Why? This treats each variable equally important and unitless;

• How? Standardize the original data set using a routine software or minus mean and then divided by standard deviation;

• To make sure if you are doing right, the mean should be zero and variance should be 1 after standardized!

APPLICATION OF EIGENVALUES• Eigenvalues can be used to infer the number of end-members that should be used in EMMA.

How?

• Sum up all eigenvalues;

• Calculate percentage of each eigenvalue in the total eigenvalue;

• The percentage should decrease from PCA component 1 to p (remember p is the number of solutes used in PCA);

• How many eigenvalues can be added up to 90% (somewhat subjective! No objective criteria for this!)? Let this number be m, which means the number of PCA components should be retained (sometimes called # of mixing spaces);

• (m +1) is equal to # of end-members we use in EMMA.

PCA PROJECTIONSPCA PROJECTIONS

-3

-1

1

3

5

-8 -3 2 7 12

U1

U2

Stream Flow

Snowpit

Snowmelt

Talus EN1-L

Talus EN1-M

Talus EN1-U

Talus EN2-L

Talus EN2-U

Talus EN4-V

Talus EN4-L

Talus EN4-U

Base Flow

Soil Water

First 2 eigenvalues are 92% and so 3 end-members appear to be correct!

FLOWPATHS: EMMAFLOWPATHS: EMMA

0

10

20

30

40

135 165 195 225 255 285

Calendar Day (1996)

Q (

103 m

3 day

-1)

Surface Flow

Talus Flow

Baseflow

ANC

R2 = 0.64

20

40

60

80

100

20 40 60 80 100

Ca2+

R2 = 0.97

20

40

60

80

100

120

20 40 60 80 100 120

Na+

R2 = 0.88

5

10

15

20

25

30

5 10 15 20 25 30

SO42-

R2 = 0.88

10

30

50

70

90

10 30 50 70 90

Si

R2 = 0.85

0

10

20

30

40

50

0 10 20 30 40 50

18O

R2 = 0.81

-19

-18

-17

-16

-15

-14

-19 -18 -17 -16 -15 -14

Pre

dic

tion

(m

ol L

-1fo

r S

i an

d

eq L

-1 f

or o

ther

s)

Observation (units same as in y axis)

EMMA VALIDATION: TRACER PREDICTIONEMMA VALIDATION: TRACER PREDICTION

NITROGEN DEPOSITION

NIWOT RIDGE NADP SITE:N-DEP INCREASED > 4x

NITROGEN IN STREAMS

PotentialSources of Nitrate andAmmonium

FLOWPATHS: EMMAFLOWPATHS: EMMA

0

10

20

30

40

135 165 195 225 255 285

Calendar Day (1996)

Q (

103 m

3 day

-1)

Surface Flow

Talus Flow

Baseflow

EMMA: NITRATE SOURCESEMMA: NITRATE SOURCES

• Under-predicts nitrate during snowmelt– Ionic pulse important

• Overpredicts nitrate during summer– Denitrification?

• 8-ha Martinelli: 30% stream nitrate atmos

• 225-ha GL4: 20% stream nitrate atmos

Dual isotopic analysis of nitrate

18O (no3)

15N (no3)

Green Lakes Valley: dual isotopes

18O (no3) time series

Hysteresis

DUAL ISOTOPE:DUAL ISOTOPE:NITRATE SOURCESNITRATE SOURCES

• 8-ha Martinelli: 60% stream nitrate atmos

• Twice EMMA

• 225-ha GL4: 20% stream nitrate atmos

• Same as EMMA

EMMA and NITRATE EMMA and NITRATE ISOTOPESISOTOPES

• First time used together

• 20% atmospheric nitrate in 220-ha stream– EMMA, dual isotopes similar results

• 60% atmospheric nitrate in 8-ha stream– EMMA underestimates: unsampled flowpath

• Talus nitrate microbial, not atmospheric

• Denitrification probably very important

11,300 river miles in Colordo

100,000 AMD sites in Western US

END OF PIPE TREATMENT STRATEGY

Millions of dollars to install

Expensive to operate

Operate for long-term

Need low-cost alternatives

CHALK CREEK MINE:GROUNDWATER SOURCE

CONTROLSDEMONSTRATION PROJECT

EPA VIII 104(b)3 Program

SUPPLEMENTAL FUNDING REQUEST

Assistance Agreement MM998404-02

Watershed approach, hydrometric, isotopic, and chemical measurements

HYDROGRAPH AND ISOTOPES

ISOTOPES OF INTERIOR STREAMS

HYDROGRAPH SEPARATION

ZINC and HYDROGRAPH

SUMMARY: Mary Murphy Mine

Sulfur-35 (35S) IN THE ENVIRONMENT

Radioactive isotope of sulfate Half-life of about 87 days Produced by spallation of argon atoms in the

atmosphere by cosmic rays

18ArN=22 O2 SO2

SO4-2

Cosmic Rays

35SO42- 35SO4

2-

16 SN=16

Mary Murphy Mine:Delta O-18 and S-352002-2003

-21

-20

-19

-18

-17

-16

-15

-14

Del

ta O

-18

0

2

4

6

8

10

12

14

16

18

20

S-35

O-18

S-35

Mine Water Surface WaterWells Snow

Tritium vs Delta O-18 Mary Murphy Mine Site 2002-2003

-21

-20

-19

-18

-17

-16

-15

-14

-13

8 10 12 14 16 18

Tritium (TU)

De

lta

O-1

8

Groundwater (Wells) Snow Mine Water Surface Water Mine GW

•Tritium = 3H•Radioactive isotope:•Half life of about 12 years•Naturally occurs in precip at about 6-8 Tritium

Units (TU)•Nuclear bomb testing in 1960’s created “bomb peak” (1000+ TU)•Can date waters younger than about 50 years:

Tritium/Tritium/33He DatingHe Dating

HeH 33

t 1 ln3He*

3H1

Precipitation

gasexchang

e

Infiltration

TTrr = Tg = Ta

PPrr = Pa = f(Hr)

gasexchange

noble gasesnoble gaseswell mixedwell mixed

CNG = f (TTr r , P Prr)

CNG

sample

1) Measure C’s

2) Derive TTrr or PPrr

3) Determine Agegas exchange

ceases

NOBLE GAS TRACERS IN GROUNDWATER

3H 3He

radioactiveradioactivedecaydecay

CNG remain constant

EXCEPT He

C3He

C3H

LEADVILLE

EPA superfund site: $100,000,000

NOT YOUR ORDINARY SUPERFUND SITE

• $1,000,000 + per year

treatment cost

•1,000,000,000 gallons of min

waste underground

• 2,000 mines, 115 mills, and

7 smelters

1818O VALUESO VALUES

RAINSNOWEMETINF-1

BMW3CT

ELKHORNMAB

NW5-CNW5-D

OG1TMW-1WCC PZ1

WO3YT

YT-BHCG-03CG-04EG-04

MARIONPWCWEFS-1SDDS

SDDS-2SPR-20SPR-23

SPR-23 (200)

0-5-10-15-20-25

Recharge isprimarily snowmelt

TRITIUM VALUESTRITIUM VALUES

RAINSNOWEMETINF-1

BMW3CT

ELKHORNMAB

NW5-CNW5-D

OG1TMW-1WCCPZ1

WO3YT

YT-BHCG-03CG-04EG-04

MARIONPWCWEFS-1SDDS

SDDS-2SPR-20SPR-23

SPR-23 (200)

2520151050

Recharge ageranges over several decades

TEMPORAL TEMPORAL VARIATION OF VARIATION OF 1818O O

AND TRITIUMAND TRITIUM

Nov/03Sep/03Aug/03Jul/03Jun/03Apr/03Feb/03Nov/02

-19

-18

-17

10 12 14 16 18 20 22 24

18 O

(‰

)

Elkhorn

INF-1

10

11

12

13

14

15

16

17

10 12 14 16 18 20 22 24

Time (# of Months Starting January 2002)

Tri

tiu

m (

TU

) Elkhorn

INF-1

18O doesn’t change so much over time at both sites;

• Tritium significantly increased after June 2003 at INF-1, indicating that significant contribution from Elkhorn.

MIXING DIAGRAMSMIXING DIAGRAMS• Potential end-members are clustered;

• The bigger the circle, the higher the uncertainty in identifying a unique end-member;

• But Elkhorn is unanimous as an end-member, which is natural groundwater well

INF-1 (Nov '02 - Sept'03)

Elkhorn

SPR 23YT

0

2

4

6

8

10

12

14

16

18

20

-20 -19 -18 -17 -16 -15

18O (‰)

Tri

tiu

m (

TU

)

INF-1 BBW-10

BMW-3 BMW-4

CG-03 CG-04

CT EFS-1

EG-04 ELKHORN

LEGH-01 LMDT-1

MAB MARION

NW-5C NW-5D

GITMW-1 PW RES

PWBEINF PWBER

PWCW PWINF

PWOF SDDS

SDDS-2 SHG07A

SHGEMSP SPR-20

SPR-23 SPR-23(200)

WCCPZ-1 WO-3

YT-BH YT

EMET

Most snowmelt infiltrates into subsurface

However, recharge rate is not known

Subsurface storage is much larger than we thought and may be enough to support groundwater harvesting for Front Range

Mountain block-piedmont connection unknown