source waters, flowpaths, and solute flux in mountain catchments mark williams
TRANSCRIPT
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