Isotope Hydrology Shortcourse

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Isotope Hydrology Shortcourse
Residence Time Approaches using Isotope Tracers

• Prof. Jeff McDonnell
• Dept. of Forest Engineering
• Oregon State University

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Outline

• Day 1
• Morning Introduction, Isotope Geochemistry
  Basics
• Afternoon Isotope Geochemistry Basics cont,
  Examples
• Day 2
• Morning Groundwater Surface Water Interaction,
  Hydrograph separation basics, time source
  separations, geographic source separations,
  practical issues
• Afternoon Processes explaining isotope evidence,
  groundwater ridging, transmissivity feedback,
  subsurface stormflow, saturation overland flow
• Day 3
• Morning Mean residence time computation
• Afternoon Stable isotopes in watershed models,
  mean residence time and model strcutures, two-box
  models with isotope time series, 3-box models and
  use of isotope tracers as soft data
• Day 4
• Field Trip to Hydrohill or nearby research site

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How these time and space scales relate to what we
have discussed so far
Bloschel et al., 1995
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This section will examine how we make use of
isotopic variability
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Outline

• What is residence time?
• How is it determined? modeling background
• Subsurface transport basics
• Stable isotope dating (18O and 2H)
• Models transfer functions
• Tritium (3H)
• CFCs, 3H/3He, and 85Kr

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Residence Time

• Mean Water Residence Time (aka turnover time,
  age of water leaving a system, exit age, mean
  transit time, travel time, hydraulic age,
  flushing time, or kinematic age)
• twVm/Q
• For 1D flow pattern twx/vpw
• where vpw q/f
• Mean Tracer Residence Time

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Why is Residence Time of Interest?

• It tells us something fundamental about the
  hydrology of a watershed
• Because chemical weathering, denitrification, and
  many biogeochemical processes are kinetically
  controlled, residence time can be a basis for
  comparisons of water chemistry

Vitvar Burns, 2001
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Tracers and Age Ranges

• Environmental tracers
• added (injected) by natural processes, typically
  conservative (no losses, e.g., decay, sorption),
  or ideal (behaves exactly like traced material)

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Modeling Approach

• Lumped-parameter models (black-box models)
• System is treated as a whole flow pattern is
  assumed constant over modeling period
• Used to interpret tracer observations in system
  outflow (e.g. GW well, stream, lysimeter)
• Inverse procedure Mathematical tool
• The convolution integral

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Convolution

• A convolution is an integral which expresses the
  amount of overlap of one function h as it is
  shifted over another function x. It therefore
  "blends" one function with another
• Its frequency filter, i.e., it attenuates
  specific frequencies of the input to produce the
  result
• Calculation methods
• Fourier transformations, power spectra
• Numerical Integration

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The Convolution Theorem

Proof
Trebino, 2002
We will not go through this!!
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Convolution Illustration of how it works
Step
1
2
3
4
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Example Delta Function

• Convolution with a delta function simply centers
  the function on the delta-function.
• This convolution does not smear out f(t).
• Thus, it can physically represent piston-flow
  processes.

Modified from Trebino, 2002
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Matrix Set-up for Convolution
length(x)length(h)-1
length(x)
S
y(t)
x(t)h
0
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Similar to the Unit Hydrograph
Precipitation
Excess Precipitation
Infiltration Capacity
Excess Precipitation
Time
Tarboton
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Instantaneous Response Function
Unit Response Function U(t)
Excess Precipitation P(t)
Event Response Q(t)
Tarboton
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Subsurface Transport Basics
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Subsurface Transport Processes

• Advection
• Dispersion
• Sorption
• Transformations

Modified from Neupauer Wilson, 2001
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Advection
Solute movement with bulk water flow
tt1
t2gtt1
t3gtt2
FLOW
Modified from Neupauer Wilson, 2001
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Subsurface Transport Processes

• Advection
• Dispersion
• Sorption
• Transformations

Modified from Neupauer Wilson, 2001
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Dispersion
Solute spreading due to flowpath heterogeneity
FLOW
Modified from Neupauer Wilson, 2001
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Subsurface Transport Processes

• Advection
• Dispersion
• Sorption
• Transformations

Modified from Neupauer Wilson, 2001
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Sorption
Solute interactions with rock matrix
FLOW
t2gtt1
tt1
Modified from Neupauer Wilson, 2001
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Subsurface Transport Processes

• Advection
• Dispersion
• Sorption
• Transformations

Modified from Neupauer Wilson, 2001
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Transformations
Solute decay due to chemical and biological
reactions
MICROBE
CO2
t2gtt1
tt1
Modified from Neupauer Wilson, 2001
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Stable Isotope Methods
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Stable Isotope Methods

• Seasonal variation of 18O and 2H in precipitation
  at temperate latitudes
• Variation becomes progressively more muted as
  residence time increases
• These variations generally fit a model that
  incorporates assumptions about subsurface water
  flow

Vitvar Burns, 2001
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Seasonal Variation in 18O of Precipitation
Vitvar, 2000
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Seasonality in Stream Water
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Example Sine-wave
Tw-1(B/A)2 1)1/2
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Convolution Movie
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Transfer Functions Used for Residence Time
Distributions
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Common Residence Time Models
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Piston Flow (PFM)

• Assumes all flow paths have transit time
• All water moves with advection
• Represented by a Dirac delta function

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Exponential (EM)

• Assumes contribution from all flow paths lengths
  and heavy weighting of young portion.
• Similar to the concept of a well-mixed system
  in a linear reservoir model

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Dispersion (DM)

• Assumes that flow paths are effected by
  hydrodynamic dispersion or geomorphological
  dispersion
• Arises from a solution of the 1-D
  advection-dispersion equation

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Exponential-piston Flow (EPM)

• Combination of exponential and piston flow to
  allow for a delay of shortest flow paths

for t? T (1-h-1), and g(t)0 for tlt T (1-h-1)
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Heavy-tailed Models

• Gamma
• Exponentials in series

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Exit-age distribution (system response function)
Confined aquifer PFM g(t) ?(t'-T)
Unconfined aquifer EM g(t) 1/T exp(-t/T)
EM
EPM
EM
PFM
PFM
EM
Maloszewski and Zuber
Kendall, 2001
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Exit-age distribution (system response function)
cont

• Partly Confined Aquifer
• EPM g(t) ?/T exp(-?t'/T ?-1) for tT (1
  - 1/?)
• g(t) 0 for t'lt T (1-1/ ?)

Kendall, 2001
Maloszewski and Zuber
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Dispersion Model Examples
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Residence Time Distributions can be Similar
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Uncertainty
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Identifiable Parameters?
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Review Calculation of Residence Time

• Simulation of the isotope input output
  relation
• Calibrate the function g(t) by assuming various
  distributions of the residence time
• Exponential Model
• Piston Flow Model
• Dispersion Model

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Input Functions

• Must represent tracer flux in recharge
• Weighting functions are used to amount-weight
  the tracer values according recharge mass
  balance!!
• Methods
• Winter/summer weighting
• Lysimeter outflow
• General equation

where w(t) recharge weighting function
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Models of Hydrologic Systems
Maloszewski et al., 1983
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Soil Water Residence Time
Stewart McDonnell, 2001
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Example from Rietholzbach
Vitvar, 1998
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Model 3
Stable deep signal
Uhlenbrook et al., 2002
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How residence time scales with basin area
Figure 1
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Contour interval 10 meters
Digital elevation model and stream network
Figure 2
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Figure 3
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K (17 ha)
Bedload (280 ha)
PL14 (17 ha)
M15 (2.6 ha)
Figure 4
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(No Transcript)
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Determining Residence Time of Old(er) Waters
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Whats Old?

• No seasonal variation of stable isotope
  concentrations gt4 to 50 years
• Methods
• Tritium (3H)
• 3H/3He
• CFCs
• 85Kr

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Tritium

• Historical tracer 1963 bomb peak of 3H in
  atmosphere
• 1 TU 1 3H per 1018 hydrogen atoms
• Slug-like input
• 36Cl is a similar tracer
• Similar methods to stable isotope models
• Half-life (l) 12.43

Tritium Input
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Tritium (cont)

• Piston flow (decay only)
• tt-17.93ln(C(t)/C0)
• Other flow conditions

Manga, 1999
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Deep Groundwater Residence Time
Spring Stollen t0 8.6 a, PD 0.22
3H-Input
3H-Input-Bruggagebiet
3H TU
3H TU
Time yr.
Time yr.
Uhlenbrook et al., 2002
lumped parameter models
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3He/3H

• As 3H enters groundwater and radioactively
  decays, the noble gas 3He is produced
• Once in GW, concentrations of 3He increase as GW
  gets older
• If 3H and 3He are determined together, an
  apparent age can be determined

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Determination of Tritiogenic He

• Other sources of 3He
• Atmospheric solubility (temp dependent)
• Trapped air during recharge
• Radiogenic production (a decay of U/Th-series
  elements)
• Determined by measuring 4He and other noble gases

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Chlorofluorocarbons (CFCs)

• CFC-11 (CFCL3), CFC-12 (CF2Cl2), CFC-13
  (C2F3Cl3) long atm residence time (44, 180, 85
  yrs)
• Concentrations are uniform over large areas and
  atm concentration are steadily increasing
• Apparent age CFC conc in GW to equivalent atm
  conc at recharge time using solubility
  relationships

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85Kr

• Radioactive inert gas, present is atm from
  fission reaction (reactors)
• Concentrations are increasing world-wide
• Half-life 10.76 useful for young dating too
• Groundwater ages are obtained by correcting the
  measured 85Kr activity in GW for radioactive
  decay until a point on the atm input curve is
  reached

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85Kr (cont)

• Independent of recharge temp and trapped air
• Little source/sink in subsurface
• Requires large volumes of water sampled by vacuum
  extraction (100 L)

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Model 3
Uhlenbrook et al., 2002
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Large-scale Basins
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Notes on Residence Time Estimation

• 18O and 2H variations show mean residence times
  up to 4 years only older waters dated through
  other tracers (CFC, 85Kr, 4He/3H, etc.)
• Need at least 1 year sampling record of
  isotopes in the input (precip) and output
  (stream, borehole, lysimeter, etc.)
• Isotope record in precipitation must be
  adjusted to groundwater recharge if groundwater
  age is estimated

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Class exerciseftp//ftp.fsl.orst.edu/pub/mcguirek
/rt_lecture

• Hydrograph separation
• Convolution
• FLOWPC
• Show your results graphically (one or several
  models) and provide a short write-up that
  includes
• Parameter identifiability/uncertainty
• Interpretation of your residence time
  distribution in terms of the flow system

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References

• Cook, P.G. and Solomon, D.K., 1997. Recent
  advances in dating young groundwater
  chlorofluorocarbons, 3H/3He and 85Kr. Journal of
  Hydrology, 191245-265.
• Duffy, C.J. and Gelhar, L.W., 1985. Frequency
  Domain Approach to Water Quality Modeling in
  Groundwater Theory. Water Resources Research,
  21(8) 1175-1184.
• Kirchner, J.W., Feng, X. and Neal, C., 2000.
  Fractal stream chemistry and its implications for
  contaminant transport in catchments. Nature,
  403(6769) 524-527.
• Maloszewski, P. and Zuber, A., 1982. Determining
  the turnover time of groundwater systems with the
  aid of environmental tracers. 1. models and their
  applicability. Journal of Hydrology, 57 207-231.
• Maloszewski, P. and Zuber, A., 1993. Principles
  and practice of calibration and validation of
  mathematical models for the interpretation of
  environmental tracer data. Advances in Water
  Resources, 16 173-190.
• Turner, J.V. and Barnes, C.J., 1998. Modeling of
  isotopes and hydrochemical responses in catchment
  hydrology. In C. Kendall and J.J. McDonnell
  (Editors), Isotope tracers in catchment
  hydrology. Elsevier, Amsterdam, pp. 723-760.
• Zuber, A. and Maloszewski, P., 2000. Lumped
  parameter models. In W.G. Mook (Editor),
  Environmental Isotopes in the Hydrological Cycle
  Principles and Applications. IAEA and UNESCO,
  Vienna, pp. 5-35. Available http//www.iaea.or.at
  /programmes/ripc/ih/volumes/vol_six/chvi_02.pdf

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Outline

• Day 1
• Morning Introduction, Isotope Geochemistry
  Basics
• Afternoon Isotope Geochemistry Basics cont,
  Examples
• Day 2
• Morning Groundwater Surface Water Interaction,
  Hydrograph separation basics, time source
  separations, geographic source separations,
  practical issues
• Afternoon Processes explaining isotope evidence,
  groundwater ridging, transmissivity feedback,
  subsurface stormflow, saturation overland flow
• Day 3
• Morning Mean residence time computation
• Afternoon Stable isotopes in watershed models,
  mean residence time and model strcutures, two-box
  models with isotope time series, 3-box models and
  use of isotope tracers as soft data
• Day 4
• Field Trip to Hydrohill or nearby research site