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Tracers: RT 1 McGuire, OSU Isotope Hydrology Shortcourse Prof. Jeff McDonnell Dept. of Forest Engineering Oregon State University Residence Time Approaches using Isotope Tracers

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Tracers: RT McGuire, OSU © Oregon State University 2 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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Tracers: RT McGuire, OSU © Oregon State University 3 How these time and space scales relate to what we have discussed so far Bloschel et al., 1995

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Tracers: RT McGuire, OSU © Oregon State University 4 This section will examine how we make use of isotopic variability

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Tracers: RT McGuire, OSU © Oregon State University 5 Outline What is residence time? How is it determined? modeling background Subsurface transport basics Stable isotope dating ( 18 O and 2 H) Models: transfer functions Tritium ( 3 H) CFCs, 3 H/ 3 He, and 85 Kr

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Tracers: RT McGuire, OSU © Oregon State University 6 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) t w =V m /Q For 1D flow pattern: t w =x/v pw where v pw =q/ Mean Tracer Residence Time Residence time distribution

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Tracers: RT McGuire, OSU © Oregon State University 7 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: RT McGuire, OSU © Oregon State University 8 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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Tracers: RT McGuire, OSU © Oregon State University 9 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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Tracers: RT McGuire, OSU © Oregon State University 10 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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Tracers: RT McGuire, OSU © Oregon State University 11 The Convolution Theorem Proof: Trebino, 2002 Y( )=F( )G( ) and |Y( )| 2 =|F( )| 2 |G( )| 2 We will not go through this!!

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Tracers: RT McGuire, OSU © Oregon State University 12 x( ) g( ) = e -a Folding g(- ) e -(-a Displacement g(t- ) e -a(t- t Multiplication x( )g(t- ) t Integration y(t) t t Shaded area 1 2 3 4 Step Convolution: Illustration of how it works

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Tracers: RT McGuire, OSU © Oregon State University 13 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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Tracers: RT McGuire, OSU © Oregon State University 14 Matrix Set-up for Convolution = [length(x)+length(h)]-1 = length(x) = = x(t)*h y(t) = 0

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Tracers: RT McGuire, OSU © Oregon State University 15 Similar to the Unit Hydrograph Time Precipitation Infiltration Capacity Excess Precipitation Tarboton

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Tracers: RT McGuire, OSU © Oregon State University 16 Instantaneous Response Function Excess Precipitation P(t) Unit Response Function U(t) Event Response Q(t) Tarboton

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Tracers: RT 17 McGuire, OSU Subsurface Transport Basics

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Tracers: RT McGuire, OSU © Oregon State University 18 Subsurface Transport Processes Advection Dispersion Sorption Transformations Modified from Neupauer & Wilson, 2001

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Tracers: RT McGuire, OSU © Oregon State University 19 Advection t=t 1 t 2 >t 1 t 3 >t 2 FLOW Solute movement with bulk water flow Modified from Neupauer & Wilson, 2001

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Tracers: RT McGuire, OSU © Oregon State University 20 Subsurface Transport Processes Advection Dispersion Sorption Transformations Modified from Neupauer & Wilson, 2001

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Tracers: RT McGuire, OSU © Oregon State University 21 Dispersion FLOW Solute spreading due to flowpath heterogeneity Modified from Neupauer & Wilson, 2001

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Tracers: RT McGuire, OSU © Oregon State University 22 Subsurface Transport Processes Advection Dispersion Sorption Transformations Modified from Neupauer & Wilson, 2001

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Tracers: RT McGuire, OSU © Oregon State University 23 Sorption t=t 1 t 2 >t 1 FLOW Solute interactions with rock matrix Modified from Neupauer & Wilson, 2001

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Tracers: RT McGuire, OSU © Oregon State University 24 Subsurface Transport Processes Advection Dispersion Sorption Transformations Modified from Neupauer & Wilson, 2001

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Tracers: RT McGuire, OSU © Oregon State University 25 Transformations t=t 1 t 2 >t 1 MICROBE CO 2 Solute decay due to chemical and biological reactions Modified from Neupauer & Wilson, 2001

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Tracers: RT 26 McGuire, OSU Stable Isotope Methods

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Tracers: RT McGuire, OSU © Oregon State University 27 Stable Isotope Methods Seasonal variation of 18 O and 2 H 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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Tracers: RT McGuire, OSU © Oregon State University 28 Vitvar, 2000 Seasonal Variation in 18 O of Precipitation

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Tracers: RT McGuire, OSU © Oregon State University 29 Seasonality in Stream Water Deines et al. 1990

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Tracers: RT McGuire, OSU © Oregon State University 30 Example: Sine-wave C in (t)=A sin( t) C out (t)=B sin( t+ ) T= -1 [(B/A) 2 –1) 1/2

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Tracers: RT McGuire, OSU © Oregon State University 31 Convolution Movie

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Tracers: RT 32 McGuire, OSU Transfer Functions Used for Residence Time Distributions

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Tracers: RT McGuire, OSU © Oregon State University 33 Common Residence Time Models

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Tracers: RT McGuire, OSU © Oregon State University 34 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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Tracers: RT McGuire, OSU © Oregon State University 35 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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Tracers: RT McGuire, OSU © Oregon State University 36 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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Tracers: RT McGuire, OSU © Oregon State University 37 Exponential-piston Flow (EPM) Combination of exponential and piston flow to allow for a delay of shortest flow paths for t (1- and g(t)=0 for t< (1- -1 ) Piston flow =

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Tracers: RT McGuire, OSU © Oregon State University 38 Heavy-tailed Models Gamma Exponentials in series

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Tracers: RT McGuire, OSU © Oregon State University 39 Exit-age distribution (system response function) Unconfined aquifer EM: g(t) = 1/T exp(-t/T) Maloszewski and Zuber Confined aquifer PFM: g(t) = (t'-T) Kendall, 2001 PFM EM EPMEM DM

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Tracers: RT McGuire, OSU © Oregon State University 40 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'< T (1-1/ ) Maloszewski and Zuber Kendall, 2001 DM

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Tracers: RT McGuire, OSU © Oregon State University 41 Dispersion Model Examples

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Tracers: RT McGuire, OSU © Oregon State University 42 Residence Time Distributions can be Similar

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Tracers: RT McGuire, OSU © Oregon State University 43 Uncertainty

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Tracers: RT McGuire, OSU © Oregon State University 44 Identifiable Parameters?

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Tracers: RT McGuire, OSU © Oregon State University 45 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: 1. Exponential Model 2. Piston Flow Model 3. Dispersion Model

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Tracers: RT McGuire, OSU © Oregon State University 46 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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Tracers: RT McGuire, OSU © Oregon State University 47 Models of Hydrologic Systems C in C out Model 1 1- C out C in 1- Model 3 Upper reservoir Lower reservoir C out C in 1- Model 2 Direct runoff Maloszewski et al., 1983

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Tracers: RT McGuire, OSU © Oregon State University 48 Stewart & McDonnell, 2001 Soil Water Residence Time

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Tracers: RT McGuire, OSU © Oregon State University 49 Example from Rietholzbach Vitvar, 1998

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Tracers: RT McGuire, OSU © Oregon State University 50 Model 3… Uhlenbrook et al., 2002 Stable deep signal

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Tracers: RT McGuire, OSU © Oregon State University 51 Figure 1 How residence time scales with basin area

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Tracers: RT McGuire, OSU © Oregon State University 52 Figure 2 Digital elevation model and stream network Contour interval 10 meters

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Tracers: RT McGuire, OSU © Oregon State University 53 Figure 3

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Tracers: RT McGuire, OSU © Oregon State University 54 M15 (2.6 ha) K (17 ha) Bedload (280 ha) PL14 (17 ha) Figure 4

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Tracers: RT McGuire, OSU © Oregon State University 55 500 m Scale -7 0 -3.5 Low High RIF

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Tracers: RT 56 McGuire, OSU Determining Residence Time of Old(er) Waters

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Tracers: RT McGuire, OSU © Oregon State University 57 Whats Old? No seasonal variation of stable isotope concentrations: >4 to 50 years Methods: Tritium ( 3 H) 3 H/ 3 He CFCs 85 Kr

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Tracers: RT McGuire, OSU © Oregon State University 58 Tritium Historical tracer: 1963 bomb peak of 3 H in atmosphere 1 TU: 1 3 H per 10 18 hydrogen atoms Slug-like input 36 Cl is a similar tracer Similar methods to stable isotope models Half-life ( ) = 12.43 Tritium Input

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Tracers: RT McGuire, OSU © Oregon State University 59 Tritium (cont) Piston flow (decay only): t t =-17.93[ln(C(t)/C 0 )] Other flow conditions: Manga, 1999

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Tracers: RT McGuire, OSU © Oregon State University 60 Spring: Stollen t 0 = 8.6 a, PD = 0.22 3H-Input-Bruggagebiet 3 H-Input lumped parameter models Time [yr.] 3 H [TU] Deep Groundwater Residence Time Time [yr.] 3 H [TU] Uhlenbrook et al., 2002

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Tracers: RT McGuire, OSU © Oregon State University 61 3 He/ 3 H As 3 H enters groundwater and radioactively decays, the noble gas 3 He is produced Once in GW, concentrations of 3 He increase as GW gets older If 3 H and 3 He are determined together, an apparent age can be determined:

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Tracers: RT McGuire, OSU © Oregon State University 62 Determination of Tritiogenic He Other sources of 3 He: Atmospheric solubility (temp dependent) Trapped air during recharge Radiogenic production ( decay of U/Th- series elements) Determined by measuring 4 He and other noble gases 3 He/ 3 H age (years) 20 0 30 10 1 5 10 50 T age (years) 20.5 years Modified from Manga, 1999

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Tracers: RT McGuire, OSU © Oregon State University 63 Chlorofluorocarbons (CFCs) CFC-11 (CFCL 3 ), CFC-12 (CF 2 Cl 2 ), & CFC-13 (C 2 F 3 Cl 3 ) 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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Tracers: RT McGuire, OSU © Oregon State University 64 85 Kr 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 85 Kr activity in GW for radioactive decay until a point on the atm input curve is reached

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Tracers: RT McGuire, OSU © Oregon State University 65 85 Kr (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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Tracers: RT McGuire, OSU © Oregon State University 66 Model 3… Uhlenbrook et al., 2002

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Tracers: RT McGuire, OSU © Oregon State University 67 Large-scale Basins

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Tracers: RT McGuire, OSU © Oregon State University 68 Notes on Residence Time Estimation 18 O and 2 H variations show mean residence times up to ~4 years only; older waters dated through other tracers (CFC, 85 Kr, 4 He/ 3 H, 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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Tracers: RT McGuire, OSU © Oregon State University 69 Class exercise ftp://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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Tracers: RT McGuire, OSU © Oregon State University 70 References Cook, P.G. and Solomon, D.K., 1997. Recent advances in dating young groundwater: chlorofluorocarbons, 3 H/ 3 He and 85 Kr. Journal of Hydrology, 191:245-265. 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 http://www.iaea.or.at/programmes/ripc/ih/volumes/vol_six/chvi_02.pdf

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Tracers: RT McGuire, OSU © Oregon State University 71 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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Plot Scale © Oregon State University Isotope Hydrology Shortcourse Prof. Jeff McDonnell Richardson Chair in Watershed Science Dept. of Forest Engineering.

Plot Scale © Oregon State University Isotope Hydrology Shortcourse Prof. Jeff McDonnell Richardson Chair in Watershed Science Dept. of Forest Engineering.

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