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

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

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

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

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

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

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

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)

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

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

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!!

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 Step Convolution: Illustration of how it works

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

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

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

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

Tracers: RT 17 McGuire, OSU Subsurface Transport Basics

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

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

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

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

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

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

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

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

Tracers: RT 26 McGuire, OSU Stable Isotope Methods

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

Tracers: RT McGuire, OSU © Oregon State University 28 Vitvar, 2000 Seasonal Variation in 18 O of Precipitation

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

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

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

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

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

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:

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

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:

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 =

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Tracers: RT McGuire, OSU © Oregon State University m Scale Low High RIF

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

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

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 hydrogen atoms Slug-like input 36 Cl is a similar tracer Similar methods to stable isotope models Half-life ( ) = Tritium Input

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

Tracers: RT McGuire, OSU © Oregon State University 60 Spring: Stollen t 0 = 8.6 a, PD = H-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

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:

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) T age (years) 20.5 years Modified from Manga, 1999

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

Tracers: RT McGuire, OSU © Oregon State University 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

Tracers: RT McGuire, OSU © Oregon State University 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)

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

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

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

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

Tracers: RT McGuire, OSU © Oregon State University 70 References Cook, P.G. and Solomon, D.K., Recent advances in dating young groundwater: chlorofluorocarbons, 3 H/ 3 He and 85 Kr. Journal of Hydrology, 191: Duffy, C.J. and Gelhar, L.W., Frequency Domain Approach to Water Quality Modeling in Groundwater: Theory. Water Resources Research, 21(8): Kirchner, J.W., Feng, X. and Neal, C., Fractal stream chemistry and its implications for contaminant transport in catchments. Nature, 403(6769): Maloszewski, P. and Zuber, A., Determining the turnover time of groundwater systems with the aid of environmental tracers. 1. models and their applicability. Journal of Hydrology, 57: Maloszewski, P. and Zuber, A., Principles and practice of calibration and validation of mathematical models for the interpretation of environmental tracer data. Advances in Water Resources, 16: Turner, J.V. and Barnes, C.J., 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 Zuber, A. and Maloszewski, P., Lumped parameter models. In: W.G. Mook (Editor), Environmental Isotopes in the Hydrological Cycle Principles and Applications. IAEA and UNESCO, Vienna, pp Available:

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