A Shortcourse on Isotope Hydrology Prof. Jeff McDonnell Dept. of Forest Engineering
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Catchment Isotope Plot Scale Scale Basics A Shortcourse on Isotope Hydrology Prof. Jeff McDonnell Richardson Chair in Watershed Science Dept. of Forest Engineering Oregon State University © Oregon State University Catchment Isotope Plot Scale Scale Basics © Oregon State University Isotopes of water = history of water Isotope Plot Scale Basics Terminology Groundwater hydrologists: GW/SW Interaction Hillslope hydrologists: Streamflow generation Watershed hydrologists: Hydrologic Flowpaths © Oregon State University Hooper (2001) Isotope Plot Scale Basics Potential usefulness to local problems Effects of logging along the Yangtze © Oregon State University Communication between polluted surface water and local groundwater Hillslope Isotope Plot Scale Hydrology Basics Basic Research Questions That Will be Addressed Groundwater-surface water interactions McGuire © Oregon State University Where does water go when it rains? How long does it reside in the catchment? What flowpath does the water take to the stream? Catchment Isotope Plot Scale Scale Basics A Useful Quote... “The role of isotopes is like the role of the aliens in the famous sci-fi movie “The Invasion of the Body Snatchers”. Isotopes and trace elements have pervaded the entire discipline (geochemistry) and they are us now!” K. Turekian, Editor Geochimica et Cosmochimica Acta ….the same could now be said for Hydrology! © Oregon State University Hillslope Isotope Plot Scale Hydrology Basics Isotope Hydrology Physical Chemical Photo: Kevin McGuire Explicit solution of water and tracer mass balance © Oregon State University Isotopic Isotope Plot Scale Basics Critical Thinking Is Inherent in Isotope Hydrology Data are scant Data are insufficient Data are wrong Hydrogeologic systems are open Mathematical solutions are inexact © Oregon State University Catchment Isotope Plot Scale Scale Basics Day 1 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: Introduction, Isotope Geochemistry Basics Afternoon: Isotope Geochemistry Basics ‘cont, Examples Day 2 Outline 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 © Oregon State University Isotope Plot Scale Basics Introduction © Oregon State University Hillslope Isotope Plot Scale Hydrology Basics Your instructor (see web page http://www.cof.orst.edu/cof/fe/watershd ) My research My teaching My other IAEA Shortcourses You (5-minute self introductions) What you are now studying Your current research projects/questions Introductions What you would like out of the course The larger university/regional context and how this course relates to interests in Isotope Hydrology in Nanjing © Oregon State University Hillslope Isotope Plot Scale Hydrology Basics Shortcourse Structure Powerpoint lectures Interactive question and answer as much as possible Examination of data, ideas and experimental sites where you are working Discussion of problems of local significance Please interrupt and ask questions whenever something is unclear, you would like to add a comment—this will add greatly to the learning experience for everyone! © Oregon State University Hillslope Isotope Plot Scale Hydrology Basics IAEA shortcouse and my connection to it The International Atomic Energy Agency (IAEA) The UNESCO-IAEA Joint International Isotope Hydrology Program The International Commission on Tracers The International Association of Hydrological Sciences PUB Initiative IGBP Biospheric Aspects of the Hydrological Cycle © Oregon State University Hillslope Isotope Plot Scale Hydrology Basics Web sites to check out IGBP http://www.igbp.kva.se/cgi-bin/php/frameset.php GEWEX http://www.gewex.org/ WCRP http://www.wmo.ch/web/wcrp/wcrp-home.html JWP http://www.igbp.kva.se/cgi-bin/php/frameset.php PUB http://www.cig.ensmp.fr/~iahs/PUBs/PUB-proposal250602.htm HELP http://www.nwl.ac.uk/ih/help/ BAHC http://www.pik-potsdam.de/~bahc/ Check these out on the web © Oregon State University Hillslope Isotope Plot Scale Hydrology Basics Related Journals where you will see papers that explore this © Oregon State University Isotope Plot Scale Basics References - Textbooks Clark, I. and Fritz, P. 1998. Environmental Isotopes in Hydrogeology. Lewis Publisher (w/ web-link) Kendall, C. and McDonnell, J.J. (eds.), 1998. Isotope Tracers in Catchment Hydrology. Elsevier (w/ web-link) Ferronsky, V. I. And Polyakov, V. A., 1982 . Environmental Isotopes in the Hydrosphere. Wiley & Sons. Mazor, E., 1991. Applied Chemical and Isotopic Groundwater Hydrology. Open University Press. © Oregon State University Catchment Isotope Plot Scale Scale Basics Isotope Tracers in Catchment Hydrology “…Isotope tracers have been among the most useful tools for understanding: -Groundwater-surface water interactions -Streamflow generation -Flowpath dynamics” Kendall, C. and J. McDonnell eds (1998). Isotope Tracers in Catchment Hydrology, Elsevier Science Publishers, 817p © Oregon State University Isotope Plot Scale Basics References - Internet USGS Isotope Interest Group Home Page (http://wwwcamnl.wr.usgs.gov/isoig/) ISOGEOCHEM Web Page with an E-mail Discussion List in Stable Isotope Geochemistry (http://geology.uvm.edu/geowww/isogeochem.html) © Oregon State University Isotope Plot Scale Basics Isotope Geochemistry Basics © Oregon State University Catchment Isotope Plot Scale Scale Basics Isotopes in Hydrology Environmental Isotopes STABLE RADIOACTIVE 2H/H 18O/16O 13C/12C Cosmogenic Primordial Fallout Products Daughter Products © Oregon State University Catchment Isotope Plot Scale Scale Basics The Isotopes of General Hydrologic Interest in Hydrology Oxygen-18 and Oxygen-16 Hydrogen-2 (Deuterium) and H-1 Tritium (H-3) (From Don Siegel, SU) © Oregon State University Catchment Isotope Plot Scale Scale Basics Isotope hydrology T © Oregon State University Kendall (2001) Catchment Isotope Plot Scale Scale Basics Isotope biogeochemistry T © Oregon State University Kendall (2001) Isotope Plot Scale Basics 1. Applications of Isotopes as Tracers: Tracers of the water itself (D, O, T) = Isotope Hydrology 2. Tracers of solutes or reactions (C, N, S) = Isotope Biogeochemistry This usage is NOT universal, but is very useful (conceptually) © Oregon State University Kendall (2001) Catchment Isotope Plot Scale Scale Basics Fundamentals Isotopes are atoms of the same element that have different numbers of neutrons. 18O and 2H are constituent part of natural water molecules—they are the water molecule Applied naturally during precipitation events Conservative at ambient temperatures Only mixing can alter concentration © Oregon State University Kendall (2001 Catchment Isotope Plot Scale Scale Basics Isotopes are atoms of the same element that have different numbers of neutrons. 16O 12C number of protons Z 6Li 1H 3He 4He 2H 3H n 10B 11B 9Be 10Be 14N 15N 13C 14C 17O 18O 7Li number of neutrons N Fig. 2.2 Part of the chart of nuclides, containing the light elements. © Oregon State University Isotope Plot Scale Basics Stable Isotopes 2H and 18O Relative amounts in earth’s hydrosphere: 18O Conservative behavior - once isotopes become part of water molecule, they change only through mixing 18O = 0.2%, 2H = 0.015% and 2H content of water changes only through fractionation associated with phase exchange processes (except for saline waters) Name Electrons Protons Neutrons Abundance 16O 8 8 8 99.76% 18O 8 8 10 0.20% © Oregon State University Isotope Plot Scale Basics Fractionation Effects Associated with Phase Changes of H2O Evaporation – vapor that forms is lighter than surrounding water Condensation – liquid that forms is heavier than surrounding vapor So, precipitation selectively removes 18O and 2H from the vapor phase © Oregon State University Catchment Isotope Plot Scale Scale Basics © Oregon State University In other words… University of Arizona Hillslope Isotope Plot Scale Hydrology Basics Commonly Used Terms: heavy vs. light isotopes the “heavy” isotope is the one with more neutrons; it is also generally the less abundant isotope. enriched vs. depleted remember to state what isotope is in short supply: does “enriched sulfate” mean that: the sulfate is enriched in heavy sulfur OR the sulfate is enriched in light sulfur? positive vs. negative -10 0/00 is more positive than –20% © Oregon State University Isotope Plot Scale Basics Non-Radioactive Some atoms of elements can have different weights. light heavy Fractionation Chemical and biological processes "sort" the light from the "heavy" versions of the elements. (From Don Siegel, SU) © Oregon State University Isotope Plot Scale Basics Fractionation Effects on 18O and 2H Equilibrium fractionation – vapor pressure of water containing light isotopes > water containing heavy isotopes, therefore vapor is enriched in light isotopes Kinetic fractionation – rapid phase changes increase fractionation because light isotopes diffuse more rapidly than heavy ones © Oregon State University Isotope Plot Scale Basics Examples of equilibrium fractionations Slow precipitation of minerals from magma Rayleigh distillation Isotopic exchange Isotopic Exchange: Shifts in isotopic composition without bulk changes in phase © Oregon State University Kendall (2001) Isotope Plot Scale Basics Fractionation in the hydrological cycle © Oregon State University Isotope Plot Scale Basics © Oregon State University Equilibrium fractionation during evaporation Kendall (2001) Catchment Isotope Plot Scale Scale Basics © Oregon State University Fractionation in d18O and dD during the hydrologic cycle Catchment Isotope Plot Scale Scale Basics Example of a Rainfall Event: Fractionation in d18O during the hydrologic cycle © Oregon State University Kendall (2001 Isotope Plot Scale Basics Fractionation Effects Associated with Phase Changes of H2O -- summary Evaporation – vapor that forms is lighter than surrounding water Condensation – liquid that forms is heavier than surrounding vapor So, precipitation selectively removes 18O and 2H from the vapor phase © Oregon State University Catchment Isotope Plot Scale Scale Basics Parts Per Mil Nomenclature Delta Isotope = Ratio sample - Ratio standard x 1000 Ratio standard …in other words…… A DELTA O-18 = -10 o/oo means there is 10 parts per thousand less O-18 in the sample than in the standard, standard "mean" oceanic water (SMOW) (From Don Siegel, SU) © Oregon State University Isotope Plot Scale Basics Isotopes in Hydrology Constituent Applied part of natural water molecules naturally during precipitation events Conservative Only at ambient temperatures mixing can alter concentration © Oregon State University Catchment Isotope Plot Scale Scale Basics Amount Some Definitions… Effect: The more rainfall, the more depleted the rain Apparent Temperature Effect: Approximately 0.5%0 for every °C for oxygen Evaporation: As rain falls through dry air, it may evaporate, resulting in heavier rain © Oregon State University Kendall (2001) Catchment Isotope Plot Scale Scale Basics Altitude More definitions… effect: On the windward (not lee) side of a mountain the rain gets lighter with increasing altitude GRADIENTS 18O: -0.15 to –0.5%0/100 meters D: -1.5 to 4%0/100 meters Continental Effect: Delta values decrease inland © Oregon State University Kendall (2001) Isotope Plot Scale Basics Geography and Seasonality of 18O and 2H Content of Precipitation Precipitation becomes lighter as air mass moves inland Precipitation becomes lighter with increasing elevation – orographic effect Precipitation becomes lighter towards the poles and is lighter in winter than summer © Oregon State University Isotope Plot Scale Basics Altitude Effect Source: IAEA © Oregon State University Isotope Plot Scale Basics Amount effect Source: IAEA © Oregon State University Isotope Plot Scale Basics Temperature Effect Source: IAEA © Oregon State University Isotope Plot Scale Basics Continental Effect Mean d O18 of the Columbia Watershed vs distanz from the West Coast -8 -9 Errorbars = 2x Stdev O18 -10 Mean d O18 -11 -12 -13 -14 -15 -16 -17 -18 0 100 200 300 400 500 600 700 800 900 1000 1100 Distanz from the West Coast [km] Starke, McDonnell and Kendall, in prep © Oregon State University Isotope Plot Scale Basics Elevation Effect Mean d O18 of Columbia Watershed vs elevation -6 -8 Errorbars = 2x Stdev mean d O18 -10 -12 -14 -16 -18 -20 0 200 400 600 800 1000 1200 1400 1600 1800 elevation [m] © Oregon State University Starke, McDonnell and Kendall, in prep Catchment Isotope Plot Scale Scale Basics Air Temperature “Effect” 20 Air Temp. (C) Singapore Nanjing 0 Arctic - 20 - 40 - 40 - 30 - 20 - 10 0 Delta O-18 (after Don Siegel, SU) © Oregon State University Isotope Plot Scale Basics Latitudinal Controls Northern Hemisphere IAEA © Oregon State University Isotope Plot Scale Basics Latitudinal Controls Southern Hemisphere © Oregon State University Isotope Plot Scale Basics Temperature Effects IAEA © Oregon State University Catchment Isotope Plot Scale Scale Basics Latitudinal Effect Lower Warmer Latitude d 18O (o/oo) 0.00 Waco, Texas -10.00 Chicago, Illinois -20.00 Barrow, Alaska -30.00 Winter Spring Summer -40.00 J F M A M J J A Fall S O N D Higher, Colder Latitude Months (From Don Siegel, SU) © Oregon State University Isotope Plot Scale Basics © Oregon State University Some spatial data (Kendall and Coplen, 2001) Isotope Plot Scale Basics summary © Oregon State University (Kendall and Coplen, 2001) Isotope Plot Scale Basics Why are 18-O and D so similar? © Oregon State University (Kendall and Coplen, 2001) Isotope Plot Scale Basics Global Meteoric Water Line …because they are related 0 d D = 8 d18 O + 10 dD - 100 - 200 - 300 - 40 - 30 - 20 - 10 0 d18 O (From Don Siegel, SU) © Oregon State University Isotope Plot Scale Basics …and they provide much information when view together © Oregon State University Kendall (2001) Isotope Plot Scale Basics IAEA © Oregon State University Hillslope Isotope Plot Scale Hydrology Basics Basic Principles of MWL 1. Each site has its own LMWL. 2. You need to collect all the rain for 2-3 years at a site to get a good average value for recharge. 3. Do not interpolate LMWL or averages from the data for the closest IAEA or other station. 4. There is lots of spatial and temporal variation in the isotopic compositions of rain. © Oregon State University Hillslope Isotope Plot Scale Hydrology Basics Basic Principles of MWL, continued 6. The GMWL or LMWL is not a tight line – they are lines through an elipse of data points. 7. Evaporation causes samples to plot below the MWL. 8. Recharge water can be very different from average rainfall. 9. Samples easily fractionate in poor quality bottles; use ones with polyseal caps. 10. Samples archive well; collect more samples than you need and analyze them in groups. © Oregon State University Catchment Isotope Plot Scale Scale Basics IAEA Stations in GNIP IAEA © Oregon State University Isotope Plot Scale Basics Sites in this region Not too many, but some… © Oregon State University (IAEA, 1981) Isotope Plot Scale Basics © Oregon State University Global Patterns (IAEA, 1981) Hillslope Plot Scale Hydrology Causes of Global Patterns in δ18 and δD The basic phenomenon is that the two isotopes of oxygen (or hydrogen) have different vapor pressures. As water changes phase, bonds are broken. As a generalization, “light” bonds (I.e., bonds between the light isotopes) are broken more easily than “heavy” bonds, and “heavy” bonds are make first. As a result, light isoptopes are preferentially concentrated in the products and heavy isotopes in the residual reactants. © Oregon State University Isotope Plot Scale Basics Globally IAEA (2001). GNIP Maps and Animations, International Atomic Energy Agency, Vienna. Accessible at http://isohis.iaea.org © Oregon State University Catchment Isotope Plot Scale Scale Basics Globally IAEA (2001). GNIP Maps and Animations, International Atomic Energy Agency, Vienna. Accessible at http://isohis.iaea.org © Oregon State University Catchment Isotope Plot Scale Scale Basics Global Atmospheric Circulation System Distills Water Isotopes Even lighter water vapor Evaporation Cold ”Light“ water vapor Heavier Rain Falls equator Hot Condensation “Heavier” Water Remains Solar Heat Raleigh Distillation (From Don Siegel, SU) © Oregon State University Isotope Plot Scale Basics IAEA (2001). GNIP Maps and Animations, International Atomic Energy Agency, Vienna. Accessible at http://isohis.iaea.org © Oregon State University Isotope Plot Scale Basics This region IAEA (2001). GNIP Maps and Animations, International Atomic Energy Agency, Vienna. Accessible at http://isohis.iaea.org © Oregon State University Isotope Plot Scale Basics This region IAEA (2001). GNIP Maps and Animations, International Atomic Energy Agency, Vienna. Accessible at http://isohis.iaea.org © Oregon State University Isotope Plot Scale Basics This region IAEA (2001). GNIP Maps and Animations, International Atomic Energy Agency, Vienna. Accessible at http://isohis.iaea.org © Oregon State University Isotope Plot Scale Basics This region IAEA (2001). GNIP Maps and Animations, International Atomic Energy Agency, Vienna. Accessible at http://isohis.iaea.org © Oregon State University Isotope Plot Scale Basics The d18O and d2H taken from the GNIP database were amount-weighted according to: n n i 1 i 1 dxw Pidi Pi where Pi and d i are the monthly precipitation amount (mm) and the isotopic composition (‰), respectively, and n is the number of months. © Oregon State University Hillslope Plot Scale Hydrology Characteristics of δD and δ180 of Precipitation: Consisten average compositions over time and space. Annual cycle of compositional changes—heavy in summer and light in winter. Large variations among storms. Often considerable variability within storms. Snow often plots along lines of higher d-exess than rain. Storms derived from different storms tracks may have consistently different meteoric water lines. © Oregon State University Catchment Isotope Isotope Plot Scale Scale Basics Basics Where I come from…. University of Waterloo © Oregon State University Isotope Plot Scale Basics Databases of H- and O-Isotopes • Global Network for Isotopes in Precipitation http://www.iaea.or.at/programs/ri/gnip/gnipmain.htm • Canadian Network for Isotopes in Precipitation http://sciborg.uwaterloo.ca/~twdedwar/cnip/cniphome.html © Oregon State University Isotope Plot Scale Basics Now, back to the MWL IAEA © Oregon State University Isotope Plot Scale Basics MWL at a single site – Woods Lake USA Doug Burns, USGS © Oregon State University Isotope Plot Scale Basics IAEA © Oregon State University Catchment Isotope Plot Scale Scale Basics Groundwater Isotopes Same as that for Average Precipitation 0 Groundwater Sample Average Precipitation dD - 100 Well Mixed System--High Dispersion - 200 - 300 - 40 - 30 - 20 - 10 0 d18 O (From Don Siegel, SU) © Oregon State University Catchment Isotope Plot Scale Scale Basics Groundwater Isotopes Different than that for Average Precipitation 0 Summer Recharge Groundwater Sample Average Precipitation - 100 dD Winter Recharge - 200 "Plug Flow" Low Dispersion Pleistocene Glacial Meltwater!! - 300 - 40 - 30 - 20 d18 O - 10 0 (From Don Siegel, SU) © Oregon State University Catchment Isotope Plot Scale Scale Basics Evaporation Enrichment in dD Relative Humidity d D (o/oo) 20.0 0.0 95% 25% -20.0 -40.0 -60.0 50% 0% Starting Isotopic Composition -80.0 -100.0 -15.0 -10.0 -5.0 0.0 5.0 d 18O (o/oo) Sometimes can detect these evaporated waters in the stream signal—e.g. the contribution of wetlands to total flow (See Burns and McD, 1998, JoH) (From Don Siegel, SU) © Oregon State University Isotope Plot Scale Basics air temperature (°C) d 18O (per mil SMOW) Seasonal Variation in 18O of Precipitation © Oregon State University 0 Neversink watershed, 1993 - 1996 -5 -10 -15 -20 20 10 0 -10 Jan-93 Vitvar, 2000 Jan-94 Jan-95 Jan-96 Vitvar, SUNY-ESF Isotope Plot Scale Basics Time Series of Water Source Isotopic Composition 18 O-Direktabfluß O-Hanggrundwasser 18 O-tieferes Grundwasser 18 O-Gesamtabfluß -4 18O-Konzentrationen [%o] 18 -6 -8 -10 -12 -14 1.1.1995 1.1.1996 1.1.1997 1.1.1998 Uhlenbrook, Freiburg U. © Oregon State University Isotope Plot Scale Basics Melt-season Variation in 18O of Precipitation © Oregon State University Isotope Catchment Isotope Hydrograph Plot Scale Scale Separation Basics Individual Rainfall Events Kendall (2001) © Oregon State University Isotope Plot Scale Basics Examples © Oregon State University Isotope Plot Scale Basics Why spend money on isotopes? Isotopes can be powerful tools for testing hypotheses about sources of water and solutes. While isotope analyses are not CHEAP, they can be much less expensive than being wrong. In many cases, they are more useful “fingerprints” of waters or solute sources than other physical constituents because… © Oregon State University Kendall (2001 Isotope Plot Scale Basics Isotopes are useful “fingerprints” because… 1. Many isotopes are relatively conservative in reactions with matrix materials. 2. Waters of different ages, recharge zones, hydrologic/geochemical history, etc., are often isotopically very distinctive. 3. If the water from one area gets to another area, it must be hydraulically and hydrologically possible for it to get there regardless of what the models predict. © Oregon State University Kendall Isotope Plot Scale Basics Isotope Hydrology Practical Applications –Groundwater replenishment –Paleo-water identification –Coastal aquifers-salinization –Groundwater dynamics (flow-path, age) –Geothermal development –Groundwater pollution –Dam leakage & sedimentation © Oregon State University Isotope Plot Scale Basics Sewering of lake dwellings What is the direction of GW flow at each dwelling? © Oregon State University Kendall (2001 Quantifying storm runoff in sewage systems Isotope Plot Scale Basics © Oregon State University Kendall (2001 Isotope Plot Scale Basics Sewering of Lake Dwellings ‘cont.… © Oregon State University Kendall (2001 Isotope Plot Scale Basics Fly-Ash Landfill and Leachate Lagoon ? Na-Cl Waters © Oregon State University Don Siegel, SU Isotope Plot Scale Basics No Evidence for Mixing -40.00 Fly Ash Lagoon d D (o/oo) -50.00 -60.00 -70.00 -80.00 -90.00 -100.00 -110.00 -15.00 -13.00 -11.00 -9.00 d 18O (o/oo) -7.00 -5.00 Don Siegel, SU © Oregon State University Isotope Plot Scale Basics © Oregon State University Where do trees sample their water Dawson, 1993 Isotope Plot Scale Basics © Oregon State University Where do trees sample their water? Dawson and Ehleringe Isotope Plot Scale Basics Large Rivers—what can we see? Agarwaal et al., 2002 © Oregon State University Isotope Plot Scale Basics Large Rivers—what can we see? Agarwaal et al., 2002 © Oregon State University Isotope Plot Scale Basics © Oregon State University Dam leakage—how would you quantify this? Isotope Plot Scale Basics Dam leakage or surface water infiltration Q Surface water H-2 Groundwater Surface water Mixing line Groundwater O-18 Suitable isotopes: • O, H, H, … 18 2 3 Fields of applications: • Coastal aquifers-sea water intrusion; • Groundwater pollution-infiltration of pollutants from surface water bodies. Isotope Hydrology Section Division of Physical and Chemical Sciences, IAEA © Oregon State University Isotope Plot Scale Basics Agarwaal et al., 2002 © Oregon State University Isotope Plot Scale Basics Agarwaal et al., 2002 © Oregon State University Hillslope Isotope Plot Scale Hydrology Basics e.g. Lake Chala in Kenya People wanted to use the Lake water for irrigation, but wanted to make sure that using lake water would have no adverse effect on the discharge of nearby springs whose waters were already being utilized. (i.e., they didn’t want to “rob Peter to pay Paul”) © Oregon State University Hillslope Isotope Plot Scale Hydrology Basics Can they tap lake water without affecting spring flow? Carol Kendall, USGS © Oregon State University Catchment Isotope Plot Scale Scale Basics Day 1 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: Introduction, Isotope Geochemistry Basics Afternoon: Isotope Geochemistry Basics ‘cont, Examples Day 2 Summary 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 © Oregon State University
