Special Issue Article
Scale and model resolution effects on the distributions of advective solute travel times in catchments
Amélie Darracq,
Georgia Destouni,
Klas Persson,
Carmen Prieto,
Jerker Jarsjö,
Corresponding Author
Amélie Darracq
Department of Physical Geography and Quaternary Geology, Stockholm University, SE-106 91, Stockholm, Sweden
Department of Physical Geography and Quaternary Geology, Stockholm University, SE-106 91, Stockholm, Sweden.===Search for more papers by this authorGeorgia Destouni
Department of Physical Geography and Quaternary Geology, Stockholm University, SE-106 91, Stockholm, Sweden
Search for more papers by this authorKlas Persson
Department of Physical Geography and Quaternary Geology, Stockholm University, SE-106 91, Stockholm, Sweden
Search for more papers by this authorCarmen Prieto
Department of Physical Geography and Quaternary Geology, Stockholm University, SE-106 91, Stockholm, Sweden
Search for more papers by this authorJerker Jarsjö
Department of Physical Geography and Quaternary Geology, Stockholm University, SE-106 91, Stockholm, Sweden
Search for more papers by this authorAmélie Darracq,
Georgia Destouni,
Klas Persson,
Carmen Prieto,
Jerker Jarsjö,
Corresponding Author
Amélie Darracq
Department of Physical Geography and Quaternary Geology, Stockholm University, SE-106 91, Stockholm, Sweden
Department of Physical Geography and Quaternary Geology, Stockholm University, SE-106 91, Stockholm, Sweden.===Search for more papers by this authorGeorgia Destouni
Department of Physical Geography and Quaternary Geology, Stockholm University, SE-106 91, Stockholm, Sweden
Search for more papers by this authorKlas Persson
Department of Physical Geography and Quaternary Geology, Stockholm University, SE-106 91, Stockholm, Sweden
Search for more papers by this authorCarmen Prieto
Department of Physical Geography and Quaternary Geology, Stockholm University, SE-106 91, Stockholm, Sweden
Search for more papers by this authorJerker Jarsjö
Department of Physical Geography and Quaternary Geology, Stockholm University, SE-106 91, Stockholm, Sweden
Search for more papers by this authorAbstract
Advective solute travel times and their distributions in hydrological catchments are useful descriptors of the dynamics and variation of the physical mass transport among and along the different source-to-recipient pathways of solute transport through the catchments. This article investigates the scale dependence and the effects of model and data resolution on the quantification of advective travel times and their distributions in the Swedish catchment areas of Norrström and Forsmark. In the surface water networks of the investigated (sub)catchments, the mean advective travel time increases with (sub)catchment scale, whereas the relative travel time variability around the mean value (coefficient of variation, CV) is scale-invariant and insensitive to model resolution. In the groundwater and for the whole (sub)catchments, both the mean value and the CV of travel times are scale-invariant, but sensitive to model resolution and accuracy. Such quantifications and results of advective travel times constitute important steps in the development of improved understanding and modelling of nutrient, pollutant and tracer transport through catchments. Copyright © 2010 John Wiley & Sons, Ltd.
REFERENCES
- Alexander RB, Elliott AH, Shankar U, McBride GB. 2002. Estimating the sources and transport of nutrients in the Waikato River Basin, New Zealand. Water Resources Research 38: 1268–1290.
- Alexander RB, Smith RA, Schwarz GE. 2000. Effect of stream channel size on the delivery of nitrogen to the Gulf of Mexico. Nature 403: 758–761.
- Amorocho J. 1961. Discussion on “Predicting storm runoff on small experimental watershed”, by N.E. Minshall. Journal of Hydraulics Division, ASCE 87(HY2): 185–191.
- Berglund S, Cvetkovic V. 1996. Contaminant displacement in aquifers: coupled effects of flow heterogeneity and nonlinear sorption. Water Resources Research 32: 23–32.
- Beven KJ. 2000. Uniqueness of place and process representations in hydrological modelling. Hydrology and Earth System Sciences 4(2): 203–213.
- Botter G, Bertuzzo E, Bellin A, Rinaldo A. 2005. On the Lagrangian formulations of reactive solute transport in the hydrologic response. Water Resources Research 41: W04008, DOI:10.1029/2004WR003544.
- Botter G, Peratoner F, Putti M, Zuliani A, Zonta R, Rinaldo A, Marani M. 2008. Observation and modeling of catchment-scale solute transport in the hydrologic response: a tracer study. Water Resources Research 44: W05409, DOI:10.1029/2007WR006611.
- Botter G, Settin T, Marani M, Rinaldo A. 2006. A stochastic model of nitrate transport and cycling at basin scale. Water Resources Research 42: W04415, DOI:10.1029/2005WR004599.
- Brunberg AK, Carlsson T, Blomqvist P, Brydsten L, Strömgren M. 2004. Identification of catchments, lake-related drainage parameters and lake habitats. Swedish Nuclear Fuel and Waste Management Company Report P-04-25, Stockholm.
- Burgman JO, Calles B, Westman F. 1987. Conclusions from a ten year study of oxygen-18 in precipitation and runoff in Sweden. In Isotope Techniques in Water Resources Development, an International Symposium. International Atomic Energy Agency: Vienna; 579–590.
- Cvetkovic V, Dagan G. 1994. Transport of kinetically sorbing solute by steady random velocity in heterogeneous porous formations. Journal of Fluid Mechanics 265: 189–215.
- Cvetkovic V, Dagan G. 1996. Reactive transport and immiscible flow in geochemical media: 2. Applications. Proceedings of the Royal Society of London, Series A 452: 303–328.
- Cvetkovic V, Haggerty R. 2002. Transport with multiple-rate exchange in disordered media. Physical Review E 65(5): DOI:10.1103/PhysRevE.65.051308.
- Cvetkovic V, Shapiro AM. 1990. Mass arrival of sorptive solute in heterogeneous porous media. Water Resources Research 26: 2057–2067.
- Dagan G. 1989. Flow and Transport in Porous Formations. Springer Verlag: Berlin.
10.1007/978-3-642-75015-1 Google Scholar
- Dagan G, Fiori A. 1997. The influence of pore-scale dispersion on concentration statistical moments in transport through heterogeneous aquifers. Water Resources Research 33(7): 1595–1606.
- Darracq A, Destouni G. 2005. In-stream nitrogen attenuation: model-aggregation effects and implications for coastal nitrogen impacts. Environmental Science and Technology 39(10): 3716–3722.
- Darracq A, Destouni G. 2007. Physical versus biogeochemical interpretations of nitrogen and phosphorus attenuation in streams and its dependence on stream characteristics. Global Biogeochemical Cycles 21: GB3003, DOI:10.1029/2006GB002901.
- Darracq A, Destouni G, Persson K, Prieto C, Jarsjö J. 2009. Quantification of advective solute travel times and mass transport through hydrological catchments. Environmental Fluid Mechanics DOI:10.1007/s10652-009-9147-2.
- Darracq A, Greffe F, Hannerz F, Destouni G, Cvetkovic V. 2005. Nutrient transport scenarios in a changing Stockholm and Mälaren valley region. Water Science and Technology 51(3–4): 31–38.
- Darracq A, Lindgren GA, Destouni G. 2008. Long-term development of phosphorus and nitrogen loads through the subsurface and surface water systems of drainage basins. Global Biogeochemical Cycles 22: GB3022, DOI:10.1029/2007GB003022.
- Destouni G. 1993. Stochastic modeling of solute flux in the unsaturated zone at the field scale. Journal of Hydrology 143: 45–61.
- Destouni G, Cvetkovic V. 1991. Field-scale mass arrival of sorptive solute into the groundwater. Water Resources Research 27: 1315–1325.
- Destouni G, Darracq A. 2006. Response to comment on “In-stream nitrogen attenuation: model aggregation effects and implications for coastal nitrogen impacts”. Environmental Science and Technology 40(7): 2487–2488.
- Destouni G, Darracq A. 2009. Nutrient cycling and N2O emissions in a changing climate: the subsurface water system role. Environmental Research Letters 4: 035008, DOI:10.1088/1748-9326/4/3/035008.
- Destouni G, Graham W. 1995. Solute transport through an integrated heterogeneous soil-groundwater system. Water Resources Research 31: 1935–1944.
- Destouni G, Hannerz F, Prieto C, Jarsjö J, Shibuo Y. 2008a. Small unmonitored near-coastal catchment areas yielding large mass loading to the sea. Global Biogeochemical Cycles 22: GB4003, DOI:10.1029/2008GB003287.
- Destouni G, Shibuo Y, Jarsjö J. 2008b. Freshwater flows to the sea: spatial variability, statistics and scale dependence along coastlines. Geophysical Research Letters 35: L18401, DOI:10.1029/2008GL035064.
- Destouni G, Lindgren G, Gren I-M. 2006. Effects of inland nitrogen transport and attenuation modeling on coastal nitrogen load abatement. Environmental Science and Technology 40(20): 6208–6214.
- Destouni G, Sassner M, Jensen KH. 1994. Chloride migration in heterogeneous soil: 2, stochastic modeling. Water Resources Research 30: 747–758 (Correction: Water Resources Research 31: 1161, 1995).
- DeWalle DR, Edwards PJ, Swistock BR, Aravena R, Drimmie RJ. 1997. Seasonal isotope hydrology of three Appalachian forest catchments. Hydrological Processes 11: 1895–1906.
- De Wit MJM. 1999. Nutrients fluxes in the Rhine and Elbe basins. Dissertation, Royal Dutch Geographical Society, Utrecht, the Netherlands.
- De Wit MJM. 2001. Nutrients fluxes at the river basin scale. I: the PolFlow model. Hydrological Processes 15: 743–759.
- Dooge JCI. 1986. Looking for hydrologic laws. Water Resources Research 22(9): 46–58.
- Eriksson N, Destouni G. 1997. Combined effects of dissolution kinetics, secondary mineral precipitation, and preferential flow on copper leaching from mining waste rock. Water Resources Research 33: 471–483.
- Fiori A, Berglund S, Cvetkovic V, Dagan G. 2002. A first-order analysis of solute flux statistics in aquifers: the combined effect of pore-scale dispersion, sampling, and linear sorption kinetics. Water Resources Research 38(8): 1137, DOI:10.1029/2001WR000678.
- Fiori A, Dagan G. 2000. Concentration fluctuations in aquifer transport: a rigorous first-order solution and applications. Journal of Contaminant Hydrology 45: 139–163.
- Fiori A, Russo D. 2008. Travel time distribution in a hillslope: insight from numerical simulations. Water Resources Research 44: W12426, DOI:10.1029/2008WR007135.
- Foussereau X, Graham W, Aakpoji A, Destouni G, Rao PSC. 2001. Solute transport through a heterogeneous coupled vadose-saturated zone system with temporally random rainfall. Water Resources Research 37(6): 1577–1588.
- Fredriksson D. 2004. Peatland investigation Forsmark. Swedish Nuclear Fuel and Waste Management Company Report P-04-127, Stockholm.
- Fritz P. 1981. River waters, in stable isotope hydrology: deuterium and oxygen-18 in the water cycle. In Technical Report Series 210, J Gat, R Gonfiantini (eds). International Atomic Energy Agency: Vienna; 177–201.
- Ginn TR, Simmons CS, Wood BD. 1995. Stochastic–convective transport with nonlinear reaction: biodegradation with microbial growth. Water Resources Research 31: 2689–2700.
- Gooseff MN, LaNier J, Haggerty R, Kokkeler K. 2005. Determining in-channel (dead zone) transient storage by comparing solute transport in a bedrock channel–alluvial channel sequence, Oregon. Water Resources Research 41: W06014, DOI:10.1029/2004WR003513.
- Greffe F. 2003. Material transport in the Norrström drainage basin: integrating GIS and hydrological process modelling. Master Thesis, Royal Institute of Technology, Stockholm, Sweden.
- Janssen GMCM, Cirpka OA, Van der Zee EATM. 2006. Stochastic analysis of nonlinear biodegradation in regimes controlled by both chromatographic and dispersive mixing. Water Resources Research 42(1): W01417, DOI:10.1029/2005WR004042.
- Jarsjö J, Destouni G, Persson K, Prieto C. 2007. Solute transport in coupled inland-coastal water systems. General conceptualization and application to Forsmark. Swedish Nuclear Fuel and Waste Management Co Report R-07-65, Stockholm, Sweden.
- Jarsjö J, Shibuo Y, Destouni G. 2004. Using the PCRaster-POLFLOW approach to GISbased modelling of coupled groundwater-surface water hydrology in the Forsmark Area. Swedish Nuclear Fuel and Waste Management Co Report R-04-54, Stockholm, Sweden.
- Jarsjö J, Shibuo Y, Destouni G. 2008. Spatial distribution of unmonitored inland water discharges to the sea. Journal of Hydrology 348(1–2): 59–72.
- Johansson P-O. 2003. Drilling and sampling in soil. Installation of groundwater monitoring wells and surface water level gauges. Swedish Nuclear Fuel and Waste Management Company Report P-03-64, Stockholm, Sweden.
- Johansson P-O, Werner K, Bosson E, Juston J. 2005. Description of climate, surface hydrology, and near-surface hydrology. Preliminary site description. Forsmark area—version 1.2. Swedish Nuclear Waste Management Company (SKB) Report R-05-06, Stockholm, Sweden.
- Lindborg T. 2005. Description of surface systems. Preliminary site description Forsmark area—version 1.2. Swedish Nuclear Fuel and Waste Management Company Report R-05-03, Stockholm, Sweden.
- Lindgren GA, Destouni G. 2004. Nitrogen loss rates in streams: scale-dependence and up-scaling methodology. Geophysical Research Letters 31: L13501, DOI: 10.1029/2004GL019996.
- Lindgren GA, Destouni G, Darracq A. 2007. The inland subsurface water system role for coastal nitrogen load dynamics and abatement responses. Environmental Science and Technology 41(7): 2159–2164.
- Lindgren GA, Destouni G, Miller AV. 2004. Solute transport through the integrated groundwater-stream system of a catchment. Water Resources Research 40: W03511, DOI:10.1029/2003WR002765.
- Malmström ME, Berglund S, Jarsjö J. 2008. Combined effects of spatially variable flow and mineralogy on the attenuation of acid mine drainage in groundwater. Applied Geochemistry 23(6): 1419–1436.
- Maloszewski P, 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.
- Malmström ME, Destouni G, Martinet P. 2004. Modeling expected solute concentration in randomly heterogeneous flow systems with multicomponent reactions. Environmental Science and Technology 38: 2673–2679.
- Marklund L, Wörman A, Geier J, Simic E, Dverstorp B. 2008. Impact of landscape topography and quaternary overburden on the performance of a geological repository of nuclear waste. Nuclear Technology 163: 165–179.
- McDonnell J, Rowe LK, Stewart MK. 1999. A combined tracerhydrometric approach to assess the effect of catchment scale on water flow path, source and age. In Integrated Methods in Catchment Hydrology—Tracer, Remote Sensing, and New Hydrometric Techniques (Proceedings of IUGG 99 Symposium HS4), C Leibundgut, J McDonnell, G Schultz (eds). IAHS Publication no. 258, IAHS; 265–273.
- McGlynn B, McDonnell J, Stewart M, Seibert J. 2003. On the relationships between catchment scale and streamwater mean residence time. Hydrological Processes 17: 175–181.
- McGuire KJ, DeWalle DR, Gburek WJ. 2002. Evaluation of mean residence time in subsurface waters using oxygen-18 fluctuations during drought conditions in the mid-Appalachians. Journal of Hydrology 261: 132–149.
- McGuire KJ, McDonnell JJ. 2006. A review and evaluation of catchment transit time modeling. Journal of Hydrology 330: 543–563.
- McGuire KJ, McDonnell JJ, Weiler M, Kendall C, McGlynn BL, Welker JM, Seibert J. 2005. The role of topography on catchment-scale water residence time. Water Resources Research 41(5): W05002.1–W05002.14.
- McGuire KJ, Weiler M, McDonnell JJ. 2007. Integrating tracer experiments with modeling to assess runoff processes and water transit times. Advances in Water Resources 30: 824–837.
- Meinardi C, Beusen A, Bollen M, Klepper O. 1994. Vulnerability to diffuse pollution of European soils and groundwater. National Institute of Public Health and Environmental Protection (RIVM), Report 4615001002, Bilthoven, the Netherlands.
- Minshall NE. 1960. Predicting storm runoff on small experimental watersheds. Journal of Hydraulics Division, ASCE 86(HY8): 17–38.
- Mourad DSJ. 2002. Application of GIS-based modelling to assess nutrient loads in rivers of the Estonian part of the lake Peipsi basin. MANTRA-East working paper 5·1.
- Nilsson AC, Borgiel M. 2004. Sampling and analyses of surface waters. Results from sampling in the Forsmark area, March 2003 to March 2004. Swedish Nuclear Waste Management Company Report P-04-146, Stockholm.
- Rinaldo A, Botter G, Bertuzzo E, Uccelli A, Settin T, Marani M. 2006. Transport at basin scales: 1. Theoretical framework. Hydrology and Earth System Sciences 10: 19–30.
- Rinaldo A, Marani A. 1987. Basin scale model of solute transport. Water Resources Research 23: 2107–2118.
- Rodgers P, Soulsby C, Waldron S. 2005. Stable isotope tracers as diagnostic tools in upscaling flow path understanding and residence time estimates in a mountainous mesoscale catchment. Hydrological Processes 19: 2291–2307.
- Rubin Y. 2003. Applied Stochastic Hydrogeology. Oxford University Press: New York.
10.1093/oso/9780195138047.001.0001 Google Scholar
- Schnoor JL. 1996. Environmental modeling: Fate and Transport of Pollutants in Water, Air and Soil. Wiley: New York.
- Seibert J, McDonnell JJ. 2002. On the dialog between experimentalist and modeler in catchment hydrology: use of soft data for multicriteria model calibration. Water Resources Research 38(11): 1241, DOI: 10.1029/2001WR000978.
- Shapiro AM, Cvetkovic V. 1998. Stochastic analysis of solute travel time in heterogeneous porous media. Water Resources Research 24: 1711–1718.
- Simic E, Destouni G. 1999. Water and solute residence times in a catchment: stochastic model interpretation of 18O transport. Water Resources Research 35(7): 2109–2120.
- Simmons CS. 1982. A stochastic-convective transport representation of dispersion in one-dimensional porous media. Water Resources Research 18: 1193–1214.
- Simmons CS, Ginn TR, Wood BD. 1995. Stochastic-convective transport with nonlinear reaction: mathematical framework. Water Resources Research 31: 2675–2688.
- Smith RA, Schwarz GE, Alexander RB. 1997. Regional interpretation of water-quality monitoring data. Water Resources Research 33: 2781–2789.
- Soulsby C, Malcolm R, Ferrier RC, Helliwell RC, Jenkins A. 2000. Isotope hydrology of the Allt a'Mharcaidh catchment, Cairngorms, Scotland: implications for hydrological pathways and residence times. Hydrological Processes 14: 747–762.
- Tetzlaff D, Seibert J, McGuire KJ, Laudon H, Burns DA, Dunn SM, Soulsby C. 2009. How does landscape structure influence catchment transit time across different geomorphic provinces? Hydrological Processes 23: 945–953.
- Tompson AFB, Bruton CJ, Pawloski GA, Smith DK, Bourcier WL, Shumaker DE, Kersting AB, Carle SF, Maxwell RM. 2002. On the evaluation of groundwater contamination from underground nuclear tests. Environmental Geology 42: 235–247.
- Turc L. 1954. The water balance of soils. Relation between precipitation, evaporation and flow. Annales Agronomiques 5: 491–569.
- Uhlenbrook S, Leibundgut C. 2002. Process-oriented catchment modeling and multiple-response validation. Hydrological Processes 16(2): 423–440.
- Wendland F. 1992. Die Nitratbelastung in den Grundwasserlandschaften der ‘alten’ Bundesländer (BRD), Berichte aus der Okologischen Forschung, Band 8, Forschungszentrum Jülich, Jülich.
- Werner K, Bosson E, Berglund S. 2006. Analysis of water flow paths: methodology and example calculations for a potential geological repository in Sweden. Ambio 35: 425–434.
- Wood EF, Sivapalan M, Beven K, Band L. 1988. Effects of spatial variability and scale with implications to hydrologic modeling. Journal of Hydrology 102: 29–47.
- Wörman A, Packman AI, Marklund L, Harvey JW, Stone S. 2006. Exact three-dimensional spectral solution to surface-groundwater interactions with arbitrary surface topography. Geophysysical Research Letters 33: L07402, DOI:10.1029/2006GL025747.
- Wörman A, Packman AI, Marklund L, Harvey JW, Stone SH. 2007. Fractal topography and subsurface water flows from fluvial bedforms to the continental shield. Geophysysical Research Letters 34: L07402, DOI:10.1029/2007GL029426.
- Yabusaki SB, Steefel CI, Wood BD. 1998. Multidimensional, multicomponent, subsurface reactive transport in nonuniform velocity fields: code verification using an advective reactive streamtube approach. Journal of Contaminant Hydrology 30(3): 299–331.
