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Partial analysis applied to scale problems in surface moisture fluxes

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Abstract

Partial analysis is applied to the problem of predicting the moisture fluxes of infiltraton and evaporation at land surfaces. The discussion covers the widely different scales of the soil particle, a soil pedon, a field, a basin and a biome. It is suggested that simplified models can be used at these different scales to provide bounding solutions to the integrated behaviour of land surface fluxes of interest in linking hydrologic models and general circulation climate models.

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References

  • Abramopoulos, F., Rosenzweig, C., and Choudhury, B.: 1988, ‘Improved Ground Hydrology Calculations for Global Climate Models (GCMs): Soil Water Movement and Evapotranspiration’,J. Climate 1(9), 921–941.

    Google Scholar 

  • Beckett, P. H. T. and Webster, R.: 1971, ‘Soil Variability: A Review’,Soil and Fertilisers 34, 1–15.

    Google Scholar 

  • Beven, K. J. and Kirkby, M. J.: 1979, ‘A Physically-Based Variable Contributing Area Model of Basin Hydrology’,Hydrol. Sci. Bull. 24, 43–69.

    Google Scholar 

  • Beven, K. J., Kirkby, M. J., Schofield, N., and Tagg, A. F.: 1984, ‘Testing a Physically-Based Flood Forecasting Model (TOPMODEL) for Three U.K. Catchments’,J. Hydrol. 69, 119–143.

    Google Scholar 

  • Bonnet, M.: 1982, ‘Methodologie de modeles de simulation en Hydrologie’, Document 34, Bureau de Recherches Geologique et Minieres, Orleans, France.

    Google Scholar 

  • Bouchet, R. J.: 1963, ‘Evapotranspiration, reele et potentielle, signification climatique’,General Assembly of Berkeley, IAHS Publ. No.62, 134–142.

    Google Scholar 

  • Brutsaert, W. H. and Stricker, H.: 1979, ‘An Advection — Aridity Approach to Estimate Actual Regional Evapotranspiration’,Water Rasour. Res. 15, 443–450.

    Google Scholar 

  • Budyko, M. I.: 1948,Evaporation under Natural Conditions, Gimiz, Leningrad. (IPST, Jerusalem, 1963).

    Google Scholar 

  • Budyko, M. I.: 1955, ‘On the Determination of Evaporation from the Land Surface’, (in Russian),Meteorol. Gydrol. No.1, 52–58.

    Google Scholar 

  • Budyko, M. I.: 1971,Klimat i zhizn, Gidrometeor. Izdat., Leningrad. Trans. by D.H. Miller as Climate and Life, Academic Press, New York, 1974.

    Google Scholar 

  • Carslaw, H. S. and Jaeger, J. C.: 1946,Conduction of Heat in Solids. Oxford University Press. First edition.

  • Carson, D. J.: 1982, ‘Current parametrization of Land-Surface Processes in Atmospheric General Circulation Models’, in Eagleson, P. S. (ed.),Land Surface Processes in Atmospheric General Circulation Models, Cambridge University Press, pp. 67–108.

  • Childs, E. C.: 1969,An Introduction to the Physical Basis of Soil Water Phenomena, Wiley Interscience Publication, London, 493 pp.

    Google Scholar 

  • Childs, E. C. and Collis-George, N.:1950, ‘The Permeability of Porous Materials’,Proc. Roy. Soc. 201A, 392–405.

    Google Scholar 

  • Clark, R. D. S.: 1980, ‘Rainfall Stormflow Analysis to Investigate Spatial and Temporal Variability of Excess Rainfall Generations’,J. Hydrol. 47, 91–110.

    Google Scholar 

  • Collins, R. E.: 1961,Flow of Fluids Through Porous Materials, Reinhold Publishing Corporation, New York.

    Google Scholar 

  • Crawford, N. H. and Linsley, R. K.: 1966,Digital Simulation in Hydrology, Stanford Watershed Model IV, Dept. Civil. Eng., Stanford. Univ., Technical Report No.39.

  • Darcy, H.: 1856,Les fontaines publiques de la ville de Dijon, Victor Dalmont, Paris.

    Google Scholar 

  • Dawdy, D. R. and O'Donnell, T.: 1965, ‘Mathematical Model of Catchment Behavior’,J. Hydraul. Div. ASCE,91(HY4), 123–137.

    Google Scholar 

  • De Backer, L. W.: 1989, ‘Background Concepts and Principles’, in H. J. Morel-Seytoux (ed.),Unsaturated Flow in Hydrologic Modeling, Theory and Practice, Kluwer Acad. Publ. pp. 3–25.

  • Delworth, T. L. and Manabe, S.: 1988, ‘The Influence of Potential Evaporation on the Variabilities of Simulated Soil Wetness and Climate’,J. Climate 1(5), 523–547.

    Google Scholar 

  • Dickinson, R. E.: 1984, ‘Modelling Evapotranspiration for Three-Dimensional Global Climate Models’, in J. E. Hansen and T. Takahashi (eds.),Climate Processes and Climate Sensitivity, Geophysical Monograph 29 A.G.U. Washington, pp. 58–72.

  • Dickinson, R. E. and Hanson, B.: 1984, ‘Vegetation-Albedo Feedbacks, J. E. Hansen and T. Takahashi (eds.),Climate Process and Climate Sensitivity, Geophysical Monograph 29, A.G.U. Washington, pp. 180–186.

  • Dooge, J. C. I.: 1973,Linear Theory of Hydrologic Systems, Tech. Bulletin. No. 1468, U.S. Agri. Res. Ser., Washington, D.C. 327 pp.

    Google Scholar 

  • Dooge, J. C. I.: 1982, ‘Parameterization of Hydrologic Processes’, in P. S. Eagleson (ed.),Land Surface Processes in Atmospheric Global Circulation Models, Cambridge Univ. Press, pp. 243–288.

  • Dooge, J. C. I.: 1986,Scale Problems in Hydrology, Fifth Chester C. Kisiel Memorial Lecture, Department of Hydrology and Water Resources, Univ. Arizona, Tucson.

    Google Scholar 

  • Dunin, F. A. and Aston, A. R.: 1981, ‘Spatial Variability in the Water Balance of an Experimental Catchment’,Aust. J. Soil Res. 19, 113–120.

    Google Scholar 

  • Dunne, T.: 1978, ‘Field Studies of Hillslope Flow Processes’, in M. J. Kirkby (ed.),Hillslope Hydrology, Wiley-Interscience, New York, pp. 227–293.

    Google Scholar 

  • Dunne, T.: 1982, ‘Models of Runoff Processes and Their Significance’, in J. R. Wallis (ed.),Studies in Geophysics: Scientific Basis of Water Resources Management, National Academy of Sciences, Washington, pp. 19–30.

    Google Scholar 

  • Dunne, T. and Black, R. D.: 1970, ‘Partial Area Contributions to Storm Runoff in a Small New England Watershed’,Water Resour. Res. 6, 1296–1331.

    Google Scholar 

  • Eagleson, P. S.: 1978, ‘Climate, Soil and Vegetation: 3. A Simplified Model of Soil Moisture Movement in the Liquid Phase’,Water Resour. Res. 14, 722–739.

    Google Scholar 

  • Eagleson, P. S.: 1982a, ‘Dynamic Hydro-Thermal Balances at Macroscale’, in P. S. Eagleson (ed.),Land Surface Processes in Atmospheric Global Circulation Models, Cambridge Univ. Press, pp. 289–357.

  • Eagleson, P. S.: 1982b, ‘Ecological Optimality in Water-Limited Natural Soil-Vegetation Systems. 1. Theory and Hypothesis’,Water Resour. Res. 19(2), 325–340.

    Google Scholar 

  • Eagleson, P. S. and Segarra, R. I.: 1985, ‘Water-Limited Equilibrium of Savanna Vegetation Systems’,Water Resour. Res. 21(10), 1483–1493.

    Google Scholar 

  • Eagleson, P. S. and Tellers, R. R.: 1982, ‘Ecological Optimality in Water-Limited Natural Soil-Vegetation Systems. 2. Tests and Applications’,Water Resour. Res. 18(2), 341–354.

    Google Scholar 

  • ECCHE: 1977,Flood Forecasting for Humid Regions of China, East China College of Hydraulic Engineering, Nanjing, China.

    Google Scholar 

  • Entekhabi, D. and Eagleson, P. S.: 1989, ‘Land Surface Hydrology Parameterization for Atmospheric General Circulation Models Including Subgrid Scale Variability’,J. of Climate 2(8), 816–831.

    Google Scholar 

  • Famiglietti, J. S. and Wood, E. F.: 1990.Evapotranspiration and Runoff from Large Land Areas: Land Surface Hydrology for Atmospheric General Circulation Models, Water Resources Program, Dept. Civil Eng. & Operations Res. Princeton Univ.

  • Fleming, G.: 1975,Computer Simulation Techniques in Hydrology, Elsevier, New York.

    Google Scholar 

  • Freeze, R. A.: 1980,A Stochastic-Conceptual Analysis of Rainfall-Runoff Processes on a Hillslope, Dept. of Geological Sciences, University of British Columbia, Vancouver B.C.

    Google Scholar 

  • Ganoulis, J. G.: 1986, ‘Sur les èchelles spatiales des hétérogénéites en milieu poreaux’,Hydrogéologie 2, 115–123.

    Google Scholar 

  • Ganoulis, J. G.: 1989, ‘Multiphase Flow in Porous Media: Description at the Pore and Macroscopic Scale’, in H. H. Morel-Seytoux (ed.),Unsaturated Flow in Hydrologic Modelling, pp. 27–52.

  • Gleick, P. H.: 1987, ‘The Development and Testing of a Water Balance Model for Climate Impact Assessment-Modelling the Sacramento Basin’,Water Resour. Res. 23(6), 1049–1061.

    Google Scholar 

  • Gupta, V. K., Rodriguez-Iturbe, I., and Wood, E. F.: (eds.): 1986,Scale Problems in Hydrology: Runoff Generation and Basin Response, Kluwer Acad. Publ. Dordrecht, Holland.

    Google Scholar 

  • Haines, W. B.: 1925, ‘Studies in the Physical Properties of Soils. II. A Note on the Cohesion Developed by Capillary Forces in an Ideal Soil’,J. Agric. Sci. 15, 529–535.

    Google Scholar 

  • Haines, W. B.: 1927, ‘Studies in the Physical Properties of Soils. IV. A Further Contribution to the Theory of Capillary Phenomena in Soil’,J. Agric. Sci. 17, 264–290.

    Google Scholar 

  • Haines, W. B.: 1930, ‘Studies in the Physical Properties of Soil. V. The Hysteresis Effect in Capillary Properties, and the Modes of Moisture Distribution Associated Therewith’,J. Agric. Sci. 20, 97–116.

    Google Scholar 

  • Hamming, R. W.: 1962,Numerical Methods for Scientists and Engineers, McGraw-Hill, New York.

    Google Scholar 

  • Hasselmann, K.: 1976, ‘Stochastic Climate Models. Part I, Theory’,Tellus 28, 473–485.

    Google Scholar 

  • Hewlett, J. D.: 1961,Soil Moisture as a Source of Base Flow from Steep Mountain Watersheds US Dept. Agric. Forest. Ser., Southeastern Forest Experiment Station, Sheville, North Carolina, Station paper No. 132. 11 pp.

    Google Scholar 

  • Hopmans, J. W.: 1987, ‘A Comparison of Various Methods to Scale Soil Hydraulic Properties’,J. Hydrol. 93, 241–256.

    Google Scholar 

  • Horsfield, H. T.: 1934, ‘Strength of Asphalt Mixtures’,J. Soc. Chem. Ind. 53, 108–111.

    Google Scholar 

  • Horton, R. E.: 1933, ‘The Role of Infiltration in the Hydrologic Circle’,Transaction of the American Geophysical Union 14, 446–460.

    Google Scholar 

  • Idso, S. B. and Brazel, A. J.: 1984, ‘Rising Atmospheric Carbon Dioxide Concentrations May Increase Streamflow,Nature 312(5989), 51–53.

    Google Scholar 

  • Kibler, D. F. and Woolhiser, D. A.: 1970, ‘The Kinematic Cascade as a Hydrological Model’, Hydrological Paper 39, Colorado State Univ.

  • Kirkby, J. J.: 1985, ‘Hillslope Hydrology’, in M. G. Anderson and T. P. Burt (eds.),Hydrological Forecasting, pp. 37–75.

  • Klemes, V.: 1985, ‘Sensitivity of Water-Resources Systems to Climate Variations’,World Climate Report 98, WMO, Geneva.

    Google Scholar 

  • Kline, S. J.: 1965,Similitude and Approximation Theory, McGraw Hill.

  • Kohler, M. A.: 1963, ‘Rainfall-Runoff Models’,Symposium on Surface Waters. General Assembly of Berkeley. IAHS Publ. No.63, 479–491.

    Google Scholar 

  • Kühnel, V.: 1989, ‘Scale Problems in Soil Moisture Flow’, Ph.D. Thesis, Dept. Civil. Eng., University College Dublin.

  • Kühnel, V., Dooge, J. C. I., O'Kane, J. P. J., and Romanowicz, R. J.: 1990,Partial Analysis Applied to Scale Problems in Surface Moisture Fluxes, CWRR EEC/NBST Project CLI-038-EIR(J), Report No. 1, Dublin.

  • Machado, D. and O'Donnell, T.: 1982, ‘A Stochastic Interpretation of a Lumped Overland Flow Model in Morel-Seytoux (ed.),Modelling of Hydrologic Processes, Water Resour. Publ., Fort Collins, Colorado. pp. 259–269.

    Google Scholar 

  • Miller, E. E. and Miller, R. D.: 1955, ‘Theory of Capillarity Flow: I. Practical Implications’,Soil. Sci. Soc. Amer. Proc. 19, 267–271.

    Google Scholar 

  • Miller, E. E. and Miller, R. D.: 1956, ‘Physical Theory for Capillary Flow Phenomena’,J. Appl. Phys. 27, 324–332.

    Google Scholar 

  • Morton, F. I.: 1965, ‘Potential Evaporation and River Basin Evaporation’,J. Hydraul. Div. ASCE.91(HY6), 67–97.

    Google Scholar 

  • Morel-Seytoux, J. J. (ed.): 1989,Unsaturated Flow in Hydrologic Modelling, Theory and Practice, NATO ASI Series C, 275, Kluwer Acad. Publ., Dordrecht, Holland.

    Google Scholar 

  • National Research Council: 1977,Climate, Climatic Change and Water Supply, Studies of Geophysics, National Academy of Sciences, Washington.

    Google Scholar 

  • Nielsen, D. R., Biggar, J. W., and Erh, K. T.: 1973, ‘Spatial Variability of Field Measured Soil-Water Properties’,Hilgardia 42, 215–259.

    Google Scholar 

  • Ol'Dekop, E. M.: 1911,Ob isparenii s poverkhnosti rechnykh basseinov, (On evaporation from the surface of river basins), Trans. Meteorol. Observ. Iurevskovo. Univ. Tartu, 4.

  • Peck, A. J., Luxmoore, R. J., and Stolzy, J. L.: 1977, ‘Effects of Spatial Variability of Soil Hydraulic Properties in Water Budget Modelling’,Water Resour. Res. 13, 348–354.

    Google Scholar 

  • Penman, H. L.: 1951,Vegetation and Hydrology, Technical Communication No. 53, Commonwealth Bureau of Soils, Harpenden.

    Google Scholar 

  • Philip, J. R.: 1957a, ‘The Theory of Infiltration: 1. The Infiltration Equation and its Solution’,Soil. Sci. 83, 345–357.

    Google Scholar 

  • Philip, J. R.: 1957b, ‘The Theory of Infiltration: 4. Sorptivity and Algebraic Infiltration Equations’,Soil. Sci. 84, 257–264.

    Google Scholar 

  • Philip, J. R.: 1960, ‘A Very General Class of Exact Solutions in Concentration-Dependent Diffusion’,Nature 185, 233.

    Google Scholar 

  • Philip, J. R.: 1969, ‘Theory of Infiltration’, in Ven Te Chow (ed.),Advances in Hydrosciences 5, 216–296.

    Google Scholar 

  • Pike, J. G.: 1964, ‘The Estimation of Annual Runoff from Meteorological Data in a Tropical Climate’,J. Hydrol. 2, 116–123.

    Google Scholar 

  • Polya, G.: 1957,How to Solve It, Doubleday and Co., Garden City, New York.

    Google Scholar 

  • Popov, E. G.: 1962, ‘Non-Uniformity of Surface Retention as a Factor of Runoff’,Bull. Int. Assn. Hydrol. Sc. 7, 21–26.

    Google Scholar 

  • Reichardt, K. and Libardi, P. L.: 1973,A New Equation for the Estimation of Soil-Water Diffusivity, Proc. of the Symp. on Isotopes and Radiation Techniques in Studies of Soil Physics, Irrigation and Drainage in Relation to Crop Production, IAEA, Vienna.

    Google Scholar 

  • Reichardt, K., Libardi, P. L., and Nielsen, D. R.: 1975, ‘Unsaturated Hydraulic Conductivity Determination by a Scaling Technique’,Soil. Sci. 120, 165–168.

    Google Scholar 

  • Richards, L. A.: 1931, ‘Capillarity Condition of Liquids Through Porous Mediums’,Physics, A Journal of General and Applied Physics, Amer. Phys. Soc. 1, 318–333.

    Google Scholar 

  • Rodriguez-Iturbe, I. and Gupta, V. K. (eds.): 1983, ‘Scale Problem in Hydrology’,J. Hydrol. 65, 1–400.

    Google Scholar 

  • Rowntree, P. R.: 1984, ‘Review of General Circulation Models for Predicting the Effects of Vegetation Change’, in E. R. C. Reynolds and F. B. Thompson (eds.),Forests, Climate, and Hydrology: Regional Impacts, United Nations University 1988, pp. 162–196.

  • Sander, G. C., Kühnel, V., Brandyk, T., Dooge, J. C. I., and O'Kane, J. P. J.: 1986,Analytical Solutions to the Soil Moisture Flow Equations, Report No. 3, EEC/NBST Project CLI-038-EIR(H), The Role of Soil Moisture in Climate Modelling, Civil Eng. Dept., University College Dublin.

  • Scheidegger, A. E.: 1960,The Physics of Flow Through Porous Media, Univ. of Toronto Press.

  • Schreiber, P.: 1904, ‘Über die Beziehungen zwischen dem Niederschlag und der Wasserführung der Flüsse in Mitteleuropa’,Z. Meteorol. 21(10).

  • Sellers, P. J.: 1987, ‘Modeling Effects of Vegetation on Climate’, in R. E. Dickinson (ed.),The Geogphysiology of Amazonia. Vegetation and Climate Interactions, Wiley-Interscience Publ. pp. 297–344.

  • Sellers, P. J., Mintz, Y., Sud, Y. C., and Dalcher, A.: 1986, ‘A Simple Biosphere Model (SiB) for Use Within General Circulation Models’,J. Atmos. Sci. 43, 505–531.

    Google Scholar 

  • Sharma, M. L. and Luxmoore, R. J.: 1979, ‘Soil Spatial Variability and its Consequences on Simulated Water Balance’,Water Resour. Res. 15, 1567–1573.

    Google Scholar 

  • Sharma, M. L., Gander, G. A., and Hunt, C. G., 1980, ‘Spatial Variability of Infiltration in a Watershed’,J. of Hydrol. 45, 101–125.

    Google Scholar 

  • Shugart, H. H., Ya Antonovsky, M., Jarvis, P. G., and Sandford, A. P.: 1986, ‘CO2, Climatic Change and Forest Ecosystems’, in B. Balin, B. R. Doos, J. Jaeger and R. A. Warwick (eds.),The Greenhouse Effect, Climatic Change and Ecosystems, SCOPE 29, Wiley, Chichester, pp. 475–521.

    Google Scholar 

  • Simmons, C. S., Nielsen, D. R., and Biggar, J. W.: 1979, ‘Scaling of Field-Measured Soil-Water Properties’,Hilgardia 47, 77–173.

    Google Scholar 

  • Soil Survey Staff: 1960,Soil Classification: A Comprehensive System — 7th Approximation. U.S. Dept. of Agriculture, Soil Conservation Service, Washington, 265 pp.

    Google Scholar 

  • Strain, B. R. and Cure, J. D.: 1985,Direct Effect of Increasing Carbon Dioxide on Vegetation. DOE/ER-0238, US Dept. of Energy, Washington DC, U.S.A.

    Google Scholar 

  • Thornthwaite, C. W. and Mather, J. R.: 1955,The Water Balance, Publ. in Climatology VIII,1, Centestor, U.S.A. 86 pp.

  • Troendle, C. A.: 1985, ‘Variable Source Area Models’, in M. G. Anderson and T. P. Burt (eds.),Hydrological Forecasting, Wiley-Interscience, pp. 347–403.

  • Turc, L.: 1954, 1955, ‘Le bilan d'eau des sols. Relation entre la precipitation, l'evaporation et l'ecoulement’,Ann. Agron. 5, 491–569 and6, 5–131.

    Google Scholar 

  • Vauclin, M., Vachaud, G., and Imberon, J.: 1981,Spatial Variability of some Soil Physical Properties over One-Hectare Field Plot., AGU Chapman Conference, Fort Collins.

  • Wagenet, R. J.: 1984,Measurement and Interpretation of Spatially Variable Leaching Processes. Proc. Int. Soc. Soil. Sci. and Soil. Sci. Soc. Amer. Workshop. Las Vegas. PUDOC Publs. Wageningen, pp. 209–236.

    Google Scholar 

  • Warrick, A. W., Mullen, G. J., and Nielsen, D. R.: 1977, ‘Scaling Field-Measured Soil Hydraulic Properties Using a Similar Media Concept’,Water Resour. Res. 13, 355–362.

    Google Scholar 

  • W.M.O.: 1975,Intercomparison of Conceptual Models Used in Operational Hydrological Forecasting. Operational Report No. 7, W.M.O., Geneva.

    Google Scholar 

  • Wood, E. F., Sivapalan, M., Beven, K., and Band, L.: 1987,Effects of Spatial Variability and Scale with Implications to Hydrologic Modelling, Proceedings of U.S.A.-Japan Seminar on Hydrology, Hawaii.

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Kuhnel, V., Dooge, J.C.I., O'Kane, J.P.J. et al. Partial analysis applied to scale problems in surface moisture fluxes. Surv Geophys 12, 221–247 (1991). https://doi.org/10.1007/BF01903420

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