Statistical Upscaling and Downscaling in Hydrology

Upscaling and downscaling methods are needed to transfer information from small-scale data to large-scale predictions and vice versa. There are two types of methods; methods focusing on how the equations and parameters of dynamic models change with scale, which are treated in other articles of this Encyclopedia, and methods focusing on how to best represent variability statistically, which is the subject of this article. This article gives a brief overview of scale concepts and illustrates first-order effects of upscaling and downscaling. The most important statistical upscaling/downscaling methods are then reviewed for various hydrological processes – rainfall, floods, soil moisture, and subsurface flow and transport. Keywords: aggregation; disaggregation; flood frequency; fractals; global circulation models; groundwater; media generation; rainfall; sampling; scale; soil moisture; stochastic rainfall models; topographic index; variogram

[1]  Ian D. Moore,et al.  A quasi-dynamic wetness index for characterizing the spatial distribution of zones of surface saturation and , 1994 .

[2]  Murugesu Sivapalan,et al.  Modeling of rainfall time series and extremes using bounded random cascades and levy‐stable distributions , 2000 .

[3]  Chris Kilsby,et al.  A weather-type conditioned multi-site stochastic rainfall model for the generation of scenarios of climatic variability and change , 2005 .

[4]  A. Karr,et al.  Statistical Inference for Point Process Models of Rainfall , 1985 .

[5]  V. Gupta,et al.  Emergence of statistical scaling in floods on channel networks from complex runoff dynamics , 2004 .

[6]  Carl E. Renshaw,et al.  Connectivity of joint networks with power law length distributions , 1999 .

[7]  Garrison Sposito,et al.  Scale Dependence and Scale Invariance in Hydrology , 1998 .

[8]  F. Alabert,et al.  Non-Gaussian data expansion in the Earth Sciences , 1989 .

[9]  N. T. Kottegoda,et al.  The derivation of areal reduction factor of storm rainfall from its scaling properties , 2001 .

[10]  E. Lorenz.  Atmospheric Predictability as Revealed by Naturally Occurring Analogues , 1969 .

[11]  A. Desbarats,et al.  Numerical estimation of effective permeability in sand-shale formations , 1987 .

[12]  Günter Blöschl,et al.  Advances in the use of observed spatial patterns of catchment hydrological response , 2002 .

[13]  Reconstruction and frequency estimates of extreme daily areal precipitation , 1996 .

[14]  J. Gómez-Hernández,et al.  To be or not to be multi-Gaussian? A reflection on stochastic hydrogeology , 1998 .

[15]  John H. Cushman,et al.  More on Stochastic Models , 1987 .

[16]  Brent Yarnal,et al.  Developments and prospects in synoptic climatology , 2001 .

[17]  Steven F. Carle,et al.  Three‐dimensional hydrofacies modeling based on soil surveys and transition probability geostatistics , 1999 .

[18]  S. P. Neuman.  Comment on ``A critical review of data on field-scale dispersion in aquifers'' by L. W. Gelhar, C. Welty, and K. R. Rehfeldt , 1993 .

[19]  Peter S. Eagleson,et al.  Climate, soil, and vegetation: 2. The distribution of annual precipitation derived from observed storm sequences , 1978 .

[20]  E. O'Loughlin.  Prediction of Surface Saturation Zones in Natural Catchments by Topographic Analysis , 1986 .

[21]  B. Hewitson,et al.  Climate downscaling: techniques and application , 1996 .

[22]  Murugesu Sivapalan,et al.  Linking flood frequency to long‐term water balance: Incorporating effects of seasonality , 2005 .

[23]  John H. Cushman,et al.  On unifying the concepts of scale, instrumentation, and stochastics in the development of multiphase transport theory , 1984 .

[24]  George Kuczera,et al.  A hidden Markov model for modelling long-term persistence in multi-site rainfall time series. 2. Real data analysis , 2003 .

[25]  Eric F. Wood,et al.  A land-surface hydrology parameterization with subgrid variability for general circulation models , 1992 .

[26]  Murugesu Sivapalan,et al.  Modeling the spatial variability of subsurface runoff using a topographic index , 1997 .

[27]  Murugesu Sivapalan,et al.  Transformation of point rainfall to areal rainfall: Intensity-duration-frequency curves , 1998 .

[28]  Martijn J. Booij,et al.  Extreme daily precipitation in Western Europe with climate change at appropriate spatial scales , 2002 .

[29]  J. Olsson,et al.  Temporal rainfall disaggregration based on scaling properties , 1998 .

[30]  Demetris Koutsoyiannis,et al.  A scaling model of a storm hyetograph , 1993 .

[31]  J. Famiglietti,et al.  Analysis and mapping of field‐scale soil moisture variability using high‐resolution, ground‐based data during the Southern Great Plains 1997 (SGP97) Hydrology Experiment , 2000 .

[32]  H. Wheater,et al.  Modelling of British rainfall using a random parameter Bartlett-Lewis Rectangular Pulse Model , 1993 .

[33]  Günter Blöschl,et al.  Spatial correlation of soil moisture in small catchments and its relationship to dominant spatial hydrological processes , 2004 .

[34]  R. Grayson,et al.  Scaling of Soil Moisture: A Hydrologic Perspective , 2002 .

[35]  Albert A. M. Holtslag,et al.  Spatial Heterogeneity of the Soil Moisture Content and Its Impact on Surface Flux Densities and Near-Surface Meteorology , 2002 .

[36]  Keith Beven,et al.  Preface to the special section on Scale Problems in Hydrology , 1997 .

[37]  Shaun Lovejoy,et al.  Multifractal Analysis Techniques and the Rain and Cloud Fields from 10−3 to 106m , 1991 .

[38]  Murugesu Sivapalan,et al.  Scale issues in hydrological modelling: A review , 1995 .

[39]  Brett C. Eaton,et al.  Scaling and regionalization of flood flows in British Columbia, Canada , 2002 .

[40]  David A. Woolhiser,et al.  A Stochastic Model of Dimensionless Thunderstorm Rainfall , 1985 .

[41]  Yizong Cheng,et al.  Statistical characterization of remotely sensed soil moisture images , 1997 .

[42]  Murugesu Sivapalan,et al.  Downward approach to hydrological prediction , 2003 .

[43]  T. Hewett.  Fractal Distributions of Reservoir Heterogeneity and Their Influence on Fluid Transport , 1986 .

[44]  R. Merz,et al.  A process typology of regional floods , 2003 .

[45]  R. Srikanthan,et al.  A space and time model for design storm rainfall , 1999 .

[46]  D. Elsworth,et al.  Multiporosity/multipermeability approach to the simulation of naturally fractured reservoirs , 1993 .

[47]  M. Hutchinson,et al.  Estimating fractal dimension of profiles: A comparison of methods , 1994 .

[48]  T. Green,et al.  Measurement, scaling, and topographic analyses of spatial crop yield and soil water content , 2004 .

[49]  Murugesu Sivapalan,et al.  An investigation into the physical causes of scaling and heterogeneity of regional flood frequency , 1997 .

[50]  G. Blöschl,et al.  Flood frequency regionalisation—spatial proximity vs. catchment attributes , 2005 .

[51]  C. Axness,et al.  Three‐dimensional stochastic analysis of macrodispersion in aquifers , 1983 .

[52]  C. L. Farmer.  Upscaling: a review , 2002 .

[53]  Y. Yortsos,et al.  Application of Fractal Geometry to the Study of Networks of Fractures and Their Pressure Transient , 1995 .

[54]  M. Bierkens,et al.  Block hydraulic conductivity of cross-bedded fluvial sediments , 1994 .

[55]  Floyd A. Huff,et al.  Time distribution of rainfall in heavy storms , 1967 .

[56]  Keith Beven,et al.  Linking parameters across scales: Subgrid parameterizations and scale dependent hydrological models. , 1995 .

[57]  Pierre M. Adler,et al.  Effective permeability of fractured porous media in steady state flow , 2003 .

[58]  Merab Menabde,et al.  Multiscaling properties of rainfall and bounded random cascades , 1997 .

[59]  Murugesu Sivapalan,et al.  Tests of a space‐time model of daily rainfall in southwestern Australia based on nonhomogeneous random cascades , 2000 .

[60]  Murugesu Sivapalan,et al.  A framework for scaling of hydrologic conceptualizations based on a disaggregation–aggregation approach , 2004 .

[61]  I. Moore,et al.  Digital terrain modelling: A review of hydrological, geomorphological, and biological applications , 1991 .

[62]  G. McCabe,et al.  Simulation of precipitation by weather type analysis , 1991 .

[63]  A. Bárdossy,et al.  Multivariate stochastic downscaling model for generating daily precipitation series based on atmospheric circulation , 2002 .

[64]  Andrew W. Western,et al.  Towards areal estimation of soil water content from point measurements: time and space stability of mean response , 1998 .

[65]  Efi Foufoula-Georgiou,et al.  Hydrologic Advances in Space-Time Precipitation Modeling and Forecasting , 1991 .

[66]  J. S. Wang,et al.  Flow and Transport in Fractured Rocks , 1991 .

[67]  K. Sreenivasan.  FRACTALS AND MULTIFRACTALS IN FLUID TURBULENCE , 1991 .

[68]  A. Robock,et al.  Temporal and spatial scales of observed soil moisture variations in the extratropics , 2000 .

[69]  Carlo De Michele,et al.  A multi-level approach to flood frequency regionalisation , 2002 .

[70]  Robert W. Masters,et al.  Comparing statistical models of physical heterogeneity in buried‐valley aquifers , 2000 .

[71]  T. Wigley,et al.  Precipitation predictors for downscaling: observed and general circulation model relationships , 2000 .

[72]  Efi Foufoula-Georgiou,et al.  A space-time downscaling model for rainfall , 1999 .

[73]  Clayton V. Deutsch,et al.  Challenges in reservoir forecasting , 1996 .

[74]  M. Seyfried.  Spatial variability constraints to modeling soil water at different scales , 1998 .

[75]  Demetris Koutsoyiannis,et al.  On the representation of hyetograph characteristics by stochastic rainfall models , 2001 .

[76]  Günter Blöschl,et al.  Observed spatial organization of soil moisture and its relation to terrain indices , 1999 .

[77]  V. Gupta,et al.  Scale Dependence and Scale Invariance in Hydrology: Spatial Variability and Scale Invariance in Hydrologic Regionalization , 1998 .

[78]  T. Wigley,et al.  Statistical downscaling of general circulation model output: A comparison of methods , 1998 .

[79]  Roger Beckie,et al.  Measurement Scale, Network Sampling Scale, and Groundwater Model Parameters , 1996 .

[80]  Murugesu Sivapalan,et al.  Process controls on regional flood frequency: Coefficient of variation and basin scale , 1997 .

[81]  K. Beven,et al.  A physically based, variable contributing area model of basin hydrology , 1979 .

[82]  Anne-Catherine Favre,et al.  Unbiased parameter estimation of the Neyman-Scott model for rainfall simulation with related confidence interval , 2004 .

[83]  D. Wilks,et al.  The weather generation game: a review of stochastic weather models , 1999 .

[84]  A. Pitman.  The evolution of, and revolution in, land surface schemes designed for climate models , 2003 .

[85]  Oscar J. Mesa,et al.  Multiscaling theory of flood peaks: Regional quantile analysis , 1994 .

[86]  Demetris Koutsoyiannis,et al.  Multivariate rainfall disaggregation at a fine timescale , 2003 .

[87]  Timothy Scheibe,et al.  Use of sedimentological information for geometric simulation of natural porous media structure , 1995 .

[88]  John D. Albertson,et al.  Temporal dynamics of soil moisture variability: 2. Implications for land surface models , 2003 .

[89]  Roberto Ranzi,et al.  On the derivation of the areal reduction factor of storms , 1996 .

[90]  T. McMahon,et al.  Stochastic generation of annual, monthly and daily climate data: A review , 2001 .

[91]  Zong-Liang Yang,et al.  Aggregation rules for surface parameters in global models , 1997 .

[92]  C. Cunnane.  Methods and merits of regional flood frequency analysis , 1988 .

[93]  David R. Dawdy,et al.  Physical interpretations of regional variations in the scaling exponents of flood quantiles , 1995 .

[94]  P. Jones,et al.  The use of weather types and air flow indices for GCM downscaling , 1998 .

[95]  Fritz Stauffer,et al.  Transport modeling in heterogeneous aquifers: 2. Three‐dimensional transport model and stochastic numerical tracer experiments , 1994 .

[96]  T. Brandsma,et al.  Statistical linkage of daily precipitation in Switzerland to atmospheric circulation and temperature , 1997 .

[97]  J. Smith,et al.  Representation of basin scale in flood peak distributions , 1992 .

[98]  Mary P. Anderson,et al.  Comment on “Universal scaling of hydraulic conductivities and dispersivities in geologic media” by S. P. Neuman , 1991 .

[99]  James P. Hughes,et al.  Statistical downscaling of daily precipitation from observed and modelled atmospheric fields , 2004 .

[100]  Günter Blöschl,et al.  Scaling issues in snow hydrology , 1999 .

[101]  A. Western,et al.  Characteristic space scales and timescales in hydrology , 2003 .

[102]  Erwin Zehe,et al.  Predictability of hydrologic response at the plot and catchment scales: Role of initial conditions , 2004 .

[103]  H. Storch,et al.  The Analog Method as a Simple Statistical Downscaling Technique: Comparison with More Complicated Methods , 1999 .

[104]  D. Veneziano,et al.  Flow through porous media with multifractal hydraulic conductivity , 2003 .

[105]  Günter Blöschl,et al.  Scaling in hydrology , 2001 .

[106]  Günter Blöschl,et al.  How well do indicator variograms capture the spatial connectivity of soil moisture , 1998 .

[107]  Zhao Ren-jun,et al.  The Xinanjiang model applied in China , 1992 .

[108]  L. Nyberg.  Spatial variability of soil water content in the covered catchment at Gårdsjön, Sweden , 1996 .

[109]  Hans Peter Schmid,et al.  Footprint modeling for vegetation atmosphere exchange studies: a review and perspective , 2002 .

[110]  R. Grayson,et al.  Toward capturing hydrologically significant connectivity in spatial patterns , 2001 .

[111]  Paul A. Witherspoon,et al.  A Model for Steady Fluid Flow in Random Three‐Dimensional Networks of Disc‐Shaped Fractures , 1985 .

[112]  S. Gorelick,et al.  Heterogeneity in Sedimentary Deposits: A Review of Structure‐Imitating, Process‐Imitating, and Descriptive Approaches , 1996 .

[113]  Ignacio Rodriguez-Iturbe,et al.  Geomorphoclimatic estimation of extreme flow probabilities , 1983 .

[114]  Robert L. Wilby,et al.  Prospects for downscaling seasonal precipitation variability using conditioned weather generator parameters , 2002 .

[115]  Jonas Olsson,et al.  Cascade-based disaggregation of continuous rainfall time series : the influence of climate , 2001 .

[116]  D. H. Pilgrim,et al.  Some problems in transferring hydrological relationships between small and large drainage basins and between regions , 1983 .

[117]  M. Anderson.  Subsurface Flow and Transport: Characterization of geological heterogeneity , 1997 .

[118]  S. P. Neuman.  Universal scaling of hydraulic conductivities and dispersivities in geologic media , 1990 .

[119]  V. Gupta,et al.  The mathematical structure of rainfall representations: 3. Some applications of the point process theory to rainfall processes , 1981 .

[120]  G. Sposito,et al.  Conditional Simulation of Geologic Media with Evolving Scales of Heterogeneity , 1998 .

[121]  Vittorio Di Federico,et al.  Scaling of random fields by means of truncated power variograms and associated spectra , 1997 .

[122]  Günter Blöschl,et al.  On the spatial scaling of soil moisture , 1999 .