Scaling in Surface Hydrology: Progress and Challenges

: This paper presents a review of the challenges in spatial and temporal scales in surface hydrology. Fundamental issues and gaps in our understanding of hydrologic scaling are highlighted and shown to limit predictive skill, with heterogeneities, nonlinearities, and non-local transport processes among the most significant difficulties faced in scaling. The discrepancy between the physical process scale and the measurement scale has played a major role in restricting the development of theories, for example, relating observational scales to scales of climate and weather models. Progress in our knowledge of scaling in hydrology requires systematic determination of critical scales and scale invariance of physical processes. In addition, viewing the surface hydrologic system as composed of interacting dynamical subsystems should facilitate the definition of scales observed in nature. Such an approach would inform the development of careful, resolution-dependent, physical law formulation based on mathematical techniques and physical laws.

[1]  Andrea Molod,et al.  A New Look at Modeling Surface Heterogeneity: Extending Its Influence in the Vertical , 2003 .

[2]  Roni Avissar,et al.  Scaling of land-atmosphere interactions: An atmospheric modelling perspective , 1995 .

[3]  P. S. Eagleson,et al.  Land Surface Hydrology Parameterization for Atmospheric General Circulation models Including Subgrid Scale Spatial Variability , 1989 .

[4]  C. Nappo.  An introduction to atmospheric gravity waves , 2002 .

[5]  Bin Li,et al.  The impact of spatial variability of land-surface characteristics on land-surface heat fluxes , 1994 .

[6]  L. A. Richards.  Capillary conduction of liquids through porous mediums , 1931 .

[7]  M. L. Kavvas,et al.  Scale Invariance and Self-Similarity in Hydrologic Processes in Space and Time , 2011 .

[8]  A S Monin,et al.  BASIC LAWS OF TURBULENT MIXING IN THE GROUND LAYER OF ATMOSPHERE , 1954 .

[9]  A. Chehbouni,et al.  Estimation of heat and momentum fluxes over complex terrain using a large aperture scintillometer , 2000 .

[10]  Numerical Simulation of Nonlinear Mesoscale Circulations Induced by the Thermal Heterogeneities of Land Surface , 1998 .

[11]  R. Neggers.  A Dual Mass Flux Framework for Boundary Layer Convection. Part II: Clouds , 2009 .

[12]  John H. Cushman,et al.  Nonequilibrium statistical mechanical derivation of a nonlocal Darcy's Law for unsaturated/saturated flow , 1994 .

[13]  W. Crow,et al.  The assimilation of remotely sensed soil brightness temperature imagery into a land surface model using Ensemble Kalman filtering: a case study based on ESTAR measurements during SGP97 , 2003 .

[14]  Shaun Lovejoy,et al.  Multifractals, cloud radiances and rain , 2006 .

[15]  M. Kavvas,et al.  Generalized Fick's Law and Fractional ADE for Pollution Transport in a River: Detailed Derivation , 2006 .

[16]  Possible self-organizing dynamics for land-atmosphere interaction (Paper 98JD02454) , 1998 .

[17]  R. Koster,et al.  Comparison and assimilation of global soil moisture retrievals from the Advanced Microwave Scanning Radiometer for the Earth Observing System (AMSR‐E) and the Scanning Multichannel Microwave Radiometer (SMMR) , 2007 .

[18]  Alessandro Marani,et al.  Fractal Structures as Least Energy Patterns - the Case of River Networks , 1992 .

[19]  Fotini Katopodes Chow,et al.  The effect of mountainous topography on moisture exchange between the “surface” and the free atmosphere , 2007 .

[20]  A. Kolmogorov.  The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers , 1991, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[21]  D. Schertzer,et al.  Functional Box-Counting and Multiple Elliptical Dimensions in Rain , 1987, Science.

[22]  M. Ek,et al.  Hyperresolution global land surface modeling: Meeting a grand challenge for monitoring Earth's terrestrial water , 2011 .

[23]  Dennis P. Lettenmaier,et al.  Simulation of spatial variability in snow and frozen soil , 2003 .

[24]  J. Kirchner.  Getting the right answers for the right reasons: Linking measurements, analyses, and models to advance the science of hydrology , 2006 .

[25]  W. J. Shuttleworth,et al.  An Agenda for Land-Surface Hydrology Research and a Call for the Second International Hydrological Decade , 2013 .

[26]  Roni Avissar,et al.  An Evaluation of the Scale at which Ground-Surface Heat Flux Patchiness Affects the Convective Boundary Layer Using Large-Eddy Simulations , 1998 .

[27]  A. P. Siebesma,et al.  A Combined Eddy-Diffusivity Mass-Flux Approach for the Convective Boundary Layer , 2007 .

[28]  Markus Weiler,et al.  Conceptualizing lateral preferential flow and flow networks and simulating the effects on gauged and ungauged hillslopes , 2007 .

[29]  J. Wieringa.  Roughness‐dependent geographical interpolation of surface wind speed averages , 1986 .

[30]  Roger A. Pielke,et al.  A parameterization of heterogeneous land surfaces for atmospheric numerical models and its impact on regional meteorology , 1989 .

[31]  A. Rinaldo,et al.  Fractal River Basins: Chance and Self-Organization , 1997 .

[32]  Paolo D'Odorico,et al.  Space-time self-organization of mesoscale rainfall and soil moisture , 2000 .

[33]  J. Kirchner.  Catchments as simple dynamical systems: Catchment characterization, rainfall‐runoff modeling, and doing hydrology backward , 2009 .

[34]  E. Foufoula‐Georgiou,et al.  A nonlocal theory of sediment transport on hillslopes , 2010 .

[35]  M. Sivapalan.  Process complexity at hillslope scale, process simplicity at the watershed scale: is there a connection? , 2003 .

[36]  Lifeng Luo,et al.  A Multiscale Ensemble Filtering System for Hydrologic Data Assimilation. Part I: Implementation and Synthetic Experiment , 2009 .

[37]  Daniel Schertzer,et al.  No monsters, no miracles: in nonlinear sciences hydrology is not an outlier! , 2010 .

[38]  S. Roy,et al.  A preferred scale for landscape forced mesoscale circulations , 2003 .

[39]  E. Foufoula‐Georgiou,et al.  A nonlocal theory of sediment buffering and bedrock channel evolution , 2008 .

[40]  Dara Entekhabi,et al.  Harmonic propagation of variability in surface energy balance within a coupled soil‐vegetation‐atmosphere system , 2011 .

[41]  Dara Entekhabi,et al.  Spectral Behaviour of a Coupled Land-Surface and Boundary-Layer System , 2010 .

[42]  Shaun Lovejoy,et al.  Multifractal Cascade Dynamics and Turbulent Intermittency , 1997 .

[43]  E. F. Bradley,et al.  Flux-Profile Relationships in the Atmospheric Surface Layer , 1971 .

[44]  L. Mahrt.  Surface Heterogeneity and Vertical Structure of the Boundary Layer , 2000, Boundary-Layer Meteorology.

[45]  I. Troen,et al.  A simple model of the atmospheric boundary layer; sensitivity to surface evaporation , 1986 .

[46]  J. Kirchner.  A double paradox in catchment hydrology and geochemistry , 2003 .

[47]  Efi Foufoula-Georgiou,et al.  Toward a unified science of the Earth's surface: Opportunities for synthesis among hydrology, geomorphology, geochemistry, and ecology , 2006 .

[48]  Christopher J. Duffy.  Scale Dependence and Scale Invariance in Hydrology , 2002 .

[49]  Charles Meneveau,et al.  Large‐eddy simulation of neutral atmospheric boundary layer flow over heterogeneous surfaces: Blending height and effective surface roughness , 2004 .

[50]  R. Maxwell,et al.  The groundwater land-surface atmosphere connection: Soil moisture effects on the atmospheric boundary layer in fully-coupled simulations , 2007 .

[51]  A generalized Fick's law to describe non-local transport effects , 2001 .

[52]  Craig T Simmons,et al.  The compleat Darcy: New lessons learned from the first English translation of les fontaines publiques de la Ville de Dijon , 2005, Ground water.

[53]  Roni Avissar,et al.  Using Similarity Theory to Parameterize Mesoscale Heat Fluxes Generated by Subgrid-Scale Landscape Discontinuities in GCMs , 1995 .

[54]  R. Pielke.  Mesoscale Meteorological Modeling , 1984 .

[55]  J. Finnigan,et al.  Scale issues in boundary-layer meteorology: Surface energy balances in heterogeneous terrain , 1995 .

[56]  Jan Polcher,et al.  A Proposed Structure for Coupling Tiled Surfaces with the Planetary Boundary Layer , 2004 .

[57]  J. Deardorff,et al.  The Counter-Gradient Heat Flux in the Lower Atmosphere and in the Laboratory , 1966 .

[58]  Larry Mahrt,et al.  The bulk aerodynamic formulation over heterogeneous surfaces , 1996 .

[59]  Fei Chen,et al.  Impact of Land-Surface Moisture Variability on Local Shallow Convective Cumulus and Precipitation in Large-Scale Models , 1994 .

[60]  J. Louis.  A parametric model of vertical eddy fluxes in the atmosphere , 1979 .

[61]  M. Levent Kavvas,et al.  Nonlinear Hydrologic Processes: Conservation Equations for Determining Their Means and Probability Distributions , 2003 .

[62]  M. Köhler,et al.  A Dual Mass Flux Framework for Boundary Layer Convection. Part I: Transport , 2009 .

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

[64]  Tammo S. Steenhuis,et al.  Drying front in a sloping aquifer: Nonlinear effects , 2004 .

[65]  Rao S. Govindaraju,et al.  Spatial averaging of unsaturated flow equations under infiltration conditions over areally heterogeneous fields 2. Numerical simulations , 1994 .

[66]  Albert A. M. Holtslag,et al.  Eddy Diffusivity and Countergradient Transport in the Convective Atmospheric Boundary Layer , 1991 .

[67]  Richard P. Hooper,et al.  Moving beyond heterogeneity and process complexity: A new vision for watershed hydrology , 2007 .

[68]  Dennis P. Lettenmaier,et al.  Parameterization of Blowing-Snow Sublimation in a Macroscale Hydrology Model , 2004 .

[69]  Models of Fractal River Basins , 1998, cond-mat/9803287.

[70]  W. Oechel,et al.  FLUXNET: A New Tool to Study the Temporal and Spatial Variability of Ecosystem-Scale Carbon Dioxide, Water Vapor, and Energy Flux Densities , 2001 .

[71]  Shaun Lovejoy,et al.  Multifractals, universality classes and satellite and radar measurements of cloud and rain fields , 1990 .

[72]  Rao S. Govindaraju,et al.  Approximate Analytical Solutions for Overland Flows , 1990 .

[73]  D. McLaughlin,et al.  Hydrologic Data Assimilation with the Ensemble Kalman Filter , 2002 .

[74]  Larry Mahrt,et al.  Grid-Averaged Surface Fluxes , 1987 .

[75]  Y. Kerr,et al.  The SMOS Mission: New Tool for Monitoring Key Elements of the Global Water Cycle This satellite mission will use new algorithms to try to forecast weather and estimate climate change from satellite measurements of the Earth's surface. , 2010 .

[76]  D. Lettenmaier,et al.  A simple hydrologically based model of land surface water and energy fluxes for general circulation models , 1994 .

[77]  G..  SCALE ISSUES IN HYDROLOGICAL MODELLING : A REVIEW , 2006 .

[78]  I. Rodríguez‐Iturbe,et al.  Comment on “On the fractal dimension of stream networks” by Paolo La Barbera and Renzo Rosso , 1990 .

[79]  Mark Z. Jacobson,et al.  Fundamentals of Atmospheric Modeling: Preface , 2005 .

[80]  Martha C. Anderson,et al.  Upscaling and Downscaling—A Regional View of the Soil–Plant–Atmosphere Continuum , 2003 .

[81]  Todd M. Scanlon,et al.  Positive feedbacks promote power-law clustering of Kalahari vegetation , 2007, Nature.

[82]  A. Rinaldo,et al.  Configuration entropy of fractal landscapes , 1998 .

[83]  Jaeyoung Yoon,et al.  Upscaling of Vertical Unsaturated Flow Model under Infiltration Condition , 2005 .

[84]  A. Banin,et al.  SCANNING ELECTRON MICROSCOPE OBSERVATIONS ON SOIL CRUSTS AND THEIR FORMATION , 1980 .

[85]  Shaun Lovejoy,et al.  Universal Multifractals: Theory and Observations for Rain and Clouds , 1993 .

[86]  A. Dyer.  A review of flux-profile relationships , 1974 .

[87]  Shaun Lovejoy,et al.  Generalized Scale Invariance in the Atmosphere and Fractal Models of Rain , 1985 .

[88]  R. Koster,et al.  Modeling the land surface boundary in climate models as a composite of independent vegetation stands , 1992 .

[89]  C. Paulson.  The Mathematical Representation of Wind Speed and Temperature Profiles in the Unstable Atmospheric Surface Layer , 1970 .

[90]  Garrison Sposito,et al.  Upscaling and downscaling methods for environmental research , 2001 .

[91]  Jiancheng Shi,et al.  The Soil Moisture Active Passive (SMAP) Mission , 2010, Proceedings of the IEEE.

[92]  D. Schertzer,et al.  Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes , 1987 .

[93]  C. Taylor,et al.  Frequency of Sahelian storm initiation enhanced over mesoscale soil-moisture patterns , 2011 .

[94]  Steven A. Margulis,et al.  The Terrestrial Water Cycle: Modeling and Data Assimilation across Catchment Scales , 2006 .