Searching for the Holy Grail of scientific hydrology: Q t =( S, R, Δt ) A as closure

Abstract. Representative Elementary Watershed concepts provide a useful scale-independent framework for the representation of hydrological processes. The balance equations that underlie the concepts, however, require the definition of boundary flux closures that should be expected to be scale dependent. The relationship between internal state variables of an REW element and the boundary fluxes will be nonlinear, hysteretic and scale-dependent and may depend on the extremes of the heterogeneities within the REW. Because of the nonlinearities involved, simple averaging of local scale flux relationships are unlikely to produce an adequate decription of the closure problem at the REW scale. Hysteresis in the dynamic response is demonstrated for some small experimental catchments and it is suggested that at least some of this hysteresis can be represented by the use of simple transfer functions. The search for appropriate closure schemes is the second most important problem in hydrology of the 21st Century (the most important is providing the techniques to measure integrated fluxes and storages at useful scales). The closure problem is a scientific Holy Grail: worth searching for even if a general solution might ultimate prove impossible to find.

[1]  William B. Haines,et al.  Studies in the physical properties of soil. V. The hysteresis effect in capillary properties, and the modes of moisture distribution associated therewith , 1930, The Journal of Agricultural Science.

[2]  R. Allan Freeze,et al.  A stochastic‐conceptual analysis of rainfall‐runoff processes on a hillslope , 1980 .

[3]  K. Beven.  Kinematic subsurface stormflow , 1981 .

[4]  Keith Beven,et al.  On hydrologic similarity: 2. A scaled model of storm runoff production , 1987 .

[5]  Keith Beven,et al.  Effects of spatial variability and scale with implications to hydrologic modeling , 1988 .

[6]  Keith Beven,et al.  On hydrological heterogeneity - Catchment morphology and catchment response , 1988 .

[7]  K. Beven,et al.  A physically based model of heterogeneous hillslopes: 2. Effective hydraulic conductivities , 1989 .

[8]  Malcolm G. Anderson,et al.  Soil water hysteresis: models and implications. , 1990 .

[9]  Keith Beven,et al.  Three‐dimensional modelling of hillslope hydrology , 1992 .

[10]  Peter C. Young,et al.  Data-based mechanistic modelling and the rainfall-flow non-linearity. , 1994 .

[11]  M. Sivapalan,et al.  A unifying framework for watershed thermodynamics: balance equations for mass, momentum, energy and entropy, and the second law of thermodynamics , 1998 .

[12]  W. Gray,et al.  A unifying framework for watershed thermodynamics: constitutive relationships , 1999 .

[13]  J. Kirchner,et al.  Fractal stream chemistry and its implications for contaminant transport in catchments , 2000, Nature.

[14]  Keith Beven,et al.  Uniqueness of place and process representations in hydrological modelling , 2000 .

[15]  Murugesu Sivapalan,et al.  Conservation equations governing hillslope responses: Exploring the physical basis of water balance , 2000 .

[16]  Keith Beven,et al.  Dalton Medal Lecture: How far can we go in distributed hydrological modelling? , 2001 .

[17]  Keith Beven,et al.  On hypothesis testing in hydrology , 2001 .

[18]  J. Kirchner,et al.  Catchment-scale advection and dispersion as a mechanism for fractal scaling in stream tracer concentrations , 2001 .

[19]  M. G. Anderson,et al.  DATA-BASED MECHANISTIC MODELLING AND VALIDATION OF RAINFALL-FLOW PROCESSES , 2001 .

[20]  Vladan Babovic,et al.  Towards the hydraulics of the hydroinformatics era , 2001 .

[21]  Keith Beven,et al.  Towards an alternative blueprint for a physically based digitally simulated hydrologic response modelling system , 2002 .

[22]  Peter C. Young,et al.  Observational data and scale‐dependent parameterizations: explorations using a virtual hydrological reality , 2002 .

[23]  Keith Beven,et al.  Towards a coherent philosophy for environmental modelling. , 2002 .

[24]  K. Beven.  Towards a coherent philosophy for modelling the environment , 2002, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[25]  Jaap Schellekens,et al.  Modelling of hydrological responses: the representative elementary watershed approach as an alternative blueprint for watershed modelling , 2003 .

[26]  P. E. O'connell,et al.  IAHS Decade on Predictions in Ungauged Basins (PUB), 2003–2012: Shaping an exciting future for the hydrological sciences , 2003 .

[27]  Peter C. Young,et al.  Top‐down and data‐based mechanistic modelling of rainfall–flow dynamics at the catchment scale , 2003 .

[28]  Jeffrey J. McDonnell,et al.  Virtual experiments: a new approach for improving process conceptualization in hillslope hydrology , 2004 .

[29]  Peter C. Young,et al.  Data-based mechanistic modelling and the simplification of environmental systems. , 2004 .

[30]  Hubert H. G. Savenije,et al.  Numerical simulations of runoff generation with surface water–groundwater interactions in the Alzette river alluvial plain (Luxembourg) , 2005 .

[31]  Isabelle Braud,et al.  Multi-criteria assessment of the Representative Elementary Watershed approach on the Donga catchment (Benin) using a downward approach of model complexity , 2005 .

[32]  Hubert H. G. Savenije,et al.  Rainfall-runoff modelling in a catchment with a complex groundwater flow system: application of the Representative Elementary Watershed (REW) approach , 2005 .

[33]  J. O'kane.  Hysteresis in hydrology , 2005 .

[34]  Erwin Zehe,et al.  Predictions of rainfall-runoff response and soil moisture dynamics in a microscale catchment using the CREW model , 2006 .

[35]  Keith Beven,et al.  A manifesto for the equifinality thesis , 2006 .

[36]  Erwin Zehe,et al.  Dynamical process upscaling for deriving catchment scale state variables and constitutive relations for meso-scale process models , 2006 .