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The Importance of Hydraulic Groundwater Theory in Catchment Hydrology: the Legacy of Wilfried Brutsaert and Jean-Yves Parlange Peter A

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The Importance of Hydraulic Groundwater Theory in Catchment Hydrology: the Legacy of Wilfried Brutsaert and Jean-Yves Parlange Peter A WATER RESOURCES RESEARCH, VOL. 49, 5099–5116, doi:10.1002/wrcr.20407, 2013 The importance of hydraulic groundwater theory in catchment hydrology: The legacy of Wilfried Brutsaert and Jean-Yves Parlange Peter A. Troch,1 Alexis Berne,2 Patrick Bogaart,3 Ciaran Harman,4 Arno G. J. Hilberts,5 Steve W. Lyon,6 Claudio Paniconi,7 Valentijn R. N. Pauwels,8 David E. Rupp,9 John S. Selker,10 Adriaan J. Teuling,11 Remko Uijlenhoet,11 and Niko E. C. Verhoest12 Received 1 March 2013; revised 21 June 2013; accepted 8 July 2013; published 4 September 2013. [1] Based on a literature overview, this paper summarizes the impact and legacy of the contributions of Wilfried Brutsaert and Jean-Yves Parlange (Cornell University) with respect to the current state-of-the-art understanding in hydraulic groundwater theory. Forming the basis of many applications in catchment hydrology, ranging from drought flow analysis to surface water-groundwater interactions, hydraulic groundwater theory simplifies the description of water flow in unconfined riparian and perched aquifers through assumptions attributed to Dupuit and Forchheimer. Boussinesq (1877) derived a general equation to study flow dynamics of unconfined aquifers in uniformly sloping hillslopes, resulting in a remarkably accurate and applicable family of results, though often challenging to solve due to its nonlinear form. Under certain conditions, the Boussinesq equation can be solved analytically allowing compact representation of soil and geomorphological controls on unconfined aquifer storage and release dynamics. The Boussinesq equation has been extended to account for flow divergence/convergence as well as for nonuniform bedrock slope (concave/convex). The extended Boussinesq equation has been favorably compared to numerical solutions of the three-dimensional Richards equation, confirming its validity under certain geometric conditions. Analytical solutions of the linearized original and extended Boussinesq equations led to the formulation of similarity indices for baseflow recession analysis, including scaling rules, to predict the moments of baseflow response. Validation of theoretical recession parameters on real-world streamflow data is complicated due to limited measurement accuracy, changing boundary conditions, and the strong coupling between the saturated aquifer with the overlying unsaturated zone. However, recent advances are shown to have mitigated several of these issues. The extended Boussinesq equation has been successfully applied to represent baseflow dynamics in catchment-scale hydrological models, and it is currently considered to represent lateral redistribution of groundwater in land surface schemes applied in global circulation models. From the review, it is clear that Wilfried Brutsaert and Jean-Yves Parlange stimulated a body of research that has led to several fundamental discoveries and practical applications with important contributions in hydrological modeling. Citation: Troch, P. A., et al. (2013), The importance of hydraulic groundwater theory in catchment hydrology: The legacy of Wilfried Brutsaert and Jean-Yves Parlange, Water Resour. Res., 49, 5099–5116, doi: 10.1002/wrcr.20407. 1Department of Hydrology and Water Resources, University of Arizona, 9Oregon Climate Change Research Institute, College of Earth, Ocean Tucson, Arizona, USA. and Atmospheric Sciences, Oregon State University, Corvallis, Oregon, 2Environmental Remote Sensing Laboratory, EPFL, Lausanne, USA. Switzerland. 10Biological & Ecological Engineering Department, Oregon State Uni- 3Copernicus Institute of Sustainable Development, Environmental Sci- versity, Corvallis, Oregon, USA. ences Group, Utrecht University, Utrecht, Netherlands. 11Hydrology and Quantitative Water Management, Wageningen Uni- 4Department of Geography and Environmental Engineering, Johns Hop- versity, Wageningen, Netherlands. kins University, Baltimore, Maryland, USA. 12Laboratory of Hydrology and Water Management, Ghent University, 5Risk Management Solutions Ltd., London, UK. Ghent, Belgium. 6Physical Geography and Quaternary Geology, Stockholm University, Corresponding author: P. A. Troch, Hydrology and Water Resources, Stockholm, Sweden. University of Arizona, 1133 E. James E. Rogers Way, Tucson, AZ 85721, 7Institut National de la Recherche Scientifique, Centre Eau Terre Envi- USA. ([email protected]) ronnement (INRS-ETE), UniversitedeQuebec, Quebec City, Quebec, Canada. ©2013. American Geophysical Union. All Rights Reserved. 8 Department of Civil Engineering, Monash University, Clayton, Victo- 0043-1397/13/10.1002/wrcr.20407 ria, Australia. 5099 TROCH ET AL.: REVIEW 1. Introduction these hypotheses. In short, it is the scientific method that guarantees advancement in our understanding rather than [2] Quantifying catchment-scale hydrological processes, parameter estimation in absence of insight, as so often states, and fluxes remains difficult due to the scale of the encountered in the literature. chosen control volume and the intrinsic heterogeneities of [5] This review paper describes the importance of hy- soil, vegetation, and topographic parameters that define draulic groundwater theory in catchment hydrology, and these processes. A bottom-up approach (i.e., building large- the role Brutsaert and Parlange have played. Because of scale predictions explicitly from direct measurement of this focus, we selected contributions that have played piv- parameters reflecting basic principles of underlying small- otal roles in developing catchment-scale theory of hydro- scale processes) that attempts to characterize all relevant logic response, and have left out many other important heterogeneities seems to be infeasible with current technol- contributions employing hydraulic groundwater theory. ogy [McDonnell et al., 2007], although important progress Section 2 summarizes the main concepts leading to hydrau- has been made using geophysical and remote sensing meth- lic groundwater theory of riparian and perched aquifers that ods (e.g., ground penetrating radar and electrical resistance drain into the catchment’s channel network. Section 3 tomography to scan subsurface soil properties at hillslope reviews several exact and approximate analytical solutions scales, visible and near IR remote sensing to map vegetation to the main equations of hydraulic groundwater theory, properties). We also lack solid theory that links small-scale many of which were proposed by Brutsaert, Parlange, their variability of soil and vegetation properties to large-scale students, and colleagues. Section 4 focuses on how hydrau- fluxes at the land surface and the subsurface [Troch et al., lic groundwater theory can be used to interpret recession 2008]. Therefore, analysis of catchment data, based on flow at catchment scales. Section 5 extends the baseflow appropriate hydrological theory, is a reasonable approach to analysis methods proposed by Brutsaert and Parlange to progress the understanding of catchment-scale processes. quantify other hydrological fluxes, such as precipitation [3] This approach is at the heart of the research executed and evaporation, as well as develop parsimonious rainfall- by Wilfried Brutsaert and Jean-Yves Parlange. While they runoff models. Section 6 reviews several extensions have addressed many different aspects of hydrology, here recently made to hydraulic groundwater theory that attempt we focus on their groundbreaking contributions regarding to relax some of the important assumptions inherent in tra- the rainfall-runoff response at the catchment scale. In a ditional hydraulic groundwater theory. In section 7, we time when distributed hydrological models became popular present studies that have formulated hydrologic similarity and seemingly the way out of the intractable problem of theory based on the pioneering work of Brutsaert and Par- identifying catchment response in light of landscape heter- lange. Finally, in Section 8, we review recent contributions ogeneity, they emphasized the scientific method: formulate to understanding hydrologic response to climate change the problem in ways that preserve the main physical prop- based on hydraulic groundwater theory. erties but reduce the dimensionality, find exact or approxi- mate solutions to the resulting flow and transport equations 2. Hydraulic Groundwater Theory to better understand the dominant modes of response, test these simplified solutions with real catchment data, develop 2.1. The Dupuit-Forchheimer Assumptions methods to derive catchment-scale parameter values from [6] Hydraulic groundwater theory of unconfined flow in these data sets, and inspire colleagues to explain observed a horizontal or sloping aquifer is founded on the Dupuit- inconsistencies between theory and observations. Forchheimer assumptions. In 1863, Dupuit postulated that [4] Their combined work on hydraulic groundwater given the aspect ratio prevelent in groundwater systems theory is a case study in the power of the scientific method that accurate descriptions of flow could be obtained by that they embraced. Hydraulic groundwater theory is simple ignoring the impact of vertical fluxes, and instead compute enough to allow derivation of exact or approximate analyti- groundwater flux assuming that water moves largely hori- cal solutions to specific flow situations defined by the initial zontally in proportion to the saturated aquifer thickness and and boundary conditions, yet it preserves the main physics the slope of the free surface of the aquifer [Dupuit, 1863]. that drives the flow (i.e., advection and diffusion driven
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