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.@en

In this synthesis paper addressing hydrologic scaling and similarity, we posit that roadblocks in the search for universal laws of hydrology are hindered by our focus on computational simulation (the third paradigm) and assert that it is time for hydrology to embrace a fourth paradigm of data-intensive science. Advances in information-based hydrologic science, coupled with an explosion of hydrologic data and advances in parameter estimation and modeling, have laid the foundation for a data-driven framework for scrutinizing hydrological scaling and similarity hypotheses. We summarize important scaling and similarity concepts (hypotheses) that require testing; describe a mutual information framework for testing these hypotheses; describe boundary condition, state, flux, and parameter data requirements across scales to support testing these hypotheses; and discuss some challenges to overcome while pursuing the fourth hydrological paradigm. We call upon the hydrologic sciences community to develop a focused effort towards adopting the fourth paradigm and apply this to outstanding challenges in scaling and similarity.@en

In just the past 5 years, the field of Earth observation has progressed beyond the offerings of conventional space-agency-based platforms to include a plethora of sensing opportunities afforded by CubeSats, unmanned aerial vehicles (UAVs), and smartphone technologies that are being embraced by both for-profit companies and individual researchers. Over the previous decades, space agency efforts have brought forth well-known and immensely useful satellites such as the Landsat series and the Gravity Research and Climate Experiment (GRACE) system, with costs typically of the order of 1 billion dollars per satellite and with concept-to-launch timelines of the order of 2 decades (for new missions). More recently, the proliferation of smartphones has helped to miniaturize sensors and energy requirements, facilitating advances in the use of CubeSats that can be launched by the dozens, while providing ultra-high (3- 5 m) resolution sensing of the Earth on a daily basis. Startup companies that did not exist a decade ago now operate more satellites in orbit than any space agency, and at costs that are a mere fraction of traditional satellite missions. With these advances come new space-borne measurements, such as real-time high-definition video for tracking air pollution, storm-cell development, flood propagation, precipitation monitoring, or even for constructing digital surfaces using structure-from-motion techniques. Closer to the surface, measurements from small unmanned drones and tethered balloons have mapped snow depths, floods, and estimated evaporation at sub-metre resolutions, pushing back on spatio-temporal constraints and delivering new process insights. At ground level, precipitation has been measured using signal attenuation between antennae mounted on cell phone towers, while the proliferation of mobile devices has enabled citizen scientists to catalogue photos of environmental conditions, estimate daily average temperatures from battery state, and sense other hydrologically important variables such as channel depths using commercially available wireless devices. Global internet access is being pursued via highaltitude balloons, solar planes, and hundreds of planned satellite launches, providing a means to exploit the "internet of things" as an entirely new measurement domain. Such global access will enable real-time collection of data from billions of smartphones or from remote research platforms. This future will produce petabytes of data that can only be accessed via cloud storage and will require new analytical approaches to interpret. The extent to which today's hydrologic models can usefully ingest such massive data volumes is unclear. Nor is it clear whether this deluge of data will be usefully exploited, either because the measurements are superfluous, inconsistent, not accurate enough, or simply because we lack the capacity to process and analyse them. What is apparent is that the tools and techniques afforded by this array of novel and game-changing sensing platforms present our community with a unique opportunity to develop new insights that advance fundamental aspects of the hydrological sciences. To accomplish this will require more than just an application of the technology: in some cases, it will demand a radical rethink on how we utilize and exploit these new observing systems.@en

In just the past 5 years, the field of Earth observation has progressed beyond the offerings of conventional space-agency-based platforms to include a plethora of sensing opportunities afforded by CubeSats, unmanned aerial vehicles (UAVs), and smartphone technologies that are being embraced by both for-profit companies and individual researchers. Over the previous decades, space agency efforts have brought forth well-known and immensely useful satellites such as the Landsat series and the Gravity Research and Climate Experiment (GRACE) system, with costs typically of the order of 1 billion dollars per satellite and with concept-to-launch timelines of the order of 2 decades (for new missions). More recently, the proliferation of smartphones has helped to miniaturize sensors and energy requirements, facilitating advances in the use of CubeSats that can be launched by the dozens, while providing ultra-high (3-5 m) resolution sensing of the Earth on a daily basis. Start-up companies that did not exist a decade ago now operate more satellites in orbit than any space agency, and at costs that are a mere fraction of traditional satellite missions. With these advances come new space-borne measurements, such as real-time high-definition video for tracking air pollution, storm-cell development, flood propagation, precipitation monitoring, or even for constructing digital surfaces using structure-from-motion techniques. Closer to the surface, measurements from small unmanned drones and tethered balloons have mapped snow depths, floods, and estimated evaporation at sub-metre resolutions, pushing back on spatio-temporal constraints and delivering new process insights. At ground level, precipitation has been measured using signal attenuation between antennae mounted on cell phone towers, while the proliferation of mobile devices has enabled citizen scientists to catalogue photos of environmental conditions, estimate daily average temperatures from battery state, and sense other hydrologically important variables such as channel depths using commercially available wireless devices. Global internet access is being pursued via high-altitude balloons, solar planes, and hundreds of planned satellite launches, providing a means to exploit the “internet of things” as an entirely new measurement domain. Such global access will enable real-time collection of data from billions of smartphones or from remote research platforms. This future will produce petabytes of data that can only be accessed via cloud storage and will require new analytical approaches to interpret. The extent to which today's hydrologic models can usefully ingest such massive data volumes is unclear. Nor is it clear whether this deluge of data will be usefully exploited, either because the measurements are superfluous, inconsistent, not accurate enough, or simply because we lack the capacity to process and analyse them. What is apparent is that the tools and techniques afforded by this array of novel and game-changing sensing platforms present our community with a unique opportunity to develop new insights that advance fundamental aspects of the hydrological sciences. To accomplish this will require more than just an application of the technology: in some cases, it will demand a radical rethink on how we utilize and exploit these new observing systems.@en