John Selker - Academia.edu (original) (raw)

Papers by John Selker

Advances in Water Resources, 2005

Applications of the axisymmetric Boussinesq equation to groundwater hydrology and reservoir engin... more Applications of the axisymmetric Boussinesq equation to groundwater hydrology and reservoir engineering have long been recognised. An archetypal example is invasion by drilling fluid into a permeable bed where there is initially no such fluid present, a circumstance of some importance in the oil industry. It is well known that the governing Boussinesq model can be reduced to a nonlinear ordinary differential equation using a similarity variable, a transformation that is valid for a certain time-dependent flux at the origin. Here, a new analytical approximation is obtained for this case. The new solution,, which has a simple form, is demonstrated to be highly accurate.

Advancing Biogeochemical Research in the Field Hydrological Sciences: The CUAHSI Hydrological Measurement Facility – Biogeochemical Component

Water Resources Research, 2014

Temperature anomalies can identify locations of seeps of groundwater into surface waters.

Water Resources Research, 2013

2] To explain the dynamic behavior of the matric potential at the wetting front of gravity driven... more 2] To explain the dynamic behavior of the matric potential at the wetting front of gravity driven fingers, we take into account the pressure across the interface that is not continuous and depends on the radius of the meniscus, which is a function of pore size and the dynamic contact angle h d . h d depends on a number of factors including velocity of the water and can be found by the Hoffman-Jiang equation that was modified for gravity effects. By assuming that water at the wetting front imbibes one pore at a time, realistic velocities are obtained that can explain the capillary pressures observed in unstable flow experiments in wettable and water repellent sands.

Late-time drainage from a sloping Boussinesq aquifer

Water Resources Research, 2013

ABSTRACT [1] Numerical solutions to the nonlinear Boussinesq equation, applied to a steeply slopi... more ABSTRACT [1] Numerical solutions to the nonlinear Boussinesq equation, applied to a steeply sloping aquifer and assuming uniform hydraulic conductivity, indicate that late-time recession discharge decreases nearly linearly in time. When recession discharge is characterized by −dQ/dt = aQb, this is equivalent to constant dQ/dt or b = 0. This result suggests that a previously reported exponential decrease with time (b = 1) of modeled recession discharge from a similar sloping aquifer represented by the same equation appears to be an artifact of the numerical solution scheme and its interpretation. Because the linearly decreasing recession discharge (b = 0) is not known from field studies, these findings challenge the application of a nonlinear Boussinesq framework assuming uniform conductivity and geometric similarity to infer hydraulic properties of sloping aquifers from observations of streamflow. This finding also questions the validity of the physical interpretation of the exponential decline in late time resulting from the commonly used linearized form of the Boussinesq equation, opposed to the full nonlinear equation, when applied under these conditions. For this reason, application of the linearized equation to infer hydraulic properties of sloping aquifers is also challenged, even if the observed recession is consistent with that of the linearized Boussinesq equation.

Water Resources Research, 2012

1] We propose a novel, accurate quantification of precipitation and evaporation, as needed to und... more 1] We propose a novel, accurate quantification of precipitation and evaporation, as needed to understand fundamental hydrologic processes. Our system uses a collection vessel placed on top of a slender rod that is securely fixed at its base. As the vessel is deflected, either by manual perturbation or ambient forcing (for example, wind), its oscillatory response is measured, here by a miniature accelerometer. This response can be modeled as a damped mass-spring system. As the mass of water within the collection vessel changes, either through the addition of precipitation or by evaporative loss, the resonant frequency experiences an inverse shift. This shift can be measured and used to estimate the change in the mass of water. We tested this concept by creating a simple prototype which was used in field conditions for a period of 1 month. The instrument was able to detect changes in mass due to precipitation with an accuracy of approximately 1 mm.

Water Resources Research, 2014

Water Resources Research, 1992

Water Resources Research, 1992

Water Resources Research, 2007

A new apparatus is presented that is capable of applying a constant fluid pressure at inflow and ... more A new apparatus is presented that is capable of applying a constant fluid pressure at inflow and outflow boundaries. The apparatus can be refilled during operation and does not rely on an overflow mechanism. The device is constructed of two vessels, one that contains the delivered fluid and the other that contains a less dense fluid. By matching the fluid densities and the areas of the vessels, the absolute elevation of the delivered fluid is maintained as the fluid is added to or removed from the system. The history of the development of the device, the underlying physical principles, and two demonstrations of the operation of a prototype device are shown.

Water Resources Research, 1990

A general procedure was developed for calibrating multiparameter probability distributions of dai... more A general procedure was developed for calibrating multiparameter probability distributions of daily precipitation to single-parameter distributions. The approach uses monthly precipitation summaries and data from U.S. Weather Bureau Technical Paper 57 (Miller and Frederick, 1966). The threeparameter beta-P model of daily precipitation amount was calibrated for 33 sites east of the Rocky Mountains. The resulting single-parameter Weibull distribution and two other single-parameter precipitation distributions were compared with respect to their fit to Paper 57 summaries and historical daily precipitation records. The Weibull model was shown to yield significant improvement over the other models in reproducing precipitation probability distributions.

Water Resources Research, 2005

1] Quality concerns drive many water studies and practices, but obtaining samples from water bodi... more 1] Quality concerns drive many water studies and practices, but obtaining samples from water bodies over time and space for quality determination is often difficult and expensive. We present a low-cost approach that allows integration of water samples over timescales of days to months to allow more widely distributed acquisition of time-integrated samples than possible with previous technology. The device is simply a submerged bottle with a small hole in the lid. In an alternative design the submerged bottle is connected by a tube to a second bottle located outside of the water. In either case, pressure changes inside the sampler arising from natural fluctuations in temperature and atmospheric pressure lead to an accumulation of water in the bottle. For example, when the sampler warms, air escapes the hole, and when it cools, water enters the hole, so with daily variation of 6°C per day the bottle will half fill in 1 month. Laboratory and environmental tests confirm the concept's function. Variants of the design for well sampling and use in deep water are also presented.

Water Resources Research, 2013

1] Based on a literature overview, this paper summarizes the impact and legacy of the contributio... more 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.

Water Resources Research, 2014

1] Though the essence of the scientific literature is to be a repository of unaffiliated truths, ... more 1] Though the essence of the scientific literature is to be a repository of unaffiliated truths, scientific advancement fundamentally stems from the insights and efforts of individuals. This dichotomy can hide exemplars for young scholars of how to contribute to scientific understanding. This section of Water Resources Research addresses eminently successful strategies for advancement of the science of hydrology by exploring the ramifications of the work from Drs. Wilfried Brutsaert and Jean-Yves Parlange, colleagues who made many of the most significant contributions to the understanding of hydrologic processes of the last 50 years. The generous scope of the special section follows the key areas of their contributions, but the content looks forward from their work. Important and novel results span solute transport, infiltration, streamflow generation, and evaporation.

High-resolution temperature sensing in the Dead Sea using fiber optics

Water Resources Research, 2014

Water Resources Research, 2010

Water Resources Research, 2013

1] Accurate estimates of water losses by evaporation from shallow water tables are important for ... more 1] Accurate estimates of water losses by evaporation from shallow water tables are important for hydrological, agricultural, and climatic purposes. An experiment was conducted in a weighing lysimeter to characterize the diurnal dynamics of evaporation under natural conditions. Sampling revealed a completely dry surface sand layer after 5 days of evaporation. Its thickness was <1 cm early in the morning, increasing to reach 4-5 cm in the evening. This evidence points out fundamental limitations of the approaches that assume hydraulic connectivity from the water table up to the surface, as well as those that suppose monotonic drying when unsteady conditions prevail. The computed vapor phase diffusion rates from the apparent drying front based on Fick's law failed to reproduce the measured cumulative evaporation during the sampling day. We propose that two processes rule natural evaporation resulting from daily fluctuations of climatic variables: (i) evaporation of water, stored during nighttime due to redistribution and vapor condensation, directly into the atmosphere from the soil surface during the early morning hours, that could be simulated using a mass transfer approach and (ii) subsurface evaporation limited by Fickian diffusion, afterward. For the conditions prevailing during the sampling day, the amount of water stored at the vicinity of the soil surface was 0.3 mm and was depleted before 11:00. Combining evaporation from the surface before 11:00 and subsurface evaporation limited by Fickian diffusion after that time, the agreement between the estimated and measured cumulative evaporation was significantly improved. a shallow water table: Diurnal dynamics of water and heat at the surface of drying sand, Water Resour. Res., 49,[4022][4023][4024][4025][4026][4027][4028][4029][4030][4031][4032][4033][4034]

Water Resources Research, 2007

1] The prediction of the time to ponding following commencement of rainfall is fundamental to hyd... more 1] The prediction of the time to ponding following commencement of rainfall is fundamental to hydrologic prediction of flood, erosion, and infiltration. Most of the studies to date have focused on prediction of ponding resulting from simple rainfall patterns. This approach was suitable to rainfall reported as average values over intervals of up to a day but does not take advantage of knowledge of the complex patterns of actual rainfall now commonly recorded electronically. A straightforward approach to include the instantaneous rainfall record in the prediction of ponding time and excess rainfall using only the infiltration capacity curve is presented. This method is tested against a numerical solution of the Richards equation on the basis of an actual rainfall record. The predicted time to ponding showed mean error 7% for a broad range of soils, with and without surface sealing. In contrast, the standard predictions had average errors of 87%, and worst-case errors exceeding a factor of 10. In addition to errors intrinsic in the modeling framework itself, errors that arise from averaging actual rainfall records over reporting intervals were evaluated. Averaging actual rainfall records observed in Israel over periods of as little as 5 min significantly reduced predicted runoff (75% for the sealed sandy loam and 46% for the silty clay loam), while hourly averaging gave complete lack of prediction of ponding in some of the cases. Citation: Assouline, S., J. S. Selker, and J.-Y. Parlange (2007), A simple accurate method to predict time of ponding under variable intensity rainfall, Water Resour. Res., 43, W03426,

Water Resources Research, 2006

1] The method of recession analysis proposed by remains one of the few analytical tools for estim... more 1] The method of recession analysis proposed by remains one of the few analytical tools for estimating aquifer hydraulic parameters at the field scale and beyond. In the method, the recession hydrograph is examined as ÀdQ/dt = f(Q), where Q is aquifer discharge and f is an arbitrary function. The observed function f is parameterized through analytical solutions to the one-dimensional Boussinesq equation for unconfined flow in a homogeneous and horizontal aquifer. While attractive in its simplicity, as originally presented it is not applicable to settings where slope is an important driver of flow, or where hydraulic parameters vary greatly with depth. We compare analytical solutions to the linearized one-dimensional Boussinesq equation for a sloping aquifer to numerical solutions of the full nonlinear equation. The behavior of the nonlinear Boussinesq equation is also assessed when the aquifer is heterogeneous wherein the lateral saturated hydraulic conductivity k varies as a power law with height z above the impermeable layer (k $ z n , n constant ! 0). All of the analytical solutions differ in key aspects from the nonlinear solution when plotted as ÀdQ/dt = f(Q) and thus are inappropriate for a Brutsaert and Nieber-type analysis. However, new analytical solutions for a sloping aquifer are derived ''empirically'' from the numerical simulations that are applicable during the late period of recession when the recession curve converges to ÀdQ/dt = aQ b , where b = (2n + 1)/(n + 1) and a is a function of the dimensions and hydraulic properties of the aquifer. Citation: Rupp, D. E., and J. S. Selker (2006), On the use of the Boussinesq equation for interpreting recession hydrographs from sloping aquifers, Water Resour. Res., 42, W12421,

Advances in Water Resources, 2005

Applications of the axisymmetric Boussinesq equation to groundwater hydrology and reservoir engin... more Applications of the axisymmetric Boussinesq equation to groundwater hydrology and reservoir engineering have long been recognised. An archetypal example is invasion by drilling fluid into a permeable bed where there is initially no such fluid present, a circumstance of some importance in the oil industry. It is well known that the governing Boussinesq model can be reduced to a nonlinear ordinary differential equation using a similarity variable, a transformation that is valid for a certain time-dependent flux at the origin. Here, a new analytical approximation is obtained for this case. The new solution,, which has a simple form, is demonstrated to be highly accurate.

Advancing Biogeochemical Research in the Field Hydrological Sciences: The CUAHSI Hydrological Measurement Facility – Biogeochemical Component

Water Resources Research, 2014

Temperature anomalies can identify locations of seeps of groundwater into surface waters.

Water Resources Research, 2013

2] To explain the dynamic behavior of the matric potential at the wetting front of gravity driven... more 2] To explain the dynamic behavior of the matric potential at the wetting front of gravity driven fingers, we take into account the pressure across the interface that is not continuous and depends on the radius of the meniscus, which is a function of pore size and the dynamic contact angle h d . h d depends on a number of factors including velocity of the water and can be found by the Hoffman-Jiang equation that was modified for gravity effects. By assuming that water at the wetting front imbibes one pore at a time, realistic velocities are obtained that can explain the capillary pressures observed in unstable flow experiments in wettable and water repellent sands.

Late-time drainage from a sloping Boussinesq aquifer

Water Resources Research, 2013

ABSTRACT [1] Numerical solutions to the nonlinear Boussinesq equation, applied to a steeply slopi... more ABSTRACT [1] Numerical solutions to the nonlinear Boussinesq equation, applied to a steeply sloping aquifer and assuming uniform hydraulic conductivity, indicate that late-time recession discharge decreases nearly linearly in time. When recession discharge is characterized by −dQ/dt = aQb, this is equivalent to constant dQ/dt or b = 0. This result suggests that a previously reported exponential decrease with time (b = 1) of modeled recession discharge from a similar sloping aquifer represented by the same equation appears to be an artifact of the numerical solution scheme and its interpretation. Because the linearly decreasing recession discharge (b = 0) is not known from field studies, these findings challenge the application of a nonlinear Boussinesq framework assuming uniform conductivity and geometric similarity to infer hydraulic properties of sloping aquifers from observations of streamflow. This finding also questions the validity of the physical interpretation of the exponential decline in late time resulting from the commonly used linearized form of the Boussinesq equation, opposed to the full nonlinear equation, when applied under these conditions. For this reason, application of the linearized equation to infer hydraulic properties of sloping aquifers is also challenged, even if the observed recession is consistent with that of the linearized Boussinesq equation.

Water Resources Research, 2012

1] We propose a novel, accurate quantification of precipitation and evaporation, as needed to und... more 1] We propose a novel, accurate quantification of precipitation and evaporation, as needed to understand fundamental hydrologic processes. Our system uses a collection vessel placed on top of a slender rod that is securely fixed at its base. As the vessel is deflected, either by manual perturbation or ambient forcing (for example, wind), its oscillatory response is measured, here by a miniature accelerometer. This response can be modeled as a damped mass-spring system. As the mass of water within the collection vessel changes, either through the addition of precipitation or by evaporative loss, the resonant frequency experiences an inverse shift. This shift can be measured and used to estimate the change in the mass of water. We tested this concept by creating a simple prototype which was used in field conditions for a period of 1 month. The instrument was able to detect changes in mass due to precipitation with an accuracy of approximately 1 mm.

Water Resources Research, 2014

Water Resources Research, 1992

Water Resources Research, 1992

Water Resources Research, 2007

A new apparatus is presented that is capable of applying a constant fluid pressure at inflow and ... more A new apparatus is presented that is capable of applying a constant fluid pressure at inflow and outflow boundaries. The apparatus can be refilled during operation and does not rely on an overflow mechanism. The device is constructed of two vessels, one that contains the delivered fluid and the other that contains a less dense fluid. By matching the fluid densities and the areas of the vessels, the absolute elevation of the delivered fluid is maintained as the fluid is added to or removed from the system. The history of the development of the device, the underlying physical principles, and two demonstrations of the operation of a prototype device are shown.

Water Resources Research, 1990

A general procedure was developed for calibrating multiparameter probability distributions of dai... more A general procedure was developed for calibrating multiparameter probability distributions of daily precipitation to single-parameter distributions. The approach uses monthly precipitation summaries and data from U.S. Weather Bureau Technical Paper 57 (Miller and Frederick, 1966). The threeparameter beta-P model of daily precipitation amount was calibrated for 33 sites east of the Rocky Mountains. The resulting single-parameter Weibull distribution and two other single-parameter precipitation distributions were compared with respect to their fit to Paper 57 summaries and historical daily precipitation records. The Weibull model was shown to yield significant improvement over the other models in reproducing precipitation probability distributions.

Water Resources Research, 2005

1] Quality concerns drive many water studies and practices, but obtaining samples from water bodi... more 1] Quality concerns drive many water studies and practices, but obtaining samples from water bodies over time and space for quality determination is often difficult and expensive. We present a low-cost approach that allows integration of water samples over timescales of days to months to allow more widely distributed acquisition of time-integrated samples than possible with previous technology. The device is simply a submerged bottle with a small hole in the lid. In an alternative design the submerged bottle is connected by a tube to a second bottle located outside of the water. In either case, pressure changes inside the sampler arising from natural fluctuations in temperature and atmospheric pressure lead to an accumulation of water in the bottle. For example, when the sampler warms, air escapes the hole, and when it cools, water enters the hole, so with daily variation of 6°C per day the bottle will half fill in 1 month. Laboratory and environmental tests confirm the concept's function. Variants of the design for well sampling and use in deep water are also presented.

Water Resources Research, 2013

1] Based on a literature overview, this paper summarizes the impact and legacy of the contributio... more 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.

Water Resources Research, 2014

1] Though the essence of the scientific literature is to be a repository of unaffiliated truths, ... more 1] Though the essence of the scientific literature is to be a repository of unaffiliated truths, scientific advancement fundamentally stems from the insights and efforts of individuals. This dichotomy can hide exemplars for young scholars of how to contribute to scientific understanding. This section of Water Resources Research addresses eminently successful strategies for advancement of the science of hydrology by exploring the ramifications of the work from Drs. Wilfried Brutsaert and Jean-Yves Parlange, colleagues who made many of the most significant contributions to the understanding of hydrologic processes of the last 50 years. The generous scope of the special section follows the key areas of their contributions, but the content looks forward from their work. Important and novel results span solute transport, infiltration, streamflow generation, and evaporation.

High-resolution temperature sensing in the Dead Sea using fiber optics

Water Resources Research, 2014

Water Resources Research, 2010

Water Resources Research, 2013

1] Accurate estimates of water losses by evaporation from shallow water tables are important for ... more 1] Accurate estimates of water losses by evaporation from shallow water tables are important for hydrological, agricultural, and climatic purposes. An experiment was conducted in a weighing lysimeter to characterize the diurnal dynamics of evaporation under natural conditions. Sampling revealed a completely dry surface sand layer after 5 days of evaporation. Its thickness was <1 cm early in the morning, increasing to reach 4-5 cm in the evening. This evidence points out fundamental limitations of the approaches that assume hydraulic connectivity from the water table up to the surface, as well as those that suppose monotonic drying when unsteady conditions prevail. The computed vapor phase diffusion rates from the apparent drying front based on Fick's law failed to reproduce the measured cumulative evaporation during the sampling day. We propose that two processes rule natural evaporation resulting from daily fluctuations of climatic variables: (i) evaporation of water, stored during nighttime due to redistribution and vapor condensation, directly into the atmosphere from the soil surface during the early morning hours, that could be simulated using a mass transfer approach and (ii) subsurface evaporation limited by Fickian diffusion, afterward. For the conditions prevailing during the sampling day, the amount of water stored at the vicinity of the soil surface was 0.3 mm and was depleted before 11:00. Combining evaporation from the surface before 11:00 and subsurface evaporation limited by Fickian diffusion after that time, the agreement between the estimated and measured cumulative evaporation was significantly improved. a shallow water table: Diurnal dynamics of water and heat at the surface of drying sand, Water Resour. Res., 49,[4022][4023][4024][4025][4026][4027][4028][4029][4030][4031][4032][4033][4034]

Water Resources Research, 2007

1] The prediction of the time to ponding following commencement of rainfall is fundamental to hyd... more 1] The prediction of the time to ponding following commencement of rainfall is fundamental to hydrologic prediction of flood, erosion, and infiltration. Most of the studies to date have focused on prediction of ponding resulting from simple rainfall patterns. This approach was suitable to rainfall reported as average values over intervals of up to a day but does not take advantage of knowledge of the complex patterns of actual rainfall now commonly recorded electronically. A straightforward approach to include the instantaneous rainfall record in the prediction of ponding time and excess rainfall using only the infiltration capacity curve is presented. This method is tested against a numerical solution of the Richards equation on the basis of an actual rainfall record. The predicted time to ponding showed mean error 7% for a broad range of soils, with and without surface sealing. In contrast, the standard predictions had average errors of 87%, and worst-case errors exceeding a factor of 10. In addition to errors intrinsic in the modeling framework itself, errors that arise from averaging actual rainfall records over reporting intervals were evaluated. Averaging actual rainfall records observed in Israel over periods of as little as 5 min significantly reduced predicted runoff (75% for the sealed sandy loam and 46% for the silty clay loam), while hourly averaging gave complete lack of prediction of ponding in some of the cases. Citation: Assouline, S., J. S. Selker, and J.-Y. Parlange (2007), A simple accurate method to predict time of ponding under variable intensity rainfall, Water Resour. Res., 43, W03426,

Water Resources Research, 2006

1] The method of recession analysis proposed by remains one of the few analytical tools for estim... more 1] The method of recession analysis proposed by remains one of the few analytical tools for estimating aquifer hydraulic parameters at the field scale and beyond. In the method, the recession hydrograph is examined as ÀdQ/dt = f(Q), where Q is aquifer discharge and f is an arbitrary function. The observed function f is parameterized through analytical solutions to the one-dimensional Boussinesq equation for unconfined flow in a homogeneous and horizontal aquifer. While attractive in its simplicity, as originally presented it is not applicable to settings where slope is an important driver of flow, or where hydraulic parameters vary greatly with depth. We compare analytical solutions to the linearized one-dimensional Boussinesq equation for a sloping aquifer to numerical solutions of the full nonlinear equation. The behavior of the nonlinear Boussinesq equation is also assessed when the aquifer is heterogeneous wherein the lateral saturated hydraulic conductivity k varies as a power law with height z above the impermeable layer (k $ z n , n constant ! 0). All of the analytical solutions differ in key aspects from the nonlinear solution when plotted as ÀdQ/dt = f(Q) and thus are inappropriate for a Brutsaert and Nieber-type analysis. However, new analytical solutions for a sloping aquifer are derived ''empirically'' from the numerical simulations that are applicable during the late period of recession when the recession curve converges to ÀdQ/dt = aQ b , where b = (2n + 1)/(n + 1) and a is a function of the dimensions and hydraulic properties of the aquifer. Citation: Rupp, D. E., and J. S. Selker (2006), On the use of the Boussinesq equation for interpreting recession hydrographs from sloping aquifers, Water Resour. Res., 42, W12421,