Biomedical subjects

Allan D Woodbury

Publications and source records attributed to Allan D Woodbury.

5 recordsLinked to original sources

PubMed2003

Extensions to minimum relative entropy inversion for noisy data.

Minimum relative entropy (MRE) and Tikhonov regularization (TR) were compared by Neupauer et al. [Water Resour. Res. 36 (2000) 2469] on the basis of an example plume source reconstruction problem originally proposed by Skaggs and Kabala [Water Resour. Res. 30 (1994) 71] and a boxcar-like function. Although Neupauer et al. [Water Resour. Res. 36 (2000) 2469] were careful in their conclusions to note the basis of these comparisons, we show that TR does not perform well on problems in which delta-like sources are convolved with diffuse-groundwater contamination response functions, particularly in the presence of noise. We also show that it is relatively easy to estimate an appropriate value for epsilon, the hyperparameter needed in the minimum relative entropy solution for the inverse problem in the presence of noise. This can be estimated in a variety of ways, including estimation from the data themselves, analysis of data residuals, and a rigorous approach using the real cepstrum and the Akaike Information Criterion (AIC). Regardless of the approach chosen, for the sample problem reported herein, excellent resolution of multiple delta-like spikes is produced from MRE from noisy, diffuse data. The usefulness of MRE for noisy inverse problems has been demonstrated.

Entropy↗

PubMedDate not supplied

Geostatistics and Bayesian updating for transmissivity estimation in a multiaquifer system in Manitoba, Canada.

In ground water flow and transport modeling, the heterogeneous nature of porous media has a considerable effect on the resulting flow and solute transport. Some method of generating the heterogeneous field from a limited dataset of uncertain measurements is required. Bayesian updating is one method that interpolates from an uncertain dataset using the statistics of the underlying probability distribution function. In this paper, Bayesian updating was used to determine the heterogeneous natural log transmissivity field for a carbonate and a sandstone aquifer in southern Manitoba. It was determined that the transmissivity in m2/sec followed a natural log normal distribution for both aquifers with a mean of -7.2 and - 8.0 for the carbonate and sandstone aquifers, respectively. The variograms were calculated using an estimator developed by Li and Lake (1994). Fractal nature was not evident in the variogram from either aquifer. The Bayesian updating heterogeneous field provided good results even in cases where little data was available. A large transmissivity zone in the sandstone aquifer was created by the Bayesian procedure, which is not a reflection of any deterministic consideration, but is a natural outcome of updating a prior probability distribution function with observations. The statistical model returns a result that is very reasonable; that is homogeneous in regions where little or no information is available to alter an initial state. No long range correlation trends or fractal behavior of the log-transmissivity field was observed in either aquifer over a distance of about 300 km.

Bayes Theorem↗

PubMedDate not supplied

Estimating deep recharge rates beneath an interlobate moraine using temperature logs.

The Sandilands area of southeastern Manitoba contains an interlobate moraine that is a major ground water recharge area. Underlying the highly permeable sediments of the moraine are up to 100 m of till and the subcrop of the Winnipeg Formation, which contains a major sandstone aquifer. Ground water flow within the till is examined using high-resolution temperature profiles and solutions to the differential equation for heat flow in porous media. These analyses indicate that recharge to the sandstone aquifer is occurring at a rate of approximately 2 x 10(-8) m/sec beneath the moraine, which is in agreement with recharge rates determined by conventional ground water hydraulics (10(-7) to 10(-10)(m/sec) and another study using multiple environmental tracers (1 x 10(-9) to 6 X 10(-9) m/sec). The use of temperature to determine ground water flux is not limited by half-lives as many environmental tracers are, and this allows for cost-effective estimation of recharge and discharge rates over longer periods.

Cost-Benefit Analysis↗

PubMedDate not supplied

Full-Bayesian inversion of the Edwards Aquifer.

The Bayesian inverse approach proposed by Woodbury and Ulrych (2000) is extended to estimate the transmissivity fields of highly heterogeneous aquifers for steady state ground water flow. Boundary conditions are Dirichlet and Neumann type, and sink and source terms are included. A first-order approximation of Taylor's series for the exponential terms introduced by sinks and sources or the Neumann condition in the governing equation is adopted. Such a treatment leads to a linear finite element formulation between hydraulic head and the logarithm of the transmissivity-denoted as ln(T)-perturbations. An updating procedure similar to that of Woodbury and Ulrych (2000) can be performed. This new algorithm is examined against a generic example. It is found that the linearized solution approximates the true solution with an R2 coefficient = 0.96 for an ln(T) variance of 9 for the test case. The addition of hydraulic head data is shown to improve the ln(T) estimates, in comparison to simply interpolating the sparse ln(T) data alone. The new Bayesian code is also employed to calibrate a high-resolution finite difference MODFLOW model of the Edwards Aquifer in southwest Texas. The posterior ln(T) field from this application yields better head fit when compared to the prior ln(T) field determined from upscaling and cokriging. We believe that traditional MODFLOW grids could be imported into the new Bayes code fairly seamlessly and thereby enhance existing calibration of many aquifers.

Bayes Theorem↗

PubMedDate not supplied

The effects of climatic variability on estimates of recharge from temperature profiles.

Using heat as a tracer allows for estimation of ground water recharge rates based on subsurface temperature measurements. While possible in theory, it may be difficult in practice to discriminate the effects of climate from the effects of ground water advection. This study uses synthetic simulations to determine the influence of variability of ground surface temperature (GST) on the ability to estimate vertical specific discharge from temperature profiles. Results suggest that in cases where temperature measurements are sufficiently deep and specific discharge is sufficiently high, estimates of specific discharges will be reasonably accurate. Increasing the number of times temperatures are measured, or producing models that incorporate variations in GST, will increase the reliability of any studies using temperatures to estimate specific discharge. Furthermore, inversions of temperature measurements should be combined with other methods of estimating recharge rates to improve the reliability of recharge estimates.

Climate↗