Leading Edge Numerical Modeling

Principal Investigator: Donald L. Baker , Ph.D. Soil Physics

Well, once upon a time. The P.I. is currently living on disability and not engaged in research, due to lack of support. This page is here merely for historical reasons. However, if someone does have some part-time research work that one can do, there are possibilities. Contact (June 2004)

The Mission

Conventional wisdom says, under the assumption that models are currently much better than available field data, "We just don't need any new models." Conventional wisdom is wrong.

Take, for example, the current wisdom that holds that "modern mass-conservative methods" for modeling vadose zone flow account for all major sources of numerical error. It is not uncommon for publications and proposals to study other sources of error to fall to the charge that the author does not understand how to use "modern methods". This has a profound impact on the decisions of what kind of engineering studies will be made of current and proposed hazardous waste sites. Then, when millions of dollars have been spent in those engineering studies, this not only creates a vested interest in maintaining that there are no other sources of error, it tends to restrict the availability of engineering study data to those investigators who contend otherwise.

At the Yucca Mountain Project in Nevada, arguably the hazardous waste site with the largest potential impact in the history of mankind, it can be hard to determine just what has been studied. Engineering data from is not available to just anyone who asks. But from outside appearances, it seems that most of the subsurface hydraulic data has been determined from air injection into well bores. Allegedly, core samples have been taken and processed for unsaturated flow data, but the scientists in charge do not respond to all inquiries.

If modern mass-conservative modeling methods are as perfect as their proponents claim, then perhaps all is well and good. But what if there is another source of numerical error in the modeling that requires another type of physical measurement? The use of Darcian interblock conductivity means in models of unsaturated flow (click here for html excerpts) requires complete knowledge of the change of unsaturated conductivity with matric suction. As far as this investigator knows, this cannot be obtained with air injection tests; it instead requires some rather more time-consuming and expensive processing of core samples. If one prejudges that current methods are "too good" for the field data, then one can make the mistake of not performing critical measurements.

This investigator seeks to bring a fresh engineering perspective to fundamentally reworking the basics of groundwater modeling, eventually integrating new modeling techniques with field and laboratory instrumentation so that models can be more effectively calibrated to field conditions. As the research offered here indicates, there remains a large, untapped store of increased accuracy, performance and computational efficiency to be wrung from finite difference and other methods to model flow and transport in the vadose zone. One draft paper (click here) shows how a combination of a new adaptive time step and a second-order Runge-Kutta method offers an order of magnitude increase in computational efficiency for smaller time steps. Another draft paper (click here) shows how in vertical infiltration, the arithmetic interblock conductivity mean can loose up to 50% of the total mass infiltrated for large space steps, a figure that can be reduced to 0.5% with appropriate approximations to Darcian means. These results were obtained using "modern mass-conservative methods", with a mass balance good to one part in ten to the eight both globally and in every time step. They demonstrate that time step discretization error and non-Darcian flow error are alive and very well, thank you, in any method that does not properly account for them.

This investigator is also working on a very challenging calibration problem for a model of nitrogen infiltration from poultry litter, made difficult by a very sparse and noisy field data set for weather and subsurface conditions. It is, admittedly, a training exercise in how to maneuver to a global calibration optimization through a minefield of local minima, without a supercomputer (click here for draft of model I/O specification). A new multi-compartment model for poultry litter degradation (click here for draft paper) was child's play by comparison.

The Company

Aquarius Engineering is currently a one-person, sole-proprietorship run by a partially disabled investigator. Small-business and other set-aside programs are welcome. If appropriate, it is also possible for the investigator to submit proposals as an affiliate Faculty member of the University of Arkansas, in association with other colleagues. Such a position would be contingent upon the proposal bringing research income to the University of Arkansas.

Principal Investigator's Background

Click here for Principal Investigator's vita. This investigator began his professional life as an Electronics Engineer, with more than a decade of cumulative experience, including development of microprocessor and field instrumentation. After a collision with a drinking driver effectively put an end to that career, this investigator returned to graduate school to gain two more degrees, culminating in a Ph.D. in Soil Physics. The unfunded Dissertation program produced two papers presented at conferences, three papers eventually accepted in refereed publication, and an SBIR proposal to the Nuclear Regulatory Commission, all before the final Dissertation. Although the NRC offered no money, it evaluated the investigator's Dissertation work as being "at the leading edge of the state of the art in the application of numerical methods to flow and transport through variably-saturated soil and rock".

The award of a U.S. Department of Energy Phase I Small Business Innovation Research contract, DE-FG02-97ER82329, in 1997 brought in much-needed equipment and funding. With this, this investigator went on to develop from his Dissertation work a new mathematical and modeling framework for Darcian interblock conductivity means in vertical unsaturated water flow. Although the Phase II award was not forthcoming, the work continues, as demonstrated by the draft papers presented here. This Investigator finds that the best way to defeat medical difficulties is to take on the toughest mental challenges that one can imagine. Although it can sometimes be as unimpressive as making sausage, it's an effectively absorbing distraction, and generally quite productive.

The Company's Research Assets

The primary research assets consist of: one Gateway 500C 1.8 GHz P4 machine running Win98se with 512 Mb memory; one mothballed 533 MHz DEC Alpha workstation running Windows NT 4.0; one 200 MHz IBM-compatible personal computer running Windows 95; the Alpha workstation runs at about ten times the speed of the 200 MHz PC; research software including Macsyma, PDEase, DEC Visual FORTRAN, Lahey FORTRAN, Absoft FORTRAN, SPSS TableCurve 2-D and 3-D, Quattro Pro 7, and Lotus 1-2-3 97; word, www and image processing software, including Word 97, Photoshop 7.0, PageMill 3.0; some removable disk drives, including CD-Rom, CD-RW, ZIP 100, and LS-120; basic electronics test equipment, including a 60 MHz oscilloscope.


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