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Though kriging is widely used as the preferred method for constructing gridded water level datasets suitable for contouring, residuals arising from using the most common (linear) drift to krige water levels in the vicinity of extraction wells often indicate large local departures from the linear drift, which correlate with areas of drawdown. These are evident in plan view (e.g. Figure 1) and cross-section (e.g. Figure 2). Using linear-log kriging, ground water levels measured in the vicinity of pumping wells are kriged using a regional-linear and point-logarithmic drift, the latter derived from the Thiem equation.

Hence, the combined regional-linear and point-logarithmic drift accounts for drawdowns (or mounding, in the case of injection wells) using a logarithmic approximation for the curvature of the potentiometric surface. Since the drift model approximates the principal physical processes that govern ground water flow and govern the auto-correlation of ground water elevation data, this approach produces maps of contoured water levels that more realistically represent physical conditions and that allow for improved interpretation of measured water-level data. Additional benefits include an improved estimate of the background hydraulic gradient and generation of an grid suitable for two-dimensional particle tracking (Figure 3).

No options available to KT3D have been disabled in making KT3D_L1. The significant arrays added to KT3D_L1 in adding the kriging and particle tracking functionality are allocatable and should not be exceeded unless the program has problems allocating the memory at run-time.

The code has been verified using a hydrologic non-linear parameter estimation code for the three cases:

Download GSLIB-Compatible KT3D_L1 Zipped file (2MB)

Disclaimer

These programs are provided FREE of charge. The authors request only that application of the software and production of results using the code is accompanied by a suitable acknowledgment. The software is provided "AS IS", without warranty of any kind, including without limitation the warranties of merchantability, fitness for a particular purpose and non-infringement. The entire risk and responsibility as to the quality and performance of the Software is borne by the user. The author(s) disclaim all other warranties.

The following text from the GSLIB KT3D program details the copyright and distribution rights pertaining to the GSLIB programs.

“Copyright (C) 1996, The Board of Trustees of the Leland Stanford Junior University. All rights reserved. The programs in GSLIB are distributed in the hope that they will be useful, but WITHOUT ANY WARRANTY. No author or distributor accepts responsibility to anyone for the consequences of using them or for whether they serve any particular purpose or work at all, unless he says so in writing. Everyone is granted permission to copy, modify and redistribute the programs in GSLIB, but only under the condition that this notice and the above Copyright notice remain intact.”

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*Software* MT3D PATH3D V4.6 ATRANS MPNE1D BIOSCREEN-AT PEST Linear-Log Kriger Applied Contaminant Transport (Textbook)	Linear-Log KrigerWater Level Kriging with a Regional-linear and Point-logarithmic Drift
	Though kriging is widely used as the preferred method for constructing gridded water level datasets suitable for contouring, residuals arising from using the most common (linear) drift to krige water levels in the vicinity of extraction wells often indicate large local departures from the linear drift, which correlate with areas of drawdown. These are evident in plan view (e.g. Figure 1) and cross-section (e.g. Figure 2). Using linear-log kriging, ground water levels measured in the vicinity of pumping wells are kriged using a regional-linear and point-logarithmic drift, the latter derived from the Thiem equation. Figure 1. Gridded Water Level data - Plan View. Figure 2. Gridded Water Level data - Section View. Hence, the combined regional-linear and point-logarithmic drift accounts for drawdowns (or mounding, in the case of injection wells) using a logarithmic approximation for the curvature of the potentiometric surface. Since the drift model approximates the principal physical processes that govern ground water flow and govern the auto-correlation of ground water elevation data, this approach produces maps of contoured water levels that more realistically represent physical conditions and that allow for improved interpretation of measured water-level data. Additional benefits include an improved estimate of the background hydraulic gradient and generation of an grid suitable for two-dimensional particle tracking (Figure 3). Figure 3. Particle Tracks with Time-of-travel A full description of the linear-log drift is given in the paper: Tonkin, Matthew J., and Larson, Steven P., 2002. "Kriging Water Levels with a Regional-linear and Point-logarithmic Drift". Ground Water, March/April 2002. Linear-log kriging freeware code - KT3D_L1 A version of the linear-log drift compatible with the popular geostatistics library GSLIB is available for download from this page, including: Documentation in Adobe PDF format. KT3D_L1.DLL - the linear-log drift function coded into KT3D_L1 as an additional drift term. Simply add the pumping data in an accessory file called Q.DAT. Forward-and-backward particle tracking integrated into the KT3D_L1 code. POST_SIM.DLL - a utility provided for converting the GSLIB output into a Surfer^TM-format or Rockware^TM-format grid file. A Visual Basic GUI driver for the gridding and particle-tracking options. An example, multiple-pumping-well data set and Surfer^TM file showing the resulting gridded surface and particle-tracks. No options available to KT3D have been disabled in making KT3D_L1. The significant arrays added to KT3D_L1 in adding the kriging and particle tracking functionality are allocatable and should not be exceeded unless the program has problems allocating the memory at run-time. The code has been verified using a hydrologic non-linear parameter estimation code for the three cases: Q(total) = zero A single pumping well Multiple pumping wells. Data for the multiple pumping-well case described in the paper was made available by the Air Force Center for Environmental Excellence (AFCEE), Cape Cod, MA, and we acknowledge their kind support. GSLIB: Geostatistical Software Library and User's Guide by Clayton Deutsch and André Journel, 1992, 340 pp, Oxford University Press. A recent publication has extended the approach described above to include boundary conditions and estimation of aquifer parameters - hydraulic conductivity in multiple 'zones' and storage. Brochu, Y. and Marcotte, D., 2003. A Simple Approach to Account for Radial Flow and Boundary Conditions When Kriging Hydraulic Head Fields for Confined Aquifers. Mathematical Geology, Vol. 35, No. 2, February 2003. One of the authors of the article (Denis Marcotte) has published on related geostatistical topics - a list of his publications can be found at his home page: http://geo.polymtl.ca/~marcotte/ Download GSLIB-Compatible KT3D_L1 Zipped file (2MB) Disclaimer These programs are provided FREE of charge. The authors request only that application of the software and production of results using the code is accompanied by a suitable acknowledgment. The software is provided "AS IS", without warranty of any kind, including without limitation the warranties of merchantability, fitness for a particular purpose and non-infringement. The entire risk and responsibility as to the quality and performance of the Software is borne by the user. The author(s) disclaim all other warranties. The following text from the GSLIB KT3D program details the copyright and distribution rights pertaining to the GSLIB programs. “Copyright (C) 1996, The Board of Trustees of the Leland Stanford Junior University. All rights reserved. The programs in GSLIB are distributed in the hope that they will be useful, but WITHOUT ANY WARRANTY. No author or distributor accepts responsibility to anyone for the consequences of using them or for whether they serve any particular purpose or work at all, unless he says so in writing. Everyone is granted permission to copy, modify and redistribute the programs in GSLIB, but only under the condition that this notice and the above Copyright notice remain intact.”