On the kriging of water table elevations using collateral information from a digital elevation model

In unconfined aquifers flowing under topographic gradients, the water table is a subdued replica of the ground surface above. This principle is the basis for using detailed collateral or secondary information from digital elevation models to supplement sparse observations from water wells in the mapping of phreatic surfaces. Data from DEM-derived secondary variables are incorporated into the estimation of water table elevations using the geostatistical method known as kriging with an external drift (KED). Two different KED models are proposed based on the choice of secondary variable. In the first, water table elevation is expressed as the sum of a deterministic trend given by topographic elevation and a residual random component representing depth to water table. In the second, depth to water table is expressed as a linear function of a deterministic trend, given by the TOPMODEL topographic index, and a residual random error. The relationship between water table depth and topographic index is derived from simplified groundwater dynamics and forms the basis of TOPMODEL-type rainfall-runoff models. The two KED models are applied to the mapping of water table elevations in the Oak Ridges Moraine (ORM), an unconfined aquifer near Toronto, Canada. Results show that KED with topographic elevation as external drift is the more robust of the two models. Despite its strong theoretical basis, the second model yields kriged water table elevations that are not always physically plausible. In part, this is because field observations of water table depth do not verify the predicated relationship with topographic index in large parts of the study area. However, this relationship may be valid in other cases and at other spatial scales. In such cases, the second model would provide a very powerful approach for mapping water table elevations and for calibrating distributed parameters of the TOPMODEL equations on water well observations.

[1]  S. K. Jenson,et al.  Extracting topographic structure from digital elevation data for geographic information-system analysis , 1988 .

[2]  D. Montgomery,et al.  Digital elevation model grid size, landscape representation, and hydrologic simulations , 1994 .

[3]  Keith Beven,et al.  On hydrologic similarity: 2. A scaled model of storm runoff production , 1987 .

[4]  F. Kenny,et al.  On the origin of the Oak Ridges Moraine , 1998 .

[5]  Norman L. Miller,et al.  A generalized power function for the subsurface transmissivity profile in TOPMODEL , 1997 .

[6]  András Bárdossy,et al.  Spatial distribution of soil moisture in a small catchment. Part 1: geostatistical analysis , 1998 .

[7]  Kevin Bishop,et al.  A TEST OF TOPMODEL'S ABILITY TO PREDICT SPATIALLY DISTRIBUTED GROUNDWATER LEVELS , 1997 .

[8]  D. Wolock,et al.  Effects of digital elevation model map scale and data resolution on a topography‐based watershed model , 1994 .

[9]  K. Beven,et al.  Toward a generalization of the TOPMODEL concepts:Topographic indices of hydrological similarity , 1996 .

[10]  K. Beven,et al.  A physically based, variable contributing area model of basin hydrology , 1979 .

[11]  J. Delhomme.  Kriging in the hydrosciences , 1978 .

[12]  L. Donald,et al.  of the INTERIOR , 1962 .

[13]  Miguel A. Mariño,et al.  Kriging of water levels in the Souss aquifer, Morocco , 1983 .

[14]  Keith Beven,et al.  Discharge and water table predictions using a generalised TOPMODEL formulation , 1997 .

[15]  G. Gambolati,et al.  A conceptual deterministic analysis of the kriging technique in hydrology , 1979 .

[16]  Dominique King,et al.  Improving the kriging of a soil variable using slope gradient as external drift , 1996 .

[17]  P. Barnett,et al.  Groundwater prospects in the Oak Ridges Moraine area, southern Ontario: application of regional geological models , 1996 .

[18]  R. B. Clapp,et al.  Cokriging model for estimation of water table elevation , 1989 .

[19]  S. P. Neuman,et al.  Analysis of nonintrinsic spatial variability by residual kriging with application to regional groundwater levels , 1984 .

[20]  P. Goovaerts.  Geostatistical approaches for incorporating elevation into the spatial interpolation of rainfall , 2000 .

[21]  Keith Beven,et al.  Including spatially variable effective soil depths in TOPMODEL , 1997 .

[22]  G. Marsily,et al.  Comparison of geostatistical methods for estimating transmissivity using data on transmissivity and specific capacity , 1987 .

[23]  Lloyd E. Dunlap,et al.  Interpolating water-table altitudes in west-central Kansas using kriging techniques. , 1981 .

[24]  Mitja Brilly,et al.  Regionalization in hydrology , 1990 .

[25]  Keith Beven,et al.  Use of spatially distributed water table observations to constrain uncertainty in a rainfall–runoff model , 1998 .

[26]  A. Maréchal.  Kriging Seismic Data in Presence of Faults , 1984 .

[27]  A. Journel,et al.  When do we need a trend model in kriging? , 1989 .

[28]  H. Wackernagel,et al.  Mapping temperature using kriging with external drift: Theory and an example from scotland , 1994 .

[29]  Giuseppe Gambolati,et al.  On the use of a main trend for the kriging technique in hydrology , 1978 .

[30]  Giuseppe Gambolati,et al.  Groundwater contour mapping in Venice by stochastic interpolators: 1. Theory , 1979 .

[31]  G. Dagan.  Flow and transport in porous formations , 1989 .

[32]  André Musy,et al.  Generalization of TOPMODEL for a power law transmissivity profile , 1997 .

[33]  R. M. Srivastava,et al.  Integrating Seismic Data in Reservoir Modeling: The Collocated Cokriging Alternative , 1992 .

[34]  Michael Edward Hohn,et al.  An Introduction to Applied Geostatistics: by Edward H. Isaaks and R. Mohan Srivastava, 1989, Oxford University Press, New York, 561 p., ISBN 0-19-505012-6, ISBN 0-19-505013-4 (paperback), $55.00 cloth, $35.00 paper (US) , 1991 .

[35]  K. Bevenb,et al.  Use of spatially distributed water table observations to constrain uncertainty in a rainfall – runoff model , 1998 .

[36]  Clayton V. Deutsch,et al.  GSLIB: Geostatistical Software Library and User's Guide , 1993 .

[37]  P. Domenico,et al.  Physical and chemical hydrogeology , 1990 .

[38]  J. Seibert.  On TOPMODEL's ability to simulate groundwater dynamics , 1999 .

[39]  R. Olea.  Geostatistics for Natural Resources Evaluation By Pierre Goovaerts, Oxford University Press, Applied Geostatistics Series, 1997, 483 p., hardcover, $65 (U.S.), ISBN 0-19-511538-4 , 1999 .