Supporting information for “Field test of a hybrid finite difference and analytic element
regional model”
D.B. Abrams
Illinois State Water Survey
2204 Griffith Drive Building 4 Room 414
Champaign, IL 61820
Phone: 217 244 1520
Email: dbabrams@illinois.edu
H.M. Haitjema
Haitjema Consulting, Inc.
2738 Brigs Bend
Bloomington, IN 47401
Phone: 812 336 2464
Email: henk@haitjema.com
D.T. Feinstein
USGS Wisconsin Water Science Center
PO Box 11166
Milwaukee, WI 53211
Phone: 414 962 2582
Fax: 414 229 5452
Email: dtfeinstein@usgs.gov
R.J. Hunt
USGS Wisconsin Water Science Center
8505 Research Way
Middleton, WI 53562-3581
Phone: 608 821 3847
Fax: 608 821 3817
Email: rjhunt@usgs.gov
December 12, 2014
Appendix S1: Hydraulic conductivity in the benchmark and hybrid models
In the primary manuscript, we assigned the same hydraulic conductivity and layer
elevations to all cells within the benchmark model that were contained within an original model
cell (see Figure 1e), referred to in this supplemental material as the checkered benchmark model.
A benchmark model whereby hydraulic conductivity and layer elevations were interpolated
between nodes of the original coarse model was also considered (Figure S1), referred to as the
smoothed benchmark model.
For purposes of testing the hybrid model performance, we sought to use the benchmark
model that was most consistent with the original MODFLOW model. It is not immediately
obvious whether this is the checkered or smoothed benchmark model! It appears, however, that
the selection of the benchmark model should include consideration of the interblock averaging
used by the original MODFLOW model. Though multiple averaging techniques are available, we
will focus on two. First, “harmonic averaging” is most consistent with uniform transmissivity in
each cell with discrete jumps at cell boundaries (Goode and Appel 1992), which we hypothesize
is conceptually similar to the checkered benchmark model. Harmonic averaging was used in the
Great Lakes Basin Model used to obtain the original MODFLOW model in the primary
manuscript. Second, “logarithmic averaging” is most consistent with continuous variations of
transmissivity between cell nodes (Goode and Appel 1992), which we hypothesize is
conceptually similar to the smoothed benchmark model.
To test our hypotheses, we compare the differences in baseflow between two original
model realizations (using harmonic and logarithmic averaging) and the two benchmark
realizations (checkered and smoothed). The two original models yield baseflows which differ
from each other (compare red with blue in Figure S2). The gages are shown in Figure 2 of the
manuscript. The two benchmark models also differ (compare purple with green). The difference
between the two benchmark models and their respective original models is in the same direction
(positive or negative) for all cases except A2-A1, E2-E1, and D2. So indeed, it appears that the
checkered benchmark model is conceptually consistent with the original model using harmonic
averaging.
Similar to the benchmark model, there is no single way to assign hydraulic conductivity
to the hybrid model. We tested two realizations, the 14 inhomogeneity zoned hybrid model that
is the focus of the manuscript and an alternative 118 inhomogeneity checkered hybrid model.
The zoned and checkered hybrid models are similar to both the smoothed and checkered baseline
models in all cases, but they are closer to the checkered baseline realization (green bar in Figure
S2) for all but two gages, D1 and E2-E1. This is because the checkered baseline model has the
same conceptual model of discrete transitions in hydraulic conductivity as the two hybrid
realizations.
References:
Goode, D.J and Appel, C.A., (1992). Finite-difference interblock transmissivity USGS WaterResources Investigations Report: 92-4124, 79 p. Technical report, United States
Geological Survey.
Figure S1: Layer 1 of the benchmark MODFLOW model with smoothed (interpolated)
transmissivity.
Figure S2: Baseflows in cubic meters per day (m3/day) modeled by the original, benchmark, and
hybrid models assuming a smooth (logarithmic) and checkered (harmonic) transmissivity
distribution. Gage locations are shown in Figure 2 of the manuscript. Where two gages are listed
(e.g. A2-A1), the baseflow reported is the difference between baseflow at these two gages.