Two digital- computer models of the ground -water reservoir of
the Tucson basin, in south - central Arizona, were constructed to study
errors in digital models and to evaluate the worth of additional basic
data to models. The two models differ primarily in degree of detail
-- the large -scale model consists of 1,890 nodes, at a 1/2 -mile spacing;
and the small -scale model consists of 509 nodes, at a l -mile spacing.
Potential errors in the Tucson basin models were classified as
errors associated with computation, errors associated with mathematical
assumptions, and errors in basic data: the model parameters of coefficient
of storage and transmissivity, initial water levels, and discharge
and recharge. The study focused on evaluating the worth of
additional basic data to the small -scale model.
A basic form of statistical decision theory was used to compute
expected error in predicted water levels and expected worth of
sample data (expected reduction in error) over the whole model associated
with uncertainty in a model variable at one given node. Discrete frequency
distributions with largely subjectively- determined parameters were
used to characterize tested variables. Ninety -one variables at sixty -
one different locations in the model were tested, using six separate
error criteria. Of the tested variables, 67 were chosen because their
expected errors were likely to be large and, for the purpose of comparison,
24 were chosen because their expected errors were not likely
to be particularly large. Of the uncertain variables, discharge /recharge and transmissivity
have the largest expected errors (averaging 155 and 115 feet, respectively,
per 509 nodes for the criterion of absolute value of error)
and expected sample worths (averaging 29 and 14 feet, respectively, per
509 nodes). In contrast, initial water level and storage coefficient
have lesser values. Of the more certain variables, transmissivity and
initial water level generally have the largest expected errors (a maximum
of 73 per feet per 509 nodes) and expected sample worths (a maximum
of 12 feet per 509 nodes); whereas storage coefficient and discharge/
recharge have smaller values. These results likely are not typical of
those from many ground -water basins, and may apply only to the Tucson
basin.
The largest expected errors are associated with nodes at which
values of discharge /recharge are large or at which prior estimates of
transmissivity are very uncertain. Large expected sample worths are
associated with variables which have large expected errors or which
could be sampled with relatively little uncertainty. Results are similar
for all six of the error criteria used.
Tests were made of the sensitivity of the method to such simplifications
and assumptions as the type of distribution function assumed
for a variable, the values of the estimated standard deviations of the
distributions, and the number and spacing of the elements of each distribution.
The results are sensitive to all of the assumptions and
therefore likely are correct only in order of magnitude. However, the
ranking of the types of variables in terms of magnitude of expected error
and expected sample worth is not sensitive to the assumptions, and thus the general conclusions on relative effects of errors in different
variables likely are valid.
Limited studies of error propagation indicated that errors in
predicted water levels associated with extreme erroneous values of a
variable commonly are less than 4 feet per node at a distance of 1 mile
from the tested node. This suggests that in many cases, prediction errors
associated with errors in basic data are not a major problem in
digital modeling.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/620122 |
| Date | 06 1900 |
| Creators | Gates, Joseph Spencer |
| Contributors | Department of Hydrology & Water Resources, The University of Arizona |
| Publisher | Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ) |
| Source Sets | University of Arizona |
| Language | en_US |
| Detected Language | English |
| Type | text, Technical Report |
| Source | Provided by the Department of Hydrology and Water Resources. |
| Rights | Copyright © Arizona Board of Regents |
| Relation | Technical Reports on Hydrology and Water Resources, No. 8 |
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