groundwater flow and transport model seaside groundwater basin ...

Seaside Model Report
October 26, 2007
Model Development
shown on Figure 1.18b. The model was calibrated in part to simulate similar areas where
groundwater levels are below sea level.
Hydraulic parameters were identified from a weighted least-squares fit of the
computed heads to the measured groundwater levels. The computer program PEST
(Watermark Numerical Computing, 2002) was used to perform the calibration. PEST
identifies parameter values such that the model fit minimizes the objective function
n
i=
1
[ ( )] 2
w h h
S = ∑ −
(3.6)
i
ci
mi
where S is the sum of weighted squared residuals, h ci is the computed head for a
particular well and time, h mi is the measured groundwater level for the particular well and
time, w i is the weight assigned to the measured groundwater level, and n is the number of
measured groundwater levels. The weight assigned to a measurement is related to the
uncertainty in the measurement according to the relation
w i
1
= (3.7)
σ
2
i
where σ
i
is the standard error of the uncertainty in the measurement.
All groundwater-level measurements are uncertain, and the uncertainty has at
least two sources. Firstly, uncertainty arises in measuring or recording groundwater
depths and in measuring, estimating, or recording measuring-point altitudes.
Additionally, uncertainty arises in the documentation of the location and construction of
wells. However, for the Seaside groundwater basin, this uncertainty type most likely is
small. Secondly, uncertainty arises because groundwater-level measurements represent
spatial and temporal point processes, but the computed heads represent spatially and
temporally average processes (Anderson and Woessner, 2002, pp.229-230, Gelhar,
1986), where the averaging depends on the effective spatial and temporal scales
represented in the model. This uncertainty increases significantly with lower-permeability
groundwater systems and with more heterogeneous and anisotropic groundwater systems.
Because the Seaside groundwater basin can be characterized as a highly heterogeneous,
highly anisotropic, and moderately permeable groundwater system, and because the
effective model spatial and temporal scales are large, the second uncertainty type is large.
Within the groundwater-level data for the Seaside groundwater basin, the standard
error for the combined effects of the two uncertainty types is about 16 ft. The first
uncertainty type has a standard of perhaps 5 ft or less, the second error type has a
standard error of most likely 15 ft or more. These combine according to the relation
σ = σ 1
+ σ
(3.8)
i i 2i
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