User's guide of Proceessing Modflow 5.0

Processing Modflow 265
Modeling Approach and Simulation Results
The aquifer is simulated using a grid of one layer, 15 columns and 15 rows. A regular grid space
of 500 ft is used for each column and row. The layer type is 0:confined and the Transmissivity
flag in the Layer Options dialog box is user-specified. Transmissivity and recharge are defined
as estimated parameters with the parameter numbers 1 and 2 (Note that the names of these two
parameters are p1 and p2).
Table 6.4 shows the optimized parameter values and the correlation coefficient matrix
calculated by PEST. A similar result obtained by UCODE is shown in Table 6.5. The diagonal
elements of the correlation coefficient matrix are always unity. The off-diagonal elements are
always between 1 and -1. The closer an off-diagonal element is to 1 or -1, the more highly
correlated are the parameters corresponding to the row and column numbers of that element. For
this example, transmissivity (parameter p1) and recharge (parameter p2) are highly correlated,
as is indicated by the value 0.9572 of the correlation coefficient matrix. This means that these
paramters are determined with a high degree of uncertainty in the parameter estimation process.
A sensitivity analysis could be used to quantify the uncertainty in the calibrated model caused
by uncertainty in the estimates of the aquifer parameters.
For our example, the only discharge is to the river and the only source is recharge. To be in
steady state, these two must balance. Recharge must therefore be equal to 1.125 cfs (the river
gain equals 11.125 cfs - 10 cfs). Spreading over the modeled area:
1.125ft
recharge'
3 /s
(15 × 15)@(500ft × 500ft) ' 2×10&8 ft/s
The estimated parameter values are acceptable.
(6.1)
Table 6.4 Optimized parameter values and the correlation coefficient matrix. Calibration result
from PEST.
Parameter Estimated 95% percent confidence limits
value lower limit upper limit
p1 1.000282E-02 9.724991E-03 1.028859E-02
p2 1.996080E-08 1.985581E-08 2.006578E-08
Note: confidence limits provide only an indication of parameter uncertainty.
They rely on a linearity assumption which may not extend as far in
parameter space as the confidence limits themselves - see PEST manual.
Correlation Coefficient Matrix ----->
1.000 0.9572
0.9572 1.000
6.4.1 Basic Model Calibration Skill with PEST/UCODE