Methods and guidelines for effective model calibration

Determining Acceptable Deviations from Independent Normal Weighted Residuals
Weighted residuals may fail the tests described above because there are too few weighted 
residuals or because of the fitting process of the regression, and not because the model is inade-
quate. The fitting process can produce correlations between residuals that, for example, result in a 
normal probability graph of weighted residuals that is not linear. This can be tested by generating 
values that conform to the expected violations, as described by Cooley and Naff (1990, p. 176). 
The steps involved in the test are as follows. 
1. Sets of normally distributed random numbers are generated with and without the regression-
induced correlations. 
2. Normal probability graphs of the weighted residuals are compared with graphs of the indepen-
dent normally distributed random numbers (called d’s by Cooley and Naff, 1990). If similar 
deviations from a straight line are apparent in these graphs, it can be concluded that the non-
linear shape of the weighted residuals graphs could result from too few weighted residuals.
3. Normal probability graphs of the weighted residuals are compared with graphs of the corre-
lated normally distributed numbers (called g’s by Cooley and Naff, 1990). If similar devia-
tions from a straight line are apparent in these graphs, it can be concluded that the nonlinear 
shape of the weighted residuals graphs could result from the regression-induced correlation.
A computer program for generating the random numbers was presented by Cooley and Naff 
(1990), and was slightly modified for use with MODFLOWP, as discussed by Hill (1992); the 
computer program is called RESANP. An output file is produced by MODFLOWP that can be used 
as the input file to RESANP; UCODE includes RESANP as a subroutine, and files with the random 
numbers are produced when input variables are set appropriately.