Methods and guidelines for effective model calibration

A. Precision of the parameter estimate
Poor: Large parameter 
composite scaled sensitivity, 
coefficient of variation, or 
confidence interval
Good: Small parameter 
composite scaled sensitivity, 
coefficient of variation, or 
confidence interval
Importance 
of the 
parameter 
to 
predictions 
of interest
Not important:
Small prediction 
scaled sensitivity
I. Acceptable
1
II. Acceptable
1
Important:
Large prediction 
scaled sensitivity
IV. Improve estimation of 
this parameter and associated 
system features.
2
III. Acceptable
1
B. Uniqueness of the parameter estimate
Poor: The absolute value of 
some of this parameter’s 
correlation coefficients are 
close to 1.0.
3
Good: All of this parameter’s 
correlation coefficients have 
absolute values less than 
about 0.95.
3
Importance 
of the 
parameter 
to 
predictions 
of interest
Not important: 
The same parameter 
pairs are extremely 
correlated.
4
I. Acceptable
1
II. Acceptable
1
Important: 
Previously correlated 
parameter pairs are 
uncorrelated.
4
IV. Improve estimation of 
this parameter and associated 
system features .
2
III. Acceptable
1

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Parameter correlation coefficients are cited in figure 16 as measures both of the uniqueness 
of the parameter estimate and the importance of parameters to the predictions of interest. In both 
cases, the correlation coefficients are variations of the parameter correlation coefficients printed at 
the end of most regression runs, as discussed above in the sections “Variances and Covariances” 
and “Correlation Coefficients.” An example of the utility of such correlation coefficients can be 
found in the following ground-water modeling example. Consider a ground-water flow model cal-
ibrated with hydraulic-head and streamflow gain or loss observation data. The calibrated model is 
being developed to predict (a) hydraulic head at a location where no measurement can be obtained, 
and (b) advective transport from the site of a contaminant spill. Correlation coefficients for all pa-
rameters are obtained using the calibrated model using all defined parameters (see section “Vari-
ances and Covariances”); the prediction correlation coefficients are obtained by adding the 
prediction hydraulic-head location and advective transport as ‘observations’ in the input file and 
again calculating the correlation matrix for the same set of parameters. A similar calculation is re-
ported by Anderman and others (1996), showing that advective-travel was affected by individual 
parameter values, while hydraulic heads were not. In this circumstance, prediction of hydraulic 
heads did not require uncorrelated parameter estimates while prediction of advective travel did.
An example analysis of predictions is presented in figure 17. Prediction scaled sensitivities 
calculated using equation 12 are compared to parameter composite scaled sensitivities of equation 
10. In the example, the predictions of interest are the cartesian components of advective travel sim-
ulated by particle tracking using the ADV Package of Anderman and Hill (1997). The figure shows 
the range and mean of the prediction scaled sensitivities for eight transported particles. The predic-
tion scaled sensitivity is defined to equal the percent change in the advective transport caused by a 
one-percent change in parameter value. The figure clearly shows that parameters T3 and T4 are 
most important to the determination of advective-transport distance in all three coordicate direc-
tions, and that the observations used in the regression provide more information for parameter T3 
than for parameter T4. This type of information can be invaluable for understanding model 
strengths and weaknesses and for planning additional modeling and data collection efforts.

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Figure 17: Composite scaled sensitivities for estimated parameters and prediction scaled sensitiv-
ities for the spatial components of predicted advective transport. The composite scaled 
sensitivites for parameters estimated in the regression are shown using black bars; those 
not estimated in the regression are shown using gray bars. The prediction scaled sensi-
tivities are defined as the percent change in the prediction given a one-percent change in 
the parameter value, so ‘Percent change’ is used to label the vetical axes.
0
2
4
6
8
10
12
14
T1
T2
T3
T4
AN
IV
RC
H1
RC
H2
GHB
1
GHB
2
AN
I
Parameter label
C
o
mp
osi
te sc
al
ed
se
nsi
tiv
it
y
East-west advective-transport distance
-60
-30
0
30
Perc
en
t c
han
ge
North-south advective-transport distance
-60
-30
0
30
Pe
rc
e
n
t c
h
a
nge
Vertical advective-transport distance
-300
-200
-100
0
100
200
300
T1
T2
T3
T4
ANIV
R
CH1
R
CH2
GH
B1
GH
B2
ANI
Parameter label
Pe
rc
e
n
t c
h
a
nge

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