Methods and guidelines for effective model calibration

Guideline 4: Include many kinds of data as observations in the regression
Guideline 4 stresses the importance of using as many kinds of observations as possible. For 
example, in ground-water flow problems, it is important to augment commonly available hydrau-
lic-head observations with flow observations. The latter serve to constrain solutions much more 
than the relatively easy to fit hydraulic heads and, therefore, using observations that reflect the rate 
and(or) direction of ground-water flow tends to promote the development of more accurate models.
MODFLOWP supports many types of observations relevant to ground-water flow problems, such 
as hydraulic heads, temporal changes in hydraulic head, streamflow gains and losses, and advective 
travel (Hill, 1992; Anderman and Hill, 1997). An advantage of UCODE is that it allows any quan-
tity to be used as an observation for which a simulated equivalent value is printed in any application 
model output file, or for which a simulated equivalent value can be calculated from the values 
printed in any application model output file. A detailed analysis of the importance of different types 
of observations and how to conduct such an analysis is presented by Anderman and others (1996).
In some circumstances, it may appear that guideline 4 could be addressed by using con-
toured values to increase the number of observations. In a ground-water example, Neuman (1982), 
Clifton and Neuman (1982), Neuman and Jacobson (1984), and Carrera and Neuman (1986) used 
kriging to interpolate hydraulic-head measurements to generate hydraulic heads used in the regres-
sion. When kriging is used, the associated kriging variances and variogram can be used to calculate 
the variance-covariance matrix on hydraulic-head observation errors needed to calculate the 
weighting. The advantage of interpolation methods is that more hydraulic-head values are avail-
able for the regression. As shown by Cooley and Sinclair (1976) and noted by Hill (1992), the dis-
advantage of interpolation methods is that the interpolated hydraulic heads are not based on the 
physics of ground-water flow, so that interpolated values generally do not respect the underlying 
processes represented in the model. This problem can be severe if aquifer properties change rapidly 
because the interpolation method would tend to make the ‘observed’ hydraulic-head distribution
unrealistically smooth. Use of interpolated values in the regression procedure produces correlation 
between the errors, so use of a full weight matrix may be important. These problems are avoided 
if the observations are used directly in the regression.