Methods and guidelines for effective model calibration

Direct Instead of Indirect Inverse Models
The most dramatically different possibility that presently exists is direct inverse modeling 
(Yeh, 1986; Sun, 1994). In direct inverse modeling, values of the dependent variable (for example, 
hydraulic head for the ground-water flow equation or concentration for the transport equation) are 
determined using usually sparse field data and these values are used directly to calculate the model 

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input values. This is in contrast to indirect methods, such as the method discussed in this work. The 
direct methods have been considered longer than the indirect methods in inverse modeling, but 
have been shown consistently to be more unstable in the presence of typical measurement errors. 
The direct methods do not use sensitivities and rarely calculate them, so that there are no equiva-
lents to the scaled sensitivities, composite scaled sensitivities, correlation coefficients, and confi-
dence intervals. Other aspects of the guidelines would still apply.
Alternative Parameterization Approach
While this work emphasizes estimating relatively few parameter values, an alternative is to 
estimate many parameter values (often a unique value for each finite element or finite-difference 
cell for numerical models) for spatially distributed system characteristics, such as hydraulic con-
ductivity in ground-water problems. Then smoothness criteria, or other types of regularization, are 
imposed to achieve a tractable regression problem. Such methods are presented by Tikkonov and 
Arsenin (1977), and tend to be most useful when very little is known about the distribution, or when 
the distribution is known to be smooth. For such a parameterization approach, the concept of start-
ing simple and building complexity might be useful when designing the regularization method.
Application of other aspects of the guidelines is unclear.

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