Methods and guidelines for effective model calibration

One-percent Scaled Sensitivities
While dimensionless sensitivities are needed to compare the importance of different types 
of observations to the estimation of parameter values, for other purposes it is useful to have dimen-
sional quantities. One-percent scaled sensitivities are calculated as 
b
b
b
ω
ii
ss
ij
b
j
∂
∂
y’
k






b
j
ω
ik
1 2
⁄
k
1
=
ND
∑
=
css
j
css
j
ss
ij
(
)
2
b
i
1
=
ND
∑
ND
⁄
1
2
---
=
ND

---

16
(11)
and approximately equal the amount that the simulated value would change if the parameter value 
increased by one percent.
The one-percent scaled sensitivities cannot be used to form a composite statistic because 
they generally have different units. Also, the omission of the weighting from equation 11 means 
that the one-percent scaled sensitivities do not reflect the influence of the observations on the re-
gression as well as the dimensionless scaled sensitivities. The omission of the weighting has an ad-
vantage, however, in that one-percent scaled sensitivities can be calculated easily for any simulated 
quantity without having to assign the weighting. In MODFLOWP, sensitivities for hydraulic heads 
are calculated for the entire grid because sensitivities are calculated using the sensitivity equation 
sensitivities. These sensitivities are used to calculate one-percent scaled sensitivities for hydraulic 
heads that can be contoured just like hydraulic heads can be contoured. The resulting one-percent 
scaled sensitivity maps can be used to identify where additional observations of hydraulic head 
would be most important to the estimation of different parameters and to compare the sensitivity 
of hydraulic heads throughout the model to different paramters. Similar maps can be produced by 
UCODE by defining every point (or many points) in the model grid as an observation. For analyt-
ical models, they would be defined at enough points to create an accurate map.