Weights should reflect:
- first of all, measure errors
- then, the importance of the observation for your predictions (i.e. observations you'd like to simulate as best as possible).
As described in "Effective Groundwater Model Calibration, Hill & Tiederman, Wiley, 2007", a good way is to set the weight = 1/S^2
where S = standard error for every measure.
For head measures, different errors sum up (errors in the measure, in the datum, well not fully penetrating...).
When it's impossible to estimate all the errors (and then sum the variances), a procedure (see Hill and Tiederman, p. 295) is:
- I assume that errors are normally distributed;
- I'm 95% sure than the measure is 25 +/-1 m a.s.l.;
-> from the tabulated standard normal distribution, at a (1 - 95% =) 5% significance level corresponds a critical value of 1.96
-> 1.96*S = 1 m
--> S = 1/1.96
--> Weight = 1/S^2.
Maybe other ways are viable.
Good work,
Giovanni Formentin
