Estimation of soil water distribution: Identifiability and observation design

Identifiability and observation design problems for the Burgers equation, a model for the nonhysteretic infiltration in nonswelling soil, are considered. In estimating initial water distribution from a finite set of measurements, the identifiability under approximation is proved. In predicting the water distributions, an algorithm for observation design problems is provided and analyzed with the maximum error bound. Also, numerical simulations are performed.