In the recent past, our research activity was dedicated to study the possibility to use the Whittle's approximation to the Gaussian maximum likelihood function for estimating the parameters of hydrological models. The calibration is carried out by comparing the periodogram of the data simulated by the model with the periodogram of the available observations. Whittle's likelihood provides asymptotically consistent and unbiased estimates for Gaussian and non-Gaussian data, even in the presence of long-range dependence. This method presents a relevant advantage: in principle, model calibration can be performed even in absence of observed data. In fact, the only information required by the Whittle's likelihood is the periodogram of the process, which can be inferred by using an alternative information, like for instance old and sparse records, regional information and so forth. This latter behaviour of the Whittle's estimator constitutes a interesting chance for the implementation to ungauged/scarcely gauged catchments. The proposed procedure was firstly applied to the case study of a Italian river basin, for which a lumped rainfall runoff model has been calibrated by emulating a scarcely gauged situation. It seems that the Whittle's estimator can be successfully applied in situations where extended records for model calibration are not available. A paper on this subject, which I authored together with my colleague Elena Toth,was published  on Water Resources Research. Here you can download it.
A software is available for download which allow the application of the method. It is a plain text source file that runs under the R environment. Please read the software documentation which is in the header of the file.
A package with the software and some test files may be downloaded here. Should you need assistance please let me know. Please drop me an e-mail when you download the software. It is still a beta and I would like to keep track of any user, so that I can inform them about any bug. Thanks for this.