Modelling processes with inadequate data: The case of multivariate streamflow simulation models

Multivariate streamflow simulation models available in the literature seem to have reached a more than acceptable level with regard to the representation of the space-time statistical features of the process.However, using these models with few or patched data prevents one taking advantage of their full potential, not to mention the case in which data need to be generated in ungauged stations. Dealing with inadequate multivariate datasets can require a greater effort than the construction of the simulation model itself. The usual approach of reconstructing missing data prior to model application has been mainly proposed for the precipitation process and can be considered as supported by sufficiently robust statistical methods. However, application of these methods is quite onerous and produces new data that are model-dependent. Moreover, to patch missing data for the runoff process, statistical procedures must be supported by hydrological arguments, owing to the nonlinear dependence between rainfall and runoff and to the serial correlation that affects streamflows. In this paper, a different view is proposed to deal with incomplete multivariate data, based on the goal of maximising the use of the existing information with procedures compatible with the standard application of the simulation model. So, missing data is not reconstructed and application of the different modules of the stochastic model is accompanied by techniques that guarantee feasibility and congruence of the solutions. The model in which these procedures are introduced is a conceptually-based contemporaneous ARMA with periodic-independent residual. Peculiar problems and solutions arise with regard to the characteristics of the residual process, which is treated as an estimate of the effective rainfall and is reproduced by a compound probability distribution. Model application in a 9-station system located in Basilicata (Southern Italy) showed the performances of the procedures proposed.

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