A. Montanari, and D. Koutsoyiannis, Is deterministic physically-based hydrological modeling a feasible target? Incorporating physical knowledge in stochastic modeling of uncertain systems, American Geophysical Union, Fall Meeting 2010, San Francisco, USA, doi:10.13140/RG.2.2.18886.68164, American Geophysical Union, 2010.
In recent years there has been an increasing focus on deterministic physically-based modeling (more often called simply physically-based modeling) of hydrological systems, with the aim to pursue a deterministic representation of the involved processes. We argue that fully deterministic physically-based hydrological modeling is not a feasible target, at least for the inherent uncertainty (also called natural variability) affecting input and output variables as well as the complex geometry of control volumes and boundaries of hydrological processes. We believe that such uncertainty calls for a stochastic representation, allowing one to estimate at the same time hydrological variables and the related, unavoidable, uncertainty. On the other hand, deterministic concepts and relationships between processes provide valuable information that must be taken into account to reduce epistemic uncertainty. We present a modeling framework where physical information is fully incorporated in a stochastic approach, thereby allowing one to take full advantage of the available knowledge while accounting for, and quantifying, the related uncertainty. Within this view, stochastic and deterministic representations are not antitethic but rather complementary and can be combined in a stochastic physically-based approach. Input and output variables can be provided in the form of probability distributions, if they are uncertain, and the hydrological model is incorporated in the form of analytical probabilistic equations. The resulting approach is not much different to what hydrologists are already used to apply, and allows one to integrate the results of the recent literature on deterministic, physically-based, modeling and uncertainty assessment.
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