How physical process knowledge adds information to predictions; an Algorithmic Information Theory perspective

Abstract:

Can the physical knowledge put into hydrological models add information to predictions? Current practise in modelling suggests that this is indeed assumed to be the case, given that physically based models play an important role in science and engineering. However, a literal interpretation of data processing inequality applied to models as signal processors seems to say that models can only lose information, not add it.
To avoid this apparent paradox we argue that model complexity should be considered in the equation. In this context it is proposed that an alternative formulation of the data processing inequality in terms of algorithmic information theory better captures the situation a hydrological modeler typically faces.