Generic and parsimonious stochastic modelling for hydrology and beyond

The old principle of parsimonious modelling of natural processes has regained its importance in the last few years. The inevitability of uncertainty and risk, and the value of stochastic modelling in dealing with them, are also again appreciated, after a period of growing hopes for radical reduction of uncertainty. Yet, in stochastic modelling of natural processes several families of models are used that are often non-parsimonious, unnatural or artificial, theoretically unjustified and, eventually, unnecessary. Here we develop a general methodology for more theoretically justified stochastic processes, which evolve in continuous time and stem from maximum entropy production considerations. The discrete-time properties thereof are theoretically derived from the continuous-time ones and a general simulation methodology in discrete time is built, which explicitly handles the effects of discretization and truncation. Some additional modelling issues are discussed with a focus on model identification and fitting, which are often made using inappropriate methods. [GRAPHICS]