# Some thoughts about stochastic hydrologic modelling inspired by the Canadian wilderness

V. Klemeš, Some thoughts about stochastic hydrologic modelling inspired by the Canadian wilderness, Seminar 17/6/2005, Athens, Department of Water Resources, Hydraulic and Maritime Engineering – National Technical University of Athens, 2005.

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[English]

PART I - MODELLING THE NUMBERS AND PATTERNS:

Hydrological science starts with observations of water, continues with recording them, i.e. converting them into "data", then proceeds to fitting the patterns of these data with mathematical models, and finally uses such models to make predictions about the behaviour of water in the frequency and the time domains. It is significant, though often overlooked that, on this route, hydrological modelling inconspicuously tends to drift ever farther from the "hydro" towards the "logic", with an implicit hope that in doing so it raises its "scientific status".

This tendency is particularly pronounced in statistical and stochastic modelling, with the consequence that many such models are constructs based on pure "dry" numbers whose original meaning does not enter the picture: they would be exactly the same regardless of what these numbers might represent. And yet, their main purpose is to predict, and make inferences about, the behaviour of the real "wet" water.

This dilemma and its consequences will be illustrated by examples some of which have been inspired by the Canadian wilderness.

PART II - TRYING TO "INJECT WATER" INTO STOCHASTIC HYDROLOGIC MODELS:

In recognition of the fact that the numbers and patterns alone do not "tell the whole story", attempts have been made to incorporate into stochastic models some of the hydrological mechanisms that have generated the "data". The most basic of these mechanisms is - to use the formulation of fluid mechanics - the flux of water through some unit volume, which is governed by the conservation of mass and momentum. In the hydrological context this translates into the transformation of "inflow" (input) to some "reservoir" (hydrological system) into its "outflow" (output).

The object of the "physics-based" stochastic modelling then is to express (or at least explain) the stochastic properties of hydrological "outputs" in terms of the properties of the "inputs" and of the "transformation mechanism" of the "reservoirs" concerned. This approach will be illustrated by a few elementary examples intended to show the inherent complexity of the stochastic behaviour of hydrological processes and the virtual impossibility to capture it by merely "fitting" mathematical constructs to their "observed records".

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