Bayesian stochastic modelling for avalanche predetermination: from a general system framework to return period computations

Stochastic models are recent but unavoidable tools for snow avalanche hazard mapping that can be described in a general system framework. For the computation of design return periods, magnitude and frequency have to be evaluated. The magnitude model consists of a set of physical equations for avalanche propagation associated with a statistical formalism adapted to the input–output data structure. The friction law includes at least one latent friction coefficient. The Bayesian paradigm and the associated simulation techniques assist considerably in performing the inference and taking estimation errors into account for prediction. Starting from the general case, simplifying hypotheses allows computing the predictive distribution of high return periods on a case-study. Only release and runout altitudes are considered so that the model can use the French database. An inversible propagation model makes it possible to work with the latent friction coefficient as if it is observed. Prior knowledge is borrowed from an avalanche path with similar topographical characteristics. Justifications for the working hypotheses and further developments are discussed. In particular, the whole approach is positioned with respect to both deterministic and stochastic hydrology.     

A Linking Test that investigates the feasibility of inverse modelling: application to a simple rainfall interception model for Mt Gambier,southeast South Australia

Interception loss has an important influence on the water yield of forested areas. Nevertheless, in most studies stemflow is not measured, therefore the question of how to determine the feasibility of optimizing interception and stemflow parameters simultaneously by matching daily simulated throughfall to fortnightly measurements of cumulative throughfall is an important one. By applying a daily empirical interception model, a goodness fit of 2·2 mm/day is obtained between observed and simulated cumulative throughfall. However, by applying the simple but robust Linking Test, it was shown that the parameters are non‐unique and falsely linked, i.e. inter‐relationships between different vegetation parameter sets give similar throughfall but non‐unique net precipitation. The Linking Test investigates the causes of obtaining falsely linked parameters and shows that objective equifinality is not the source of the problem. Objective equifinality occurs when an inappropriate objective function is used. The Linking Test also shows that falsely linked parameters are not caused by measuring throughfall on a non‐daily basis (termed frequency sampling equifinality). By expanding the interception model to the second degree, it was found that the non‐uniqueness is due to the inherent nature of interception and stemflow functions that behave similarly and therefore can easily compensate each other (termed similarity equifinality). It is also shown that a simple daily empirical exponential interception model developed for conifers in the uplands of the United Kingdom is suitable to model interception in Pinus radiata plantations in the Mediterranean climate of southern Australia by using only daily gross precipitation data and two parameters. Copyright © 2009 John Wiley & Sons, Ltd.