Why don’t avalanche-dynamics models of higher complexity necessarily lead to better predictions?

The avalanche-dynamics approach has a long history in avalanche prediction. In the absence of computers, scientists and engineers focused on idealized models in which avalanches were seen as rigid sliding blocks. Although the resulting governing equation was very simple, the use of empirical rules made the model outcomes quite realistic, the errors being counterbalanced by common sense and experience of practitioners. To improve the earliest models, scientists explored two complementary paths. The first was to provide a more physical framework for avalanches. In the 1960s, Bruno Salm suggested that flowing snow can be regarded as a continuum, an idea which has encountered great success, but which, at that time, faced considerable computational difficulties. A second path was the development of analytical and numerical models to solve the governing equations of continuum models. In the 1970s, French and Soviet scientists played a key role in the development of the Saint-Venant models for flowing avalanches. Since the 1990s, these models have been made available worldwide. Paradoxically, the substantial increase in model complexity can lead us to lose sight of the empirical nature of the assumptions used to build the models. Human expertise should still be of paramount importance when evaluating the relevance of numerical outputs. In 2004, Salm sounded an alarm, stating that excessive confidence was placed in the accuracy of model outputs. The problem of predictability and accuracy of models used for environmental purposes has attracted growing attention in recent years, but the debate seems an endless story as it is extremely difficult to determine the source of errors and remove them. In this talk, I will present the conclusions of experimental campaigns conducted in the laboratory to study avalanches of fluid. In this setting, an avalanche of fluid results from the sudden release of a fixed volume of fluid down a sloping bed. Both fluid properties and flow geometry are imposed. Using high-resolution flow-visualization techniques, we are also able to monitor the internal evolution of the avalanche from release to runout. The experimental data can then be compared with models of varying complexity. For Newtonian fluids (i.e., fluids whose rheological behavior is linear), we have found that the model accuracy increases with its degree of complexity. Surprisingly, for viscoplastic fluids (non-linear rheology), simple models perform much better than sophisticated models (such as the Saint-Venant equations). Our conclusions do not differ from the lessons learnt in other fields, such as atmospheric sciences, in which small nonlinearities in the governing equations are known to produce large errors, which accumulate to give false predictions. There is no feasible reason why governing equations such as the Saint-Venant equations, which are unable to provide accurate predictions in well-controlled experiments should miraculously outperform other methods when applied to complex natural phenomena such as snow avalanches. Such models are certainly valuable in avalanche expertise as they provide a precise conceptual framework that link physical processes to universal principles such as conservation of mass and momentum. But, in agreement with Salm’s warning, our experiments show that the returns from using sophisticated models may be minimal or diminishing unless we take notice of the errors and biases introduced by these models.