Adding expert contributions to the spatiotemporal modelling of avalanche activity under different climatic influences

type="main" xml:id="rssc12095-abs-0001"> We address the question of introducing expert knowledge in a hierarchical Bayesian spatiotemporal model. Specifically, we combine avalanche count data and an expert prior judgement about avalanche climatology to cluster French Alpine townships into two coherent groups. A spatial regression defines the a priori probability of belonging to each group and an innovative method is proposed to elicit its parameters by working with an expert on replicates of simulated maps. As a benefit of the extra data knowledge, we show the existence of robust north–south clusters of decreasing–increasing avalanche activity resulting from the interaction of local climate change patterns with altitude distribution. Spatial dependence of avalanche activity has also been inferred and is characterized by an anisotropy, with longer dependence along the north-west–south-east axis.

[1]  Martin Beniston,et al.  CLIMATIC CHANGE AT HIGH ELEVATION SITES: AN OVERVIEW , 1997 .

[2]  D. Mcclung,et al.  Numerical avalanche prediction: Kootenay Pass, British Columbia, Canada , 1994, Journal of Glaciology.

[3]  Pierre Etchevers,et al.  Reanalysis of 44 Yr of Climate in the French Alps (1958-2002): Methodology, Model Validation, Climatology, and Trends for Air Temperature and Precipitation , 2009 .

[4]  N. Eckert,et al.  Mapping extreme snowfalls in the French Alps using max‐stable processes , 2013 .

[5]  W. Wong,et al.  The calculation of posterior distributions by data augmentation , 1987 .

[6]  Jon A. Krosnick,et al.  Global warming vs. climate change, taxes vs. prices: Does word choice matter? , 2011 .

[7]  Karl W. Birkeland,et al.  Snow Avalanche Climatology of the Western United States Mountain Ranges , 2000 .

[8]  Ying C. MacNab,et al.  Spline smoothing in Bayesian disease mapping , 2007 .

[9]  Judith Rousseau,et al.  Combining expert opinions in prior elicitation , 2010 .

[10]  N. Eckert,et al.  Projected changes of snow conditions and avalanche activity in a warming climate: a case study in the French Alps over the 2020-2050 and 2070-2100 periods , 2014 .

[11]  N. Eckert,et al.  Snow and weather climatic control on snow avalanche occurrence fluctuations over 50 yr in the French Alps , 2011 .

[12]  Rémy Garçon,et al.  Expertise humaine des prévisions hydrométéorologiques et communication de leurs incertitudes dans un contexte décisionnel , 2009 .

[13]  Juan Ignacio López-Moreno,et al.  Effects of climate change on the intensity and frequency of heavy snowfall events in the Pyrenees , 2011 .

[14]  A. O'Hagan,et al.  Statistical Methods for Eliciting Probability Distributions , 2005 .

[15]  Vincent Jomelli,et al.  Probabilistic analysis of recent snow avalanche activity and weather in the French Alps , 2007 .

[16]  Kerrie L. Mengersen,et al.  Elicitator: An expert elicitation tool for regression in ecology , 2010, Environ. Model. Softw..

[17]  Kerrie Mengersen,et al.  Elicitation by design in ecology: using expert opinion to inform priors for Bayesian statistical models. , 2009, Ecology.

[18]  Lukas Stoffel,et al.  On forecasting large and infrequent snow avalanches , 2009 .

[19]  Nicolas Eckert,et al.  Bayesian stochastic modelling for avalanche predetermination: from a general system framework to return period computations , 2008 .

[20]  Hao Zhang.  Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics , 2004 .

[21]  M. Beniston.  Warm winter spells in the Swiss Alps: Strong heat waves in a cold season? A study focusing on climate observations at the Saentis high mountain site , 2005 .

[22]  Y. Durand,et al.  Reanalysis of 47 Years of Climate in the French Alps (1958–2005): Climatology and Trends for Snow Cover , 2009 .

[23]  C. Keylock,et al.  Temporal trends in avalanche activity in the French Alps and subregions: from occurrences and runout altitudes to unsteady return periods , 2013, Journal of Glaciology.

[24]  Jorge Mateu,et al.  Estimating Space and Space-Time Covariance Functions for Large Data Sets: A Weighted Composite Likelihood Approach , 2012 .

[25]  N. Eckert,et al.  A model for spatio‐temporal clustering using multinomial probit regression: application to avalanche counts , 2012 .

[26]  R. Christensen,et al.  A New Perspective on Priors for Generalized Linear Models , 1996 .

[27]  C. Wikle.  Hierarchical Models in Environmental Science , 2003 .

[28]  N. Eckert,et al.  Cross-comparison of meteorological and avalanche data for characterising avalanche cycles: The example of December 2008 in the eastern part of the French Alps , 2010 .

[29]  P. Diggle,et al.  A Class of Convolution‐Based Models for Spatio‐Temporal Processes with Non‐Separable Covariance Structure , 2010 .

[30]  Mark A. Burgman,et al.  Expert Status and Performance , 2011, PloS one.

[31]  Chih-Hsiang Ho,et al.  Volcanic hazard assessment incorporating expert knowledge: Application to the yucca mountain region, Nevada, USA , 1997 .

[32]  James S. Hodges,et al.  Variational Bayesian methods for spatial data analysis , 2011, Comput. Stat. Data Anal..

[33]  T. Gneiting.  Nonseparable, Stationary Covariance Functions for Space–Time Data , 2002 .

[34]  Éric Parent,et al.  Hierarchical Bayesian modelling for spatial analysis of the number of avalanche occurrences at the scale of the township , 2007 .

[35]  N. Eckert,et al.  Extracting the temporal signal from a winter and summer mass-balance series: application to a six-decade record at Glacier de Sarennes, French Alps , 2011, Journal of Glaciology.

[36]  N. Eckert,et al.  Assessing the Response of Snow Avalanche Runout Altitudes to Climate Fluctuations Using Hierarchical Modeling: Application to 61 Winters of Data in France , 2010 .

[37]  Lyle Brenner,et al.  Overconfidence in Probability and Frequency Judgments: A Critical Examination , 1996 .

[38]  N. Eckert,et al.  A spatio-temporal modelling framework for assessing the fluctuations of avalanche occurrence resulting from climate change: application to 60 years of data in the northern French Alps , 2010 .

[39]  Y. Durand,et al.  Analysis and forecast of extreme new-snow avalanches: a numerical study of the avalanche cycles of February 1999 in France , 2010, Journal of Glaciology.

[40]  C. Holmes,et al.  Bayesian auxiliary variable models for binary and multinomial regression , 2006 .

[41]  Purushottam W. Laud,et al.  A Predictive Approach to the Analysis of Designed Experiments , 1994 .