Abstract Modelling extreme environments
Extreme value analysis can help us understand unusual events in our physical environment, particularly given current concerns about climate change, providing a mathematically sound and statistically ecient basis for modelling. For example, reliable design and assessment of ood and coastal defences and marine structures requires estimation of both marginal and dependence characteristics of extreme environments.
Incorporation of covariate e ects is necessary for good modelling. For example, by expressing the parameters of extreme value distributions as smooth functions of storm direction, we can model the directional variation of extreme ocean storms [1, 2, 3]. Similarly we can estimate seasonal, temporal and spatial variation. Characterisation of dependence structure [4] is also critical for good modelling of joint occurrences of rare events [5, 6, 7]. For example, in a spatial context, rare events are often spatially clustered. The most extreme environmental loads on a marine structure may correspond to joint occurrence of large waves, winds and currents [8].
This talk will illustrate some current methodologies for covariate and dependence modelling in extreme value analysis in application to extreme ocean environments [9].
References
[1] Davison, A.C. and Smith, R. L., Models for exceedances over high thresholds, J. R. Statist. Soc. B , 1990, 52, 393.
[2] Ewans, K. C. and P. Jonathan, The e ffect of directionality on Northern North Sea extreme wave design criteria, J. O shore Mechanics Arctic
Engineering, 2008, 130, 10.
[3] D. Randell and Y. Wu and P. Jonathan and K. C. Ewans, OMAE2013-10187: Modelling covariate e ects in extremes of storm severity on
the Australian North West Shelf, Proc. 32nd Conf. O shore Mech. Arct. Eng., 2013, (preprint at www.lancs.ac.uk/jonathan).
[4] Ledford, A. W. and Tawn, J. A., Modelling dependence within joint tail regions,J. R. Statist. Soc. B ,1997, 59, 475-499.
[5] He ernan, J. E. and J. A. Tawn, A conditional approach for multivariate extreme values, J. R. Statist. Soc. B, 2004, 66, 497.
[6] Davison, A.C. and Gholamrezaee, M. M., Geostatistics of extremes, Proc. Roy. Soc. A, 2012, 468, 581-608.
[7] Davison, A. C., Padoan, S. A. and Ribatet, M., Statistical Modelling of Spatial Extremes, Statistical Science, 2012, 27, 161-186.
[8] Jonathan, P., J. Flynn and K. C. Ewans, Joint modelling of wave spectral parameters for extreme sea states, Ocean Engineering, 2010, 37,
1070.
[9] Jonathan, P. and Ewans, K. C., Statistical modelling of extreme ocean environments for marine design, Ocean Engineering, 2013, 62, 91-109.
Abstract Locating and quantifying gas emission sources using remotely obtained concentration data
We describe [1] a method for detecting, locating and quantifying sources of gas emissions to the atmosphere using remotely obtained gas concentration data; the method is applicable to gases of environmental concern. We demonstrate its performance using methane data collected from aircraft. Atmospheric point concentration measurements are modelled as the sum of a spatially and temporally smooth atmospheric background concentration, augmented by concentrations due to local sources. We model source emission rates with a Gaussian mixture model [2] and use aMarkov random eld to represent the atmospheric background concentration component of the measurements. A Gaussian plume atmospheric eddy dispersion model represents gas dispersion between sources and measurement locations. Initial point estimates of background concentrations and source emission rates are obtained using mixed l2-l1 optimisation over a discretised grid of potential source locations. Subsequent reversible jump Markov chain Monte Carlo inference [3] provides estimated values and uncertainties for the number, emission rates and locations of sources unconstrained by a grid. Source area, atmospheric background concentrations and other model parameters are also estimated. We investigate the performance of the approach rst using a synthetic problem, then apply the method to real airborne data from a 1600km2 area containing two land lls, then a 225km2 area containing a gas are stack.
References
[1] B. Hirst and P. Jonathan and F. Gonzalez del Cueto and D. Randell and O. Kosut, Locating and quantifying gas emission sources using
remotely obtained concentration data, Atmospheric Environment (accepted, preprint at www.lancs.ac.uk/jonathan), 2013.
[2] Z. Zhang and K. L. Chan and Y. Wu and C. Chen, Learning a multivariate Gaussian mixture model with the reversible jump MCMC algorithm,
Statistics and Computing, 2004, 14, 343-355.
[3] Green, P.J., Reversible jump Markov chain Monte Carlo computation and Bayesian model determination, Biometrika, 1995, 82, 711-732.