NHESS Natural Hazards and Earth System Sciences NHESS Nat. Hazards Earth Syst. Sci. 1684-9981 Copernicus Publications Göttingen, Germany 10.5194/nhess-13-545-2013 Bayesian hierarchical modelling of North Atlantic windiness Vanem E. 1 Breivik O. N. 1 Department of Mathematics, University of Oslo, P.O. Box 1053 Blindern, 0316 Oslo, Norway 04 03 2013 13 3 545 557 Copyright: © 2013 E. Vanem 2013 This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/ This article is available from https://nhess.copernicus.org/articles/13/545/2013/nhess-13-545-2013.html The full text article is available as a PDF file from https://nhess.copernicus.org/articles/13/545/2013/nhess-13-545-2013.pdf

Extreme weather conditions represent serious natural hazards to ship operations and may be the direct cause or contributing factor to maritime accidents. Such severe environmental conditions can be taken into account in ship design and operational windows can be defined that limits hazardous operations to less extreme conditions. Nevertheless, possible changes in the statistics of extreme weather conditions, possibly due to anthropogenic climate change, represent an additional hazard to ship operations that is less straightforward to account for in a consistent way. Obviously, there are large uncertainties as to how future climate change will affect the extreme weather conditions at sea and there is a need for stochastic models that can describe the variability in both space and time at various scales of the environmental conditions. Previously, Bayesian hierarchical space-time models have been developed to describe the variability and complex dependence structures of significant wave height in space and time. These models were found to perform reasonably well and provided some interesting results, in particular, pertaining to long-term trends in the wave climate. In this paper, a similar framework is applied to oceanic windiness and the spatial and temporal variability of the 10-m wind speed over an area in the North Atlantic ocean is investigated. When the results from the model for North Atlantic windiness is compared to the results for significant wave height over the same area, it is interesting to observe that whereas an increasing trend in significant wave height was identified, no statistically significant long-term trend was estimated in windiness. This may indicate that the increase in significant wave height is not due to an increase in locally generated wind waves, but rather to increased swell. This observation is also consistent with studies that have suggested a poleward shift of the main storm tracks.

 References Bader, J., Mesquita, M. D.&nbsp;S., Hodges, K.&nbsp;I., Keenlyside, N., Østerhus, S., and Miles, M.: A review on {N}orthern {H}emisphere sea-ice, storminess and the {N}orth {A}tlantic {O}scillation: Observations and projected changes, Atmos. Res., 101, 809–834, 2011. Beauchamp, J.&nbsp;J. and Olson, J.&nbsp;S.: Corrections for Bias in Regression Estimates After Logarithmic Transformation, Ecology, 54, 1403–1407, 1973. Bender, F. A.-M., Ramanathan, V., and Tselioudis, G.: Changes in extratropical storm track cloudiness 1983-2008: observational support for a poleward shift, Clim. Dynam., 38, 2037–2053, 2012. Caires, S., Swail, V.&nbsp;R., and Wang, X.&nbsp;L.: Projection and Analysis of Extreme Wave Climate, J. Climate, 19, 5581–5605, 2006. Collins, M., Chandler, R.&nbsp;E., Cox, P.&nbsp;M., Huthnance, J.&nbsp;M., and Rougier, J.: Quantifying future climate change, Nat. Climate Change, 2, 403–409, 2012. Debernard, J.&nbsp;B. and Røed, L.&nbsp;P.: Future wind, wave and storm surge climate in the {N}orthern {S}eas: a revisit, Tellus, 60A, 427–438, 2008. Ferguson, R.: River Loads Underestimated by Rating Curves, Water Resour. Res., 22, 74–76, 1986. Gastineau, G. and Soden, B.&nbsp;J.: Model projected changes of extreme wind events in response to global warming, Geophys. Res. Lett., 36, L10810, <a href="http://dx.doi.org/10.1029/2009GL037500">https://doi.org/10.1029/2009GL037500</a>, 2009. Grabemann, I. and Weisse, R.: Climate change impact on extreme wave conditions in the {N}orth {S}ea: an ensemble study, Ocean Dynam., 58, 199–212, 2008. IPCC: {C}limate {C}hange 2007: The Physical Sciences Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge University Press, 2007. IPCC: Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation, Cambridge University Press, 2012. Kushnir, Y., Cardone, V., Greenwood, J., and Cane, M.: The Recent Increase in North Atlantic Wave Heights, J. Climate, 10, 2107–2113, 1997. Natvig, B. and Tvete, I.&nbsp;F.: Bayesian Hierarchical Space-time Modeling of Earthquake Data, Methodol. Comput. Appl. Probability, 9, 89–114, 2007. Stephenson, D.&nbsp;B., Collins, M., Rougier, J.&nbsp;C., and Chandler, R.&nbsp;E.: Statistical problems in the probabilistic prediction of climate change, Environmetrics, 23, 364–372, 2012. Stow, C.&nbsp;A., Reckhow, K.&nbsp;H., and Qian, S.&nbsp;S.: A {B}ayesian Approach to Retransformation Bias in Transformed Regression, Ecology, 87, 1472–1477, 2006. Talley, L.&nbsp;D., Pickard, G.&nbsp;L., Emery, W.&nbsp;J., and Swift, J.&nbsp;H.: Descriptive Physical Oceanography an introduction, Elsevier, 6th Edn., 2011. Tebaldi, C. and Knutti, R.: The use of the multi-model ensemble in probabilistic climate projections, Phil. Trans. Roy. Soc. A, 365, 2053–2075, 2007. Uppala, S.&nbsp;M., Kållberg, P.&nbsp;W., Simmons, A.&nbsp;J., Andrae, U., Da&nbsp;Costa&nbsp;Bechtold, V., Fiorino, M., Gibson, J.&nbsp;K., Haseler, J., Hernandez, A., Kelly, G.&nbsp;A., Li, X., Onogi, K., Saarinen, S., Sokka, N., Allan, R.&nbsp;P., Andersson, E., Arpe, K., Balmaseda, M.&nbsp;A., Beljaars, A. C.&nbsp;M., Van&nbsp;de Berg, L., Bidlot, J., Bormann, N., Caires, S., Chevallier, F., Dethof, A., Dragosavac, M., Fisher, M., Fuentes, M., Hagemann, S., Hólm, E.&nbsp;Hoskins, B.&nbsp;J., Isaksen, L., Janssen, P. A. E.&nbsp;M., Jenne, R., McNally, A.&nbsp;P., Mahfouf, J.-F., Morcrette, J.-J., Rayner, N.&nbsp;A., Saunders, R.&nbsp;W., Simon, P., Sterl, A., Trenberth, K.&nbsp;E., Untch, A., Vasiljevic, D., Vitebro, P., and Woolen, J.: The {ERA}-40 re-analysis, Q. J. Roy. Meteorol. Soc., 131, 2961–3012, 2005. Vanem, E.: Long-term time-dependent stochastic modelling of extreme waves, Stochastic Environ. Res. Risk Assess., 25, 185–209, 2011. Vanem, E. and Bitner-Gregersen, E.: Stochastic modelling of long-term trends in the wave climate and its potential impact on ship structural loads, Appl. Ocean Res., 37, 235–248, 2012. Vanem, E. and Walker, S.-E.: Identifying trends in the ocean wave climate by time series analyses of significant wave height data, Ocean Eng., 60, 148–160, 2013 Vanem, E., Huseby, A.&nbsp;B., and Natvig, B.: Bayesian Hierarchical Spatio-Temporal Modelling of Trends and Future Projections in the Ocean Wave Climate with a CO}{<sub>2</sub> Regression Component, submitted, 2012{a}. Vanem, E., Huseby, A.&nbsp;B., and Natvig, B.: A B}ayesian Hierarchical Spatio-Temporal Model for Significant Wave Height in the {N}orth {A}tlantic, Stochastic Environ. Res. Risk Assess., 26, 609–632, 2012{b. Vanem, E., Huseby, A.&nbsp;B., and Natvig, B.: A Stochastic Model in Space and Time for Monthly Maximum Significant Wave Height, in: Proc. Ninth International Geostatistics Congress (Geostats 2012), 505–517, 2012{c}. Vanem, E., Huseby, A.&nbsp;B., and Natvig, B.: Modeling Ocean Wave Climate with a B}ayesian Hierarchical Space-Time Model and a Log-Transform of the Data, Ocean Dynam., 62, 355–375, 2012{d. Wallcraft, A.&nbsp;J., Kara, A.&nbsp;B., Barron, C.&nbsp;N., Metzger, E.&nbsp;J., Pauley, R.&nbsp;L., and Bourassa, M.&nbsp;A.: Comparison of monthly mean 10 m wind speeds from satellites and NWP products over the global ocean, J. Geophys. Res., 114, D16109, <a href="http://dx.doi.org/10.1029/2008JD011696">https://doi.org/10.1029/2008JD011696</a>, 2009. Wang, X.&nbsp;J., Zwiers, F.&nbsp;W., and Swail, V.&nbsp;R.: North {A}tlantic Ocean Wave Climate Change Scenarios for the Twenty-First Century, J. Climate, 17, 2368–2383, 2004. Wang, X.&nbsp;L. and Swail, V.&nbsp;R.: Changes of Extreme Wave Heights in Northern Hemisphere Oceans and Related Atmospheric Circulation Regimes, J. Climate, 14, 2204–2221, 2001. Wang, X.&nbsp;L. and Swail, V.&nbsp;R.: Trends of {A}tlantic Wave Extremes as Simulated in a 40-Yr Wave hindcast Using Kinematically Reanalyzed Wind Fields, J. Climate, 15, 1020–1035, 2002. Wang, X.&nbsp;L. and Swail, V.&nbsp;R.: Climate change signal and uncertainty in projections of ocean wave heights, Climate Dynamics, 26, 109–126, 2006. Wikle, C.&nbsp;K., Berliner, L.&nbsp;M., and Cressie, N.: Hierarchical {B}ayesian space-time models, Environ. Ecol. Stat., 5, 117–154, 1998. Wikle, C.&nbsp;K., Milliff, R.&nbsp;F., Nychka, D., and Berliner, L.&nbsp;M.: Spatiotemporal Hierarchical {B}ayesian Modeling: Tropical Ocean Surface Winds, J. Am. Stat. Assoc., 96, 382–397, 2001. Yin, J.&nbsp;H.: A consistent poleward shift of the storm tracks in simulations of 21st century climate, Geophys. Res. Lett., 32, L1801, <a href="http://dx.doi.org/10.1029/2005GL023684">https://doi.org/10.1029/2005GL023684</a>, 2005.