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Franzke, C. L. E., O'Kane, T. J., Berner, J., Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820 and Lucarini, V. ORCID: https://orcid.org/0000-0001-9392-1471 (2015) Stochastic climate theory and modeling. Wiley Interdisciplinary Reviews: Climate Change, 6 (1). pp. 63-78. ISSN 1757-7799 doi: https://doi.org/10.1002/wcc.318

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Williams, P. ORCID: https://orcid.org/0000-0002-9713-9820 (2012) Comment on “A modified leapfrog scheme for shallow water equations” by Wen-Yih Sun and Oliver M.T. Sun. Computers & Fluids, 62. p. 91. ISSN 0045-7930 doi: https://doi.org/10.1016/j.compfluid.2012.02.023

McCann, D. W., Knox, J. A. and Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820 (2012) An improvement in clear-air turbulence forecasting based on spontaneous imbalance theory: the ULTURB algorithm. Meteorological Applications, 19 (1). pp. 71-78. ISSN 1469-8080 doi: https://doi.org/10.1002/met.260

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Amezcua, J., Kalnay, E. and Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820 (2011) The effects of the RAW filter on the climatology and forecast skill of the SPEEDY model. Monthly Weather Review, 139 (2). pp. 608-619. ISSN 0027-0644 doi: https://doi.org/10.1175/2010MWR3530.1

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Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820, Guilyardi, E. ORCID: https://orcid.org/0000-0002-2255-8625, Madec, G., Gualdi, S. and Scoccimarro, E. (2010) The role of mean ocean salinity in climate. Dynamics of Atmospheres and Oceans, 49 (2-3). pp. 108-123. ISSN 0377-0265 doi: https://doi.org/10.1016/j.dynatmoce.2009.02.001

Knox, J. A., McCann, D. W. and Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820 (2009) "Application of the Lighthill-Ford theory of spontaneous imbalance to clear-air turbulence forecasting" :Reply. Journal of the Atmospheric Sciences, 66 (8). pp. 2511-2516. ISSN 0022-4928 doi: https://doi.org/10.1175/2009JAS3084.1

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Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820, Haine, T., Read, P., Lewis, S. and Yamazaki, Y. (2009) QUAGMIRE v1.3: a quasi-geostrophic model for investigating rotating fluids experiments. Geoscientific Model Development, 2 (1). pp. 13-32.

Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820 (2009) Rapid climate change: an overview for economists. International Journal of Green Economics, 3 (1). pp. 63-76. ISSN 1744-9928 doi: https://doi.org/10.1504/IJGE.2009.026492

Knox, J.A., McCann, D.W. and Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820 (2008) Application of the Lighthill-Ford theory of spontaneous imbalance to clear-air turbulence forecasting. Journal of the Atmospheric Sciences, 65 (10). pp. 3292-3304. ISSN 1520-0469 doi: https://doi.org/10.1175/2008JAS2477.1

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Palmer, T.N. and Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820 (2008) Introduction. Stochastic physics and climate modelling. Philosophical Transactions of the Royal Society. Part A, 366 (1875). pp. 2421-2427. ISSN 1364-503X doi: https://doi.org/10.1098/rsta.2008.0059

Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820, Haine, T.W.N. and Read, P.L. (2008) Inertia-Gravity Waves Emitted from Balanced Flow: Observations, Properties, and Consequences. Journal of the Atmospheric Sciences, 65 (11). pp. 3543-3556. ISSN 1520-0469 doi: https://doi.org/10.1175/2008JAS2480.1

Read, P., Yamazaki, H., Lewis, S., Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820, Wordsworth, R. and Miki-Yamazaki, K. (2007) Dynamics of convectively driven banded jets in the laboratory. Journal of the Atmospheric Sciences, 64 (11). pp. 4031-4052. ISSN 1520-0469 doi: https://doi.org/10.1175/2007JAS2219.1

Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820, Guilyardi, E. ORCID: https://orcid.org/0000-0002-2255-8625, Sutton, R. T. ORCID: https://orcid.org/0000-0001-8345-8583, Gregory, J. M. ORCID: https://orcid.org/0000-0003-1296-8644 and Madec, G. (2007) A new feedback on climate change from the hydrological cycle. Geophysical Research Letters, 34 (8). L08706. ISSN 0094-8276 doi: https://doi.org/10.1029/2007GL029275

Lewis, A. C., Evans, M. J., Methven, J. ORCID: https://orcid.org/0000-0002-7636-6872, Watson, N. M., Lee, J. D., Hopkins, J. R., Purvis, R., Arnold, S. R., McQuaid, J., Whalley, L. K., Pilling, M. J., Heard, D. E., Monks, P. S., Parker, A. E., Reeves, C. E., Oram, D. E., Mills, G., Bandy, B. J., Stewart, D., Coe, H., Williams, P. I. ORCID: https://orcid.org/0000-0002-9713-9820 and Crosier, J. (2007) Chemical composition observed over the mid-Atlantic and the detection of pollution signatures far from source regions. Journal of Geophysical Research, 112. D10S39. ISSN 0148-0227 doi: https://doi.org/10.1029/2006JD007584

Methven, J. ORCID: https://orcid.org/0000-0002-7636-6872, Arnold, S. R., Stohl, A., Evans, M. J., Avery, M., Law, K., Lewis, A. C., Monks, P. S., Parrish, D. D., Reeves, C. E., Schlager, H., Atlas, E., Blake, D. R., Coe, H., Crosier, J., Flocke, F. M., Holloway, J. S., Hopkins, J. R., McQuaid, J., Purvis, R., Rappengluck, B., Singh, H. B., Watson, N. M., Whalley, L. K. and Williams, P. I. ORCID: https://orcid.org/0000-0002-9713-9820 (2006) Establishing Lagrangian connections between observations within air masses crossing the Atlantic during the International Consortium for Atmospheric Research on Transport and Transformation experiment. Journal of Geophysical Research, 111. D23S62. ISSN 0148-0227 doi: https://doi.org/10.1029/2006JD007540

Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820, Guilyardi, E. ORCID: https://orcid.org/0000-0002-2255-8625, Sutton, R. T. ORCID: https://orcid.org/0000-0001-8345-8583, Gregory, J. M. ORCID: https://orcid.org/0000-0003-1296-8644 and Madec, G. (2006) On the climate response of the low-latitude Pacific Ocean to changes in the global freshwater cycle. Climate Dynamics, 27 (6). pp. 593-611. ISSN 0930-7575 doi: https://doi.org/10.1007/s00382-006-0151-7

Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820 and Galvin, J. F. P. (2006) A multitude of gravity waves. Weather, 61 (6). p. 180. ISSN 0043-1656 doi: https://doi.org/10.1256/wea.134.04

Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820 (2006) Storm in a teacup. Weather, 59 (4). pp. 96-98. ISSN 0043-1656 doi: https://doi.org/10.1256/wea.152.03

Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820, Haine, T. W. N. and Read, P. L. (2005) On the generation mechanisms of short-scale unbalanced modes in rotating two-layer flows with vertical shear. Journal Of Fluid Mechanics , 528. pp. 1-22. ISSN 0022-1120 doi: https://doi.org/10.1017/S0022112004002873

Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820 (2005) Modelling climate change: the role of unresolved processes. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 363 (1837). pp. 2931-2946. ISSN 1364-503X doi: https://doi.org/10.1098/rsta.2005.1676

Read, P. L., Yamazaki, Y. H., Lewis, S. R., Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820, Miki-Yamazaki, K., Sommeria, J., Didelle, H. and Fincham, A. (2004) Jupiter's and Saturn's convectively driven banded jets in the laboratory. Geophysical Research Letters, 31 (22). L22701. ISSN 0094-8276 doi: https://doi.org/10.1029/2004GL020106

Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820, Haine, T. and Read, P. (2004) Stochastic resonance in a nonlinear model of a rotating, stratified shear flow, with a simple stochastic inertia-gravity wave parameterization. Nonlinear Processes in Geophysics, 11 (1). pp. 127-135. ISSN 1023-5809

Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820, Read, P.L. and Haine, T.W.N. (2004) A calibrated, non-invasive method for measuring the internal interface height field at high resolution in the rotating, two-layer annulus. Geophysical & Astrophysical Fluid Dynamics, 98 (6). pp. 453-471. ISSN 0309-1929 doi: https://doi.org/10.1080/03091920412331296366

Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820 (2003) Spontaneous generation and impact of inertia-gravity waves in a stratified, two-layer shear flow. Geophysical Research Letters, 30 (24). 2255. ISSN 0094-8276 doi: https://doi.org/10.1029/2003GL018498

Haine, T. and Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820 (2002) The role of nonhydrostatic dynamics in controlling development of a surface ocean front. Ocean modelling, 4 (2). pp. 121-135. ISSN 1463-5003 doi: https://doi.org/10.1016/S1463-5003(01)00014-2

Book or Report Section

Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820 and Joshi, M. M. (2016) Clear-air turbulence in a changing climate. In: Sharman, R. and Lane, T. (eds.) Aviation turbulence: processes, detection, prediction. Springer, pp. 465-480. ISBN 9783319236292 doi: https://doi.org/10.1007/978-3-319-23630-8_23

Book

von Larcher, T. and Williams, P. D. ORCID: https://orcid.org/0000-0002-9713-9820, eds. (2015) Modeling atmospheric and oceanic flows: insights from laboratory experiments and numerical simulations. John Wiley & Sons, Hoboken, pp368. ISBN 9781118855935

Palmer, T. and Williams, P. ORCID: https://orcid.org/0000-0002-9713-9820, eds. (2010) Stochastic physics and climate modelling. Cambridge University Press, Cambridge, UK, pp496. ISBN 9780521761055