Publications

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2025

• "Quantifying the effects of climate change on aircraft take-off performance at European airports"
  Williams, J., Williams, P. D., Guerrini, F. and Venturini, M., Aerospace, 12(3), 165, 2025. doi:10.3390/aerospace12030165

2024

• "Update to aircraft observations and reanalysis depictions of trends in the North Atlantic winter jet stream wind speeds and turbulence"
  Tenenbaum, J. and Williams, P. D., Quarterly Journal of the Royal Meteorological Society, 150(761), pp 2533-2535, 2024. doi:10.1002/qj.4676

• "Nonlinear diffusion-limited two-dimensional colliding-plume simulations with very high-order numerical approximations"
  Straka, J. M., Williams, P. D. and Kanak, K. M., Quarterly Journal of the Royal Meteorological Society, 150(759), pp 663-705, 2024. doi:10.1002/qj.4616

2023

• "Comparison of very high order (O3-18) flux and Crowley flux, and (O3-17) WENO flux schemes with a 2D nonlinear test problem"
  Straka, J. M., Kanak, K. M. and Williams, P. D., Quarterly Journal of the Royal Meteorological Society, 149(757), pp 3669-3710, 2023. doi:10.1002/qj.4579

• "Evidence for large increases in clear-air turbulence over the past four decades"
  Prosser, M. C., Williams, P. D., Marlton, G. J. and Harrison, R. G., Geophysical Research Letters, 50(11), e2023GL103814, 2023. doi:10.1029/2023GL103814

• "Clear-air turbulence trends over the North Atlantic in high-resolution climate models"
  Smith, I. H., Williams, P. D. and Schiemann, R., Climate Dynamics, 61(7-8), pp 3063-3079, 2023. doi:10.1007/s00382-023-06694-x

• "The role of airspeed variability in fixed-time, fuel-optimal aircraft trajectory planning"
  Wells, C. A., Kalise, D., Nichols, N. K., Poll, I. and Williams, P. D., Optimization and Engineering, 24(2), pp 1057-1087, 2023. doi:10.1007/s11081-022-09720-9

• "Minimising emissions from flights through realistic wind fields with varying aircraft weights"
  Wells, C. A., Williams, P. D., Nichols, N. K., Kalise, D. and Poll, I., Transportation Research Part D: Transport and Environment, 117, 103660, 2023. doi:10.1016/j.trd.2023.103660

2022

• "Aircraft observations and reanalysis depictions of trends in the North Atlantic winter jet stream wind speeds and turbulence"
  Tenenbaum, J., Williams, P. D., Turp, D., Buchanan, P., Coulson, R., Gill, P. G., Lunnon, R. W., Oztunali, M. G., Rankin, J. and Rukhovets, L., Quarterly Journal of the Royal Meteorological Society, 148(747), pp 2927-2941, 2022. doi:10.1002/qj.4342

• "Can a climate model successfully diagnose clear-air turbulence and its response to climate change?"
  Williams, P. D. and Storer, L. N., Quarterly Journal of the Royal Meteorological Society, 148(744), pp 1424-1438, 2022. doi:10.1002/qj.4270

• "The performance of filtered leapfrog schemes in benchmark simulations"
  Williams, P. D., Straka, J. M. and Kanak, K. M., Quarterly Journal of the Royal Meteorological Society, 148(743), pp 784-808, 2022. doi:10.1002/qj.4231

• "Modelling the effect of electric aircraft on airport operations and infrastructure"
  Doctor, F., Budd, T., Williams, P. D., Prescott, M. and Iqbal, R., Technological Forecasting and Social Change, 177, 121553, 2022. doi:10.1016/j.techfore.2022.121553

• "Reviewing the impacts of climate change on air transport operations"
  Gratton, G. B., Williams, P. D., Padhra, A. and Rapsomanikis, S., The Aeronautical Journal, 126(1295), pp 209-221, 2022. doi:10.1017/aer.2021.109

2021

• "Pro-L* – A probabilistic L* mapping tool for ground observations"
  Thompson, R. L., Morley, S. K., Watt, C. E. J., Bentley, S. N. and Williams, P. D., Space Weather, 19(2), e2020SW002602, 2021. doi:10.1029/2020SW002602

• "Reducing transatlantic flight emissions by fuel-optimised routing"
  Wells, C. A., Williams, P. D., Nichols, N. K., Kalise, D. and Poll, I., Environmental Research Letters, 16(2), 025002, 2021. doi:10.1088/1748-9326/abce82

2020

• "Impact of climate variabilities on trans-oceanic flight times and emissions during strong NAO and ENSO phases"
  Kim, J.-H., Kim, D., Lee, D.-B., Chun, H.-Y., Sharman, R. D., Williams, P. D. and Kim, Y.-J., Environmental Research Letters, 15(10), 105017, 2020. doi:10.1088/1748-9326/abaa77

• "Accounting for variability in ULF wave radial diffusion models"
  Thompson, R. L., Watt, C. E. J. and Williams, P. D., Journal of Geophysical Research: Space Physics, 125(8), e2019JA027254, 2020. doi:10.1029/2019JA027254

• "The impacts of climate change on Greek airports"
  Gratton, G., Padhra, A., Rapsomanikis, S. and Williams, P. D., Climatic Change, 160(2), pp 219-231, 2020. doi:10.1007/s10584-019-02634-z

• "Multi-diagnostic multi-model ensemble forecasts of aviation turbulence"
  Storer, L. N., Gill, P. G. and Williams, P. D., Meteorological Applications, 27(1), e1885, 2020. doi:10.1002/met.1885

2019

• "Evaluation of ARM tethered-balloon system instrumentation for supercooled liquid water and distributed temperature sensing in mixed-phase Arctic clouds"
  Dexheimer, D., Airey, M., Roesler, E., Longbottom, C., Nicoll, K., Kneifel, S., Mei, F., Harrison, R. G., Marlton, G. and Williams, P. D., Atmospheric Measurement Techniques, 12(12), pp 6845-6864, 2019. doi:10.5194/amt-12-6845-2019

• "Increased shear in the North Atlantic upper-level jet stream over the past four decades"
  Lee, S. H., Williams, P. D. and Frame, T. H. A., Nature, 572(7771), pp 639-642, 2019. doi:10.1038/s41586-019-1465-z

• "Uncertainty and scale interactions in ocean ensembles: From seasonal forecasts to multidecadal climate predictions"
  Zanna, L., Brankart, J. M., Huber, M., Leroux, S., Penduff, T. and Williams, P. D. Quarterly Journal of the Royal Meteorological Society, 145(S1), pp 160-175, 2019. doi:10.1002/qj.3397

• "Multi-model ensemble predictions of aviation turbulence"
  Storer, L. N., Gill, P. G. and Williams, P. D., Meteorological Applications, 26(3), pp 416-428, 2019. doi:10.1002/met.1772

• "A review of high impact weather for aviation meteorology"
  Gultepe, I., Sharman, R., Williams, P. D., Zhou, B., Ellrod, G., Minnis, P., Trier, S., Griffin, S., Yum, S. S., Gharabaghi, B., Feltz, W., Temimi, M., Pu, Z., Storer, L. N., Kneringer, P., Weston, M. J., Chuang, H.-Y., Thobois, L., Dimri, A. P., Dietz, S. J., França, G. B., Almeida, M. V. and Neto, F. L. A., Pure and Applied Geophysics, 176(5), pp 1,869-1,921, 2019. doi:10.1007/s00024-019-02168-6

• "Aviation turbulence: dynamics, forecasting, and response to climate change"
  Storer, L. N., Williams, P. D. and Gill, P. G., Pure and Applied Geophysics, 176(5), pp 2,081-2,095, 2019. doi:10.1007/s00024-018-1822-0

2017

• "A self-calibrating wide range electrometer for in-cloud measurements"
  Harrison, R. G., Marlton, G. J., Nicoll, K. A., Airey, M. W. and Williams, P. D., Review of Scientific Instruments, 88(12), 126109, 2017. doi:10.1063/1.5011177

• "A census of atmospheric variability from seconds to decades"
  Williams, P. D., Alexander, M. J., Barnes, E. A., Butler, A. H., Davies, H. C., Garfinkel, C. I., Kushnir, Y., Lane, T. P., Lundquist, J. K., Martius, O., Maue, R. N., Peltier, W. R., Sato, K., Scaife, A. A. and Zhang, C., Geophysical Research Letters, 44(21), pp 11,201-11,211, 2017. doi:10.1002/2017GL075483

• "Global response of clear-air turbulence to climate change"
  Storer, L. N., Williams, P. D. and Joshi, M. M., Geophysical Research Letters, 44(19), pp 9,976-9,984, 2017. doi:10.1002/2017GL074618

• "A miniature oscillating microbalance for sampling ice and volcanic ash from a small airborne platform"
  Airey, M. W., Harrison, R. G., Nicoll, K. A., Williams, P. D. and Marlton, G. J., Review of Scientific Instruments, 88(8), 086108, 2017. doi:10.1063/1.4998971

• "Increased light, moderate, and severe clear-air turbulence in response to climate change"
  Williams, P. D., Advances in Atmospheric Sciences, 34(5), pp 576-586, 2017. doi:10.1007/s00376-017-6268-2

• "Stochastic parameterization: toward a new view of weather and climate models"
  Berner, J., Achatz, U., Batté, L., Bengtsson, L., Cámara, A., Christensen, H. M., Colangeli, M., Coleman, D. R. B., Crommelin, D., Dolaptchiev, S. I., Franzke, C. L. E., Friederichs, P., Imkeller, P., Järvinen, H., Juricke, S., Kitsios, V., Lott, F., Lucarini, V., Mahajan, S., Palmer, T. N., Penland, C., Sakradzija, M., von Storch, J.-S., Weisheimer, A., Weniger, M., Williams, P. D. and Yano, J.-I., Bulletin of the American Meteorological Society, 98(3), pp 565-588, 2017. doi:10.1175/BAMS-D-15-00268.1

2016

• "Improved climate simulations through a stochastic parameterization of ocean eddies"
  Williams, P. D., Howe, N. J., Gregory, J. M., Smith, R. S. and Joshi, M. M., Journal of Climate, 29(24), pp 8763-8781, 2016. doi:10.1175/JCLI-D-15-0746.1

• "Editorial: Focus on stochastic flows and climate statistics"
  Marston, J. B. and Williams, P. D., New Journal of Physics, 18(9), 090201, 2016. doi:10.1088/1367-2630/18/9/090201

• "On the detection and attribution of gravity waves generated by the 20 March 2015 solar eclipse"
  Marlton, G. J., Williams, P. D., and Nicoll, K. A., Philosophical Transactions of the Royal Society A, 374(2077), 20150222, 2016. doi:10.1098/rsta.2015.0222

• "Coordinated weather balloon solar radiation measurements during a solar eclipse"
  Harrison, R. G., Marlton, G. J., Williams, P. D., and Nicoll, K. A., Philosophical Transactions of the Royal Society A, 374(2077), 20150221, 2016. doi:10.1098/rsta.2015.0221

• "Impact of the North Atlantic Oscillation on transatlantic flight routes and clear-air turbulence"
  Kim, J.-H., Chan, W. N., Sridhar, B., Sharman, R. D., Williams, P. D., and Strahan, M., Journal of Applied Meteorology and Climatology, 55(3), pp 763-771, 2016. doi:10.1175/JAMC-D-15-0261.1

• "Transatlantic flight times and climate change"
  Williams, P. D., Environmental Research Letters, 11(2), 024008, 2016. doi:10.1088/1748-9326/11/2/024008

2015

• "Is there a rhythm of the rain? An analysis of weather in popular music"
  Brown, S., Aplin, K. L., Jenkins, K., Mander, S., Walsh, C., and Williams, P. D., Weather, 70(7), pp 198-204, 2015. doi:10.1002/wea.2464

• "The composite-tendency Robert–Asselin–Williams (RAW) filter in semi-implicit integrations"
  Amezcua, J. and Williams, P. D., Quarterly Journal of the Royal Meteorological Society, 141(688), pp 764-773, 2015. doi:10.1002/qj.2391

• "The dynamics of baroclinic zonal jets"
  Williams, P. D. and Kelsall, C. W., Journal of the Atmospheric Sciences, 72(3), pp 1137-1151, 2015. doi:10.1175/JAS-D-14-0027.1

• "A balloon-borne accelerometer technique for measuring atmospheric turbulence"
  Marlton, G. J., Harrison, R. G., Nicoll, K. A., and Williams, P. D., Review of Scientific Instruments, 86(1), 016109, 2015. doi:10.1063/1.4905529

• "Advanced Review: Stochastic climate theory and modeling"
  Franzke, C. L. E., O'Kane, T. J., Berner, J., Williams, P. D. and Lucarini, V., Wiley Interdisciplinary Reviews: Climate Change, 6(1), pp 63-78, 2015. doi:10.1002/wcc.318

2013

• "Intensification of winter transatlantic aviation turbulence in response to climate change"
  Williams, P. D. and Joshi, M. M., Nature Climate Change, 3(7), pp 644-648, 2013. doi:10.1038/nclimate1866

• "Achieving seventh-order amplitude accuracy in leapfrog integrations"
  Williams, P. D., Monthly Weather Review, 141(9), pp 3037-3051, 2013. doi:10.1175/MWR-D-12-00303.1

• "Mathematics applied to the climate system: outstanding challenges and recent progress"
  Williams, P. D., Cullen, M. J. P., Davey, M. K. and Huthnance, J. M., Philosophical Transactions of the Royal Society A, 371(1991), 20120518, 2013. doi:10.1098/rsta.2012.0518

2012

• "Whether weather affects music"
  Aplin, K. L. and Williams, P. D., Eos, 93(36), pp 347-348, 4 September 2012. doi:10.1029/2012EO360007

• "Climatic impacts of stochastic fluctuations in air–sea fluxes"
  Williams, P. D., Geophysical Research Letters, 39, L10705, 2012. doi:10.1029/2012GL051813

• "Comment on "A modified leapfrog scheme for shallow water equations" by Wen-Yih Sun and Oliver M. T. Sun"
  Williams, P. D., Computers & Fluids, 62, p 91, 2012. doi:10.1016/j.compfluid.2012.02.023

• "An improvement in clear-air turbulence forecasting based on spontaneous imbalance theory: the ULTURB algorithm"
  McCann, D. W., Knox, J. A. and Williams, P. D., Meteorological Applications, 19(1), pp 71-78, 2012. doi:10.1002/met.260

2011

• "Meteorological phenomena in Western classical orchestral music"
  Aplin, K. L. and Williams, P. D., Weather, 66(11), pp 300-306, 2011. doi:10.1002/wea.765

• "The RAW filter: an improvement to the Robert–Asselin filter in semi-implicit integrations"
  Williams, P. D., Monthly Weather Review, 139(6), pp 1996-2007, 2011. doi:10.1175/2010MWR3601.1

• "The effects of the RAW filter on the climatology and forecast skill of the SPEEDY model"
  Amezcua, J., Kalnay, E. and Williams, P. D., Monthly Weather Review, 139(2), pp 608-619, 2011. doi:10.1175/2010MWR3530.1

• "Generation of inertia–gravity waves in the rotating thermal annulus by a localised boundary layer instability"
  Jacoby, T. N. L., Read, P. L., Williams, P. D. and Young, R. M. B., Geophysical and Astrophysical Fluid Dynamics, 105(2-3), pp 161-181, 2011. doi:10.1080/03091929.2011.560151

2010

• "Testing the limits of quasi-geostrophic theory: application to observed laboratory flows outside the quasi-geostrophic regime"
  Williams, P. D., Read, P. L. and Haine, T. W. N., Journal of Fluid Mechanics, 649, pp 187-203, 2010. doi:10.1017/S0022112009993405

• "The role of mean ocean salinity in climate"
  Williams, P. D., Guilyardi, E., Madec, G., Gualdi, S. and Scoccimarro, E., Dynamics of Atmospheres and Oceans, 49(2-3), pp 108-123, 2010. doi:10.1016/j.dynatmoce.2009.02.001

2009

• "A proposed modification to the Robert–Asselin time filter"
  Williams, P. D., Monthly Weather Review, 137(8), pp 2538-2546, 2009. doi:10.1175/2009MWR2724.1

• "Reply to comments on 'Application of the Lighthill–Ford theory of spontaneous imbalance to clear-air turbulence forecasting'"
  Knox, J. A., McCann, D. W. and Williams, P. D., Journal of the Atmospheric Sciences, 66(8), pp 2511-2516, 2009. doi:10.1175/2009JAS3084.1

• "Rapid climate change: an overview for economists"
  Williams, P. D., International Journal of Green Economics, 3(1), pp 63-76, 2009. doi:10.1504/IJGE.2009.026492

• "QUAGMIRE v1.3: a quasi-geostrophic model for investigating rotating fluids experiments"
  Williams, P. D., Haine, T. W. N., Read, P. L., Lewis, S. R. and Yamazaki, Y. H., Geoscientific Model Development, 2(1), pp 13-32, 2009. doi:10.5194/gmd-2-13-2009

2008

• "Inertia–gravity waves emitted from balanced flow: observations, properties, and consequences"
  Williams, P. D., Haine, T. W. N. and Read, P. L., Journal of the Atmospheric Sciences, 65(11), pp 3543-3556, 2008. doi:10.1175/2008JAS2480.1

• "Application of the Lighthill–Ford theory of spontaneous imbalance to clear-air turbulence forecasting"
  Knox, J. A., McCann, D. W. and Williams, P. D., Journal of the Atmospheric Sciences, 65(10), pp 3292-3304, 2008. doi:10.1175/2008JAS2477.1

• "Sudden stratospheric warmings as noise-induced transitions"
  Birner, T. and Williams, P. D., Journal of the Atmospheric Sciences, 65(10), pp 3337-3343, 2008. doi:10.1175/2008JAS2770.1

• "Introduction. Stochastic physics and climate modelling"
  Palmer, T. N. and Williams, P. D., Philosophical Transactions of the Royal Society A, 366(1875), pp 2421-2427, 2008. doi:10.1098/rsta.2008.0059

2007

• "Dynamics of convectively driven banded jets in the laboratory"
  (Corrigendum)
  Read, P. L., Yamazaki, Y. H., Lewis, S. R., Williams, P. D., Wordsworth, R., Miki-Yamazaki, K., Sommeria, J. and Didelle, H., Journal of the Atmospheric Sciences, 64(11), pp 4031-4052, 2007. doi:10.1175/2007JAS2219.1

• "A new feedback on climate change from the hydrological cycle"
  Williams, P. D., Guilyardi, E., Sutton, R. T., Gregory, J. M. and Madec, G., Geophysical Research Letters, 34, L08706, 2007. doi:10.1029/2007GL029275

2006

• "On the climate response of the low-latitude Pacific Ocean to changes in the global freshwater cycle"
  Williams, P. D., Guilyardi, E., Sutton, R. T., Gregory, J. M. and Madec, G., Climate Dynamics, 27(6), pp 593-611, 2006. doi:10.1007/s00382-006-0151-7

2005

• "Modelling climate change: the role of unresolved processes"
  Williams, P. D., Philosophical Transactions of the Royal Society A, 363(1837), pp 2931-2946, 2005. doi:10.1098/rsta.2005.1676

• "On the generation mechanisms of short-scale unbalanced modes in rotating two-layer flows with vertical shear"
  Williams, P. D., Haine, T. W. N. and Read, P. L., Journal of Fluid Mechanics, 528, pp 1-22, 2005. doi:10.1017/S0022112004002873

2004

• "A calibrated, non-invasive method for measuring the internal interface height field at high resolution in the rotating, two-layer annulus"
  Williams, P. D., Read, P. L. and Haine, T. W. N., Geophysical and Astrophysical Fluid Dynamics, 98(6), pp 453-471, 2004. doi:10.1080/03091920412331296366

• "Jupiter's and Saturn's convectively driven banded jets in the laboratory"
  Read, P. L., Yamazaki, Y. H., Lewis, S. R., Williams, P. D., Miki-Yamazaki, K., Sommeria, J., Didelle, H. and Fincham, A., Geophysical Research Letters, 31(22), L22701, 2004. doi:10.1029/2004GL020106

• "Storm in a teacup"
  Williams, P. D., Weather, 59(4), pp 96-98, 2004. doi:10.1256/wea.152.03

• "Stochastic resonance in a nonlinear model of a rotating, stratified shear flow, with a simple stochastic inertia–gravity wave parameterization"
  Williams, P. D., Haine, T. W. N. and Read, P. L., Nonlinear Processes in Geophysics, 11(1), pp 127-135, 2004. doi:10.5194/npg-11-127-2004

2003

• "Spontaneous generation and impact of inertia–gravity waves in a stratified, two-layer shear flow"
  Williams, P. D., Read, P. L. and Haine, T. W. N., Geophysical Research Letters, 30(24), 2255, 2003. doi:10.1029/2003GL018498

2002

• "The role of nonhydrostatic dynamics in controlling development of a surface ocean front"
  Haine, T. W. N. and Williams, P. D., Ocean Modelling, 4(2), pp 121-135, 2002. doi:10.1016/S1463-5003(01)00014-2

Special Issues Edited

• "Focus on Transportation and the Environment"
  Coffel, E., Dedoussi, I., Barrett, S. and Williams, P. D. (eds.), details at iopscience.iop.org/journal/1748-9326/page/Transportation_and_the_Environment, Environmental Research Letters, 2021.

• "A Census of Atmospheric Variability From Seconds to Decades"
  Williams, P. D. (ed.), details at agupubs.onlinelibrary.wiley.com/hub/issue/10.1002/(ISSN)1944-8007.ATMOS_VARIABILITY, Geophysical Research Letters, 2017.

• "Focus on Stochastic Flows and Climate Statistics"
  Marston, J. B. and Williams, P. D. (eds.), details at iopscience.iop.org/1367-2630/focus/Focus%20on%20Stochastic%20Flows%20and%20Climate%20Statistics, New Journal of Physics, 2016.

• "Mathematics Applied to the Climate System"
  Williams, P. D., Cullen, M. J. P., Davey, M. K. and Huthnance, J. M. (eds.), details at http://rsta.royalsocietypublishing.org/site/2013/1991.xhtml, Philosophical Transactions of the Royal Society A, 371(1991), 2013.

• "Stochastic Physics and Climate Modelling"
  Palmer, T. N. and Williams, P. D. (eds.), details at http://rsta.royalsocietypublishing.org/site/issues/stochastic-climate.xhtml, Philosophical Transactions of the Royal Society A, 366(1875), pp 2419-2641, 2008.

Books Edited

• "Modeling Atmospheric and Oceanic Flows: Insights from Laboratory Experiments and Numerical Simulations"
  von Larcher, T. and Williams, P. D. (eds.), details at www.wiley.com/buy/9781118855935, John Wiley & Sons, pp 368, Print ISBN 978-1-118-85593-5, Online ISBN 9781118856024, 2015. doi:10.1002/9781118856024

• "Stochastic Physics and Climate Modelling"
  Palmer, T. N. and Williams, P. D. (eds.), details at www.cambridge.org/9780521761055, Cambridge University Press, pp 496, ISBN 978-0-521-76105-5, 2009.

Books Chapters

• "The jet stream and climate change"
  Stendel, M., Francis, J., White, R., Williams, P. D. and Woollings, T., Chapter 15 (pp 327-357) in Climate Change: Observed Impacts on Planet Earth (Third Edition), Edited by Trevor M. Letcher, details at www.elsevier.com/books/climate-change/letcher/978-0-12-821575-3, Elsevier, pp 848, ISBN 978-0-12-821575-3, 2021. doi:10.1016/B978-0-12-821575-3.00015-3

• "Aviation Turbulence: Dynamics, Forecasting, and Response to Climate Change"
  Storer, L. N., Williams, P. D. and Gill, P. G., Chapter 9 (pp 219-234) in Aviation Meteorology: Observations and Models, Edited by Ismail Gultepe and Wayne F. Feltz, details at www.springer.com/978-3-030-30981-7, Birkhäuser, pp 340, ISBN 978-3-030-30981-7, 2020.

• "A Review of High Impact Weather for Aviation Meteorology"
  Gultepe, I., Sharman, R., Williams, P. D., Zhou, B., Ellrod, G., Minnis, P., Trier, S., Griffin, S., Yum, S. S., Gharabaghi, B., Feltz, W., Temimi, M., Pu, Z., Storer, L. N., Kneringer, P., Weston, M. J., Chuang, H.-Y., Thobois, L., Dimri, A. P., Dietz, S. J., França, G. B., Almeida, M. V. and Neto, F. L. A., Chapter 2 (pp 7-60) in Aviation Meteorology: Observations and Models, Edited by Ismail Gultepe and Wayne F. Feltz, details at www.springer.com/978-3-030-30981-7, Birkhäuser, pp 340, ISBN 978-3-030-30981-7, 2020.

• "A "Forecast Factory""
  Williams, P. D., Chapter on 1922 (pp 124-125) in Weather: An Illustrated History: From Cloud Atlases to Climate Change, Andrew Revkin and Lisa Mechaley, details at www.sterlingpublishing.com/9781454921400, Sterling Publishing, pp 224, ISBN 978-1-4549-2140-0, 2018.

• "Clear-air turbulence in a changing climate"
  Williams, P. D. and Joshi, M. M., Chapter 23 (pp 465-480) in Aviation Turbulence: Processes, Detection, Prediction, Edited by Robert Sharman and Todd Lane, details at www.springer.com/book/9783319236292, Springer, pp 523, ISBN 978-3-319-23629-2, 2016. doi:10.1007/978-3-319-23630-8_23

• "Leapfrogging into the future: How child's play is at the heart of weather and climate models"
  Williams, P. D., Chapter 45 (pp 168-171) in 50 Visions of Mathematics, Edited by Sam Parc, Foreword by Dara Ó Briain, details at ukcatalogue.oup.com/product/9780198701811.do, Oxford University Press, pp 208, ISBN 978-0-19-870181-1, 2014.

Books Reviewed

• "The Goldilocks Planet: The Four Billion Year Story of Earth's Climate" by Jan Zalasiewicz and Mark Williams
  Williams, P. D., Weather, 68(6), p 167, 2013. doi:10.1002/wea.2143

• "Atmospheric Dynamics" by Mankin Mak
  Williams, P. D., Bulletin of the American Meteorological Society, 93(2), pp 242-243, 2012.

• "Eloquent Science: A Practical Guide to Becoming a Better Writer, Speaker and Atmospheric Scientist" by David M. Schultz
  Williams, P. D., Progress in Physical Geography, 34(5), pp 729-731, 2010. doi:10.1177/03091333100340050102

Book Forewords

• Foreword to "Science of Weather, Climate and Ocean Extremes" by John Hay
  Williams, P. D., Elsevier, pp 396, ISBN 9780323855419 (paperback) and 9780323900775 (ebook), 2022.

Meeting Summaries

• "Research Collaborations for Better Predictions of Aviation Weather Hazards"
  Chun, H.-Y., Kim, J.-H., Lee, D.-B., Kim, S.-H., Strahan, M., Pettegrew, B., Gill, P., Williams, P. D., Schumann, U., Tenenbaum, J., Lee, Y.-G., Choi, H.-W., Song, I.-S., Park, Y.-J. and Sharman, R. D., Bulletin of the American Meteorological Society, 98(5), pp ES103-ES107, 2017. doi:10.1175/BAMS-D-17-0010.1

Non-refereed

• "Improved turbulence forecasts for the aviation sector"
  Williams, P. D., Research Excellence Framework (REF) Impact Case Study, 2021, on-line at results2021.ref.ac.uk/impact/2bbca9b9-cc5f-4ad7-b7ad-7e1b2393e8d3.

• "Meteorology: A New Journal for a New Age of Weather Research"
  Williams, P. D., Meteorology, 1(1), pp 2-3, 2022. doi:10.3390/meteorology1010002

• "Climate change means longer take-offs and fewer passengers per aeroplane - new study"
  Gratton, G. and Williams, P. D., The Conversation, 13 February 2020, on-line at theconversation.com/climate-change-means-longer-take-offs-and-fewer-passengers-per-aeroplane-new-study-131613.

• "Atmospheric turbulence research leads to smoother, safer, and cleaner flights"
  Williams, P. D., University of Oxford Department of Physics Newsletter, Number 15, pp 22-23, Autumn 2019.

• "Making flights smoother, safer, and cleaner"
  Williams, P. D., Floreat Domus, pp 14-15, June 2019.

• "Stronger turbulence causes a stir"
  Williams, P. D. and Storer, L. N., University of Reading Connecting Research: The Forum blog, 9 October 2017, on-line at blogs.reading.ac.uk/the-forum/2017/10/09/stronger-turbulence-causes-a-stir.

• "Volcanic Disruption"
  Harrison, G., Airey, M., Marlton, G., Nicoll, K. and Williams, P. D., Meteorological Technology International, pp 54-56, September 2017.

• "Close Encounter with Jupiter"
  Yau, A., Dombard, A., Peterson, W. K. and Williams, P. D., AGU Eos Editors' Vox blog, 25 May 2017, on-line at eos.org/editors-vox/close-encounter-with-jupiter.

• "Passagiere müssen sich auf holprigere Flüge einstellen - wegen des Klimawandels"
  Williams, P. D., Neue Energie, pp 54-55, May 2017.

• "Guest post: Air passengers face a bumpier ride due to climate change"
  Williams, P. D., Carbon Brief, 6 April 2017, on-line at www.carbonbrief.org/guest-post-air-passengers-face-bumpier-ride-climate-change.

• "The politics of climate change may be stalling - but business is rising to the challenge"
  Williams, P. D., University of Reading Connecting Research: The Forum blog, 25 January 2017, on-line at blogs.reading.ac.uk/the-forum/2017/01/25/the-politics-of-climate-change-may-be-stalling-but-business-is-rising-to-the-challenge/.

• "The Impacts of Climate Change on Aviation: Scientific Challenges and Adaptation Pathways"
  Puempel, H. and Williams, P. D., ICAO Environmental Report 2016: On Board A Sustainable Future, pp 205-207, 2016, on-line at www.icao.int/environmental-protection/Pages/ENV2016.aspx.

• "New Geophysical Research Letters Editorial and Revisions Policies"
  Diffenbaugh, N., Beal, L., Cardenas, M. B., Cobb, K., Cronin, M., Dombard, A., Ilyina, I., Lavraud, B., Newman, A. V., Peterson, W. K., Ritsema, J., Stroeve, J., Thornton, J. A. and Williams, P. D., Eos, 97(17), p 23-24, 2016, on-line at eos.org/agu-news/new-geophysical-research-letters-editorial-revisions-policies. doi:10.1029/2016EO056437

• "Controversy: A Crucial Ingredient for Scientific Progress"
  Williams, P. D., AGU Eos Editors' Vox blog, 13 June 2016, on-line at eos.org/editors-vox/controversy-a-crucial-ingredient-for-scientific-progress.

• "Soundtrack to a storm"
  Aplin, K. L. and Williams, P. D., Weather, 71(4), p 91, 2016. doi:10.1002/wea.2726

• "Postcards from the Field"
  Williams, P. D., Eos, 97(5), inside back cover, 1 March 2016.

• "Letters: Weather scientists cite Bob Dylan too"
  Brown, S., Aplin, K. L., Jenkins, K., Mander, S., Walsh, C., and Williams, P. D., The BMJ, 352(8041), p 112, 23 January 2016. doi:10.1136/bmj.i265

• "Correction"
  Astronomy and Geophysics, 56(4), p 10, August 2015. doi:10.1093/astrogeo/atv145

• "Let's share our music of the spheres"
  Aplin, K. L. and Williams, P. D., Astronomy and Geophysics, 56(3), p 8, June 2015. doi:10.1093/astrogeo/atv086

• "Weather and Climate Modelling"
  Williams, P. D., Institute of Physics Environmental Physics Group newsletter, p 9, September 2013.

• "Moon's a balloon: Balloon-borne measurements for Earth weather and space weather"
  Harrison, G., Nicoll, K., Marlton, G. and Williams, P. D., Meteorological Technology International, pp 78-82, August 2013.

• "Weather and music: Response"
  Aplin, K. L. and Williams, P. D., Weather, 67(2), pp 54-55, 2012. doi:10.1002/wea.1890

• "Correction [to "How mathematical models can aid understanding of climate"]"
  Balcerak, E., Eos, 93(5), p 51, 31 January 2012. doi:10.1029/2012EO050007

• "How mathematical models can aid understanding of climate"
  Williams, P. D., Cullen, M. J. P. and Huthnance, J. M., Eos, 92(51), p 482, 20 December 2011. doi:10.1029/2011EO510010

• "How Mathematical Models Can Aid Our Understanding of Climate"
  Williams, P. D., Cullen, M. and Huthnance, J., Mathematics Today, 47(6), p 274, December 2011.

• "Secretary's Report 2009-2010 from the 19th Annual General Meeting held on 26th May 2010"
  Williams, P. D., Institute of Physics Environmental Physics Group newsletter, p 8, October 2010.

• "Geophysical Research Letters: New Policies Improve Top-Cited Geosciences Journal"
  Calais, E., Diffenbaugh, N., D'Odorico, P., Harris, R., Knorr, W., Lavraud, B., Mueller, A., Peterson, W., Rignot, E., Srokosz, M., Strutton, P., Tyndall, G., Wysession, M. and Williams, P., Eos, 91(38), p 337, 21 September 2010.

• "Working Group E report: What Is Climate?"
  Chandler, R. (Chair), Williams, P. D. (Rapporteur), Anderson, C., Crommelin, D., Farmer, C., Held, H., Huthnance, J., Jupp, T., Stainforth, D., Tett, S., Turasie, A., Watkins, N. and Yip, S. Isaac Newton Institute for Mathematical Sciences satellite workshop on Probabilistic Climate Prediction, University of Exeter, 20-23 September 2010.

• "Computer Simulation and the Environment"
  Williams, P. D., Institute of Physics Environmental Physics Group Newsletter, pp 7-8, October 2009.

• "Report from breakout group 1: How can work in nonlinear PDEs most benefit climate prediction?"
  Williams, P. D. (Chair) and Wlasak, M. (Rapporteur), on-line at www.maths.ox.ac.uk/groups/oxpde/events/upcoming-events, Workshop on the Mathematics of Weather and Climate Prediction, Met Office, Exeter, 2009.

• "European Meteorological Society Young Scientists Travel Award Report"
  Williams, P. D., on-line at www.emetsoc.org/awards/award_descriptions.php, October 2009.

• "Sudden Stratospheric Warmings as Noise-Induced Transitions"
  Williams, P. D. and Birner, T., NCAS Annual Report 2008-2009, p 25, 2009.

• "MP–Scientist Pairing Scheme: a knowledge transfer case study"
  Williams, P. D., Using NERC Science, on-line at www.nerc.ac.uk/using/casestudies/pairing.asp, March 2009.

• "A multitude of gravity waves"
  Williams, P. D. and Galvin, J. F. P., Weather, 61(6), p 180, 2006. doi:10.1256/wea.134.04

• "Modelling planetary atmospheres: problems and solutions"
  Williams, P. D., The Observatory, 125(1187), pp 204-207, August 2005.

• "Working Group 3 report: The parameterisation problem in weather and climate models"
  Ghil, M., Berloff, P., Buizza, R., Hermanson, L., Miller, M., Palmer, T., Roulstone, I., Sardeshmukh, P. and Williams, P. D., In Proceedings of the Workshop on Representation of Sub-Grid Processes using Stochastic–Dynamic Models, pp xvii-xxii, ECMWF, 6-8 June 2005.

• "Climate change prediction: a challenging scientific problem"
  Williams, P. D., Institute of Physics Environmental Physics Group Newsletter, pp 5-6, Spring 2005.

• "Global Warming, Local Warning: a study of the likely impacts of climate change upon South East England"
  Williams, P. D., commissioned by Dr. Caroline Lucas MEP, published by the European Parliament, Brussels, pp 16, 2004.

• "Climate change and the thermohaline circulation"
  Williams, P. D., Institute of Physics Environmental Physics Group Newsletter, pp 9-10, Spring 2004.

• "QUAGMIRE: QUAsi-Geostrophic Model for Investigating Rotating fluids Experiments. Reference Manual for Version 1.2"
  Williams, P. D., Haine, T. W. N., Read, P. L., Lewis, S. R. and Yamazaki, Y. H., AOPP Technical Memorandum Series 2004.3, Department of Physics, University of Oxford, pp 27, 2004.

• "Storm in a teacup"
  Williams, P. D., The Grove: Lincoln College Murray Society Newsletter, 1(11), Summer 2003.

• "Nonlinear interactions of fast and slow modes in rotating, stratified fluid flows"
  Williams, P. D., D.Phil. thesis, Department of Physics, University of Oxford, pp 205, 2003.

• "Royal Meteorological Society Legacies Fund Report"
  Williams, P. D., on-line at www.rmets.org/activities/awards/grants/detail.php?ID=264, April 2003.

• "Finger on the button"
  Williams, P. D., The Oxford Student, 28 February 2002.

• "Interactions of 'fast' and 'slow' modes in rotating, stratified flows"
  Williams, P. D., D.Phil. Third Year Report, Department of Physics, University of Oxford, pp 6, 2002.

• "Interactions of 'fast' and 'slow' modes in rotating, stratified flows"
  Williams, P. D., D.Phil. Second Year Report, Department of Physics, University of Oxford, pp 52, 2001.

• "Interactions of 'fast' and 'slow' modes in rotating, stratified flows"
  Williams, P. D., D.Phil. First Year Report, Department of Physics, University of Oxford, pp 59, 2000.

• "Comparison of the Non-Hydrostatic, Hydrostatic and Convectively-Adjusted Navier–Stokes Equations in Physical Oceanography"
  Williams, P. D., M.Phys. report, Department of Physics, University of Oxford, pp 50, 1998.