Multiweek weather
This page provides a general introduction to the kinds of forecasts I provide. For further information or access to live forecasts please contact me.
Imperfect knowledge of the state of the Earth system, combined with sensitivity to initial state, limits predictions. Useful advanced warning of extreme weather requires lead times of weeks, as do decisions on investments sensitive to energy markets. An original mathematical method allows us to make computationally efficient multiweek predictions not possible with traditional methods, better even than with supercomputers used by government facilities such as NOAA in the USA, the Met. Office in the UK, and the ECMWF in Europe.
How is this possible? Many of the models run by government agencies try to describe the flows [1–3] of ocean and atmosphere at high resolution, and to include as many other processes as possible. The calculations seek the most complete description of the Earth system that they can manage. If instead we use mathematical methods designed to focus on just variables of interest, [4] we can sacrifice extensive knowledge of the Earth system, but often enough obtain better forecasts for the variables we are interested in. Others have studied similar approaches that apply simplified linear equations of motion to fewer variables, notably the Linear Inverse Model (LIM), [5,6] and the method of empirical model reduction (EMR). [7–9]
Ghil and Lucarini have written an useful review that covers many of the mathematical methods used to study weather and climate. [10] Methods of incorporating observations used in this work are discussed by Bishop. [11]
Figure 1 shows a forecast of the Northern Hemisphere geopotential height at 500 hPa. This is the gravity-adjusted height at which the atmospheric pressure is 500 hPa. The geopotential height for 500 hPa is a popular choice when a limited number of fields are included. [10,12] The quantity plotted is an anomaly. This means the difference between the observed or forecast height, and the height normally expected for the time of year. The normally expected value is usually estimated as the average over a range of years chosen as a reference. This is called the climate average. The choice of years can affect the average, and it is worth checking that different choices do not affect the results. The method used to obtain climate properties used here is a little more elaborate, and is taken from work by Albers and Newman. [5]
References
[1] D. J. Acheson, Elementary Fluid Dynamics (Oxford University Press, Oxford, 1990).
[2] H. Ockendon and J. R. Ockendon, Viscous Flow (Cambridge University Press, Cambridge, 1995).
[3] G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, 1973).
[4] R. Zwanzig, Nonequilibrium Statistical Mechanics (Oxford University Press, New York, 2001).
[5] J. Albers and M. Newman, A Priori Identification of Skillful Extratropical Subseasonal Forecasts, Geophysical Research Letters 46, 12527 (2019).
[6] C. Penland and P. D. Sardeshmukh, The Optimal Growth of Tropical Sea Surface Temperature Anomalies, J. Clim. 8, 1999 (1995).
[7] S. Kravtsov, D. Kondrashov, and M. Ghil, Multilevel Regression Modeling of Nonlinear Processes: Derivation and Applications to Climatic Variability, J. Clim. 18, 4404 (2005).
[8] S. Kravtsov, D. Kondrashov, and M. Ghil, Empirical Model Reduction and the Modelling Hierarchy in Climate Dynamics and the Geosciences, in Stochastic Physics and Climate Modelling, edited by T. Palmer and P. Williams (Cambridge University Press, Cambridge, 2010), pp. 35–72.
[9] D. Kondrashov, M. D. Chekroun, and M. Ghil, Data-Driven Non-Markovian Closure Models, Physica D 297, 33 (2015).
[10] M. Ghil and V. Lucarini, The Physics of Climate Variability and Climate Change, Rev. Mod. Phys. 92, 035002 (2020).
[11] C. H. Bishop, J. S. Whitaker, and L. Lei, Gain Form of the Ensemble Transform Kalman Filter and Its Relevance to Satellite Data Assimilation with Model Space Ensemble Covariance Localization, Journal of the American Meteorological Society 145, 4575 (2017).
[12] J. G. Charney, R. Fjortoft, and J. von Neumann, Numerical Integration of the Barotropic Vorticity Equation, Tellus 2, 237 (1950).