Posts Tagged 'Numerical Weather Prediction'

A Prescient Vision of Modern Weather Forecasting

Published March 3, 2022 Irish Times Closed
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Lewis Fry Richardson in 1931.

One hundred years ago, a remarkable book was published by Cambridge University Press. It was a commercial flop: although the print run was just 750 copies, it was still in print thirty years later. Yet, it held the key to forecasting the weather by scientific means. The book, Weather Prediction by Numerical Process, was written by Lewis Fry Richardson, a brilliant, eccentric mathematician. He described in detail how the mathematical equations that govern the evolution of the atmosphere could be solved by numerical means to deduce future weather conditions from a set of observations [TM230 or search for “thatsmaths” at irishtimes.com].

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Improving Weather Forecasts by Reducing Precision

Published May 6, 2021 Irish Times Closed
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Weather forecasting relies on supercomputers, used to solve the mathematical equations that describe atmospheric flow. The accuracy of the forecasts is constrained by available computing power. Processor speeds have not increased much in recent years and speed-ups are achieved by running many processes in parallel. Energy costs have risen rapidly: there is a multimillion Euro annual power bill to run a supercomputer, which may consume something like 10 megawatts [TM210 or search for “thatsmaths” at irishtimes.com].

The characteristic butterfly pattern for solutions of Lorenz’s equations [Image credit: source unknown].

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Weather Forecasts get Better and Better

Published November 5, 2020 Irish Times Closed
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Weather forecasts are getting better. Fifty years ago, predictions beyond one day ahead were of dubious utility. Now, forecasts out to a week ahead are generally reliable  [TM198 or search for “thatsmaths” at irishtimes.com].

Anomaly correlation of ECMWF 500 hPa height forecasts over three decades [Image from ECMWF].

Careful measurements of forecast accuracy have shown that the range for a fixed level of skill has been increasing by one day every decade. Thus, today’s one-week forecasts are about as good as a typical three-day forecast was in 1980. How has this happened? And will this remarkable progress continue?

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Does Numerical Integration Reflect the Truth?

Published July 23, 2020 Occasional Closed
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Many problems in applied mathematics involve the solution of a differential equation. Simple differential equations can be solved analytically: we can find a formula expressing the solution for any value of the independent variable. But most equations are nonlinear and this approach does not work; we must solve the equation by approximate numerical means. The big question is:

“Does the numerical solution resemble the true solution of the equation?”

The answer is: “Not necessarily”.

There are often specific criteria that must be satisfied to ensure that the answer `crunched out’ by the computer is a reasonable approximation to reality. Although the principles of numerical stability are quite general, they are best illustrated by simple examples. We will look at some of these below.

CFL-Criterion-1

Smooth curve: True solution. Black dots: stable solution. Red dots: unstable solution (time step too large).

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Grad, Div and Curl on Weather Maps: a Gateway to Vector Analysis

Published January 9, 2020 Occasional Closed
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Vector analysis can be daunting for students. The theory can appear abstract, and operators like Grad, Div and Curl seem to be introduced without any obvious motivation. Concrete examples can make things easier to understand. Weather maps, easily obtained on the web, provide real-life applications of vector operators.

GradDivCurl-MSLP

Fig. 1. An idealized scalar field representing the mean sea-level atmospheric pressure over the North Atlantic area.

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Spin-off Effects of the Turning Earth

Published June 6, 2019 Irish Times Closed
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Gaspard-Gustave de Coriolis (1792-1843).

On the rotating Earth, a moving object deviates from a straight line, being deflected to the right in the northern hemisphere and to the left in the southern hemisphere. The deflecting force is named after a nineteenth century French engineer, Gaspard-Gustave de Coriolis [TM164 or search for “thatsmaths” at irishtimes.com].

Coriolis was interested in the dynamics of machines, such as water mills, with rotating elements. He was not concerned with the turning Earth or the oceans and atmosphere surrounding it. But it is these fluid envelopes of the planet that are most profoundly affected by the Coriolis force.

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A Pioneer of Climate Modelling and Prediction

Published April 4, 2019 Irish Times Closed
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Norman-Phillips

Norman Phillips (1923-2019)

Today we benefit greatly from accurate weather forecasts. These are the outcome of a long struggle to advance the science of meteorology. One of the major contributors to that advancement was Norman A. Phillips, who died in mid-March, aged 95. Phillips was the first person to show, using a simple computer model, that mathematical simulation of the Earth’s climate was practicable [TM160 or search for “thatsmaths” at irishtimes.com].

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