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].
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?Posts Tagged 'Numerical Weather Prediction'
Weather Forecasts get Better and Better
Published November 5, 2020 Irish Times Leave a CommentTags: Geophysics, Numerical Weather Prediction
Does Numerical Integration Reflect the Truth?
Published July 23, 2020 Occasional Leave a CommentTags: Numerical Analysis, Numerical Weather Prediction
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.

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 Leave a CommentTags: Analysis, Numerical Weather Prediction
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.

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 Leave a CommentTags: Fluid Dynamics, Geophysics, Numerical Weather Prediction

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.
A Pioneer of Climate Modelling and Prediction
Published April 4, 2019 Irish Times Leave a CommentTags: Climate Modelling, Numerical Weather Prediction

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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