Tag: Numerical Weather Prediction

Joining Forces to Improve Weather Forecasts

Since 1950, there has been a quiet but steady revolution in meteorology, and especially in numerical weather prediction (NWP). The growth in accuracy, range and scope of weather forecasts over the past half-century has been spectacular. As late as the mid-1970s, forecasts were seriously unreliable. The diagram illustrates the inexorable increase in skill of the … Continue reading Joining Forces to Improve Weather Forecasts →

Earth’s Digital Twins can help us to avert Disaster

Imagine another Earth, just like ours, but running a year ahead. Observing it, we could foretell events over the coming weeks or months, and take action to avoid catastrophes. There is no such planet! Even if there were, conditions there would diverge rapidly from ours, so it would provide no guidance on our future. But … Continue reading Earth’s Digital Twins can help us to avert Disaster →

Margules’ Tendency Equation and Richardson’s Forecast

During World War One, long before the invention of computers, the English Quaker mathematician Lewis Fry Richardson devised a method of solving the equations and made a test forecast by hand. The forecast was a complete failure: Richardson calculated that the pressure at a particular point would rise by 145 hPa in 6 hours. This … Continue reading Margules’ Tendency Equation and Richardson’s Forecast →

DLWP: A New Age of Weather Forecasting

Before the age of computers, weather forecasters analysed observations plotted on paper charts, drew isobars and other features and — based on their previous knowledge and experience — constructed charts of conditions at a future time, often one day ahead. They combined observational data and rules of thumb based on physical principles to predict what … Continue reading DLWP: A New Age of Weather Forecasting →

A Prescient Vision of Modern Weather Forecasting

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 … Continue reading A Prescient Vision of Modern Weather Forecasting →

Improving Weather Forecasts by Reducing Precision

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 … Continue reading Improving Weather Forecasts by Reducing Precision →

Weather Forecasts get Better and Better

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 … Continue reading Weather Forecasts get Better and Better →

Does Numerical Integration Reflect the Truth?

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 … Continue reading Does Numerical Integration Reflect the Truth? →

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

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. Weather charts provide great examples of scalar … Continue reading Grad, Div and Curl on Weather Maps: a Gateway to Vector Analysis →

Spin-off Effects of the Turning Earth

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, … Continue reading Spin-off Effects of the Turning Earth →