In addition to some beautiful photos and maps and descriptions of upland challenges in Ireland and abroad, the November issue of *The Summit*, the Mountain Views Quarterly Newsletter for hikers and hillwalkers, describes a method to find the length of a walk based on ideas originating with the French naturalist and mathematician George-Louis Leclerc, Comte de Buffon [TM224 or search for “thatsmaths” at irishtimes.com].

## Posts Tagged 'Geophysics'

### Buffon’s Noodle and the Mathematics of Hillwalking

Published December 2, 2021 Irish Times ClosedTags: Geometry, Geophysics

### Earth System Models simulate the changing climate

Published September 16, 2021 Irish Times ClosedTags: biology, Climate Modelling, Geophysics

The climate is changing, and we need to know what changes to expect and how soon to expect them. Earth system models, which simulate all relevant components of the Earth system, are the primary means of anticipating future changes of our climate [TM219 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Earth System Models simulate the changing climate’

### Changing Views on the Age of the Earth

Published August 19, 2021 Irish Times ClosedTags: Geophysics, History, Ireland

### Simple Models of Atmospheric Vortices

Published July 29, 2021 Occasional ClosedTags: Fluid Dynamics, Geophysics

Atmospheric circulation systems have a wide variety of structures and there is no single mechanistic model that describes all their characteristics. However, we can construct simple kinematic models that capture some primary aspects of the flow. For simplicity, we will concentrate on idealized extra-tropical depressions. We will not consider hurricanes and tropical storms in any detail, because the effects of moisture condensation and convection dominate their behaviour.

From a hilltop, the horizon lies below the horizontal level at an angle called the “dip”. Around AD 1020, the brilliant Persian scholar al-Biruni used a measurement of the dip, from a mountain of known height, to get an accurate estimate of the size of the Earth. It is claimed that his estimate was within 1% of the true value but, since he was not aware of atmospheric refraction and made no allowance for it, this high precision must have been fortuitous [TM213 or search for “thatsmaths” at irishtimes.com].

### Was Space Weather the cause of the Titanic Disaster?

Published April 1, 2021 Occasional ClosedTags: Geophysics

Space weather, first studied in the 1950’s, has grown in importance with recent technological advances. It concerns the influence on the Earth’s magnetic field and upper atmosphere of events on the Sun. Such disturbances can enhance the solar wind, which interacts with the magnetosphere, with grave consequences for navigation. Space weather affects the satellites of the Global Positioning System, causing serious navigation problems [TM208 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Was Space Weather the cause of the Titanic Disaster?’### We are living at the bottom of an ocean

Published January 7, 2021 Irish Times ClosedTags: Geophysics

Anyone who lives by the sea is familiar with the regular ebb and flow of the tides. But we all live at the bottom of an ocean of air. The atmosphere, like the ocean, is a fluid envelop surrounding the Earth, and is subject to the influence of the Sun and Moon. While sea tides have been known for more than two thousand years, the discovery of tides in the atmosphere had to await the invention of the barometer [TM202 or search for “thatsmaths” at irishtimes.com].

### Ireland’s Mapping Grid in Harmony with GPS

Published November 19, 2020 Irish Times ClosedTags: Geophysics, Maps, Spherical Trigonometry

The earthly globe is spherical; more precisely, it is an oblate spheroid, like a ball slightly flattened at the poles. More precisely still, it is a triaxial ellipsoid that closely approximates a “geoid”, a surface of constant gravitational potential [TM199 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Ireland’s Mapping Grid in Harmony with GPS’

### Weather Forecasts get Better and Better

Published November 5, 2020 Irish Times ClosedTags: Geophysics, Numerical Weather Prediction

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?### A Ring of Water Shows the Earth’s Spin

Published February 13, 2020 Occasional ClosedTags: Geophysics, Mechanics

Around 1913, while still an undergraduate, American physicist Arthur Compton described an experiment to **demonstrate the rotation of the Earth** using a simple laboratory apparatus.

### Spin-off Effects of the Turning Earth

Published June 6, 2019 Irish Times ClosedTags: Fluid Dynamics, Geophysics, Numerical Weather Prediction

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.

### Joseph Fourier and the Greenhouse Effect

Published March 21, 2019 Irish Times ClosedTags: Applied Maths, Fourier analysis, Geophysics

Jean-Baptiste Joseph Fourier, French mathematician and physicist, was born in Auxerre 251 years ago today. He is best known for the mathematical techniques that he developed in his analytical theory of heat transfer. Over the past two centuries, his methods have evolved into a major subject, harmonic analysis, with widespread applications in number theory, signal processing, quantum mechanics, weather prediction and a broad range of other fields [TM159 or search for “thatsmaths” at irishtimes.com].

### A Zero-Order Front

Published August 30, 2018 Occasional ClosedTags: Fluid Dynamics, Geophysics, modelling

Sharp gradients known as fronts form in the atmosphere when variations in the wind field bring warm and cold air into close proximity. Much of our interesting weather is associated with the fronts that form in extratropical depressions.

Below, we describe a simple mechanistic model of frontogenesis, the process by which fronts are formed.

### The Miraculous Spiral on Booterstown Strand

Published August 16, 2018 Irish Times ClosedTags: biology, Geometry, Geophysics

We all know what a spiral looks like. Or do we? Ask your friends to describe one and they will probably trace out the form of a winding staircase. But that is actually a helix, a curve in three-dimensional space. A spiral is confined to a plane – it is a flat curve. In general terms, a spiral is formed by a point moving around a fixed centre while its distance increases or decreases as it revolves [see TM145, or search for “thatsmaths” at irishtimes.com].

Continue reading ‘The Miraculous Spiral on Booterstown Strand’

### Tides: a Tug-of-War between Earth, Moon and Sun

Published August 2, 2018 Irish Times ClosedTags: Fluid Dynamics, Geophysics

All who set a sail, cast a hook or take a dip have a keen interest in the water level, and the regular ebb and flow of the tides. At most places the tidal variations are **semi-diurnal**, with high and low water twice each day [see TM144, or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Tides: a Tug-of-War between Earth, Moon and Sun’

### Trigonometric Comfort Blankets on Hilltops

Published July 5, 2018 Irish Times ClosedTags: Geophysics, Maps, Spherical Trigonometry

On a glorious sunny June day we reached the summit of Céidín, south of the Glen of Imall, to find a triangulation station or *trig pillar*. These concrete pillars are found on many prominent peaks throughout Ireland, and were erected to aid in surveying the country [see TM142, or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Trigonometric Comfort Blankets on Hilltops’

### Waves Packed in Envelopes

Published April 26, 2018 Occasional ClosedTags: Fluid Dynamics, Geophysics, Wave Motion

In this article we take a look at group velocity and at the extraction of the envelope of a wave packet using the ideas of the Hilbert transform.

### Staying Put or Going with the Flow

Published February 1, 2018 Irish Times ClosedTags: Algorithms, Geophysics, Numerical Analysis

The atmospheric temperature at a fixed spot may change in two ways. First, heat sources or sinks may increase or decrease the thermal energy; for example, sunshine may warm the air or radiation at night may cool it. Second, warmer or cooler air may be transported to the spot by the air flow in a process called advection. Normally, the two mechanisms act together, sometimes negating and sometimes reinforcing each other. What is true for temperature is also true for other quantities: pressure, density, humidity and even the flow velocity itself. This last effect may be described by saying that “the wind blows the wind” [TM132 or search for “thatsmaths” at irishtimes.com].

### Energy Cascades in Van Gogh’s Starry Night

Published January 4, 2018 Irish Times ClosedTags: Fluid Dynamics, Geophysics

“*Big whirls have little whirls that feed on their velocity,*

*And little whirls have lesser whirls, and so on to viscosity.*“

We are all familiar with the measurement of speed, the distance travelled in a given time. Allowing for the direction as well as the magnitude of movement, we get velocity, a vector quantity. In the flow of a viscous fluid, such as treacle pouring off a spoon, the velocity is smooth and steady. Such flow is called laminar, and variations of velocity from place to place are small. By contrast, the motion of the atmosphere, a fluid with low viscosity, can be irregular and rapidly fluctuating. We experience this when out and about on a gusty day. Such chaotic fluid flow is called turbulence, and this topic continues to challenge the most brilliant scientists [TM130 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Energy Cascades in Van Gogh’s Starry Night’

### Inertial Oscillations and Phugoid Flight

Published July 13, 2017 Occasional ClosedTags: Applied Maths, Fluid Dynamics, Geophysics

The English aviation pioneer Frederick Lanchester (1868–1946) introduced many important contributions to aerodynamics. He analysed the motion of an aircraft under various consitions of lift and drag. He introduced the term **“phugoid”** to describe aircraft motion in which the aircraft alternately climbs and descends, varying about straight and level flight. This is one of the basic modes of aircraft dynamics, and is clearly illustrated by the flight of gliders.

### The Water is Rising Fast

Published April 20, 2017 Irish Times ClosedTags: Fluid Dynamics, Geophysics

Seventy percent of the Earth is covered by water and three quarters of the world’s great cities are on the coast. Ever-rising sea levels pose a real threat to more than a billion people living beside the sea. As the climate warms, this is becoming a greater threat every year [TM113 or search for “thatsmaths” at irishtimes.com].

### Mercator’s Marvellous Map

Published May 21, 2015 Irish Times ClosedTags: Geometry, Geophysics, Spherical Trigonometry

Try to wrap a football in aluminium foil and you will discover that you have to crumple up the foil to make it fit snugly to the ball. In the same way, it is impossible to represent the curved surface of the Earth on a flat plane without some distortion.** ** [See this week’s *That’s Maths* column (TM068): search for “thatsmaths” at irishtimes.com].

The Hodograph is a vector diagram showing how velocity changes with position or time. It was made popular by William Rowan Hamilton who, in 1847, gave an account of it in the Proceedings of the Royal Irish Academy. Hodographs are valuable in fluid dynamics, astronomy and meteorology.

### Mode-S: Aircraft Data improves Weather Forecasts

Published April 2, 2015 Irish Times ClosedTags: Algebra, Geometry, Geophysics

A simple application of vectors yields valuable new wind observations for weather forecasting [see this week’s *That’s Maths* column (TM065) or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Mode-S: Aircraft Data improves Weather Forecasts’

### Falling Bodies [1]: Sky-diving

Published November 13, 2014 Occasional ClosedTags: Fluid Dynamics, Geophysics, Mechanics

Aristotle was clear: heavy bodies fall faster than light ones. He arrived at this conclusion by pure reasoning, without experiment. Today we insist on a physical demonstration before such a conclusion is accepted. Galileo tested Aristotle’s theory: he dropped bodies of different weights simultaneously from the Leaning Tower of Pisa and found that, to a good approximation, they hit the ground at the same time.

### El Niño likely this Winter

Published November 6, 2014 Irish Times ClosedTags: Fluid Dynamics, Geophysics, modelling, Physics

This week’s *That’s Maths* column in *The Irish Times* (**TM056** or search for “thatsmaths” at irishtimes.com) is about El Niño and the ENSO phenomenon.

In 1997-98, abnormally high ocean temperatures off South America caused a collapse of the anchovy fisheries. Anchovies are a vital link in the food-chain and shortages can bring great hardship. Weather extremes associated with the event caused 2000 deaths and 33 million dollars in damage to property. One commentator wrote that the warming event had “more energy than a million Hiroshima bombs”.

### Gauss’s Great Triangle and the Shape of Space

Published July 10, 2014 Occasional ClosedTags: Gauss, Geophysics, Maps

In the 1820s Carl Friedrich Gauss carried out a surveying experiment to measure the sum of the three angles of a large triangle. Euclidean geometry tells us that this sum is always 180º or two right angles. But Gauss himself had discovered other geometries, which he called non-Euclidean. In these, the three angles of a triangle may add up to more than two right angles, or to less.

Continue reading ‘Gauss’s Great Triangle and the Shape of Space’

### Breaking Weather Records

Published April 24, 2014 Occasional ClosedTags: Geophysics, Number Theory, Probability

In arithmetic series, like 1 + 2 + 3 + 4 + 5 + … , each term differs from the previous one by a fixed amount. There is a formula for calculating the sum of the first *N* terms. For geometric series, like 3 + 6 + 12 + 24 + … , each term is a fixed multiple of the previous one. Again, there is a formula for the sum of the first *N* terms of such a series. Continue reading ‘Breaking Weather Records’

### Simulating the Future Climate

Published March 6, 2014 Irish Times ClosedTags: Computer Science, Geophysics, Numerical Analysis

The Earth’s climate is changing, and the consequences may be very grave. This week, *That’s Maths* in *The Irish Times* ( TM040 ) is about computer models for simulating and predicting the future climate.

### Interesting Bores

Published January 2, 2014 Irish Times ClosedTags: Applied Maths, Fluid Dynamics, Geophysics, Mechanics, Wave Motion

This week’s *That’s Maths* column in the* Irish Times* ( TM036 ) is about bores. But don’t be put off: they are very interesting.

“I wonder if I shall fall right through the earth”, thought Alice as she fell down the rabbit hole, “and come out in the antipathies”. In addition to the author of the “Alice” books, Lewis Carroll – in real life the mathematician Charles L. Dodgson – many famous thinkers have asked what would happen if one fell down a hole right through the earth’s centre.

Galileo gave the answer to this question: *an object dropped down a hole piercing the earth diametrically would fall with increasing speed until the centre, where it would be moving at about 8 km per second, after which it would slow down until reaching the other end, where it would fall back again, oscillating repeatedly between the two ends.*

Continue reading ‘A Hole through the Earth’