Atmospheric dynamics

Professor Joanna Haigh, Imperial College London, UK


Before her retirement in 2019 she was Professor of Atmospheric Physics at Imperial College London, and co-director of the Grantham Institute for Climate Change and the Environment. She is a former head of the Department of Physics at Imperial College London. She is also a Fellow of the Royal Society, and a former president of the Royal Meteorological Society.

Joanna is known for her work on solar variability, and also works on radiative transfer, stratosphere-troposphere coupling and climate modelling. She was Editor of the Journal of the Atmospheric Sciences and a Lead Author on the Third Assessment Report of the Intergovernmental Panel on Climate Change. She is a Fellow of the Institute of Physics. In 2004 she received the Institute of Physics’ Charles Chree Medal and Prize and in 2010 the Royal Meteorological Society Adrian Gill prize for her work on solar variability and its effects on climate.


What makes the wind blow? In this talk we will consider the location and strength of trade winds, mid-latitude depressions and fronts, tropical storms as well as smaller scale weather features, and why some places have much more varied weather than others.

My notes from the talk (if they don’t make sense then it is entirely my fault)

This book is an introductory text on the atmospheric environment.

The primitive equations are a set of nonlinear differential equations that are used to approximate global atmospheric flow and are used in most atmospheric models. They consist of three main sets of balance equations:

A continuity equation: Representing the conservation of mass.

Conservation of momentum: Consisting of a form of the Navier–Stokes equations that describe hydrodynamical flow on the surface of a sphere under the assumption that vertical motion is much smaller than horizontal motion (hydrostasis) and that the fluid layer depth is small compared to the radius of the sphere

A thermal energy equation: Relating the overall temperature of the system to heat sources and sinks

In general, nearly all forms of the primitive equations relate the five variables u, v, ω, T, W, and their evolution over space and time.

The equations were first written down by Vilhelm Bjerknes


Professor Lynch uses seven variables u, v, w, p, T, r, rw

The globe is divided into cells, like the checkers of a chess-board.

x, u represents the west-east direction and y, v represents the south-north direction

The horizontal momentum equation is basically Newton’s second law. The equation is made up of five parts: acceleration; the Coriolis effect, curvature effect, pressure gradient and friction.

Coriolis effect

The Earth’s rotation means that we experience an apparent force known as the Coriolis force. This deflects the direction of the wind to the right in the northern hemisphere and to the left in the southern hemisphere. This is why the wind-flow around low and high-pressure systems circulates in opposing directions in each hemisphere.

The Coriolis effect was described by the 19th-century French physicist and mathematician Gustave-Gaspard de Coriolis in 1835. He formulated theories of fluid dynamics through studying waterwheels, and realized the same theories could be applied to the motion of fluids on the surface of the Earth.

One of the most common examples of the Coriolis effect in action is seen through the deflection of winds on Earth.


Gaspard-Gustave de Coriolis (21 May 1792 – 19 September 1843) was a French mathematician, mechanical engineer and scientist. He is best known for his work on the supplementary forces that are detected in a rotating frame of reference, leading to the Coriolis effect. He was the first to apply the term travail (translated as “work”) for the transfer of energy by a force acting through a distance.

The geostrophic wind is the theoretical wind that would result from an exact balance between the Coriolis force and the pressure gradient force. This condition is called geostrophic balance. The geostrophic wind is directed parallel to isobars (lines of constant pressure at a given height). This balance seldom holds exactly in nature. The true wind almost always differs from the geostrophic wind due to other forces such as friction from the ground. Thus, the actual wind would equal the geostrophic wind only if there were no friction and the isobars were perfectly straight. Despite this, much of the atmosphere outside the tropics is close to geostrophic flow much of the time and it is a valuable first approximation. Geostrophic flow in air or water is a zero-frequency inertial wave.


The effect of surface friction


Wind doesn’t blow parallel to the isobars, but is deflected toward lower pressure; this happens close to the ground where terrain and vegetation provide friction.

Storm Bronagh was the second storm of the 2018/19 storm season. It brought gusts up to 78 mph to parts of England and Wales.

It brought widespread strong winds and heavy rain, with the strongest gusts being recorded across the hills and coasts of England and Wales.

The footprint of Storm Bronagh was clearly visible in surface analyses based on WOW observations. The dense network of WOW observations over England and Wales, along with other sources of observations, meant that we could track this storm in great detail. See below for the evolution of the storm. At each time step an analysis chart showing the position of the low pressure centre and associated weather fronts has been provided, along with an analysis produced from WOW observations. The colours on which represent temperature, the arrows are wind vectors, and the dark blue lines show surface pressure.

The UK Met Office Weather Observation Website (WOW). WOW allows anyone to submit their own weather data, anywhere in the world.


The analysis chart above left at 0000 UTC 21 September 2018 shows storm Bronagh centred across northern England. The centre of the storm is now over NE England. Cooler air can be seen moving into the West behind the cold front. The wind is still very strong across Eastern England.

This storm continued to deepen rapidly as it moved eastward into the North Sea.

Having moved across the UK overnight, the satellite image below left shows the centre of storm Bronagh approaching Denmark the following day, 21 September 2018. Image copyright Met Office / NOAA / NASA


The rain-radar image above right at 2230 UTC 20 September 2018 shows rainfall associated with storm Bronagh, with several bands of intense convection embedded within the fronts bringing torrential rainfall at times.

The map below left shows the daily rainfall totals 0900 UTC 20 to 0900 UTC 21 September 2018 from storm Bronagh. Upland areas of Wales, the southern Pennines and North York Moors recorded over 50mm of rain, with 78.6mm at Capel Curig (Conwy) and 71.6mm at Middleton (Derbyshire). Both mid-Wales and the Sheffield area experienced localised flooding.


The map above right shows maximum gust speeds from storm Bronagh. The strongest winds were across southern England and Wales with gusts of 40 to 50 Kt (46 to 58 mph). Exposed coastal locations recorded 50 to 60 Kt or more

Convergence into the centre of low pressure


Near-surface wind converging into a low-pressure system.

Near-surface wind converging into a low-pressure system. A modest friction force allows the velocity to have an inward component rather than being geostrophic, and the resultant of all forces is nonzero and toward the centre of the storm, causing wind to spiral. The wind speeds up during the air’s inward spiral, especially in a tropical cyclone (pictured).

The mean sea-level pressure (MSLP) is the atmospheric pressure at mean sea level (PMSL). This is the atmospheric pressure normally given in weather reports on radio, television, and newspapers or on the Internet. When barometers in the home are set to match the local weather reports, they measure pressure adjusted to sea level, not the actual local atmospheric pressure. January 2020


Mean Sea-Level Pressure in Black (hPa) 500-1000 hPa Thickness in Red (dam)

Atmospheric circulation is the large-scale movement of air and together with ocean circulation is the means by which thermal energy is redistributed on the surface of the Earth.

The Earth’s atmospheric circulation varies from year to year, but the large-scale structure of its circulation remains fairly constant. The smaller scale weather systems – mid-latitude depressions, or tropical convective cells – occur “randomly”, and long-range weather predictions of those cannot be made beyond ten days in practice, or a month in theory.


Idealised depiction (at equinox) of large-scale atmospheric circulation on Earth.

The large-scale atmospheric circulation “cells” shift polewards in warmer periods (for example, interglacials compared to glacials), but remain largely constant as they are, fundamentally, a property of the Earth’s size, rotation rate, heating and atmospheric depth, all of which change little.

The Hadley cell, named after George Hadley, is a global scale tropical atmospheric circulation that features air rising near the Equator, flowing poleward at a height of 10 to 15 kilometres above the earth’s surface, descending in the subtropics, and then returning equatorward near the surface. This circulation creates the trade winds, tropical rain-belts and hurricanes, subtropical deserts and the jet streams. Hadley cells are the low-altitude overtuning circulation that have air sinking at roughly zero to 30-degree latitude.

Air masses are large bodies of air that create distinctive weather conditions across the globe.

An air mass is defined as a body or ‘mass’ of air with uniform weather conditions, such as similar temperature and humidity. Air masses may cover several million square kilometres and extend high up into the atmosphere.

They are primarily defined by the area in which they originate, this is called the ‘source region’. The characteristics of an air mass can then be modified as they travel across the globe. Where two air masses of different temperatures meet, a boundary forms which is termed a ‘front’.


The UK is at the meeting point of several different types of weather from different directions. There are 5 main air masses that affect the UK. These are polar continental, arctic maritime, polar maritime, tropical maritime and tropical continental. Each brings unique weather to the UK.


When there are two air masses which are characteristically different, their collision is often also the cause strong meteorological phenomena. When the two air masses of distinct moisture levels collide, then they usually give rise to a higher moisture level. According to the reports given by major weather analysts, it is said that when these weather fronts pass over a certain area, then it causes a change in weather and gives rise to such events as thunderstorms, tornadoes, and gusty winds. These air masses included in the weather front have features like humidity or the temperature, and their direction is guided by the wind in the form of “Jet streams, and even underlying mountains and other geological features can influence their paths as well.

Types of Weather Fronts

Following are the types of weather fronts which are formed by the characterized features of two air masses, and are categorized as:

Cold Fronts: These are caused by drops in temperature, and normally lie within a sharp surface trough. They produce sharper change in the weather and move up to two times more powerfully than the warm fronts in the air, causing rapidly developing thunderstorms. They come in association with the low-pressure area, and form a line of showers if enough moisture is present in the front.

Warm Fronts: The warm fronts especially lie within the broader troughs of low pressure than the cold fronts, though these move more slowly upwards in the area. Their locations are often also marked on meteorological maps with semicircular red lines in the direction of travel.

Occluded Front: When the cold front in the air takes over the warm front, this causes the dominance of the cooler air in the air mass. As it takes over the warm front, it gives rise to two forms of “occlusions” in the air, and these characterize the mature forms of the storm systems.

Stationary Front: This is actually a non-moving kind of boundary between two different air masses, and remains in the same area for most of the time. A wide variety of weather is found along this area, and is visible in the form of clouds or precipitation. When these fronts are formed into smaller zones, they come to be known as “shear lines”.

Movements of Weather Fronts

The movement of weather fronts is guided by the winds moving them aloft, within which can be noticed the fact that usually the cold and occluded fronts move into the northwest to southeast direction, while warm fronts move from the southwest to the northeast direction in the Northern Hemisphere. Usually, however, this is effectively the opposite in the Southern hemisphere. The weather fronts’ movement is generally caused by the gradient front, or through the Coriolis Effect.

Effect of Fronts on Weather

These weather fronts impose a significant level of control on the weather conditions when they advance forward towards each other and, in some cases, will collide and then form violent storm conditions as a result. It is seen that these thunderstorms are most unusual, as the cold front makes the warm air pushed upwards. If there is any moisture present in the air, then it leads to the formation of the clouds.

A weather front represents a boundary between two different air masses, such as warm and cold air. If cold air is advancing into warm air, a cold front is present. On the other hand, if a cold air mass is retreating and warm air is advancing, a warm front exists. Otherwise, a stationary front is present if the cold air is neither advancing nor retreating from the warm air mass.


In a cold front set-up, the boundary between the cold and warm air masses is relatively steep (see above right), typically causing the warm air in front of it to rise rapidly. This rising air creates energetic, billowing cumulonimbus clouds leading to showers and thunderstorms. After the cold front passes, skies typically clear rapidly and temperatures cool due to the advancing cool air.

With a warm front, boundary between warm and cold air is more gradual than that of a cold front, which allows warm air to slowly rise and clouds to spread out into gloomy, overcast stratus clouds. Precipitation ahead of a warm front typically forms into a large shield of steady rain or snow. After the warm front passes, fair and milder weather is typical, however, a cold front is likely not far behind.

A front’s strength can be assessed by the difference in temperatures between the two air masses or temperature gradient. Basically, the larger the temperature gradient (as in 30s on one side and 60s on the other) the stronger the front is (example of a strong front above). Of course, a stronger front leads to a greater potential of precipitation, while a weak front may only bring a few clouds, a decrease in humidity, and/or a shift in winds.


Cumulonimbus (from Latin cumulus, “heaped” and nimbus, “rainstorm”) is a dense, towering vertical cloud, forming from water vapor carried by powerful upward air currents. If observed during a storm, these clouds may be referred to as thunderheads. Cumulonimbus can form alone, in clusters, or along cold front squall lines. These clouds are capable of producing lightning and other dangerous severe weather, such as tornadoes and hailstones. Cumulonimbus progress from overdeveloped cumulus congestus clouds and may further develop as part of a supercell. Cumulonimbus is abbreviated Cb.


Stratus clouds are low-level clouds characterized by horizontal layering with a uniform base, as opposed to convective or cumuliform clouds that are formed by rising thermals. More specifically, the term stratus is used to describe flat, hazy, featureless clouds of low altitude varying in colour from dark grey to nearly white. The word “stratus” comes from the Latin prefix “strato-“, meaning “layer”. Stratus clouds may produce a light drizzle or a small amount of snow. These clouds are essentially above-ground fog formed either through the lifting of morning fog or through cold air moving at low altitudes over a region. Some call these clouds “high fog” for the fog-like cloud. While light rain may fall, this cloud does not indicate much meteorological activity.


Cold air is more dense than warm air, so when a warm air mass meets a cold air mass, the cold air ends up below the warm air. Once the air has risen, it cools and clouds can form. Credit: CMMAP

Cyclogenesis is the development or strengthening of cyclonic circulation in the atmosphere (a low-pressure area). Cyclogenesis is an umbrella term for at least three different processes, all of which result in the development of some sort of cyclone, and at any size from the microscale to the synoptic scale.

How does the weather change during and after a cold front?

What type of weather is associated with occluded and stationary fronts?

Low pressure systems in the middle latitudes are called mid-latitude cyclones.

Mid latitude cyclones usually develop along either the polar jet stream or the sub-tropical jet stream.

A mid latitude cyclone goes through a life cycle of four stages.

Before the Cyclone:

A stationary front forms a boundary between a cold and warm air mass;

These fronts can be found along the jet stream


Stages of a cyclone:


1) A wave or ‘kink’ in the front develops. The wave begins to rotate and the low-pressure system is born. Precipitation.

2) Open stage. The drier, cooler, more dense air begins to close in on warm air. This stage the warm and cold fronts become easily noticeable and more developed.


3) Occluded stage. The low-pressure system becomes fully developed. The cold front catches-up to the warm front and creates an occluded front, this is part of the low-pressure system. The storm is biggest in this stage.


4) Dissolving stage. The occluded front becomes larger and the supply of warm air is cut-off and pushed aloft. The low pressure begins to gradually dissipate.


Eye in The Sky – 27 January 2020


A rather classic image of the UK in a polar maritime airmass in winter with heavy showers across Western areas. Note the trough across the Southwest which will continue to organise itself and head Northeast.

Curvilinear flow and the gradient wind balance

The “gradient wind” is a flow around a curved path where there are three forces involved in the balance:

Pressure gradient force

Coriolis force

Centrifugal force (a term which physics teachers hate)

This is important in regions of strong curvature (near high- or low-pressure centres)


With small scale curvilinear flow, you can ignore the Coriolis effect e.g. tornado

Tropical Cyclones (or hurricanes or typhoons depending where they are)

A tropical cyclone is a rapidly rotating storm system characterized by a low-pressure centre, a closed low-level atmospheric circulation, strong winds, and a spiral arrangement of thunderstorms that produce heavy rain or squalls.


Hurricane Isabel (2003) as seen from orbit during Expedition 7 of the International Space Station. The eye, eyewall, and surrounding rainbands, characteristics of tropical cyclones in the narrow sense, are clearly visible in this view from space.


A tropical cyclone’s primary energy source is heat from the evaporation of water (latent heat of evaporation) from the surface of a warm ocean, previously heated by sunshine. A surface wind is necessary. They only form over the ocean where the temperature is greater than 27oC. The maximum intensity is proportional to the difference between the inflow temperature and the outflow temperature.

Hurricane Dorian was the most intense tropical cyclone on record to strike the Bahamas, and is regarded as the worst natural disaster in the country’s history. It was also one of the most powerful hurricanes recorded in the Atlantic Ocean in terms of 1-minute sustained winds, with these winds peaking at 295 km/h.


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