Climate-based questions for students and teachers. A team of students and academics at the University of Oxford developed these Maths for Planet Earth questions.
Climate is the average weather over a long time period (30 years) for a particular region or place. The climate affects a number of environmental factors within the region including the type and growth of vegetation and wildlife. The climate is determined by large scale factors such as the Earth’s orbit around the Sun, the position of the continents and the composition of the atmosphere. Weather describes the short-term state of our atmosphere. This may include information about the air temperature, precipitation, air pressure and cloud cover. Our local weather changes daily due to the movement of air in our atmosphere.
I can investigate the relationship between climate and weather.
2 dice
Tally chart for numbers 2-12 Graph paper
In pairs, throw the two dice about 100 times and record the combined score shown each time.
Draw a bar graph of the results.
The results should show a smoothish distribution, with a score of 7 being most frequent. Ask each group to predict what their score will be if they throw the dice one more time – they can’t. However, with one more throw, the mean of all the scores will stay about the same (about 7). In the same way, the weather may be very different from day to day but the climate, the weather we ‘expect’, stays about the same.
If you don’t have access to dice, you can do this activity online at https://www.metlink.org/blog/weather-climate-extreme-weather-and-chaos-theory/
Can the students design a concept cartoon to illustrate the difference between weather and climate? See https://www.stem.org.uk/system/files/elibrary-resources/legacy_files_migrated/1292WEATHER.PDF and http://www.millgatehouse.co.uk/concept-cartoons-research/
A YouTube video showing an owner and his dog, as an analogy for weather and climate
Resource produced in collaboration with MEI
Brief overview of session ‘logic’
Mathematical opportunities offered
Download the resources
Resource produced in collaboration with MEI
Brief overview of session ‘logic’
Mathematical opportunities offered
Download the resources
Resource produced in collaboration with MEI
Brief overview of session ‘logic’
Mathematical opportunities offered
Download the resources
Resource produced in collaboration with MEI
Brief overview of session ‘logic’
Mathematical opportunities offered
Download the resources
Energy and Climate Change
Energy is needed in the form of electricity to power our lives, and to fuel our travel and industry. Since 1990, total world energy consumption has increased by over 55% and is projected to increase by another third by 2040.
Globally, oil accounts for over 30% of total energy use, followed by coal, gas and nuclear at 4%. This mix is different when you look only at electricity production, and different again on a country by country level.
A sustainable energy transition is a shift from an energy intensive society based on fossil fuels to energy efficiency with low carbon and renewable energy sources.
The Paris Agreement is a legally binding global climate change agreement, adopted by 189 nations at the Paris climate conference (COP21) in December 2015. It sets out a global framework to avoid dangerous climate change by limiting global warming to well below 2°C and pursuing efforts to limit it to 1.5°C.
Significant changes in energy production, transmission and use are necessary to achieve these commitments.
This should lead to co-benefits including improved air quality and reductions in energy poverty.
Since 2019, the costs of developing new power plants based on hydroelectric power, onshore wind, solar photovoltaic (PV), biomass and geothermal energy have become comparable to the costs of new oil and gas fuel plants.
Physicists play an essential role in all aspects of climate change research and policy decisions as well as in development of technologies and new ideas for preventing and mitigating the effects of future, damaging climate change.
Energy and Core Physics
Energy is a fundamental concept in physics and a key topic in any physics curriculum. The Earth’s climate system is driven by energy stores and transfers. Development of clean, sustainable energy generation and distribution methods relies on understanding the core physics involved. The climate system and sustainable energy production therefore provide engaging and relevant sources of examples for enhancing the teaching and learning of energy as a topic in Physics. They give teachers an obvious opportunity to engage their students in an appreciation of the importance of the physics already in the school curriculum in solving many of the problems surrounding accelerated climate change, as illustrated in the following, brief summary of potential links.
Energy is transferred by radiation from the Sun, increasing the thermal store in the Earth’s atmosphere and ocean systems. Energy transfers within these systems take place through the physical processes of conduction, convection, radiation and changes of state. Seasonal and longer term, natural variations in heating and cooling of the Earth are a result of the alignment of the Earth in space and its orbital motion around the Sun. Land and ice surfaces are heated differentially according to the absorptive or reflective nature of the surface type and rocks are heated internally due to energy released during radioactive decay and large scale, convective motion of the Earth’s interior.
Successful and sustainable, low carbon generation of electricity to meet current and future demands relies on understanding and exploiting many of these natural, physical processes. Atmospheric convection causes winds to drive wind turbines and also generates the ocean waves exploited in wave power devices. The relative motion of the Earth, Moon and Sun causes the ocean tides exploited in tidal barrages and undersea-current driven turbines. Seasonal changes, weather patterns and latitude can all affect the output of solar energy devices as can reflection and absorption of radiation by the materials they are made from. Geothermal energy relies on energy transfers due to radioactive heating of rocks, local volcanism or simply the heat capacity of the soil acting as a thermal store of energy.
Many large-scale electricity generation methods depend on the basic principle of a turbine turning a generator which relies on understanding the principles of electromagnetic induction and factors affecting potential power output and efficiency. Electricity distribution on a large scale, via the National Grid, involves minimising energy dissipation into the surroundings by transmitting electricity at very high potential difference and low current thus reducing thermal transfers of energy within the cables. Domestic uses of electricity involve devices with varying levels of energy efficiency and informed choice of the most efficient appliances and how long they are used for can lead to reductions in an individual’s energy demands, carbon footprint and household bills.
Energy Efficiency
Improving energy efficiency saves individuals money, reduces waste, conserves resources and cuts emissions of greenhouse gases and other pollutants. Discussing personal, financial savings and more immediately obvious environmental impacts can lead to engagement with climate change by an indirect route with valid applications in the physics curriculum. This is also a good opportunity to reinforce accurate vocabulary using the terms energy stores, transfers and pathways as well as the concept of energy dissipation and avoiding terms such as energy saving (https://spark.iop.org/collections/energy-new-curriculum). Examples can be given of more relevant applications of the Sankey Diagram as a tool for accounting for energy transfers in the atmosphere:
(see also http://www.sankey-diagrams.com/greenhouse-effect-explanation-with-sankey-diagram/ and https://www.metlink.org/wp-content/uploads/2020/11/PhysRev-25_energybudgets.pdf)
By Cmglee – Own work, CC BY-SA 3.0
This could be used to illustrate a more complex example of a Sankey diagram and lead to a discussion of the possible effects of changes to some of the pathways, reinforcing the concept of energy conservation as both sides must remain balanced.
Wind Turbine Example
In a wind turbine, 20% of the energy from the wind is converted to electricity. Lost wind leads to a loss of 30 % of the energy, friction between the wind and the blades of the turbine and the wind leads to a loss of 25% of the energy, and the rest of the energy is lost due to friction in the electric generator.
2. Draw a Sankey diagram for the wind turbine, considering that the output in electrical energy is 20 kJ.
Find out about how to borrow weather instruments in order to be able to carry out a microclimate investigation with your school here, or more about urban heat islands here.
What are microclimates?
What are the different types of microclimates?
What is an urban microclimate?
Urban precipitation
Smog
Urban winds
A microclimate is the distinctive climate of a small-scale area, such as a garden, park, valley or part of a city. The weather variables in a microclimate, such as temperature, rainfall, wind or humidity, may be subtly different from the conditions prevailing over the area as a whole and from those that might be reasonably expected under certain types of pressure or cloud cover. Indeed, it is the amalgam of many, slightly different local microclimates that actually makes up the microclimate for a town, city or wood.
It is these subtle differences and exceptions to the rule that make microclimates so fascinating to study, and these notes help to identify and explain the key differences which can be noticed by ground-level observations.
In truth, there is a distinctive microclimate for every type of environment on the Earth’s surface, and as far as the UK is concerned they include the following:
Upland areas have a specific type of climate that is notably different from the surrounding lower levels. Temperature usually falls with height at a rate of between 5 and 10 °C per 1000 m, depending on the humidity of the air. This means that even quite modest upland regions, such as The Cotswolds, can be significantly colder on average than somewhere like the nearby Severn Valley in Gloucestershire.
Occasionally, a temperature inversion can make it warmer above, but such conditions rarely last for long. With higher hills and mountains, the average temperatures can be so much lower that winters are longer and summers much shorter. Higher ground also tends to be windier, which makes for harsher winter weather. The effect of this is that plants and animals are often different from those at low levels.
Hills often cause cloud to form over them by forcing air to rise, either when winds have to go over them or they become heated by the sun. When winds blow against a hill-side and the air is moist, the base of the cloud that forms may be low enough to cover the summit. As the air descends on the other (lee) side, it dries and warms, sometimes enough to create a föhn effect. Consequently, the leeward side of hills and mountain ranges is much drier than the windward side. The clouds that form due to the sun’s heating sometimes grow large enough to produce showers, or even thunderstorms. This rising air can also create an anabatic wind on the sunny side of the hill. Sunshine-facing slopes (south-facing in the Northern Hemisphere, north-facing in the Southern Hemisphere) are warmer than the opposite slopes.
Apart from temperature inversions, another occasion when hills can be warmer than valleys is during clear nights with little wind, particularly in winter. As air cools, it begins to flow downhill and gathers on the valley floor or in pockets where there are dips in the ground. This can sometimes lead to fog and/or frost forming lower down. The flow of cold air can also create what is known as a katabatic wind.
The coastal climate is influenced by both the land and sea between which the coast forms a boundary. The thermal properties of water are such that the sea maintains a relatively constant day to day temperature compared with the land. The sea also takes a long time to heat up during the summer months and, conversely, a long time to cool down during the winter. In the tropics, sea temperatures change little and the coastal climate depends on the effects caused by the daytime heating and night-time cooling of the land. This involves the development of a breeze from off the sea (sea breeze) from late morning and from off the land (land breeze) during the night. The tropical climate is dominated by convective showers and thunderstorms that continue to form over the sea but only develop over land during the day. As a consequence, showers are less likely to fall on coasts than either the sea or the land.
Around the Poles, sea temperatures remain low due to the presence of ice, and the position of the coast itself can change as ice thaws and the sea re-freezes. One characteristic feature is the development of powerful katabatic winds that can sweep down off the ice caps and out to sea.
In temperate latitudes, the coastal climate owes more to the influence of the sea than of the land and coasts are usually milder than inland during the winter and cooler in the summer. However, short-term variations in temperature and weather can be considerable. The temperature near a windward shore is similar to that over the sea whereas near a leeward shore, it varies much more. During autumn and winter, a windward shore is prone to showers while during spring and summer, showers tend to develop inland. On the other hand, a sea fog can be brought ashore and may persist for some time, while daytime heating causes fog to clear inland. A lee shore is almost always drier, since it is often not affected by showers or sea mist and even frontal rain can be significantly reduced. When there is little wind during the summer, land and sea breezes predominate, keeping showers away from the coast but maintaining any mist or fog from off the sea.
Tropical rainforests cover only about 6% of the earth’s land surface, but it is believed they have a significant effect on the transfer of water vapour to the atmosphere. This is due to a process known as evapotranspiration from the leaves of the forest trees. Woodland areas in more temperate latitudes can be cooler and less windy than surrounding grassland areas, with the trees acting as a windbreak and the incoming solar radiation being ‘filtered’ by the leaves and branches. However, these differences vary depending on the season, i.e. whether the trees are in leaf, and the type of vegetation, i.e. deciduous or evergreen. Certain types of tree are particularly suitable for use as windbreaks and are planted as barriers around fields or houses.
These are perhaps the most complex of all microclimates. With over 75% of the British population being classed as urban, it is no surprise that they are also the most heavily studied by students of geography and meteorology. Therefore, the rest of these notes focus on the various elements that constitute an urban microclimate.
The table below summarises some of the differences in various weather elements in urban areas compared with rural locations.
| Sunshine duration | 5 to 15% less |
| Annual mean temperature | 0.5-1.0 °C higher |
| Winter maximum temperatures | 1 to 2 °C higher |
| Occurrence of frosts | 2 to 3 weeks fewer |
| Relative humidity in winter | 2% lower |
| Relative humidity in summer | 8 to 10% lower |
| Total precipitation | 5 to 10% more |
| Number of rain days | 10% more |
| Number of days with snow | 14% fewer |
| Cloud cover | 5 to 10% more |
| Occurrence of fog in winter | 100% more |
| Amount of condensation nuclei | 10 times more |
Marked differences in air temperature are some of the most important contrasts between urban and rural areas shown in the table above. For instance, Chandler (1965) found that, under clear skies and light winds, temperatures in central London during the spring reached a minimum of 11 °C, whereas in the suburbs they dropped to 5 °C.
Indeed, the term urban heat island is used to describe the dome of warm air that frequently builds up over towns and cities.
The formation of a heat island is the result of the interaction of the following factors:
The precise nature of the heat island varies from urban area to urban area, and it depends on the presence of large areas of open space, rivers, the distribution of industries and the density and height of buildings. In general, the temperatures are highest in the central areas and gradually decline towards the suburbs. In some cities, a temperature cliff occurs on the edge of town. This can be clearly seen on the heat profile below for Chester.
As noted previously, the greater presence of condensation nuclei over urban areas can lead to cities being wetter and having more rain days than surrounding rural areas. Indeed, it was often said that Rochdale, the famous mill town, had significantly smaller amounts of rain on Sundays when the town’s factories were closed.
However, other factors play a major role, especially the heat islands. These can enhance convectional uplift, and the strong thermals that are generated during the summer months may serve to generate or intensify thunderstorms over or downwind of urban areas. Storms cells passing over cities can be ‘refuelled’ by contact with the warm surfaces and the addition of hygroscopic particles. Both can lead to enhanced rainfall, but this usually occurs downwind of the urban area.
Smogs were common in many British cities in the late 19th and early 20th centuries, when domestic fires, industrial furnaces and steam trains were all emitting smoke and other hygroscopic pollutants by burning fossil fuels. The smogs were particularly bad during the winter months and when temperature inversions built up under high pressure, causing the pollutants to become trapped in the lower atmosphere and for water vapour to condense around these particles.
One of the worst of these ‘pea-soup fogs’ was the London smog of the winter of 1952/53. Approximately 4,000 people died during the smog itself, but it is estimated that 12,000 people may have died due to its effects. As a result, the Clean Air Act of 1956 was introduced to reduce these emissions into the lower atmosphere. Taller chimney stacks and the banning of heavy industry from urban areas were just two of the measures introduced and, consequently, fewer smogs were recorded in the UK during the 1960s and 1970s.
Research in the 1990s has shown, however, that another type of smog – photochemical – is now occurring in some urban areas as a result of fumes from car exhausts and the build up of other pollutants in the lower atmosphere which react with incoming solar radiation. The presence of a brown-coloured haze over urban areas is an indication of photochemical smog, and among its side effects are people experiencing breathing difficulties and asthma attacks.
Tall buildings can significantly disturb airflows over urban areas, and even a building 100 metres or so high can deflect and slow down the faster upper-atmosphere winds. The net result is that urban areas, in general, are less windy than surrounding rural areas.
However, the ‘office quarter’ of larger conurbations can be windier, with quite marked gusts. This is the result of the increased surface roughness that the urban skyline creates, leading to strong vortices and eddies. In some cases, these faster, turbulent winds are funnelled in between buildings, producing a venturi effect, swirling up litter and making walking along the pavements quite difficult.
Web page reproduced with the kind permission of the Met Office
Question to consider: Adaptation to climate change needs to be addressed in all urban policies. Discuss.
The impact of 3 urban policies in Paris on climate change adaptation and mitigation
Acceptable risks are those deemed so low that additional efforts at risk reduction, in this case climate adaptation efforts, are not justified. Tolerable risks relate to situations where adaptive, risk management efforts are required and effective for risks to be kept within reasonable levels. The scope of risks that fall within the tolerable area is influenced by adaptation opportunities and constraints. Therefore, the categorization of risks varies across spatial, jurisdictional, and temporal. Opportunities and constraints may be physical, technological, economic, institutional, legal, cultural, or environmental in nature.
Intolerable risks may be related to threats to core social objectives associated with health, welfare, security or sustainability. Risks become intolerable when practicable or affordable adaptation options to avoid escalating risks become unavailable. Therefore, a limit is a point when an intolerable risk must be accepted; the objective itself must be relinquished; or some adaptive transformation must take place to avoid intolerable risk. Such a discontinuity may take several forms such as individual’s decision to relocate, an insurance company’s decision to withdraw coverage, or a species’ extinction. The alternative to such discontinuities is an escalating and unmediated risk of losses. While individuals have their own perspectives about what are acceptable, tolerable or intolerable risks, collective judgements about risk are also codified through mechanisms such as engineering design standards, air and water quality standards, and legislation that establishes goals for regulatory action. There are also international agreements that establish norms and rights relevant to climate change risks, such as the Universal Declaration of Human Rights, the International Covenant on Civil and Political Rights, and the International Covenant on Economic, Social and Cultural Rights. Further, these high level responses often shape the constraints and opportunities to adaptation and responses to risk at lower levels through the distribution of resources, institutional design, and support of capacity development. If these risks and discontinuities have global-scale consequences, they can be linked to ‘key vulnerabilities’ to climate change. Consistent with our framing of adaptation limits, such key vulnerabilities would need to be assessed in terms of the limits they imply for specific social actors, species and ecosystems.
A number of factors will limit strategy adoption and preclude elimination of all climate change effects. The first outside circle represents the “adaptation needs”, i.e. the set of adaptation actions that would be required to avoid any negative effect (and capture all positive effects) from climate change. It can be reduced by climate change mitigation, i.e. by limiting the magnitude of climate change.
The second circle represents the subset of adaptation actions that are possible considering technical and physical limits. Improving what can be done, for instance through research and development, can expand this circle. The area between the first and second circles is the area of “unavoidable impacts” that one cannot adapt to (for instance, it is impossible to restore outdoor comfort under high temperature). The third circle represents the subset of adaptation actions that are desirable considering limited resources and competing priorities: some adaptation actions will be technically possible, but undesirable because they are too expensive and there are better alternative ways of improving welfare (e.g., investing in health or education). This circle can be expanded through economic growth, which increases resources that can be dedicated to adaptation. Finally, the last circle represents what will be done, taking into account the fact that market failures or practical, political, or institutional constraints will make it impossible to implement some desirable actions. The area between the first and the last circles represents residual impacts (i.e. the impacts that will remain after adaptation, because adapting to them is impossible, too expensive, or impossible due to some barriers).
Key regional risks from climate change and the potential for reducing risks through adaptation and mitigation
WG2 Assessment box spm2 table 1: Africa, Asia, Australasia, Central/ South America, Europe, North America, Ocean, Polar Regions, Small Islands, Key.
Could economic approaches bias adaptation policy and decisions against the interests of the poor, vulnerable populations, or ecosystems?
(WG2 FAQ 17.2)
A narrow economic approach can fail to account adequately for such items as ecosystem services and community value systems, which are sometimes not considered in economic analysis or undervalued by market prices, or for which data is insufficient. This can bias decisions against the poor, vulnerable populations, or the maintenance of important ecosystems. For example, the market value of timber does not reflect the ecological and hydrological functions of trees nor the forest products whose values arise from economic sectors outside the timber industry, like medicines. Furthermore some communities value certain assets (historic buildings, religious sites) differently than others. Broader economic approaches, however, can attach monetary values to non-market impacts, referred to as externalities, placing an economic value on ecosystem services like breathable air, carbon capture and storage (in forests and oceans) and usable water. The values for these factors may be less certain than those attached to market impacts, which can be quantified with market data, but they are still useful to provide economic assessments that are less biased against ecosystems.
But economic analysis, which focuses on the monetary costs and benefits of an option, is just one important component of decision making relating to adaptation alternatives, and final decisions about such measures are almost never based on this information alone. Societal decision making also accounts for equity – who gains and who loses – and for the impacts of the measures on other factors that are not represented in monetary terms. In other words, communities make decisions in a larger context, taking into account other socioeconomic and political factors. What is crucial is that the overall decision-framework is broad, with both economic and non-economic factors being taken into consideration. A frequently used decision-making framework that provides for the inclusion of economic and non-economic indicators to measure the impacts of a policy, including impacts on vulnerable groups and ecosystems, is multicriteria analysis (MCA). But as with all decision making approaches, the a challenge for MCA and methods like it is the subjective choices that have to be made about what weights to attach to all the relevant criteria that go into the analysis, including how the adaptation measure being studied impacts poor or vulnerable populations, or how fair it is in the distribution of who pays compared to who benefits.
The impact of 3 urban policies in Paris on climate change adaptation and mitigation
Urban policies have many goals, such as enhancing the quality of life and the city’s economic competitiveness by means of affordable housing and office space, amenities and efficient public services.
They also have social objectives aimed at poverty and social segregation issues, safety and security, and public health and environmental goals, such as reducing air and water pollution and preserving natural areas. Urban policies now also face new challenges from climate change, including adaptation and mitigation needs.
Five possible policy goals:
The graph below shows the effectiveness of 3 policies in Paris as measured against these policy goals. The three policies are:
1) a greenbelt policy,
2) a public transport subsidy and
3) a zoning policy to reduce the risk of flooding with building prohibited in flood prone areas.
By implementing all three policies, the outcome, considering both positive and negative impacts on the five policy goals, is better than a ‘do nothing scenario’ measured against the five policy goals. Therefore, climate goals can be reached more efficiently and with higher social acceptability, if they are implemented through taking into account existing strategic urban planning, rather than by creating new, independent climate-specific plans.
Additional Source:
Trade-offs and synergies in urban climate policies, V. Viguié & S. Hallegatte, Nature Climate Change 2, 334–337 (2012), doi:10.1038/nclimate1434
Use this Global Atmospheric Circulation practice exercise.
Changes to the Global Atmospheric Circulation as the climate changes.
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