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Margules, M. (1893) Luftbewegungen in einer rotierenden Spharoidschale. Sitzungsberichte der
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Ludwig Boltzmann Festschrift, J. A. Barth, Leipzig
Pichler, H. (2001) Von Margules zu Lorenz. In:
Hammerl, C., Lenhardt, W., Steinacker, R. and
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Platzman, G. W. (1967) A retrospective view of

An introduction to weather and climate derivatives John E. Thornes
University of Birmingham

The weather derivatives market has grown from being virtually non-existent in 1997
(Price Waterhouse Coopers 2001) to an estimated $10 billion global market by 2002. The market in Europe is just beginning to take off, as indicated by the establishment of the Met
Office and London-based Umbrella Brokers’ joint venture WeatherXchange (www.weather xchange.com) in June 2001 and the Londonbased Liffe (www.liffeweather.com) weather futures market and European weather index in
July 2001. These two Internet sites give a good introduction to the basic concepts of weather derivatives. Since the early 1980s, derivatives have been used by companies to manage their exposure to risk, be it due to currency exchanges or a host of other financial uncertainties. The financial derivatives markets are by far the biggest trading markets in the world, and derivatives are the most widely used and understood tool for risk-management purposes. They are also extremely cost-effective compared to more traditional insurance policies. A derivative can be defined as a contract between two parties that defines how payments will be made between them at the end of a contract period according to an agreed outcome.

Richardson’s book on weather prediction. Bull.
Am. Meteorol. Soc., 48, pp. 514±550
Richardson, L. F. (1922) Weather prediction by numerical process. Cambridge University Press
(reprinted by Dover Publications, New York,
1965, with a new introduction by Sydney
Chapman)
Â
Correspondence to: Dr P. Lynch, Met Eireann,
Glasnevin Hill, Dublin 9, Ireland. e-mail: Peter.
Lynch@met.ie
# Royal Meteorological Society, 2003. doi: 10.1256/wea.146.02

A weather derivative will be based on an agreed weather outcome such as the severity of a winter. The weather derivatives market is one of the last derivatives markets to be developed and has grown rapidly with the advantage of existing derivatives skills. The weather derivatives market was kick-started by the utility companies in the USA, following deregulation and considerable interest in the 1998/99 mild winter attributed to La Nina. This mild winter,
Ä
leading to significant loss of sales by the energy companies, had a big impact on the American economy ± encouraging companies to hedge their weather risk in subsequent winters ± for the first time.
Weather risk can be divided into two broad categories (Keller 2002) ± `extreme events’ and
`regional climate anomalies’. Extreme events such as floods, hurricanes, windstorms and hailstorms are often referred to as `catastrophes’, and traditionally the insurance market handles these high-risk low-probability events. Catastrophes usually wreak their havoc in a few hours or, at most, a few days.
Regional climate anomalies, on the other hand, are usually caused by unusual regional weather that may be persistent for weeks or months. Weather conditions such as drought or a heatwave, or persistent rain or cloudy conditions, may be low-risk high-probability events in a region that nevertheless cause financial problems to local companies and organisations.
For example, a theme park or open-air swimming pool may be concerned about revenue fluctuations as a result of poor weather in the summer months. A ski resort may be con193

Weather Vol. 58 cerned about a mild winter with little snow or temperatures that are too high to enable snowmaking machines to perform effectively. A jacket manufacturer may be concerned about lower sales in a mild winter, as might a road salt mining company. Up to now the costs from these regional climate anomalies have been borne by businesses under operational expenses. The weather derivatives market has been developed to cope with these kinds of risk to business. They allow companies to control
(or hedge) the effects of the weather on demand for their products, thereby reducing fluctuations in their cash flow. Derivatives are designed to hedge changes in the volumes of sales rather than in the price of goods.
Up to now the weather derivatives market has been concerned with fluctuations in weather away from the normal climate average.
Contracts are let (e.g. call, put, collar or swap options (see below)) on a monthly or seasonal basis based on historical weather records and short-term seasonal forecasts. The mean and standard deviation of the climate are assumed constant. In the future the potential of weather derivatives to hedge against climate change ± to produce a `climate derivative’ ± will enable contracts to be let over a number of years as the climate fluctuates. Climate derivatives will hedge against changes in the mean and/or standard deviation of the climate. This should be of great interest to companies that have longterm exposure to the climate, e.g. power companies that have considerable capital tied up in infrastructure such as power lines, and the railway industry with its huge number of overhead electric cables. Also it could be useful for companies that have to try to assess the long-term future demand for their products, for example water companies ± should they invest and build new dams?

Weather derivatives terminology and examples A generic weather derivatives contract has been defined by Zeng (2000) to include seven parameters:
(i) Contract type (swap, call, put, collar, etc.). 194

May 2003
(ii) Contract period (e.g. from 1 November
2002 to 31 March 2003).
(iii) An official weather station from which the weather data will be obtained.
(iv) Definition of the weather index (W) underlying the contract.
(v) Strike (S) or prenegotiated thresholds.
(vi) Tick (k) or payment (P).
(vii)Premium.
At the end of the contract if W is different from S by an agreed amount then the buyer
(seller) of the contract will receive from the seller (buyer) an amount equal to: P = k (W ±
S) depending on the type of contract.
Swaps

Swaps are contracts where two organisations agree to exchange their risk in order to stabilise their cash flow when the weather conditions are volatile. A swimsuit manufacturer may buy a swap against the average temperature in summer being too low in return for sacrificing extra revenue if it turns out to be a hot summer
(e.g. if W = 24 8C, S = 22 8C, and k = £100 000 per degC, then P = £200 000 and manufacturer pays seller; if W = 19 8C, S = 22 8C, and k = £100 000 per degC, then P = £300 000 and seller pays manufacturer).
Swaps can also be negotiated between organisations that have conflicting weather risks.
For example, a colder than average winter with lots of snow is good for the skiing industry but expensive for the highway authorities who have to clear the roads. A swap could be arranged to minimise financial risk to both parties. If it is a cold winter the ski companies will subsidise the winter maintenance costs (which is also useful for vital road access to the resorts) and if it is a mild winter the highway authority will subsidise the ski companies. These kinds of swaps can be agreed at no cost or premium due to the mutual benefits.
Call options and put options

Call options (sometimes called cap options) are contracts that compensate a buyer if a weather variable rises above a predetermined level. For example, an airport might buy a call option

Weather Vol. 58 against the number of days that the wind speed exceeds a certain threshold that is likely to stop the flying of small commercial aircraft. The airport would be compensated for their loss of revenue on those days when flying was restricted. On the other hand, the airport loses its premium if there are no windy days that cause problems (e.g. if W = 30 gale days, S = 25 gale days, and k = £10 000 per gale day, then
P = £50 000 and seller pays airport; if W < S then airport loses the premium).
Put options (sometimes called floor options) compensate a buyer if a weather variable falls below a given threshold. For example, a ski resort could be compensated if the amount of snow falls below a given threshold (e.g. if
W = 25 cm of snow, S = 30 cm of snow, and k = £20 000 per cm of snow, then P = £100 000 and seller pays ski resort; if W > S then ski resort loses the premium).
Collars

A collar is like a swap in that protection is given against adverse weather, but if the weather is favourable then no payouts are made and only premiums are paid. The difference to a swap is that payments only take place if the weather is outside an agreed upper and lower band. This allows for close to normal weather conditions to provide small fluctuations in revenue but protects against weather extremes. For example, a gas company will not only suffer a loss of revenue in a very mild winter but also in a very cold winter if they run out of gas and have to buy at inflated prices (e.g. S could be defined to trigger a payout if the average winter temperature is below ±5 8C or above 5 8C).
Data standards for contract settlement

In order to agree on whether or not contracts should be paid out, very strict rules are agreed on the source of the weather data to be used.
The Weather Risk Management Association
(2002) has recently published a report entitled
European weather data settlement procedures which recommends that climate data be used, although it is likely that either climate or synoptic data will be used depending on availability. As long as both parties agree in advance

which data are to be used, this should not cause a problem. In the USA the National
Weather Service maintains high standards of data collection across the country and there has been little difficulty in all parties agreeing on the weather data to be used. Heating degree days (HDDs) and cooling degree days (CDDs) are often used instead of temperature. In
Europe and in other parts of the world, HDDs and CDDs are not commonly used and therefore standard weather data are more likely to be utilised. There are about 8000 synoptic sites around the globe approved by the World
Meteorological Organization, and in Europe reliable data extend back to about 1974 for synoptic data and 1961 for climate data.
Negotiation of contracts

There are many organisations that offer consultancy advice to potential users of weather derivatives. Considerable research is currently being undertaken to calculate the agreed prices of weather risk contracts. Climate (and/or synoptic) data are used to establish the basic probabilities of certain weather events occurring over a coming month or season at a given location. Long-range forecasts are used to improve the probability prediction, and ensemble predictions are also now being made available. Potential clients

Weather derivatives have already been sold to a variety of customers around the world from a variety of sectors. Recent estimates have suggested that up to 70% of UK companies are exposed to weather risk in one way or another and that in the USA at least $1 trillion (US $1 trillion is $1 million million) of their economy is weather-sensitive.
The most affected industries include utilities, insurance and reinsurance, transportation, retailing and agriculture. In the USA, exchanges (e.g. Chicago Mercantile Exchange) already list futures and options for the following weather-sensitive commodities: corn, oats, soybeans, soybean oil, soybean meal, wheat, live cattle, feeder cattle, live hogs, cocoa, coffee, sugar, cotton, orange juice, crude oil,
195

Weather Vol. 58 heating oil, gasoline, propane and electricity production. As these are global commodities, trading takes place all year round. Futures are contracts to sell/buy a commodity at an agreed price at a stipulated future date.
Conclusion

Weather and climate derivatives present a new and exciting way of hedging against unseasonable weather and climate. There is no doubt that this is a sensible approach to risk management and that companies will be able to handle fluctuations in demand for their products, caused by the weather, much more effectively.
Weather and climate derivatives will also stimulate research into the probability of certain weather and climate events occurring on differing temporal and spatial scales.

The science of weather:
Radiation fog and steam fog*
Malcolm Walker
Education Officer, Royal Meteorological
Society

Figure 1 shows fog over Bute Park in Cardiff,
South Wales, UK. Figure 2 shows fog over the
St. Lawrence River at Quebec in Canada. The kind of fog that occurred at Cardiff is called radiation fog. The kind that occurred at Quebec is called steam fog.
Radiation fog forms when the sky is clear and the wind speed no more than Beaufort force 1. Typically, it forms at night and dissipates during the day. In midwinter, however, particularly in latitudes where the sun is low in the sky (e.g. north-west Europe), it may linger all day. When the sky is clear at night, land surfaces radiate heat to space and therefore cool.
Sea and lakes surfaces do not, however, cool by more than a small amount overnight (much less than 1 degC). If the air in contact with a surface is cooled to its dew-point temperature,
* Previously published as part of the Royal Meteorological Society’s educational material.

196

May 2003
References
Keller, J. L. (2002) Weather risk assessment at the dawn of ensemble numerical weather prediction.
In: Proceedings of the American Meteorological
Society: 3rd Symposium on Environmental Applications, Orlando, pp. J9±J15
Price Waterhouse Coopers (2001) The weather risk management industry: Report to the Weather Risk
Management Association. www.wrma.org
Weather Risk Management Association (2002)
European weather data settlement procedures. www.wrma.org Zeng, L. (2000) Weather derivatives and weather insurance: Concept, application, and analysis.
Bull. Am. Meteorol. Soc., 81, pp. 2075±2082
Correspondence to: Dr J. E. Thornes, School of
Geography, Earth and Environmental Sciences,
University of Birmingham, Birmingham B15 2TT.
# Royal Meteorological Society, 2003. doi: 10.1256/wea.132.02

small water droplets form (condensation). If there is no wind, droplets of dew form (on, for example, grass). If there is a gentle breeze, turbulent mixing spreads cooling upwards so that a shallow layer of radiation fog forms, as in
Fig. 1. When the wind is stronger, stratus cloud tends to form. Radiation fog does not form over the sea because the temperature of the sea’s surface stays much the same day and night. If the dew-point temperature lies below about ±0.5 8C, hoar frost forms instead of dew.
It does not form between 0 and ±0.5 8C because latent heat is released when condensation occurs and this heat is sufficient to melt the tiny ice crystals that make up hoar frost as they form. During the day, the sun’s rays heat the ground beneath the fog. Most of the rays are actually reflected from the top of the fog but some reach the surface, otherwise it would not be daylight in the fog! The ground is gradually heated until the dew-point temperature is exceeded. The fog then dissipitates, often very quickly. Steam fog forms when cold air flows over water that is more than 9 or 10 degC warmer than the air. Over sea water, steam fog is called sea smoke. Condensation results mainly from the cold air mixing with the air that is in contact with the water surface. However, convec-