© Nuffield Foundation 2011 Nuffield Free-Standing Mathematics Activity Climate prediction

Is the Earth’s temperature in balance? Climate prediction

Incoming solar radiation Outgoing radiation The change in Earth’s temperature depends on the difference between incoming and outgoing radiation

Climate prediction The outgoing radiation depends only on the temperature of the Earth, T kelvins (K). The amount of outgoing radiation is given by the Stefan-Boltzman Law: Outgoing radiation = σT 4 where σ = 5.67 x 10 –8 Js –1 m –2 K –4 Let ’ s start by assuming that the (average) temperature of the Earth ’ s surface is 283  K. Then the outgoing radiation = σ T 4 = 364 Js –1 m –2 (to 3sf) This is the energy lost per square metre of the Earth’s surface per second.

Climate prediction Change in temperature of the Earth = where the heat capacity of the Earth = 4 x 10 8 JK –1 m –2 New temperature of the Earth = old temperature + temperature change

Climate prediction What would happen if the amount of radiation from the Sun were suddenly to increase? For example, if radiation input went up to 370 Js –1 m –2 Change in temperature of the Earth = = 0.47 K New temperature of the Earth = old temperature + temperature change = K After one year

Reflect on your work Why does an exponential function give a better long-term prediction than any of the polynomials? Climate prediction