© Nuffield Foundation 2011

Nuffield Free-Standing Mathematics Activity

Climate prediction

Is the Earth’s temperature in balance?

Climate prediction

Climate prediction

Incoming solar

radiation

Outgoing radiation

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

Climate predictionThe 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 = σT4 where σ = 5.67 x 10–8 Js–1m–2K–4

Let’s start by assuming that the (average) temperature of the Earth’s surface is 283K.

Then the outgoing radiation = σT4 = 364 Js–1m–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

= capacity heat

seconds in time radiation outgoing - radiation incoming

where the heat capacity of the Earth = 4 x 108 JK–1m–2

New temperature of the Earth

= old temperature + temperature change

Climate predictionWhat would happen if the amount of radiation from the Sun were suddenly to increase? For example, if radiation input went up to 370 Js–1m–2

Change in temperature of the Earth =

810 4

606024365364 - 370

= 0.47 K

New temperature of the Earth

= old temperature + temperature change

= 283.47 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