Climate Change A simple climate model Dudley Shallcross and Tim Harrison, Bristol University

Simple climate model A simple climate model Students can use an excel spreadsheet to run it Simple factors to change Can look at feedbacks on climate Ideas and questions e-mail d.e.shallcross@bris.ac.uk or t.g.harrison@bris.ac.uk

Granny’s model of climate 1 Earth Sun Temperature of the Earth ~ 10o C

Big problema: clouds and ice From sun (100) Scattered out to space by clouds (24) by the surface (6) (skiing) Surface Land/water Ice 30% of incoming solar radiation reflected back out to space without being absorbed (Earth’s albedo A = 0.3)

Granny’s model of climate 2 Earth Sun With clouds and ice Temperature of the Earth ~ - 18o C

Granny is now very cold What can she do to warm herself up? Move closer? (Earth’s distance to the Sun varies but not enough to make up this loss in heat) Get a blanket? (In effect this is what Greenhouse gases do)

CO2 O3

Granny’s model of climate 3 (with blankets) Earth Sun with clouds and ice and greenhouse gases Temperature of the Earth ~ 16o C

Thanks to Mike Stuart 2008 www.disphoria.co.uk For the granny cartoons

Essential Background Physics Black Body Radiation   All bodies radiate energy as electro-magnetic radiation. A black body absorbs all radiation falling on it. It emits radiation as a function of its surface temperature without favouring particular frequencies. The Stefan-Boltzmann Law relates how the total energy emitted by a black body relates to the temperature by   Equation 1 where I is the energy per unit area emitted per second (Watts m-2 s-1), T is the Absolute Temperature (K) and  is the Stefan-Boltzmann constant (5.67 x 10-8 W m-2 K-4).

Model 1: Heat in, heat out Balanced Flux model We know that the energy from the Sun reaching the top of the atmosphere, the so-called solar constant S, is 1370 Wm-2. If we take the radius of the Earth to be RE, in this very simple model we can see that the Earth absorbs solar radiation over an area R2 (i.e. a flat atmosphere) but emits energy from an area 4R2 (i.e. from the entire surface).

Energy Out Energy In Out = TE4 4RE2 IN = S x Area IN = 1370 πRE2 W m-2 Area of Earth normal to Solar Radiation S = πRE2 Surface area of Earth = 4πRE2 Solar Flux, per unit area, S

Surface temperature looks OK Energy in = Energy out 1370 x RE2 = TE4 x 4 RE2 TE4 = 1370 4 x 5.67x10-8 TE = 279 K (note for later we will call 1370/4 = FS)

Big problema: clouds and ice From sun (100) Scattered by Clouds (24) the surface (6) Surface Land/water Ice 30% of incoming solar radiation reflected back out to space without being absorbed (Earth’s albedo A = 0.3)

Re-calculate TE 24% of solar flux is reflected by clouds 6% Scattered by surface TE = 255 K (- 18 o C) Cold

Terrestrial Radiation The Earth also acts as a blackbody radiator TE = 288 K so most of the irradiance from the Earth is in the infra-red part of the spectrum and peaks at about 10 m. Solar Radiation 5900 K Terrestrial Radiation 288 K Wavelength m little overlap between the incoming solar radiation and the outgoing infra-red radiation from the Earth’s surface. separated by a gap at around 4 m shortwave (SW) radiation longwave (LW) radiation

Atmospheric Window (C-F bonds absorb ir energy)

Model 2: One layer atmosphere FS(1-A) FgIR Fa Atmosphere FS(1-A)VIS Fa Fg Ground VIS IR

FS = Energy Flux from the Sun (1370/4) A = Albedo or reflectivity of Earth typically ~ 0.3 FS(1-A) FgIR Fa Atmosphere FS(1-A)VIS Fa Fg Ground VIS IR

VIS = Transmittance of UV/Vis light from the Sun through the Earth’s atmosphere to the ground. If all the light is absorbed VIS = 0.0 and if all the light passes through VIS = 1.0 FS(1-A) FgIR Fa Atmosphere FS(1-A)VIS Fa Fg Ground VIS IR

IR = Transmittance of IR light from the Earth through the Earth’s atmosphere to space. If all the ir light is absorbed IR = 0.0 and if all the ir light passes through IR = 1.0 FS(1-A) FgIR Fa Atmosphere FS(1-A)VIS Fa Fg Ground VIS IR

Fa = Energy flux from the atmosphere, in a balanced flux model the flux upwards and the flux downwards are the same. FS(1-A) FgIR Fa Atmosphere FS(1-A)VIS Fa Fg Ground VIS IR

FgIR = The IR energy flux from the ground modified by the transmittance properties of the Earth’s atmosphere that now escapes to space. FS(1-A) FgIR Fa Atmosphere FS(1-A)VIS Fa Fg Ground VIS IR

FS(1-A)VIS = The UV/Vis energy flux reaching the ground from the Sun modified by the transmittance properties of the Earth’s atmosphere. FS(1-A) FgIR Fa Atmosphere FS(1-A)VIS Fa Fg Ground VIS IR

Fg = The IR energy flux from the Earth’s surface. FS(1-A) FgIR Fa Atmosphere FS(1-A)VIS Fa Fg Ground VIS IR

Fluxes at the top of the atmosphere must balance FS(1-A) FgIR Fa Atmosphere FS(1-A)VIS Fa Fg Ground VIS IR

Fluxes at the ground must balance FS(1-A) FgIR Fa Atmosphere FS(1-A)VIS Fa Fg Ground VIS IR

Simply balance energy fluxes At the surface FS(1-A) VIS + Fa = Fg (a) And at the top of the atmosphere, Fg IR + Fa = FS(1-A) (b) If the two fluxes are in balance Fg = FS(1-A)(1 + VIS) / (1 + IR )

Finally Fg = TE4 = FS(1-A)(1 + VIS) / (1 + IR ) Assuming FS = 336 Wm-2 A = 0.3 VIS = 0.8 IR = 0.1 TE = 287 K

Example calculations TE = [ FS(1-A)(1 + VIS) / σ(1 + IR )]0.25 FS /Wm-2 336 336 336 336 A 0.3 0.0 0.0 0.3 VIS 1.0 1.0 1.0 1.0 IR 1.0 1.0 0.0 0.0 TE /K 254 278 330 302

Example calculations TE = [ FS(1-A)(1 + VIS) / σ(1 + IR )]0.25 FS /Wm-2 336 336 336 336 A 0.3 0.0 0.0 0.3 VIS 1.0 1.0 1.0 1.0 IR 1.0 1.0 0.0 0.0 TE /K 254 278 330 302

Example calculations TE = [ FS(1-A)(1 + VIS) / σ(1 + IR )]0.25 FS /Wm-2 336 336 336 336 A 0.3 0.0 0.0 0.3 VIS 1.0 1.0 1.0 1.0 IR 1.0 1.0 0.0 0.0 TE /K 254 278 330 302

Example calculations TE = [ FS(1-A)(1 + VIS) / σ(1 + IR )]0.25 FS /Wm-2 336 336 336 336 A 0.3 0.0 0.0 0.3 VIS 1.0 1.0 1.0 1.0 IR 1.0 1.0 0.0 0.0 TE /K 254 278 330 302

Example calculations TE = [ FS(1-A)(1 + VIS) / σ(1 + IR )]0.25 FS /Wm-2 336 336 336 336 A 0.3 0.0 0.0 0.3 VIS 1.0 1.0 1.0 1.0 IR 1.0 1.0 0.0 0.0 TE /K 254 278 330 302

Quick Questions TE. =. [ FS(1-A)(1 + VIS) / σ(1 + IR ) ]0 Quick Questions TE = [ FS(1-A)(1 + VIS) / σ(1 + IR ) ]0.25 Assuming FS = 336 Wm-2 A = 0.3 VIS = 0.8 IR = 0.1 TE = 287 K 1 If the Earth were to move closer to the Sun such that the solar constant increases by 10% calculate the effect on the surface temperature of the Earth. 2 If the Earth’s ice caps were to grow such that 25% of the surface was covered in ice (it is about 6% now) calculate the effect on the surface temperature of the Earth.

Quick Questions TE. =. [ FS(1-A)(1 + VIS) / σ(1 + IR ) ]0 Quick Questions TE = [ FS(1-A)(1 + VIS) / σ(1 + IR ) ]0.25 Assuming FS = 336 Wm-2 A = 0.3 VIS = 0.8 IR = 0.1 TE = 287 K 1 If the Earth were to move closer to the Sun such that the solar constant increases by 10% calculate the effect on the surface temperature of the Earth. 294 K (up 7 K) 2 If the Earth’s ice caps were to grow such that 25% of the surface was covered in ice (it is about 6% now) calculate the effect on the surface temperature of the Earth. 265 K (- 8 C)

Secrets in the Ice Snow accumulation lays down record of environmental conditions Compacted to ice preserving record Drill ice core & date

Climate Change Correlation of temperature with CH4 and CO2

Milankovitch Cycles Climate shifts correspond to three cycles related to Earth’s orbit Effect intensity of solar radiation Caused by gravitational attraction between the planets (mainly Jupiter) and Earth Predictions from cycles match major glacial/interglacial periods and minor periodic oscillations in climate record

Milankovitch Cycles Obliquity of Earth’s axis of rotation (tilt) changes from 22° (currently23.5°) to 24.5°  41,000 years Precession (wobble) changes the quantity of incident radiation at each latitude during a season  22,000 years Eccentricity of Earth’s orbit varies from nearly circular to elliptical. At low eccentricity orbits the average Earth-sun distance is less  100,000 years

Source: OSTP Global Average Temperature is Increasing This steady increase of CO2 in the atmosphere has caused greater retention of heat and a gradual warming of the earth: global average surface temperature has risen by about 1°F over the last century. The 13 warmest years this century have all occurred since 1980, with 1998 the warmest on record. The term global warming is used to describe the enhanced greenhouse effect resulting from human activities. Source: OSTP

Indicators of the Human Influence on the Atmosphere during the Industrial Era Concentrations of atmospheric greenhouse gases and their radiative forcing have continued to increase as a result of human activities. Since 1750, carbon dioxide has increased by 31%, methane by 151% and nitrous oxide by 17%. Present concentrations of CO2 and methane are higher now than at any time during the last 420,000 years, the period for which there are reliable ice core data, and probably significantly longer. The current rate of CO2 increase is unprecedented during at least the past 20,000 years. About 75% of the anthropogenic emissions of CO2 to the atmosphere during the past 20 years is from fossil fuel burning, the remainder from deforestation and other land-use changes. The greatest warming effect currently stems from CO2, followed by methane, halocarbons and nitrous oxide. Cooling effects stem from the depletion of stratospheric ozone and generally from relatively short-lived aerosols. Ice cores in Greenland show the large increase in anthropogenic SO2 emissions during the Industrial Era (graph b). Source: IPCC TAR 2001

Climate Change Correlation of temperature with CH4 and CO2

Variations of the Earth’s Surface Temperature* Over the past 140 years (graph a), the global average surface temperature has increased over the 20th century by about 1.1°F (0.6°C). While the record shows a great deal of variability, the upward trend is unambiguous. Most of the warming occurred during the 20th century, during two periods, 1910 to 1945 and since 1976. Graph b shows that the 20th century warming is likely to be the largest during any century over the past 1000 years for the Northern hemisphere, with the 1990s the warmest decade and 1998 the warmest year of the millennium. Night-time minimum air temperatures over land have increased at the greatest rate; this has lengthened the frost-free season in many mid- and high-latitude regions. *relative to 1961-1990 average Source: IPCC TAR 2001

Projected Changes in Annual Temperatures for the 2050s Global Warming Predictions of Earth’s Surface Global climate models project that the warming will not be evenly distributed - land areas will experience greater warming than the oceans, higher latitude regions (regions closer to the poles) are expected to warm more than equatorial regions, and the northern hemisphere is projected to warm more than the southern hemisphere. The U.S. may experience warming of between 5 and 10°F. A 2.5 - 10.4°F global increase may not seem like a lot, but in fact, this temperature rise is happening at an extremely rapid rate, a rate of change not seen on the planet for at least the last 10,000 years. It is the combined threat of the unusually large magnitude of this temperature increase and the speed at which it is occurring that causes great concern among scientists. The projected change is compared to the present day with a ~1% increase per year in equivalent CO2 Source: The Met Office. Hadley Center for Climate Prediction and Research

Temperature Projections Global average temperature is projected to increase by 1.0 to 10 °C from 1990 to 2100 Projected temperature increases are greater than those in the SAR (1.8 to 6.3°C) Projected rate of warming is unprecedented for last 10,000 years Temperature Projections The global average surface temperature is projected to increase by 2.5 to 10.4°F (1.4 to 5.8°C) over the period 1990 to 2100. These results span the full range of scenarios used in the TAR (35 SRES scenarios). The projected temperature increases are greater than those in the SAR (top end of the range is nearly doubled), which were 1.8 to 6.3°F (1.0 to 3.5°C). The revised higher estimates of projected warming are due primarily to the lower projected sulphur dioxide emissions in the TAR scenarios relative to the SAR scenarios (less of a cooling effect); i.e., a result of the assumption that we will produce fewer pollutants when producing electricity. The projected rate of warming is much larger than the observed changes during the 20th century and is very likely to be unprecedented for at least the last 10,000 years. The magnitude of the warming at the upper end of the range is of the same order as the warming the earth experienced emerging from the depth of the last ice age 20,000 years ago to the warmth of the present interglacial beginning about 10,000 years ago. Source: IPCC TAR 2001

Model simulation of recent climate Natural forcings only (solar, volcanic etc. variability) Anthropogenic forcings only (human-induced changes) The Met Office

Simulated global warming 1860-2000: Natural & Man-made factors Observed simulated by model Temperature rise o C 0.0 0.5 1.0 1850 1900 1950 2000 Hadley Centre

Factors affecting climate system Establishing a link between global warming and man-made greenhouse gas pollution? This figure shows how changes in greenhouse gases and aerosols have affected climate since pre-industrial times to present. Anything in pink shows substances that tend on average to warm the surface of the Earth. In contrast, anything in the blue part of the graph tends on average to cool the surface. The height of the rectangular bar indicates a mid-range estimate of how much they warm or cool the Earth’s surface and the error bars show the uncertainty range.. So firstly it’s important to point out that it’s not only CO2 that’s involved in climate change. There are a whole host of other atmospheric chemical and physical parameters. The second feature to point out is the uncertainty that still remains in each of these which is continually being reduced and you’ll be pleased to hear that the UK atmospheric research community is leading the way on reducing this uncertainty, particularly with respect to our understanding of CO2. The impact of direct anthropogenic emissions on the atmosphere is often relatively easy to assess, especially if they are tied to major industrial activities, where accurate and detailed records. Classical examples are the release of chlorofluorocarbons and the emission of CO2 from fossil fuel combustion. However, things get more complex where human activities release compounds that impact upon other parts of the atmosphere, for example, stratospheric ozone, or where human activities release a precursor compound, which is transformed in the atmosphere to a compound that may be climatically active, for example tropospheric ozone. Stratospheric and tropospheric ozone are indirect greenhouse gases and their effect on climate is complex. The global mean radiative forcing of the climate system for the year 2000, relative to 1750 (IPCC, 2001).

Impacts of Climate on the UK UK will become warmer High summer temperatures more frequent Very cold winters increasingly rare Winters will become wetter and summers may become drier