{"id":3984,"date":"2010-07-05T09:00:45","date_gmt":"2010-07-05T14:00:45","guid":{"rendered":"http:\/\/www.realclimate.org\/?p=3984"},"modified":"2010-07-13T11:44:00","modified_gmt":"2010-07-13T16:44:00","slug":"a-simple-recipe-for-ghe","status":"publish","type":"post","link":"https:\/\/www.realclimate.org\/index.php\/archives\/2010\/07\/a-simple-recipe-for-ghe\/","title":{"rendered":"A simple recipe for GHE"},"content":{"rendered":"
\n

According to some recent reports (e.g. PlanetArk<\/a>; The Guardian<\/a>), the public concern about global warming may be declining. It’s not clear whether this is actually true: a poll conducted by researchers at Stanford<\/a> suggests otherwise. In any case, the science behind climate change has not changed<\/a> (also see America’s Climate Choices<\/a>), but there certainly remains a problem in communicating the science to the public.<\/p>\n

This makes me think that perhaps a new simple mental picture of the situation is needed. We can look at climate models, and they tell us what we can expect, but it is also useful to have an idea of why increased greenhouse gas concentrations result in higher surface temperatures. The saying “Everything should be made as simple as possible, but not simpler<\/a>” has been attributed to Albert Einstein, which also makes me wonder if we – the scientists – need to reiterate the story of climate change in a different way. <\/p>\n

Gavin has already discussed this<\/a> (also see here<\/a> and here<\/a>), but it may be necessary to tell story over again, with a slightly different slant. So how can we explain how the greenhouse effect (GHE) work in both simple terms and with a new angle? I also want to explain why the middle atmosphere cools with increasing greenhouse gas concentrations associated with an increased GHE. Here I will try to present a conceptual and comprehensive picture of GHE, explaining both the warming in the lower part of the atmosphere as well as the cooling aloft, and where only the most central features are included. Also, it is important to provide a good background, and we need to start with some very fundamental facts.<\/p>\n

<\/p>\n

Four main physical aspects<\/strong>
\nSeveral factors are involved, and hence it may be useful to write a simple recipe for the GHE. This recipe then involves four main ingredients: (i) the relationship between temperature and light, (ii) the planetary energy balance, (iii) the distance light travels before being absorbed, and (iv) the relationship between temperature and altitude. <\/p>\n

(i) Temperature and light<\/strong>
\nEnergy can be transmitted in many different ways, involving photons<\/a> (light or electromangetic radiation<\/a>), conduction, and motion. Most of these require a medium, such as a gas, fluid, or a solid, but space is basically a void through which photons represent virtually the only form for energy transfer. Hence, planets tend to gain or lose energy to space in the form of photons, and we often refer to the energy loss as ‘radiative heat loss’. <\/p>\n

A fundamental law of physics, known as the Planck’s law<\/a>, says that radiative heat loss from any object depends on its temperature. Planck’s law also explains the colour of the light, or its wavelength, and hence explains why iron gets red hot<\/a> when heated sufficiently. <\/p>\n

\"\"<\/a>
Figure 1. Illustration of Planck's law, where the different curves represent objects with different temperature. The y-axis is marks the intensity and the x-axis the wave length (colour) of the light emitted by bodies with a given temperature (PDF-version<\/a> and R-script<\/a> generating the figure.)<\/em><\/figcaption><\/figure>\n

Planck’s law predicts that the light from an object with a temperature of 6000K \u2013 such as the solar surface \u2013 produces light that is visible, whereas objects with a temperature of 288K produce light with a wavelength that our eyes are not able to see (infra red<\/a>). This is illustrated in Figure 1 showing how the light intensity (y-axis; also referred to as ‘flux density<\/a>‘) and the colour of the light (wave length) vary for objects with different temperatures (here represented by different curves). The yellow curve in the figure represents the solar surface and the light blue curve the earth.<\/p>\n

(ii) The planetary energy balance<\/strong>
\nThe planetary energy balance says that our planet loses heat at the same rate as it receives energy from the sun (otherwise it would heat or cool over time). This is because energy cannot just be created or destroyed (unless it involves nuclear reactions or takes place on quantum physics scales). <\/p>\n

The planets’ distance from the sun and the brightness of its surface dictates how much energy it receives from the sun, as the light gets dimmer when it spreads out in space, as described by Gauss’ theorem<\/a>. <\/p>\n

\"\"<\/a>
Figure 2. A schematic of the solar system, where the energy received by the earth is the sunlight intercepted by its cross-section, and where the heat loss on average is due to thermal emission from the whole surface area of the planet. As the sunlight travels away from the sun, it spreads out over larger space and gets dimmer.<\/em><\/figcaption><\/figure>\n

The energy flowing from the sun is intercepted by the earth with energy density described by the ‘solar constant<\/a>‘ (S0<\/sub>=1366W\/m2<\/sup><\/em>), and the amount of energy intercepted is the product between this flux density and the earth’s disc (minus the reflected light due to the planet’s albedo: A ~0.3<\/em>). The average heat loss is given by the product of earth’s surface and its black body radiation<\/a>: <\/p>\n

S0<\/sub>\/4 (1-A) = \u03c3T4<\/sup><\/em>, <\/p>\n

where \u03c3=5.67 x 10-8<\/sup>W\/(m2<\/sup> K4<\/sup>)<\/em> is the Stefan-Boltzman constant<\/a>. This gives a value of 255K, known as the emission temperature<\/a>. <\/p>\n

Figure 3 shows a comparison between observed surface temperature and calculated emission temperature for the planets in the solar system, based on the balance between energy from the sun and heat loss due to black body emission. In these simple calculations, the greenhouse effect is neglected, and the black body radiation can be derived from Planck’s law. The calculations agree quite well with the observations for most of the objects in our solar system, except for Venus<\/a> which is known to harbour a strong GHE and has a hotter surface than Mercury despite being about twice as far away from the sun.<\/p>\n

\"\"<\/a>
Figure 3. Comparison between calculated emission temperature and the observed surface temperatures for planets and moons in our solar system. The calculations estimate the reduction in the energy flux density with distance away from the sun (Gauss' theorem<\/a>) and the black body radiation<\/a> describing the rate of planetary heat loss. Here, the greenhouse effect has been neglected in the calculations, but the GHE does affect the observed surface temperatures. Venus is a bright planet (high albedo) with a thick atmosphere mostly made up of CO2<\/sub>, which explains higher surface temperature than inferred from a pure energy balance (PDF-version<\/a> and R-script<\/a> generating the figure).<\/em><\/figcaption><\/figure>\n

(iii) Light absorption<\/strong>
\nIt is also clear that our planet is largely heated at the surface because the light from the sun \u2013 which is visible for our eyes \u2013 penetrates the atmosphere without much absorption (hence we can see the sun from the ground). However, the atmosphere is a medium of gas and particles that can absorb and scatter light, depending on their wavelength (hence explain why the sky is blue and sunsets orange<\/a>).<\/p>\n

The distance light travels before being absorbed \u2013 optical depth<\/a> \u2013 can vary with the light’s wavelength and the medium through which is travels. The optical depth in our atmosphere is different for visible and infra-red light.<\/p>\n

Infra-red light is absorbed by molecules, which in turn get more energetic, and the excited molecules will eventually re-emit more infra-red light in any random direction or transfer excess energy to other molecules through collisions. In a optically thick (opaque) atmosphere, there will be a cascade of absorption and re-emission. <\/p>\n

Hence, whereas the planet is heated at the surface, it’s main heat loss takes place from a height about 5.5 km above the ground<\/a>, where most of the radiation is free to escape out to space. The optical depth dictates how deep into the planet’s atmosphere the origin is for most of the planet’s infra-red light (the main planetary heat loss) that can be seen from space. Furthermore, it is the temperature at this level that dictates the magnitude of the heat loss (Planck’s law), and the vertical temperature change (lapse rate) is of course necessary for a GHE. The temperature at this level is the emission temperature, not to be confused by the surface temperature. <\/p>\n

We know that the optical depth is affected by CO2<\/sub> \u2013 in fact, this fact is the basis for measuring CO2<\/sub> concentrations with infra-red gas analysers<\/a>. Molecules composed of three or more atoms tend to act as greenhouse gases because they can possess energy in terms of rotation and vibrations which can be associated with the energy of photons at the infra-red range. This can be explained by theory<\/a> and be demonstrated in lab experiments<\/a>. Other effects are present too, such as pressure and Doppler broadening<\/a>, however, these are secondary effects in this story.<\/p>\n

(iv) The relationship between temperature and altitude<\/strong>
\nThere is a well-known relationship between temperature and height in the troposphere, known as the ‘lapse rate<\/a>‘ (the temperature decreases with height at a rate -6K\/km). The relationship between temperature and altitude can also be seen in the standard atmosphere<\/a>. The lapse rate can be derived from theory for any atmosphere that is the hydrostatically<\/a> stable condition with maximum vertical temperature gradient, but it is also well-known within meteorology. Thus, given the height and value of the emission temperature, we can get a simple estimate for the surface temperature: 255K + 5.5km * 6K\/km = 288K<\/em> (=15o<\/sup>C; close to the global mean estimated from observations given by NCDC<\/a> of ~14o<\/sup>C).<\/p>\n

Enhanced greenhouse effect<\/strong>
\nThe term known as the ‘enhanced greenhouse effect’ describes a situation where the atmosphere’s becomes less transparent to infra-red light (reduced<\/del>increased optical depth), and that the heat loss must take place at higher levels. Moreover, an observer in space cannot see the infra-red light from as deep levels as before because the atmosphere has become more opaque. <\/p>\n

\"\"<\/a>
Figure 4. A simple schematic showing how the planet is heated at the surface, how the temperature (blue) decreases with height according to the lapse rate, and how infra-red light (wiggly arrows) is absorbed and re-emitted at various stages on its way up through the atmosphere. Energy is also transferred through vertical motion (convection), evaporation, and condensation too (latent heat), but that doesn't affect this picture, as they all act to restore the vertical structure toward the hydrostatically stable lapse rate in the long run. At the top of the atmosphere, the infra-red light escapes freely out to space, and this is where the planet's main heat loss takes place. This level is determined by the optical depth, and the heat loss depends on the temperature here. (click on figure for animation)<\/em><\/figcaption><\/figure>\n

The effect of heightened level of heat loss on the surface temperature is illustrated in Figure 4, where the emission temperature and lapse rate are given if we assume an energy balance and a hydrostatically stable<\/a> atmosphere on average (a generally hydrostatically unstable atmosphere would be bad news).<\/p>\n

Hence, a reduced<\/del>increased optical depth explains why atmospheres are not easily ‘saturated<\/a>‘ and why planets such as Venus have surface temperatures that are substantially higher<\/a> than the emission temperature. Planets with a thin atmosphere and insignificant greenhouse effect, on the other hand, have a surface temperature that is close the<\/del>to the estimates from the planetary energy balance model (Figure 3).<\/p>\n

Feedback processes<\/strong>
\nThe way the atmosphere reacts to changes in the optical depth is more complicated, due to a number of different feedback mechanisms taking place. But to get a simple overview, it is useful to keep in mind that the optical depth is sensitive to how much water vapour (humidity) there is in the air, and that the lapse rate is sensitive to the composition of the atmosphere (i.e. humidity). Furthermore, the albedo A<\/em> is affected by clouds, snow, ice, and vegetation, all of which affect the way the earth receives energy from the sun. <\/p>\n

In our simple picture, feedback processes affect changes in the height of the level where most heat loss takes place, the slope of the lapse rate, and heating at the surface (and hence the emission temperature).<\/p>\n

So why is the upper atmosphere cooled then?<\/strong>
\nThe upper atmosphere, comprising the stratosphere and mesosphere, is expected to cool during an AGW, as shown by the GCMs. So what is happening there? This is when the picture becomes more complicated.<\/p>\n

Since CO2<\/sub> mostly absorbs\/re-emits infra-red light at around 14 microns, an increased concentration in the troposphere will reduce the upward infra-red radiation at this band. The total energy is roughly constant, but it is made up from increased emissions at other bands because it’s warmer. There is less absorption by CO2<\/sub> of upwelling infra-red light above the troposphere, but increased emission as a function of increased concentrations. Thus there is a cooling.<\/p>\n

Controversy?<\/strong>
\nCan this picture be falsified, e.g. if other factors were to play a role too? For instance, can this situation be altered by changes in the sun? <\/p>\n

Changes in the sun can of course affect the amount of energy received by the earth through changes in its output, variations in the intensity of UV-light, or perhaps even clouds through galactic cosmic rays. But it’s hard to see any systematic long-term trend in the level of solar activity over the last 50<\/a> years, and it is difficult to see how solar activity may have an effect while other factors, such as GHGs, don’t. Gavin and I recently published a study<\/a> on the response to both solar activity and GHGs, and found similar magnitude for both forcings in both observations and the GISS GCM. <\/p>\n

There have been claims of negative feedbacks, such as the “iris effect<\/a>“. One would expect negative feedbacks in general to dampen the response to most forcings, unless they involve a particular process that is active for a particular forcing. In other word, why would a negative feedback act for GHGs but not for solar forcing? Many feedbacks, such as changes in atmospheric moisture, cloudiness, and atmospheric circulation should be similar for most forcings. <\/p>\n

Another question is why we do see a global warming trend if the negative feedbacks were most important (Figure 5). Negative feedbacks usually imply quiet conditions in a complex system, whereas positive feedbacks tend to lead to instabilities, often manifested as internal and spontaneous oscillations (see Figure 5). It is reasonable to expect the feedback processes to affect natural variations as well as forced changes such as an enhanced GHE, orbital changes, volcanoes, or changes in the sun.<\/p>\n

\"\"<\/a>
Figure 5. Estimates of the global and annual mean temperature based on a number of different data sets, including both traditional analyses as well as re-analyses<\/a> (also see the last 15 years<\/a>).<\/em><\/figcaption><\/figure>\n

The point about negative feedback also brings up another interesting issue: Negative feedbacks usually act to restore a system to a particular zero-level state<\/em>. What would the zero-state be for our climate? No greenhouse effect or some preferred level of greenhouse warming? There is already a natural GHE that, together with other atmospheric effects, can account for about 32o<\/sup>C higher global mean surface temperature. What makes this state so special, and can we explain the present natural GHE in the presence of negative feedbacks (consider starting from a state with no GHE)? <\/p>\n

Hence, claims of negative feedback is controversial because all these tough questions then need to be addressed. We can write down a simple recipe for the GHE, but it is indeed challenging to reconcile a presence of a negative feedback with our observations, or explain the current observed global warming in any other terms.<\/p>\n\n<\/div> ","protected":false},"excerpt":{"rendered":"

According to some recent reports (e.g. PlanetArk; The Guardian), the public concern about global warming may be declining. It’s not clear whether this is actually true: a poll conducted by researchers at Stanford suggests otherwise. In any case, the science behind climate change has not changed (also see America’s Climate Choices), but there certainly remains […]<\/p>\n","protected":false},"author":11,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[1],"tags":[],"class_list":{"0":"post-3984","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-climate-science","7":"entry"},"aioseo_notices":[],"post_mailing_queue_ids":[],"_links":{"self":[{"href":"https:\/\/www.realclimate.org\/index.php\/wp-json\/wp\/v2\/posts\/3984","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.realclimate.org\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.realclimate.org\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.realclimate.org\/index.php\/wp-json\/wp\/v2\/users\/11"}],"replies":[{"embeddable":true,"href":"https:\/\/www.realclimate.org\/index.php\/wp-json\/wp\/v2\/comments?post=3984"}],"version-history":[{"count":193,"href":"https:\/\/www.realclimate.org\/index.php\/wp-json\/wp\/v2\/posts\/3984\/revisions"}],"predecessor-version":[{"id":4428,"href":"https:\/\/www.realclimate.org\/index.php\/wp-json\/wp\/v2\/posts\/3984\/revisions\/4428"}],"wp:attachment":[{"href":"https:\/\/www.realclimate.org\/index.php\/wp-json\/wp\/v2\/media?parent=3984"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.realclimate.org\/index.php\/wp-json\/wp\/v2\/categories?post=3984"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.realclimate.org\/index.php\/wp-json\/wp\/v2\/tags?post=3984"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}