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<h2 class="hd hd-2 unit-title">Instrumental record and atmospheric composition</h2>
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<h2>The instrumental record of Earth's climate and the composition of the atmosphere</h2>
<p>In this section we will discuss the temperature of the Earth over the period for which instrumental observations exist. We will seek to understand the spatial and seasonal patterns of temperature, as well as longer term trends that have been observed. We will also discuss the composition of the atmosphere, and how it may have changed in time. With a particular focus on gases that interact with terrestrial radiation strongly - the greenhouse gases.</p>
<p><i>Instructors: Kerry Emanuel and Dan Cziczo</i></p>
<h2>Module outline</h2>
<p>This module is broadly in two parts. First we shall focus on the spatial and seasonal patterns of temperature over the globe, and how they may have changed over the period of time for which we have thermometer measurements. We will then discuss the composition of the atmosphere, and temporal evolution of greenhouse gases over roughly the same period. We will briefly recap some of our previous discussion on planetary energy balance and the greenhouse effect in between the two, to get us thinking about the possible connections between the temperature of the Earth and its atmospheric composition. The module discusses:</p>
<ul>
<li>The history of <b>global temperature</b> and <b>atmospheric composition</b> over the instrumental period</li>
<li>The <b>spatial patterns</b> of temperature change that have occurred</li>
<li>Changes to the <b>ocean</b> and <b>cryosphere</b> over the instrumental period</li>
<li>A recap of <b>planetary energy balance</b> and <b>the greenhouse effect</b></li>
<li>Different <b>forcing agents</b> in the atmosphere and how they have changed with time and <b>the greenhouse effect</b></li>
</ul>
<h2>Background reading</h2>
<p>Changes to the atmospheric composition and temperature are discussed in sections 2.2 and 2.4 of <a href="http://www.climatechange2013.org/images/uploads/WGIAR5_WGI-12Doc2b_FinalDraft_Chapter02.pdf" target="_blank">chapter 2</a> of the <a href="http://www.ipcc.ch/report/ar5/wg1/" target="_blank">IPCC 5th Assessment report</a>. Students interested in other aspects of observed changes to the climate system may also which to read other sections of chapter 2, or sections of chapter 3 and 4 which discuss ocean and cryosphere observations respectively.</p>
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The utility of satellites
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<p>Satellites are useful for monitoring global temperature change because:</p>
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<text>They can probe multiple levels in the atmosphere and give a sense of the vertical profile of temperature.</text>
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<text>They have much greater spatial coverage of the globe than direct thermometer measurements.</text>
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<text>They can easily look over both land and oceanic areas.</text>
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<text>All of the above.</text>
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<h3 class="hd hd-3 problem-header" id="Impacts_of_changes_to_the_mean_and_standard-deviation_of_temperature-problem-title" aria-describedby="block-v1:MITx+12.340x+1T2020+type@problem+block@Impacts_of_changes_to_the_mean_and_standard-deviation_of_temperature-problem-progress" tabindex="-1">
Impacts of changes to the mean and standard-deviation of temperature
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<p>The temperature in Cape Town, South Africa, rarely gets below freezing, even in the winter months. Which of the following changes to the temperature distribution at Cape Town would cause the largest increase in the number of days with minimums below freezing?</p>
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<text>An increase in the mean and decrease in the variance.</text>
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<text>A decrease in the mean and and increase in the variance.</text>
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<input type="radio" name="input_Impacts_of_changes_to_the_mean_and_standard-deviation_of_temperature_2_1" id="input_Impacts_of_changes_to_the_mean_and_standard-deviation_of_temperature_2_1_choice_hotwater" class="field-input input-radio" value="choice_hotwater"/><label id="Impacts_of_changes_to_the_mean_and_standard-deviation_of_temperature_2_1-choice_hotwater-label" for="input_Impacts_of_changes_to_the_mean_and_standard-deviation_of_temperature_2_1_choice_hotwater" class="response-label field-label label-inline" aria-describedby="status_Impacts_of_changes_to_the_mean_and_standard-deviation_of_temperature_2_1">
<text>A decrease in the mean and a decrease in the variance.</text>
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<text>An increase in the mean and an increase in the variance.</text>
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Ocean acidification
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<p>What is responsible for the downward trend in ocean pH over the late 20th century?</p>
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<text>The upper ocean is warming, driving the ocean to become more acidic.</text>
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<text>The increasing atmospheric concentration of carbon dioxide is driving an increase in the concentration of dissolved carbon dioxide in the ocean, thus increasing its acidity.</text>
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<text>Marine organisms are changing their photosynthesis and respiration patterns, changing the acidity of the ocean.</text>
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<text>A warmer upper ocean is encouraging upwelling of deep acidic ocean waters.</text>
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Albedo and surface temperature
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<p>In the above video, we once again discussed the importance of energy balance in setting the planet's temperature. At the end of the video, it was pointed out that, given its albedo, the surface temperature of Venus should be lower than that of Earth, according to the 'bare-rock model'. In reality, the surface temperature of Venus is close to 700 K! What is a possible explanation for this discrepancy?</p>
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<text>Venus is closer to the sun.</text>
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<text>Venus has a very thick carbon dioxide atmosphere.</text>
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<text>Venus has a very thick Nitrogen atmosphere.</text>
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The thick atmosphere of Venus
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<p>The reason Venus has such a high surface temperature despite its high albedo is its thick greenhouse atmosphere. The one-layer model of the atmosphere introduced here only increased Venus' surface temperature to near 300 K, not nearly close to the actual surface temperature of Venus of 700 K. But we can add multiple atmospheric layers to mimic a very thick atmosphere to the one layer model. Using the <a href="/courses/course-v1:MITx+12.340x+1T2020/courseware/Resources/Resources:Nlayer/">multi-layer radiative model</a> in the resources section, and reproduced below, find how many atmospheric layers are required to increase the surface temperature of Venus to 700 K. You may assume the Solar constant at the distance from the sun of Venus is 2600 W m[mathjaxinline]^{-2}[/mathjaxinline], and the albedo of Venus is 0.7.</p>
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<text>2</text>
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<text>3</text>
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<text>4</text>
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<input type="radio" name="input_The_thick_atmosphere_of_Venus_2_1" id="input_The_thick_atmosphere_of_Venus_2_1_choice_emit" class="field-input input-radio" value="choice_emit"/><label id="The_thick_atmosphere_of_Venus_2_1-choice_emit-label" for="input_The_thick_atmosphere_of_Venus_2_1_choice_emit" class="response-label field-label label-inline" aria-describedby="status_The_thick_atmosphere_of_Venus_2_1">
<text>5</text>
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<text>6</text>
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<text>&gt;6</text>
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<h3 class="hd hd-3 problem-header" id="The_lifetime_of_gases_in_the_atmosphere-problem-title" aria-describedby="block-v1:MITx+12.340x+1T2020+type@problem+block@The_lifetime_of_gases_in_the_atmosphere-problem-progress" tabindex="-1">
The lifetime of gases in the atmosphere
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<p>A gas has an abundance in the atmosphere of 100 gigatonnes. Its rate of emission is 200 megatonnes per year. What is its lifetime?</p>
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<text>2 years</text>
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<text>half a year</text>
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<text>5000 years</text>
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Global warming potential
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<p>Consider two greenhouse gases A and B. Emitting 1 gigatonne of gas A causes an instantaneous radiative forcing of 5 W m<sup>-2</sup>, while emitting 1 gigatonne of gas B causes an instantaneous radiative forcing of only 0.5 W m<sup>-2</sup>. However, gas B has an atmospheric lifetime of 100 years, while gas A has a lifetime of only 5 years. Which gas has the higher global warming potential over a 100 year time frame? What about over a 20 year time frame? You may assume that each greenhouse gas stays in the atmosphere for its entire lifetime without any depletion, whereupon the concentration is instantaneously reduced to zero.
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<text>A over 20 years, B over 100 years.</text>
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<text>A in both cases.</text>
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<text>B in both cases.</text>
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<h2 class="hd hd-2 unit-title">Problem Set: Instrumental record</h2>
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<h2>Problem Set: Instrumental record</h2>
<p>This problem set is aimed at testing your understanding of the material presented in the videos of this sequence. By now you should have some familiarity with the seasonal and spatial patterns of temperature over the globe, and how they have changed over the instrumental period. You should also have some knowledge of the main long-lived greenhouse gases in the atmosphere, and how their concentration has been changing. Additionally, by now you should have a good understanding of planetary energy balance and the one-layer greenhouse model. This model was covered in the Climate Physics module as well as this module.</p>
<p>This problem set contains three problems, each of which has multiple parts. Problems may ask you to choose the correct answer between a list of alternatives, or may ask you to enter an answer in directly. Be sure to follow the instructions for each problem carefully to ensure you receive full credit for your responses.</p>
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<h2 class="hd hd-2 unit-title">Problem 1: Estimating the Mean Temperature</h2>
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<h2>Estimating the Mean Temperature</h2><p>Estimating the mean temperature of the Earth from thermometer measurements must take into account the point nature of observations, as well as the inherent error associated with thermometers. In this problem, we will investigate the error characteristics of averaging many measurements, each of which is uncertain.</p>
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1a
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<p>Consider the region pictured, with thermometers placed at
the locations given:</p>
<img src="/assets/courseware/v1/82773dac0d5e29ba7575aa7870963de2/asset-v1:MITx+12.340x+1T2020+type@asset+block/images_Psets_obsnetwork_cartoon.png" width="560" height="420"/>
<p>Suppose we know the temperature of the region is
10[mathjaxinline]^{\circ}[/mathjaxinline]C everywhere. If the
thermometers were all perfect, they would all read
10[mathjaxinline]^{\circ}[/mathjaxinline]C exactly. However,
the actual readings of the thermometers are:</p>
<table style="width:30%;">
<tr>
<th>Thermometer #</th>
<th>Reading ([mathjaxinline]^\circ[/mathjaxinline]C)</th>
</tr>
<tr>
<td>1</td>
<td>9.0</td>
</tr>
<tr>
<td>5</td>
<td>9.8</td>
</tr>
<tr>
<td>10</td>
<td>10.1</td>
</tr>
</table>
<p>One estimate for the average temperature of the region is
the arithmetic mean of these thermometers. Estimate the
temperature of the region by taking the arithmetic mean of
the three measurements.</p>
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1b
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<html>
<p>Suppose we now have access to more thermometers.</p>
<table style="width:30%;">
<tr>
<th>Thermometer #</th>
<th>Reading ([mathjaxinline]^\circ[/mathjaxinline]C)</th>
</tr>
<tr>
<td>1</td>
<td>9.0</td>
</tr>
<tr>
<td>2</td>
<td>10.9</td>
</tr>
<tr>
<td>3</td>
<td>9.4</td>
</tr>
<tr>
<td>4</td>
<td>10.9</td>
</tr>
<tr>
<td>5</td>
<td>9.8</td>
</tr>
<tr>
<td>6</td>
<td>9.9</td>
</tr>
<tr>
<td>7</td>
<td>10.6</td>
</tr>
<tr>
<td>8</td>
<td>9.1</td>
</tr>
<tr>
<td>9</td>
<td>9.3</td>
</tr>
<tr>
<td>10</td>
<td>10.1</td>
</tr>
<tr>
<td>11</td>
<td>9.7</td>
</tr>
<tr>
<td>12</td>
<td>9.6</td>
</tr>
<tr>
<td>13</td>
<td>9.2</td>
</tr>
<tr>
<td>14</td>
<td>10.7</td>
</tr>
<tr>
<td>15</td>
<td>11.0</td>
</tr>
<tr>
<td>16</td>
<td>11.5</td>
</tr>
<tr>
<td>17</td>
<td>9.8</td>
</tr>
<tr>
<td>18</td>
<td>8.9</td>
</tr>
<tr>
<td>19</td>
<td>11.2</td>
</tr>
<tr>
<td>20</td>
<td>10.0</td>
</tr>
</table>
<p>Calculate the temperature of the region using the arithmetic mean of the first eight thermometers.</p>
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<p>Now use <u>all</u> the thermometers to calculate an estimate of the mean temperature of the region.</p>
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1d
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Should you expect your estimate to get closer to the true value (10[mathjaxinline]^\circ[/mathjaxinline]C) as you add more measurements?
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<html><p>It can be shown that the expected error in an estimate of the mean temperature of our region based on a number of point measurements is given by</p>
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\textrm{Error} = \frac{\varepsilon}{\sqrt{N}},
[/mathjax]
<p>where [mathjaxinline]N[/mathjaxinline] is the number of thermometers and [mathjaxinline]\epsilon[/mathjaxinline] is the average error in a single measurement.</p>
<p>Estimate the number of thermometers required to find the temperature of the region accurate to 0.01[mathjaxinline]^\circ[/mathjaxinline]C, assuming the average error in a single thermometer measurement is 0.5[mathjaxinline]^\circ[/mathjaxinline]C.</p>
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1f
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<h2 class="hd hd-2 unit-title">Problem 2: Sea level change</h2>
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<h2>Sea level change</h2><p>Sea level may change as a result of global warming directly through expansion of sea water as it warms, as well as through addition of water through melting of land ice.</p><p>The following table shows the density ([mathjaxinline]\rho[/mathjaxinline]) of sea water as a function of temperature.</p><table style="width:30%;"><tr><th>[mathjaxinline]T[/mathjaxinline] ([mathjaxinline]^\circ[/mathjaxinline]C)</th><th>[mathjaxinline]\rho[/mathjaxinline] (kg/m[mathjaxinline]^3[/mathjaxinline])</th></tr><tr><td>0</td><td>1031.364</td></tr><tr><td>2</td><td>1031.205</td></tr><tr><td>4</td><td>1030.997</td></tr><tr><td>6</td><td>1030.763</td></tr><tr><td>8</td><td>1030.445</td></tr><tr><td>10</td><td>1030.106</td></tr></table>
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2a
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<p>If 1 kg of seawater is warmed from 4[mathjaxinline]^\circ[/mathjaxinline]C to 8[mathjaxinline]^\circ[/mathjaxinline]C, by what percentage will its volume increase? Please <b>do not</b> include a percentage ("%") sign in your solution.</p>
<p><i>Hint:</i> Remember [mathjaxinline]\rho=\frac{m}{V}[/mathjaxinline], where [mathjaxinline]\rho[/mathjaxinline] is density, [mathjaxinline]m[/mathjaxinline] is mass, and [mathjaxinline]V[/mathjaxinline] is volume.</p>
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<p>Assuming the ocean depth is on average 4 km, use your previous answer to estimate the global sea-level rise (in meters) for a 4[mathjaxinline]^\circ[/mathjaxinline]C change in ocean temperature.</p>
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What is one possible reason that the estimate in part (b) is <u>larger</u> than the 0.5 - 1 m sea level rise predicted by the end of the 21st century for a similar increase in Earth's surface temperature?
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<text>The part (b) estimate does not consider ice melt</text>
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<text>The ocean may not warm 4[mathjaxinline]^\circ[/mathjaxinline]C through its entire depth</text>
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<text>The ocean only covers 70% of the globe</text>
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2d
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<p>The total amount of ice in the Greenland ice sheet is estimated to be 2.85 million cubic km.</p>
<p>Assume the Earth's surface is 70% covered by ocean, and that the Earth's radius is 6300 km. How many meters would sea level rise if the entire Greenland ice sheet were to melt?</p>
<p>(You may further assume that the density of ice is 916.9 kg/m[mathjaxinline]^3[/mathjaxinline], and that once melted it attains the density of fresh water at 0[mathjaxinline]^\circ[/mathjaxinline]C, 1000 kg/m[mathjaxinline]^3[/mathjaxinline].)</p>
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2e
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<p>In the last glacial maximum (LGM) 15000 years ago, sea level was believed to be nearly 100 m lower than today. The global temperature was believed to be between 5[mathjaxinline]^\circ[/mathjaxinline]C and 10[mathjaxinline]^\circ[/mathjaxinline]C cooler, and there were vast ice sheets over the North American and Eurasian continents.</p>
<p>Based on your previous answers, which components of sea level rise contributed most to the rise in sea level between the LGM and the present?</p>
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<text>Thermal expansion</text>
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<text>Ice melt</text>
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<text>They both contributed roughly equally</text>
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<h2 class="hd hd-2 unit-title">Problem 3: The Montreal protocol and CFCs</h2>
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<h2>The Montreal protocol and CFCs</h2><p>The Montreal protocol was an international agreement to limit the production of gases that deplete the ozone layer, signed in 1987. An important class of ozone depleting gases are Chlorofluorocarbons, or CFCs. As well as their ability to destroy ozone in the stratosphere, they are very strong greenhouse gases. In this problem we explore some of the properties of the most common CFCs.
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3a
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<p>Consider a simple model for the evolution of the concentration of a certain gas in the atmosphere,
[mathjax]
\frac{dC}{dt} = E - \frac{C}{\tau},
[/mathjax]
where [mathjaxinline]C[/mathjaxinline] is the concentration of the gas [Tg], [mathjaxinline]E[/mathjaxinline] is the emission rate [Tg/yr], and [mathjaxinline]t[/mathjaxinline] is time [yr]. The time-scale [mathjaxinline]\tau[/mathjaxinline] [yr] represents the lifetime of the gas in the atmosphere, before it is removed, either by chemical reactions or deposition to the surface.
</p>
<p>
The common CFC Trichlorofluoromethane (CCl<sub>3</sub>F), also known as CFC-11, has an atmospheric lifetime of approximately 55 years. Suppose that all emission of CFC-11 ceased on January 1, 1988, a few months after the signing of the Montreal Protocol. Using the simple equation given above, find what year the concentration of CFC-11 would be reduced to one-fifth of its concentration at the beginning of 1988.
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3b
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<p>Another important CFC is Dichlorodifluoromethane (CCl<sub>2</sub>F<sub>2</sub>), or CFC-12. This gas has a longer life-time of 140 years in the atmosphere. Assuming the emission of this gas is also reduced to zero at the beginning of 1988, calculate the concentration of CFC-12 as a fraction of its value in 1988 in the year that was the answer to the previous question. That is, find the concentration of CFC-12 when the concentration of CFC-11 is one fifth of its 1988 value.
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3c
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<p>An immediate halt to all emission of CFCs is unrealistic. Even in the case where all production of CFCs stopped immediately, the emissions, coming from old appliances slowly leaking into the atmosphere, would continue for some decades. Suppose instead that the Montreal Protocol enforced an immediate halving of CFC emissions in 1988 until the year 2018, whereupon emissions were required to be halved again.
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Using the same model as in the previous question, by what fraction would the concentration of CFC-11 be reduced in 2018?
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3d
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<p>CFC-11 and CFC-12 are very potent greenhouse gases. Suppose the emission of 1 Tg of CFC-11 causes a 1.0 W m<sup>-2</sup> instantaneous perturbation in the radiation budget. The emission of the 1 Tg of CFC-12 causes a 1.5 W m<sup>-2</sup> radiative forcing. </p>
<p>The 100 year global warming potential for CFC-11 is estimated to be 4750. Global warming potential is a measure of how much energy would be trapped by the emission of one molecule of a given gas over a specified time period, in this case 100 years, relative to CO<sub>2</sub>. Global warming potential depends on both the atmospheric lifetime of a gas, as well as its ability to absorb infra-red radiation. </p>
<p>
Use the information on the lifetimes and relative radiative forcing strengths of CFC-11 and CFC-12, as well as the global warming potential of CFC-11 to estimate the global warming potential of CFC-12. You may assume that the radiative forcing of each species is simply proportional to its concentration.</p>
<p><i>Hint:</i> Use the model from part (a) to calculate the total energy absorbed by the instantaneous injection of 1 Tg of each CFC into the atmosphere over 100 years. The ratio of these two energies is the ratio of the global warming potentials.
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3e
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<p>The global warming potential for CFC-12 is more than twice that of CFC-11, but the instantaneous radiative impact of CFC12 is only 1.5 times that of CFC-11. What factor accounts for this discrepancy?
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<text>The emissions of CFC-12 are larger than those of CFC-11</text>
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