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<h2>Climate modeling</h2>
<p>So far in 12.340x, we have covered much of the basic physics and chemistry of the Earth's climate system. Climate scientists use these foundations to understand how our planet's climate has changed in the past, and how it will change in the future. However, as you now know, the climate system is extremely complex, and while its individual components can be understood with simple mathematical models, its evolution as a whole cannot be predicted analytically. As such, numerical climate models are an important tool used by scientists to advance our understanding of the Earth's climate system, and the ways in which it may change or evolve over time.</p>
<p>In this final segment of the course, we will discuss <b>General Circulation Models (GCMs)</b>, used frequently by scientists to model the Earth's climate.</p>
<p><i>Instructor: Kerry Emanuel</i></p>
<h2>Module outline</h2>
<p>In this module, we will give a broad overview of GCMs. Specifically, the module will address the following questions:</p>
<ul>
<li>What equations do climate models solve?</li>
<li>How do climate models solve these equations?</li>
<li>What are the constraints on the numerical methods used in models?</li>
<li>How has the state of climate modeling evolved over time?</li>
<li>What components of the climate system are simulated in a climate model?</li>
<li>What are the capabilities and limitations of today's models?</li>
<li>How do we evaluate the performance of climate models?</li>
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<h2>Final exam</h2>
<p>There is no problem set for this week's material (although it may be tested on the final exam). In place of the problem set, we suggest that you take this light week to review content across the other weeks of the course in preparation for the final.</p>
<p>The final exam will be offered from May 17, 2020 at 12:00 UTC to May 22, 2020 at 12:00 UTC, and is designed to take 3 hours. It will be accessible via the navigation pane on the left during that time.</p>
<h2>Exit survey</h2>
<p>Don't forget to take the <b>important exit survey</b>, which is accessible via the navigation pane to the left.</p>
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<h2 class="hd hd-2 unit-title">Equations of climate models</h2>
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Time derivatives in fixed and moving reference frames
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<p>Consider measurements of the temperature as a function of time taken in the following situations:
<ol><li>Measurements taken aboard a hot-air balloon as it floats above a lake.</li><li>Measurements taken by instruments on board an aeroplane as it flies in the stratosphere.</li><li>An ocean buoy taking measurements during the passage of a tropical cyclone.</li><li>Measurements taken by a weather balloon rising through the atmosphere.</li></ol>
In which situation would the time derivative of the measured time series be a good approximation of the time derivative of temperature in a frame of reference <i>following the flow</i>? This is also known as the <it>Lagrangian</it> derivative.</p>
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Vertical coordinate systems in climate models
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<p>Many climate models use a "sigma" vertical coordinate in which the model levels are placed at dicrete values of the variable,
[mathjax]
\sigma = p/p_s.
[/mathjax]
Here [mathjaxinline]p[/mathjaxinline] is the pressure, and [mathjaxinline]p_s[/mathjaxinline] is the value of the pressure at the surface.</p>
<p>Which of the following is an advantage of using a "sigma" vertical coordinate in a climate model?</p>
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<text>The computation of the pressure gradient is simplified.</text>
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<text>Higher accuracy can be acheived with a small number of vertical levels.</text>
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<text>The model levels never intersect the ground.</text>
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<text>It reduces model errors.</text>
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The Courant-Friedrichs-Lewy (CFL) condition
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<p>Suppose we would like to model a flow with typical velocities of up to 10 m/s. This flow includes many types of waves, the fastest of which are long-wavelength gravity waves, whose phase speed may be up to 40 m/s. If we use a model with a grid spacing of 1 km, which of the following is a possible time step with which we would be able to successfully simulate the flow?</p>
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Remember, simulations may become unstable if they violate the "CFL condition" as described in the video.
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<text>Climate models use more powerful computers than weather forecast models. The Japanese Earth Simulator was the fastest super computer in the world between 2002 and 2004.</text>
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<text>Climate models include more processes than weather forecast models. In particular, the coupling of an atmospheric model to an ocean model allows for the prediction of weather much farther ahead.</text>
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<text>When we examine climate models we consider different statistics -- such as the global temperature averaged over a sufficiently long time periods -- to the variables typically predicted by weather forecast models -- e.g., whether it will rain in the town of Cairns tomorrow. </text>
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<h3 class="hd hd-3 problem-header" id="Which_processes_do_we_parameterize_-problem-title" aria-describedby="block-v1:MITx+12.340x+1T2020+type@problem+block@Which_processes_do_we_parameterize_-problem-progress" tabindex="-1">
Which processes do we parameterize?
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<p> Which one of the following processes must be parameterized in a climate model?</p>
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<text>convective clouds</text>
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<text>cloud-radiative interactions</text>
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<text>surface fluxes of sensible and latent heat</text>
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<text>cloud-aerosol interactions</text>
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<text>all of the above</text>
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<p>Many of the figures from this video come from <a href="http://www.climatechange2013.org/images/report/WG1AR5_Chapter09_FINAL.pdf" target="_blank">Chapter 9</a> of the IPCC 5th Assessment Report. We encourage you to read through this chapter for more information on the performance of climate models in reproducing different aspects of the Earth's climate. In particular, section 9.1 provides a nice overview of the different model components in the type of climate models used in IPCC assessments.</p>
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Uncertainty in future global temperature changes
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<p>Consider the following sources of uncertainty in model projections of future global mean surface temperature:
<ol><li>Internal variability</li><li>Model error and differences between models</li><li>Uncertainty in the emissions of greenhouse gases and other forcing agents by humans</li></ol>
Which of these sources of uncertainty is most important for projections of the global mean surface temperature 10 years into the future? Which is most important for predicting the global mean temperature one century into the future?
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<text>Internal variability is most important for both timescales.</text>
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<text>Model error is most important for both timescales.</text>
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<text>Internal variability is most important for short term predictions, but the other sources become dominant for predictions a century ahead.</text>
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<text>All sources of uncertainty are roughly equally important at all timescales.</text>
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