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EdGCM Workshop Guide |
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Education -
General
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Written by Mark Chandler and Ana Marti
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Monday, 06 March 2006 |
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Page 4 of 5
The NASA/GISS Global Climate Model
The climate model used by the EdGCM software was developed at NASA’s Goddard Institute for Space Studies (NASA/GISS). This type of 3-dimensional computer model is known as a grid-point Global Climate Model (GCM). A grid point GCM divides the atmosphere into a series of discrete grid cells. EdGCM’s model grid has 7776 grid cells in the atmosphere, with each horizontal column corresponding to 8° latitude by 10° longitude and containing 9 vertical layers. The computer model numerically solves fundamental physical equations, which describe the conservation of mass, energy, momentum, and moisture in each cell, while taking into account the transport of quantities between cells. It then uses the Ideal Gas Law to relate pressure to temperature, two of the most important climate variables. Parameterizations, based on empirical data or simplified physical hypotheses, are used to calculate quantities that are not handled by the fundamental equations, or which occur at spatial scales that are finer than the scale of the model’s grid. For example, plants, convective clouds, and river run-off are all parameterized in GCMs (see below for more information about parameterizations).
Global Climate Models Described
At the heart of a GCM is a model of the Earth’s atmosphere. There are five fundamental physical equations that are used to describe the evolving state of the atmosphere: the conservation of mass, conservation of energy, conservation of momentum, conservation of moisture and the ideal gas law (to approximate the equation of state).
 Fundamental physics equations used in the GISS GCM (Hansen et al., 1983)
There are two basic forms of the fundamental equations used to simulate the atmosphere in global climate models. These define two distinct families of models: Cartesian grid point GCMs and spectral GCMs. In a Cartesian grid point model the atmosphere is divided horizontally and vertically into a series of grid cells. The equations are solved for each cell in the grid, while taking into account the transport of various quantities between grid cells. In a spectral model the conservation equations are expressed as continuous functions (made up of a series of sine and cosine curves), which define the global distribution of climate variables such as temperature, pressure, winds, and humidity.
 Source: Henderson-Sellers, 1985, A Climate Modelling Primer
 The GISS GCM uses 3 standard resolutions: 8 x 10, 4 x 5, and 2 x 2.5 (latitude x longitude).
The main components of the atmospheric portion of a GCM are those that represent the atmospheric dynamics and the interactions of the Sun’s radiation with the planet. The dynamics calculations help define the general circulation of the atmosphere as well as smaller-scale eddy circulations, such as the cyclonic storm systems that control much of the weather in the mid-latitudes. The radiation calculations determine the energy balance of the Earth by evaluating the reflection and absorption of solar radiation by the surface and atmosphere, and by the remittance of thermal energy back to space. The radiation calculations in a GCM must take into account cloud thickness and cloud distribution (horizontal and vertical), surface conditions (land vs. ocean, topography, vegetation types, snow and ice cover), and all significant greenhouse gases and aerosols.
 Schematic of the parameterizations in the GISS GCM Model II
While climate models of varying complexity exist, defining simple vs. complex climate models is not necessarily straightforward. That’s because climate models may be considered more complex if they incorporate additional dimensions, increase the spatial or temporal resolution at which calculations are applied, represent the physics more completely, or incorporate parameterizations that describe additional components of the climate system (e.g. oceans, vegetation, ground hydrology, ice sheets, the carbon cycle, etc.). Perhaps the most important of these “additions” to the atmospheric model are the coupling of the atmospheric GCMs to 3-D ocean circulation models.
Ocean General Circulation Models
Global Climate Models have evolved over time to include more and more of the physical and chemical components of the climate system. Many characteristics of the Earth that were supplied as boundary conditions in earlier models can now be simulated in the latest models. Moreover, as new scientific studies advance our understanding of the Earth’s physical environment, climate models incorporate the new findings by altering or adding to existing calculations. Ultimately, this allows climate models to describe the climate system in greater detail and with improved precision.
Probably the most significant change to the traditional structure of global climate models was the advent of models that coupled an atmospheric GCM to a 3-dimensional ocean GCM. 3-D ocean models have been under development for nearly as long as atmospheric models and some of the most important experiments, commanding the most computing resources, have employed coupled ocean-atmosphere GCMs for a decade or more. However, coupled GCMs have only recently become a standard for use in simulating the broad array of climate experiments underway that study everything from climates of the geologic past to the many scenarios that seek to represent the potential states of future climate. Some of the lag in incorporating fully dynamic oceans into global climate models has been due to the added pressure on computational resources that the ocean calculations represent: the ocean’s cover nearly two-thirds of the surface of the Earth; they circulate slowly compared to the atmosphere, requiring longer simulations; on average key features in the ocean (e.g. eddies, western boundary currents, upwelling, and deep water formation) occur at finer scales than analogous atmospheric circulation phenomena (which tend to average 1000’s of kilometers instead of 10’s of kilometers as with the oceans). On the other hand, much of the delay in developing and applying coupled ocean-atmosphere models was simply related to the fact that we knew precious little about the how physical oceans operated. The past two decades has seen an astounding increase in our understanding Earth’s oceans and how they operate over both short and long time scales. It may be that the ultimate reason that coupled oceans models have become a standard component of global climate models is because they have simply reached a point where scientists have much more confidence in the results they produce.
Climate Model Parameterizations
Climate models built for predictive purposes would, ideally, be derived entirely on fundamental laws of nature. For example, the ideal gas law (Table 4-1) makes it possible for a GCM to always determine an exact relationship between temperature (T) and pressure (p), which are two critical variables used in the determination of the energy balance and movement of the atmosphere. However, our knowledge of the exact workings of many of the processes in the climate system is still limited. Furthermore, many of those processes operate on scales too fine for existing computers to simulate. Therefore, models simulate a number of the key components of the climate system by using series of calculations that are derived from statistical or empirical relationships between variables. These types of calculations are called parameterizations and they range from simple one-line equations (for example, an equation that instructs a portion of an ocean grid cell to freeze at a fixed temperature based on a constant salinity) to highly complex sequences of equations that describe cloud processes, vegetation, continental ice sheets, atmospheric chemistry, ground hydrology, and more. In fact, many parameterizations are themselves models that are designed to simulate just one part of the climate system. However, when carefully linked to an atmospheric GCM, an ocean model, and other parameterizations, they make up a virtual Earth Climate System Model. Such models, that couple together atmospheric and oceanic GCMs with complex parameterizations of are increasingly becoming the successors to GCMs.
How do GCMs represent the Earth?
Although the key equations in a global climate model are fundamental laws of nature that presumably apply on all planets, they contain a number of constants that are specific to the Earth. Such values as the radius of the planet, the force of gravity, the mass of the atmosphere, and the R constant used in the ideal gas law, all must be assigned appropriately for a GCM to be representative of the Earth’s climate as opposed to some other spherical body with an atmosphere. However, simply assigning the appropriate constants is not enough. A number of other conditions are required as well:
Boundary Conditions: Every GCM experiment must have assigned at the outset a group of fixed conditions that describe features that effect the climate, but are not altered in return by climate model calculations. These specified features are called the model’s boundary conditions. The most important boundary conditions are the description of the land-ocean distribution and the topography. Next, the land surface cover is usually specified, including the locations and heights of continental ice sheets, the seasonal distribution of vegetation, and the location and extent of lakes. For certain types of experiments, particularly those that attempt to reproduce past climates, the annual cycle of sea surface temperatures and sea ice might even be specified as a boundary condition, assuming observations of such exist. However, since it is implicit that anything assigned as a boundary condition is not subject to change by the model, specifying characteristics will limit the overall impact of other changes within the simulated climate system.
Initial Conditions: In addition to boundary conditions, GCMs must be initiated with a number of initial conditions. Initial conditions are just as the name implies, the description of the initial state of the model. From the standpoint of the atmosphere, the initial conditions specify the starting temperature, pressure, winds, and humidity for every location in the atmosphere. Though based on observations, small inaccuracies in the initial conditions can lead to unique results as an experiment proceeds. For this reason, critical experiments are commonly run multiple times, with the only difference in the simulations being slight perturbations of the initial conditions. The range of answers in such an ensemble of runs places a somewhat crude error-bar on the accuracy of the experiment.
Climate Forcings: Once the initial and boundary conditions are supplied a GCM experiment applies a number of climate forcings that impact the results of the run more dramatically. Usually, one or more of these forcing factors are the focus of the experiment. The best-known examples are the greenhouse gas forcing experiments that describe the increase of temperatures during the 20th century and forecast the global warming that will take place in future decades. Like boundary conditions, climate forcings are also specified in an experiment, but they are often altered so that they change with time, or adjust spatially, throughout the course of a simulation. In this way the effect of the altered forcing on climate can be examined. Again, the most common example are the greenhouse gas experiments that increase the trace amounts of gases such as carbon dioxide, methane, chlorofluorocarbons, and nitrogen oxides. Other examples of forcings that regularly impact Earth’s climate include the dust and sulphuric acid droplets ejected into the atmosphere during large volcanic explosions, aerosols produced by human pollution, or changes in the Sun’s luminosity that accompany sunspot cycles. All of these forcings have been the focus of global climate model experiments and have helped lead to a better understanding of how our climate system responds to change.
Climate Feedbacks: For the most part, the direct impact of the above climate forcings is relatively small compared with their overall effects. The reason for this is that operating within the climate system are a large variety of feedback mechanisms, which can either dampen or amplify the impact of the original forcing. While the number of feedback mechanisms, and the timescales over which they act, is virtually limitless, there are three feedback mechanisms that are illustrative of the process, and which are dominant mechanisms effecting global warming and cooling scenarios: the water vapor feedback, the cloud feedback, and the ice albedo feedback.
As greenhouse gases increase in the atmosphere they absorb more of the thermal radiation being emitted from the planet’s surface, thus trapping heat and warming the atmosphere. Even for relatively large increases in gases like carbon dioxide, this direct radiative heating of the atmosphere is not dramatic. However, the minor heating has several effects. Two of the most significant are both positive feedbacks, meaning they amplify the initial effect of the forcing. The direct heating of the atmosphere by carbon dioxide causes more water to be evaporated from the surface of the ocean. This leads to an increase in the water vapor content of the atmosphere, particularly in the tropics. The water is itself a powerful greenhouse gas, which heats the atmosphere further, causing more water to evaporate from the ocean setting up a positive feedback loop. Similarly, a positive feedback loop is set in motion as the initial heating of the atmosphere by CO2 (and increased water vapor) causes sea ice to melt and less precipitation to fall in the form of snow. The reduced surface area covered by highly reflective ice and snow reduces the surface albedo, thus an increased percentage of incoming solar radiation is absorbed instead of reflected to space. This then leads to further heating of the planet, and another positive feedback loop.
The cloud feedback is thought to be far more complex, so much so that not all climate models agree on the sign of the feedback. We know that low altitude clouds tend to reflect more sunlight, while high clouds have an overall heat-trapping effect, because they are cold, and reemit their absorbed energy to space at a much cooler temperature than the surface. A number of GCM simulations have shown that as greenhouse gases increase and the globe warms low cloud amounts decrease as the warmer atmosphere makes it more difficult to condense atmospheric water vapor. This is a positive feedback towards warming. However, if high clouds also decrease a negative feedback ensues that could mitigate the low cloud change. While there is general agreement among global climate models that the combined cloud feedback is positive, there is definitely more uncertainty and variation in the results. Moreover, there are atmospheric scientists who believe that the clouds produced by GCMs are simply not accurate enough to yet determine the true nature of the cloud feedback.
Climate Sensitivity: The National Academy Press defines climate sensitivity in their publication "Climate Change Science" as:
"The sensitivity of the climate system to a forcing is most commonly expressed in terms of the global mean temperature change that would be expected after a time sufficiently long for both the atmosphere and the ocean to come to equilibrium with the change in climate forcing."
Publications, like those of the Intergovernmental Panel on Climate Change (IPCC), will refer to illustrative simulation climate sensitivity results to describe the expected climate change in the coming decades. For example, the sensitivity of climate to a doubling of CO2 is expected to be between 2 and 4 degrees Celsius, based on a wide range of climate model predictions.
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