PRESENTER: Let's now do an actual experiment here with our one-dimensional energy balance model where we've now generalized the energy balance model to allow for discrete latitude zones. And we calculate the energy balance as we did before between the incoming solar radiation, the outgoing long-wave radiation, the reflected radiation. We use the same energy balance principles that we used in the zero-dimensional model, but now we're allowing for different solutions of the energy balance model and different latitude zones.

And importantly, we are going to allow for these fluxes, these lateral fluxes of energy F between latitude zones, which represent the very important role that atmospheric and oceanic motions play in transporting heat on the whole from low latitudes to higher latitudes to make up for the imbalance between outgoing and incoming radiation at the tropics and at the poles. There's a surplus of energy at the equator, a deficit of energy at the poles. And so we need these lateral fluxes to make up for that imbalance

So let's take a look at a problem that was first attacked using this sort of approach, the one-dimensional energy balance modeling approach. We're going to use a program that was written in MATLAB. And you can see, this is sort of the heart of the program. It does the energy bounce calculations for each latitude zone. Here, we've specified the lateral heat flux transport coefficient F.

We're using gray body parameters for the energy balance of the sort you saw before in the zero-dimensional model. And we are now accounting for the possibility that the albedo will be vastly different depending on whether a particular latitude zone is ice covered, in which case it has a relatively high albedo, or not ice covered, in which case it has relatively low albedo.

And we will determine whether or not a latitude band is likely to be ice covered through a simple threshold, a parameterization here where if the average temperature for that latitude band is below minus 10 degrees Celsius in the annual average, then it will be ice covered. And that's the assumption that we'll be making. It's not a bad assumption if you look overall at the relationship between mean annual temperatures and which latitude zones are indeed mostly covered by ice in the real world.

And we will perform experiments in which we slowly change the solar constant from a relatively high value larger than today's solar constant to a relatively low value. And we'll see how the temperature of the Earth and of different latitude zones changes. And then we'll increase the solar constant from that low value to the high original value and again, see how Earth's temperature changes. Now we know that changing albedo will be coming into the problem. There will be transport of heat between different latitude zones. So this is a more sophisticated model than the sorts of models that we've looked at so far.

PRESENTER: Now that we're dealing with an additional degree of freedom-- we've now got the latitude to deal with-- we'll have to do a little bit of geometry. We have to take into account the geometry of Earth's tilt and the variation in incoming solar radiation at the top of the atmosphere as a function of latitude. So all those calculations-- the geometry and the distribution of insulation as a function of latitude-- is calculated in some subroutines.

And that is incorporated, of course, into our solution of the one-dimensional energy balance model. So let's actually run that model, It's simply run by me executing the command one_dim_ebm-- One-Dimensional Energy Balance Model. OK. And when it's done, first of all, it calculates the insulation at the top of the atmosphere as a function of latitude, where we, of course, have very high values of solar installation near the equator, very low values near the pole.

And it is now varying the solar constant. We're describing that through a solar multiplier. So it varies the solar constant from 40% larger than its current value, a multiplier of 1.4, the way to 40% lower than its current value, a multiplier of 0.6. And a multiplier of 1 is the current value of the solar constant.

What the red curve shows is what happens to the average temperature of the earth, which is constructed by averaging over all the latitude bands, each of which has its own temperature, as you lower the solar constant from a value that's 40% larger than it is today to, let's say, the current-day value.

By the time you decrease the solar multiplier to the current day value, you get a temperature somewhere in the range of 15 degrees Celsius or so, which we know is, in fact, a pretty reasonable estimate of the average temperature of the earth. And as we decrease it further, the temperature, of course, decreases, but something very interesting happens.

Suddenly, we reach a critical point where the temperature drops quite rapidly to well below freezing and, of course, continues to drop further as we lower the solar multiplier further. What's happening here is as Earth temperature is getting colder and colder, the latitude zones that are occupied by ice are spreading further and further towards the equator until eventually we reach a point where the entire earth becomes covered with ice and the albedo plummets dramatically. Sorry, the albedo increases dramatically, and Earth's temperature, therefore, plummets dramatically.

Now we have an ice-covered Earth as we continue to lower the solar constant. It, of course, continues to cool, but the ice cover isn't changing. We have a frozen Earth. Now what happens if we instead start out with a solar constant that is 40% below the current value and continue to increase it? Well, that's what's shown by the blue curve. And something very interesting happens.

As you start with a frozen, ice-covered Earth, solar constant 40% lower than today, it, of course, warms as we increase the solar multiplier, but it's still ice-covered. It's still ice-covered. It's still ice-covered. And it actually remains ice-covered, and the temperature remains very low-- the average temperature of the earth remains well below 0-- all the way until we reach a solar constant of 30% larger than today.

At that point, we now suddenly begin to melt away the ice fairly rapidly. And as soon as we do that, Earth temperature increases very rapidly. Now we have an ice-free Earth, and we're back where we begun. And if we increase the solar multiplier to 1.4, we are precisely where we started out.

PRESENTER: OK, so what happened here? We found that this system has a very interesting and non-intuitive property that for a given value of the governing parameters-- for example, for a solar constant of 1,370 watts per meter squared, Earth's temperature can potentially have two very different values. It doesn't have a unique value. It can either have a value similar to what we see today or a temperature below 30 degrees below 0 Celsius for the current day solar constant.

And what determines which of those two temperatures it's likely to have is the prior history. The properties of the system depend on its prior history. If we had started out with a frozen Earth and increased the solar constant to its current-day value, we would still have a frozen Earth.

And that's because the ice, once it accumulates and increases the albedo, which is reflecting away most of the solar radiation, it's fairly difficult to get rid of that ice, and only when you turn up the solar constant to a very high value are you able to melt away the ice, suddenly lower Earth's albedo from the albedo of an essentially frozen planet, and Earth's temperature can warm quite a bit.

On the other hand, if you start out with a very warm Earth and slowly lower the solar constant, you're not going to form ice until Earth's average temperature gets well below 0 degrees Celsius, and the various latitude zones now start dropping below that critical threshold temperature of minus 10 degrees Celsius, which is the temperature we specified represents when a latitude zone becomes ice-covered. And then, at that point, of course, the albedo increases dramatically, and Earth's surface temperature cools rapidly.

So the temperature of the Earth depends not only on the value of the governing parameters-- in this case, the solar constant-- but the prior history of the system. That is a property that's known as hysteresis, when the properties of a system depend on its prior history, not just on the governing parameters. It is an intrinsically nonlinear property. It's a property of complex systems which exhibit non-linear behavior. And in particular, in this case, bi-stable behavior that for a given value of the parameter, there are two stable points in terms of Earth's surface temperature.

And under some circumstances in systems like this, it's possible to undergo transitions rapidly between these two stable states. That is one theory for explaining the dramatic changes in the meridional overturning circulation of the North Atlantic Ocean that has taken place in the past, and we've talked a little bit about that in the past. We'll talk a little bit more about that in the future.

This is an example of a non-linear and, in this case, a bi-stable system. And in general, as our models become more complex-- in this case, we've generalized the model from 0 dimensions to 1 dimension. We've allowed for the possibility of a temperature dependent albedo. As soon as we start to make our models more complex, more detailed, more sophisticated, we introduce the possibility of very unusual, potentially unusual behavior of the system, this sort of non-linear behavior. And this is something that we'll talk quite a bit more about in this course.

It's relevant to the issue of thresholds and the possibility that as we continue to warm Earth's climate, we will pass certain critical thresholds where the climate system will undergo rapid transitions from its current state to some new state.

Finally, it's worth noting that this original model, constructed by a Russian scientist named Budyko decades ago in the mid 20th century, represented a real conundrum for climate scientists because it suggested that once Earth goes into a frozen ice-covered state, which it has in the past, it is very difficult to get out of that state. Even at current values of the solar constant, the Earth cannot come out of this frozen state.

The solution, it turns out, to this problem has to do with carbon cycle feedbacks and what happens with the Earth's carbon cycle when this happens. We'll talk more about that later on in the course.

Complex Climate Modelling includes:

• Water in oceanic grid boxes interacts horizontally and vertically with other boxes
• Oceanic grid boxes model currents, temperature, and salinity
• Influence of vegetation and terrain is included
• Atmosphere is divided into 3-D grid boxes, each with its own local climate
• Air in grid boxes interacts horizontally and vertically with other boxes

PRESENTER: OK, so we're going to run a GCM, a very famous GSM, in fact. This is the GCM that was constructed back in the mid-1980s, which was used for a number of very famous climate modeling experiments by James Hansen and his group at the NASA Goddard Institute for Space Studies that we'll be talking about a little bit more later on in this lesson. So that model has actually been taken and put in a format that can be run on a PC, on a Mac or a PC.

Of course by modern standards, the computational requirements of climate models written in the 1980s are far exceeded by current day state of the art models. But because they are a couple of decades old, they can in fact be run fairly efficiently now on simple laptops and PCs like we're going to do. Now, this model is available at the website EdGCM.com.

I would have had students in the class download the model and run it themselves. That was possible a few years ago. Unfortunately, now you actually have to pay to obtain the model. And so I will be doing some experiments with the model. And you will be watching me do these experiments rather than actually downloading it and running it yourself. But if you felt so motivated, you could indeed download this climate model and do the very same sorts of experiments that we're doing right here on your PC, or your Mac, or whatever computer you have.

So let's go ahead. I'm going to look at this Doubled CO2 experiment. If we click here, we can get some information about what that experiment is. It basically takes the CO2 concentration from 1958 and instantaneously doubles that CO2 concentration. And then we see how the climate model responds to that sudden increase in CO2.

Now, because of the presence of a large ocean that has large thermal capacity in this model, it takes quite a bit of time for the climate model to equilibrate to do that increase in CO2 concentrations, in fact, several decades to near a century. So this underscores the point that when we're looking at transient climate change, whether we're looking at observations are looking at the results of a climate model, we are in fact observing a system that is not in equilibrium. And that might take quite a bit of time to equilibrate to whatever change enforcing is imposed.

So ultimately, we know that this model will warm the amount that is consistent with the sensitivity of the model in response to that CO2 doubling. But it will not achieve that equilibrium warming for several decades, again, to nearly a century. And so what I'm going to do now is actually continue a run of that model that I started previously. And I'm just going to click on that. And I should be able to run.

PRESENTER: OK, so I'm running that experiment. It started in 1957. Then we instantaneously doubled the CO2 concentration. And now we're letting the model equilibrate to that instantaneously doubling of CO2.

And when it comes into equilibrium, it should have warmed by an amount that is consistent with the sensitivity of this particular model. And again, this is the NASA Goddard Institute for Space Studies climate model from the 1980s that was used in a series of famous experiments by James Hansen, by climate scientist James Hansen.

So we're running the model. I've been running this for several days, in fact. And as you can see, I'm now all the way up through September 2012. So we started out in December 1957. The model has now reached September 2012.

And as you can see, I get about one simulation day per second. So it takes the better part of a day running this climate model to simulate anything approaching a century, a long time period. But that's quite fast. By comparison, say, with where things stood in the 1980s when it would take that long to run a simulation like this on a state of the art computer, now we can run it on a desktop.

So we're letting the days tick off day by day. The model is solving all of the equations of motion. It's solving the governing equations of the atmosphere and the ocean. It's calculating the radiative fluxes, the incoming solar radiation. It's computing the distribution of infrared radiation within the Earth's system, the diffusion of heat into a mixed layer ocean.

It's solving the full set of governing three-dimensional equations that describes the coupled ocean atmosphere, cryosphere system. The ocean in this model is fairly simple by modern standards. Today climate models of this sort simulate the complex motions of the ocean currents.

This particular model treats the ocean simply as a slab of water with an appropriate amount of thermal inertia. It can absorb heat. It can give up heat to the atmosphere. It can respond to radiative imbalances.

There is a parameterization of heat transport. So the ocean transports a certain amount of heat poleward. As we know, it needs to. But that heat transport is fixed. It's not variable as it is in modern-day climate models which allow for changes in the intensity of the ocean currents.

So the ocean is pretty primitive by modern standards. And many of the components of this model are in fact primitive by the standards of state of the art models today. But as we'll see, this model is sophisticated enough to have made some surprisingly accurate predictions.

OK, so we're closing in on the end of 2012. And what I'll do is I'll let this model run out to the end of 2012 so I have one more complete year of data. And then we'll start looking at the output of this climate model simulation.

PRESENTER: OK so let's look at the simulation results. And by the way, there are a number of experiments that can be performed using EdGCM. One of them is the doubled CO2 experiment that we just talked about.

And you can see how there are various settings. You can tell the model what component, what ocean model to use, a mixed layer model with a parameterization of heat fluxes, or a simpler model if you choose to do so. You can change how vegetation and topography is parameterized. So there are lots of different settings in the model that one can change.

And there are various presort of determined experiments that you can just run off of the main menu in EdGCM. But if you liked, you could design your own experiment. You could set all these settings to use that particular version of the model that you want to use. You could specify exactly how to change forcings, whether they be natural forcings like CO2 or other anthropogenic forcings, methane, and CFCs.

You can change natural forcings like solar output or even the Earth orbital geometry changes that we know are important on very long time scales. So there are a variety of experiments that you can perform. And a number of the sort of predetermined experiments are indicated here.

You can simulate the last Ice Age. You can simulate Snowball Earth. We've alluded to the fact that in the past there were periods in Earth's evolution where we believe Earth was entirely frozen. And you can do that Snowball Earth experiment With EdGCM.

But we're going to continue to analyze this CO2 doubling experiment that we were running. And we will look at the output now. As you can see here-- well, we'll do that in a moment.

PRESENTER: OK, so unfortunately there are quite a few bugs still in EdGCM. And sometimes it freezes up and you have to restart it, which I've done here. So forgive the lack of continuity. But we're going to pick up where we left off. So we have the [INAUDIBLE] doubling experiment. As you can see, we now have years 1958 through 2012 completed. So we've got more than 50 years of output of this [INAUDIBLE] doubling experiment. And this most recent year, 2012, you saw me complete it a little bit earlier.

So we will extract the time series, various variables. You can see that I've selected precipitation, surface air temperature, ocean ice cover, snow cover, water content of the atmosphere, sea surface temperature, and the ground albedo. Or if you like, we could select instead the planetary albedo, which would include both the ground and, for example, cloud albedo. So I've selected these variables.

And now what I'm going to do is generate time series, annual averages for each of these variables for each of the years of the simulation. So I'll be able to plot out time series of the various quantities. And you can see it calculating the annual averages right now. It's going through each month of each year and calculating an annual average. So we'll let it finish that process. And then we will look at the output shortly.

PRESENTER: OK, so we've calculated all of those values, those annual values of these various quantities that we selected here. Now we're going to extract them, and they are now available to plot. You can see the period is 1958 to 2012. And the quantities we have are the atmospheric water vapor. We have the ocean surface temperature, ocean ice cover. We've got the planetary albedo. We've got surface air temperature. We've got sea surface temperature. And we can start plotting these and seeing what they look like.

Let's start out with the surface air temperature. So this is the global average surface air temperature for the model. And it should be plotting that up for us shortly. There it is. So we can expand that window a little bit. We can change the scale here. So let's go from 9 and 8.5 to 23 on the vertical scale, just to get a finer vertical scale on this.

So the red curve shows us how average global land temperatures are changing over time in the model. The blue curve shows us how the open ocean temperatures are changing the model. Open ocean is going to be warmer, as you can see, by several degrees than land. It's the part of the ocean surface that isn't frozen. And the ocean, in general, warms up more than the land and is warmer than land on average because it doesn't go to as high latitudes, particular in the southern hemisphere.

So ocean temperatures are going to be warmer than land temperatures. The open ocean, the blue curve, is warmer than the full ocean, which includes ice-covered regions of the ocean. It's the green curve. And the black is the global average temperature. It's the average of all the regions, whether they're open ocean, ice-covered ocean, or land. That's what the black curve represents. Let's zoom in on that curve.

So we can say we started out in 1958 with a global average temperature of about 13.8 degrees Celsius, roughly what the global average temperature is prior to the increase in CO2 that's taken place since then. And we've warmed up by 2010 or 2012 to a temperature that's close to 17.8 degrees. So we've gone from about 13.8 to about 17.8. We've warmed up by about 4 degrees Celsius in response to that instantaneous CO2 doubling that took place in 1958.

So you can see how long it's taking the global temperature to equilibrate to that increase in CO2-- many decades. Although we can see that we are asymptotically approaching a new equilibrium value. If we were to extend this several decades into the future, as it turns out, we would probably see a net warming of 4.5 degrees Celsius relative to that initial temperature of 13.8 degrees Celsius.

And that is consistent with the fact that this particular model-- the GISS climate model, the NASA Goddard Institute for Space Studies climate model from the 1980s-- has a relatively high climate sensitivity of about 4.5 degrees Celsius equilibrium climate sensitivity for CO2 doubling. And that's consistent with the transient result that we're seeing here, as the temperature is approaching its equilibrium response to that instantaneous CO2 doubling.

But we can look at many other quantities in this model, in addition to surface temperatures. And so that's what we'll do next.

PRESENTER: OK. So we looked at surface temperature. Let's look at some other quantities here. These are all global averages. We'll look at the global average snow cover over time.

And we can see that's expressed as percentage-- the percentage of the land surface area that's covered by snow. That's what it looks like. If we look at the global average, that's the black curve. We can zoom in on that. We go from 5 or so to 12.

The global snow cover is decreasing in percentage from about 11% in the annual mean to a little over 7%, as we might expect. As the Earth is warming, snow cover is decreasing. In fact, that's one of the complimentary observations that we looked at earlier in the course that in addition to the warming of the Earth, we see that global snow cover is decreasing. That's just as the models projected to as surface temperatures warm.

We can-- no, I won't save that image-- we could look at the ocean ice cover. And again, we'll focus in on the global mean, so let's try to focus on that black curve. We'll go from a minimum of 1 to a maximum of 5.

And that's the black curve is a global average ice cover, and it is decreasing significantly as the Earth is warming. Again, as we might expect and as we have seen in the observations. Global ice cover is decreasing over time fairly dramatically. Northern hemisphere snow cover, where we have widespread records, is decreasing significantly as the model projects it too. And of course surface temperatures are warming.

So we can look at various variables other than surface temperature in this model and get some sense of what else is going-- what else is going on in this model. What else does this model project that we could look to the observations and see if the things that the models project should happen as we increase CO2 concentrations are indeed happening.

And why don't we take a look at global mean precipitation. And global mean precipitation is increasing. It's wetter over the oceans than it is over land, and the global average, the average of land and ocean regions is the black curve.

If we zoom in on that curve, OK, that gives us an idea of how precipitation is changing. Precipitation, in this case, is expressed as millimeters per day. And in the global average, we've gone from a little over 3 millimeters of precipitation per day in 1958 to something approaching about 3 and 1/2 millimeters of precipitation per day in 2012.

So in the global average, precipitation is increasing. That is also one of the robust projections of climate models. As we increase the surface temperature of the Earth, warmer oceans evaporate more water vapor into the atmosphere. The rate of evaporation increases. And to conserve water, that means that the rate of precipitation has to increase as well. In other words, we get a more vigorous hydrological cycle-- faster evaporation and faster precipitation of water out of the atmosphere.

And so the models project that global precipitation should increase, but what we saw previously in the observations was that, in fact, precipitation is a variable where there are very large regional differences. Certain regions become wetter, but other regions become drier. And so this is a case where looking at the global average, looking at a single time series, is going to be somewhat misleading. We really need to go to the actual spatial patterns of response in the models to see if we can make sense of what the model is projecting, and so that's what we'll do next.

PRESENTER: OK, so we've now gone to the Maps option. Previously we looked at Time Series, which give us a single number averaged over some region of the globe, typically the entire globe or the oceans or the land regions. But we can also look at the detailed latitudinal and longitudinal structure of these trends in various variables produced from the model.

The easiest way to do that is to pick, say, a five-year period at the beginning of the simulation and a five-year period at the end of the simulation so that we average out some of the year-to-year fluctuations. And we have an early baseline that we can compare to some later average in the model.

And I've already computed averages for various variables here-- snow cover, precipitation, soil moisture, surface air temperature, ocean mixed layer temperature. I've computed those all for a base period of 1958 to 1963, the first five years of the model simulation. And now what I'm going to do is calculate the spatial patterns of those variables for the last five years of the simulation.

So let's do that right now-- 2008, '09, '10, '11, '12. We're going to calculate the averages over that period. And it's doing that right now. You can see it going through the individual months for each of those five years. And it's going to calculate the averages of all those variables for each of the grid boxes in this model.

And the model is fairly low resolution. So as we'll see, the individual latitude-longitude grid boxes are in the order of seven degrees latitude and longitude. So it's a pretty coarse description of the surface. State of the art climate models today are run at much higher resolutions. But this is an earlier climate model. And at that time, it was necessary to resolve the Earth's surface into fairly coarse latitude-longitude grid boxes to run the models efficiently.

So now we're going to take a look at the spatial patterns of some of these variables, and in particular, the difference between the most recent five years and the first five years of the simulation, giving us a sense of how the model simulation is projecting changes over time and over the surface of the Earth.

PRESENTER: OK. So I've extracted the last five years of the simulation, the period 2008 through 2012, the average for that five-year period. And I'm now going to read it into the Data Browser, where it's available to plot. Then as a baseline, I am going to take the first five years, the average over the first five years of the simulation, read that into the Data Browser.

And you can see that I've got each of these five variables now, Ocean Mixed-Layer Temperature, Precipitation, Snow Cover, Soil Moisture, and Surface Air Temperature, all annual averages for each of these two five-year periods. And what I'm going to do next is to take the difference.

Let me select Surface Air Temperature. We're going to take the difference between the last five years and the first five years of the simulation. And that'll give us the spatial pattern of the trend in temperature over the globe.

So I want Data one minus Data two. It's going to plot that out for me. Unfortunately, it uses a nonsensical color scale. So I am going to change the color scale so that it is more meaningful.

OK. So the warm colors all indicate warming. The cold colors would indicate cooling. Of course, the entire globe is warming in this simulation, warming more at high latitudes, particularly in the northern hemisphere, where, as we know, sea ice is decreasing markedly. And so that ice albedo feedback is kicking in, giving us that additional warming at high latitudes in the northern hemisphere.

And there's some interesting structure in the southern hemisphere, as well, perhaps a little bit more warming over the land regions than over most of the ocean regions, although the variations are fairly small. So that's the projected surface air temperature pattern.

Of course, as I've said before, this is a fairly primitive climate model by modern standards. And a lot of the more interesting variations in ocean circulation and atmospheric circulation that give us more complicated patterns of surface temperature changes in the projections of current state-of-the-art climate models are not really resolved in this relatively primitive model.

But that's what the surface pattern of warming looks like. And we can now look at the patterns of some other variables.

PRESENTER: OK. So now I've selected Precipitation. And we're going to look at the change in precipitation over the surface of the globe. "Annual" means surface-- precipitation. Differenced-- the first five years minus-- the last five years minus the first five years of the simulation.

OK-- Data one minus Data two. And this is what we get. Again, let's use a more sensible scale. So we'll go from minus 3.09 to plus 3.09.

So we can see that overall, precipitation is increasing over the globe, as we already saw when we plotted out the global average precipitation. But there are some strong regional variations. There is a concentration of increased precipitation in a band near the equator.

The largest increases in precipitation are near the equator, where we have the Intertropical Convergence Zone rising motion in the atmosphere. And since the surface is warmer and there's more water vapor in the atmosphere, we get more rainfall in the region where rainfall tends to occur, which is this Intertropical Convergence Zone.

But as we go to the subtropics, we can see large patches of white. And what that's indicating is that in fact, in the descending branch of the Hadley circulation, where we tend to see deserts, that region is actually expanding poleward somewhat. And so that region of drying is now expanding towards the poles. And that's why we see these large areas of at least small decreases in rainfall in subtropical regions, contrasting with the large increases we see closer to the equator.

And then as we get into higher latitudes again, you can start to see that there's a larger tendency, again, for increased precipitation in the subpolar latitudes. And that is associated with a migration poleward of the mid-latitude band of frontal precipitation in both hemispheres.

So when we look at the pattern of rainfall, there's a far richer pattern of regional variation that tells us that, in fact, if we want to understand projected changes in rainfall, it's important not to just look at global averages or hemispheric averages. But look at the underlying pattern of changes, which is fairly complex, even in this case.

But of course, this is a relatively simple model. In state-of-the-art models today, the patterns of projected change in variables like rainfall are even more complex, even more regionally variable, because these models are able to resolve important changes in ocean and atmosphere circulation that impact on regional precipitation, for example, changes in the El Niño-Southern Oscillation phenomenon, which has a large impact on regional patterns of rainfall.

But even in this fairly basic, this fairly primitive model from the 1980s, we can see this pattern of latitudinal variation in how rainfall changes. Even on the average, there is an increase in global rainfall. That change in rainfall is strongly regionally variable. And there are some regions in the subtropics where this model projects a modest decrease in rainfall.

So we'll leave our discussion of EdGCM there. This, again, is a relatively primitive climate model by modern standards. And yet we can see some of the changes that we know are projected by more state-of-the-art climate models, with regard to changes in temperature, changes in rainfall, changes in sea ice.

And so as we go on into our next couple of lessons and we start to look at projections of state-of-the-art climate models, we will see that many of these predictions with the earliest models are borne out by more realistic models that are available today.

Figures (left to right):

• Solar effect on atmospheric temperature
  • temperature ranges from -1.1^ºF to 1.1^ºF
• Volcanic effect on atmospheric temperature
  • temperature ranges from -1.4^ºF to 1.1^ºF
• Human-generated greenhouse gas effect on atmospheric temperature
  • temperature ranges from -2.2^ºF to 2.2^ºF
• Combined effect of human and natural forces on atmospheric temperature
  • temperature ranges from -2.2^ºF to 2.2^ºF

Atmospheric Temperature Change: The model-predicted pattern of atmospheric temperature change taking into account the impacts of both natural and human influences (far right) looks much like the greenhouse gas pattern alone (second from right). This is because human-generated increases in greenhouse gas concentrations are believed to have dominated atmospheric temperature changes over the past century (shown are the model-simulated trends in annual average temperatures from 1890-1999)