## 04 September 2009

### One dimensional climate models

Some time back, I described the simplest meaningful climate model, and then gave a brief survey of the 16 climate models.

The next 4 I'll take up are the 4 1 dimensional climate models. These are the models that vary only in longitude, only time, only in latitude, or only in the vertical. It'll be in that order. This turns out to be the order of difficulty, and the order of interest. It isn't until the vertical that we'll get to how exactly it is that the greenhouse effect works.

On the other hand, with the model in latitude we'll see some powerful statements about the fact that energy has to move from the equator towards the pole. Not just the fact, but how much, and how it changes with latitude.

In the model with only time, we can look a little more at things we were thinking towards with the simplest model -- what happens if the solar output varies, or if the earth's albedo does. More is involved, and required, than just that. We'll have to start paying attention to how energy is taken up in the atmosphere, ocean, ice, and land. Not a very large amount of attention -- we can't tell the difference between the poles and the equator, or upper vs. lower atmosphere or ocean. But it's a start.

But for now, let's look at the simplest model in longitude only. As with any of our models, they start with the conservation of energy. The energy coming in is, as before, from the sun. How much energy arrives does not depend on what longitude we're at. Remember, even though the sun rises in the east and sets in the west -- east and west being matters of longitude -- the sun does eventually rise everywhere.

Energy coming in has to be balanced by energy going out. If it weren't, things would be changing over time and there is no time in this model. One part of the energy going out is the solar energy that gets bounced straight out. This fraction is called the albedo. Now albedo is something that can depend on longitude. For instance, land is more reflective than ocean. And along, say, 30 E, the earth is mostly land, while along, say 170 W, it is almost entirely ocean. Clouds can be anywhere. So ... we arrive at one of those unpleasant realities -- we have to get some data.

Normal business. The process arrives at telling us that we need to find averaged albedo over time (say some years) and all latitudes for each longitude. (We don't have to average over elevation because albedo is defined as the energy bounced out -- from whatever level of the atmosphere -- divided by the energy coming in.)

Once we have that, we can compute the temperatures at each longitude that will permit us to balance, with terrestrial radiation out, the incoming energy. These temperatures should be something like the blackbody temperature of the earth we found in the simplest model. But they'll vary some.

The next piece of data we'll need are the observed blackbody temperatures, by longitude. Then we'll compare the simplest model to the observations.

One thing which is possible, and we'll be looking for in our comparison, is that now we've added longitude, a new thing can happen. In the simplest model, the energy coming in had to be balanced, right there, by energy going out. Now that we have longitude, it's possible for energy to shift from one longitude to another. The Gulf Stream and North Atlantic Currents, for instance, move a lot of energy from west to east. If no energy is being transported, on the average, then the temperature for a longitude will be just what we expect. If there's a mismatch, energy has to be getting moved from one longitude to another.

I haven't collected the data yet, so I don't really know how it will turn out. I expect that clouds will cover the albedo differences between land and ocean to a fair extent, so the temperatures we'll compute will be fairly constant. I also expect that heat transport by longitude will be small -- the Gulf Stream's eastward warm current is balanced at least partly by a cool current (relative to local temperatures, that is!) at the equator.

On the other hand, I haven't looked at the data yet, so there is room for surprise. That'll be fun. Means we get to learn more than we expected.