Monday, September 15, 2014

The Grid Box

by Ben Brown-Steiner

The above image is taken from a popular indie game called Minecraft that gives players free access to an environment with in which they can interact with water, land, lava, and other natural resources. It’s blocky textures are a unique style for modern games, but serves as a wonderful example of how climate modelers look at our world.
The Earth is huge and complex. It’s easy to lose yourself observing the infinite details in an ant colony, a thunderstorm, or a sunset. And while that can be fun, if we’re to understand what’s happening over the entire planet, we need to divide it up into parcels and we need to try and understand how each chunk interacts to its surroundings.
Climate scientists who use models are become comfortable with viewing the Earth as a set of boxes. In order to get our increasingly powerful computers to create realistic simulations of our world, we have to divide up the atmosphere, the oceans and the land into grid boxes. For each grid box the computer tracks a single value for each variable. A grid box has one temperature, one value for cloudiness, one relative humidity, and so on. And a typical climate model has a time step of roughly 20 to 30 minutes.
Currently, we consider a high-resolution global climate model to have boxes that are around 60 kilometers or 35 miles per side. That’s roughly the length of Cayuga Lake. So a global climate model isn’t capable of seeing Cayuga Lake! How is it possible that a grid box that encompasses nearly all of Cayuga Lake and that jumps forward in time every 30 minutes has any chance of being realistic?
It’s because, somehow, astonishingly, the movement of mass and energy in the real world is amazingly organized. To some degree, it’s intelligible, which means that we can study it, take some notes, and understand the basic principles of how the it operates.
            Even though you could be standing in a parking lot in direct sunlight blinded and sweating and someone 100 feet away could be lounging in the breeze under a shady tree, if you average all of the temperatures in a region and track those values over time, you find smooth and regular patterns. If you average every temperature in a day (from the high temperature in the afternoon to the low temperature at night) and draw a graph, you can see the regular and repeating cycle of our seasons.
If you are examining a region’s climate you look at these average cycles. You ask questions like: Are the seasonal highs and lows changing over time? Is it drier, on average, this decade than it was last decade? How does the average state of our region influence the surrounding regions and the global climate? These questions are the questions of climate science and the purpose of these questions is to examine averages. In this sense, a large, abstracted grid box, is a really great way of looking at the big picture.
What, however, if you care about the high temperature tomorrow? If you want to know whether you should bring an umbrella on your walk right now, you do not ask a climate scientist. If you did, you would get a funny look and perhaps a response like this: the average daily high for September in Ithaca is 70 degrees and on average it rains 3.5 inches.
If you ask the question “What’s the weather going to be tomorrow?” you would ask a meteorologist, and the meteorologist, because they don’t have to worry about the entire globe all at once, can zoom in on smaller atmospheric patterns. They can run simulations with time steps as short as 10 seconds and grid boxes as small as one mile (~1.5 km) per side.
To look at a concrete example, let’s say you’re a climate modeler trying to capture interactions between clouds, the Earth’s surface, and solar radiation. You recognize that the real world is complicated and chaotic, but you know that there is some underlying structure that you can model. You take a look at a satellite photo over the ocean and it looks like this (from NASA):

How are you going to recreate this reality in your model? Clearly, you’ll have to simplify. If this particular picture is 100 miles per side, you know that your computers can’t capture that level of detail and have any chance of running on your computer. You need grid boxes. What size grid box is appropriate? If you had the computational power, you could build something like this:

Even though you know you’ll have to make simplifications, and parameterize (we’ll talk about these in another post) some of the small cloud features, you can still represent the overall cloud system you see in the satellite photo. But then your IT staff tells you that there’s no way you can run the model at that resolution. You need to try a somewhat coarser resolution:

You aren’t all that happy with this one since you lose a lot of detail and you’ll have to make different and broader assumptions. For instance, you’ll have to completely forget about resolving individual clouds. You’ll have to start representing cloudiness in a grid box as a percentage (real climate models do this). After some time, you hear from your IT staff that you can run this resolution, but it will take three months to run 1 year of your simulated Earth at this resolution. For your purposes, that’s not practical. Since you don’t want to give up you decide to go to an even coarser resolution with grid boxes of roughly 35 miles per side:

This one leaves out even more detail. You can hardly recognize this as a system of clouds anymore. But in exchange you can run your model at this resolution much more quickly and you’ll be able to examine the details of what you think is going on with much more confidence and data points. Right now, this is the grid box size of many climate models. And even though they use this resolution, they can be used to understand our Earth. The following image is an example of North America viewed through a variety of resolutions used today:

            The top left resolution is a course resolution used in the past. The top right is roughly the resolution of the average climate model today. The bottom left image is roughly the resolution that is considered high resolution today (the resolution that doesn’t quite see Cayuga Lake) and the bottom right resolution is one used more by meteorological models than climate models.
            As we’ve mentioned before, a model by definition is a simplification. It’s not going to simulate reality, and you are going to have to make sacrifices. But if you are careful and you understand what parts of reality you’re ignoring and what parts of reality you’re including in your model, you are able to interpret your results and hopefully discover something new that wasn’t understood before. The history of weather and climate modeling is a wonderful history of practical limitations, amazing ingenuity and cleverness, and glorious tales of scientific advancement of our understanding or our Earth.

1 comment:

tonyon said...

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