9 April 2009

Weather & Climate Models- Trust me this is interesting!

Posted by Dan Satterfield

His name was Richardson.

Lewis Fry Richardson. He was a British mathematician, and as a Quaker, also a pacifist. When World War one began, he enlisted as an ambulance driver to serve his country while adhering to his ideals.

Richardson had the bright idea that the mathematical equations that govern the air, could be used to predict the weather. He decided to make a forecast, and divided the forecast area into squares.  Then he assigned such variables as current temperature, pressure, and humidity to each of these grids. He believed that if he solved all the equations for each grid, he would come up with a forecast of the weather 8 hours in the future.
It took him months! No computers around in World War One, and no one really wanted to help him!

Lewis Fry Richardson- Ctsy UK Met. Office

Lewis Fry Richardson- Ctsy UK Met. Office

Did it work??

Total failure dude. (I can relate my friend, I can definitely relate!)

He did not give up though, and kept working on it for years. He had the idea of having thousands of people in a stadium, who would each do one calculation, and pass it on to the next person. This would make it possible to solve all of the complex calculus equations, in a short period of time, and produce an accurate forecast!

With the advent of computers in the 1950′s, this idea took on a whole new meaning.  While Richardson’s first forecast failed spectacularly, the attempts showed much promise by 1960. If only Richardson could see the models I look at every day now!

The rapid increase in computing power has revolutionized weather forecasting. In 1979, I was told that an accurate 7 day forecast would not be possible in my lifetime. Computers were just not fast enough. In 1980, an extended forecast was 3 days. I produce a 7 day forecast everyday now, and some stations put on a 10 day forecast. The 5 day forecast is as accurate as a 3 day forecast was just 20 years ago!

Let me explain how they work. No math, I promise!!

Grab a map of North America or Europe, or wherever you are in the world. A map that covers several thousand kilometers. Now get a box of sugar cubes. The kind you put in your tea or coffee. Put them down on the map. Now imagine that the cubes cover the entire map. Now, we tell the computer model what the weather conditions are in every single one of those cubes. We then use the mathematical equations that describe the atmosphere, to move the weather from one cube to another.

If there is a south wind over Texas, then the cubes over Oklahoma will get warmer. How fast they get warmer, will depend on the wind speed, the elevation, and whether or not the sun is shining. Actually there are a ton of variables, and they can all be described using equations of math. Some better than others. We have to decide how often we are going to move the weather, from one cube to another. Modern weather models use a time period of just a few minutes. We call this the time step of the model. We also have to decide how big are cubes are going to be.

Imagine a map covered with sugar cubes

Imagine a map covered with sugar cubes

This is very important, because the smaller the cubes, the more accurate the forecast. Imagine we have a cube that is 50 kilometers wide on each side. We will give one value of the current weather to that cube, when we tart the model. Will the weather be the same across that entire cube? No, of course not. We will have to average the weather over the cube and this will introduce error into the forecast. The smaller the cube, the less error.

Here’s the rub.

The smaller the cube, and the shorter the time step, the more time it takes to run the model!

I also neglected to tell you something. We have a map covered with a a layer of sugar cubes right? What about the rest of the atmosphere? What about the weather up high. What about the jet stream? We have to have a bunch of sugar cubes in layers on our map. Each one has to be given a value for the weather happening now, before we can run the model!

The best resolution model run by NOAA over North America is called the NAM. North American Mesoscale model. The cubes are 12 km square in the NAM and there are 70 layers of them. The top layer is over 20 miles high! The model is run 4 times a day on a multi-million dollar supercomputer. It makes a forecast out to 84 hours in the future. Other models have bigger cubes and forecast the atmosphere out to 10 or twelve days. They take longer to run of course.

NWP model forecast of temperatures and winds at 5000 ft. From NOAA and weather.unisys.com

NWP model forecast of temperatures and winds at 5000 ft. From NOAA and weather.unisys.com

So why isn’t the three day forecast always perfect??

The cubes are still too big for one thing. We also do not know the weather over all of North America exactly is another. The NAM covers large areas of ocean, where there may be no weather observations at all! We have to guess. We do a pretty good job of it too.

There is more error. The equations are not perfect, so even if we did know the weather everywhere, and could tell the model exactly what the weather is doing right now, it would still make a less than perfect forecast! There is more though. what about clouds?? How do you tell the model what a cloud looks like, and how do you tell the model what to do with rain and snow that falls.

The rain will affect the temperature and humidity. If the rainfall is wrong, more error!

Lastly, there is chaos.

If we had perfect equations, and perfect knowledge of the initial weather, the forecast would still go wrong!

The atmosphere is a chaotic thing. This was described brilliantly by Ed Lorenz. He famously asked the question “Does a butterfly flapping it’s wings in Mexico cause a blizzard in Kansas”? Tiny changes at molecular level will eventually add up to big errors.

The current thinking is that the limit to very accurate numerical weather model forecasts is somewhere between 2 and 4 weeks. We have a long, long way to go, to get there though!

You might wonder about Climate models used by the IPCC to forecast climate change. They are similar, but since they must run for hundreds of years, the cubes are huge. Climate scientists are not interested in the weather the model comes up with. They ARE interested in the climate it comes up with, and the changes in climate that it comes up with.
How good are these Climate models??
Look at the image below.

Climate Model Hindcast from IPCC

Climate Model Hindcast from IPCC

When we start the models back in the early 1900′s, they do a very good job of predicting the Earths temperature through the 20th century. Notice the difference when we do not include greenhouse gases rising. The model blows it. Only when we include natural and human caused changes in the atmosphere, does the model get it right.

Those same models say we will see a catastrophic rise in temperature in the next 100 years, if we do not do smething to reduce CO2, and other greenhouse gases.

Yea, it’s scary isn’t it. Now you know why so many climate scientists have a bad feeling in the pit of their stomach, and they cannot seem to convince the public why.

See, I told you this was interesting!

Later,

Dan

Credits:
The Forgiving Air by Richard Somerville (He goes into great detail, and also with no Math! Buy the book.)
COMET NWP Model Matrix
NCEP (National Centers for Environmental Prediction-NOAA)
Unisys