Chapter 4 - Simulating the Weather

Scientists like to tinker with things. We push here and poke there and try to understand what's going on in the center. Long ago, atmospheric scientists found out that experimenting with the weather was fraught with problems. The idea of changing the weather to see if a theory is right conjures up scenes from a late night movie, where townspeople run through the countryside carrying torches and searching for the mad scientist. The concept has seen some real discussion and has received some political attention for in one state it is illegal to enter a plane equipped for cloud seeding.

When computers of reasonable size began to appear in the early 1950s, meteorologists were some of the first users. For the first decade, research meteorologists just explored this new tool trying to make it look like the atmosphere and seeing what would make it break down. When transistors became available and the reliability of the computers became reasonable, the simulations were fed with real data and the results looked promising, but a 24-hour forecast of the weather which took 36 hours to compute was still a research tool. Operational meteorologists and programmers succeeded in reprogramming these models, and in the late 60s and early 70s the model results were good enough that they became useful to forecasters. The NWS began sending facsimile copies to any meteorologist who wanted them; faxes were rare, expensive and temperamental things in those days. Since that time, the major meteorological centers around the world have adopted them as important cogs in the weather forecast systems.

Of course, the problem is that a computer model is not the real atmosphere. The fact that the operational computer simulations do so well leads the scientific community to believe that the models do simulate the atmosphere. The models are one major reason why the weather forecast accuracy has doubled every decade since operational modeling began. Yet, for all their successes, there have been errors. Without well trained people interpreting them, the weather forecasts would be fraught with blunders.

Simulating the weather involves four steps: bringing all the data together in such a way that the simulations can go on, preparing the data for the simulations, running the simulations and interpreting the results of the simulations.

Just collecting and moving the data around the world is a big job in itself; weather data are apolitical. Even in the darkest Cold War days, weather data were officially and continuously exchanged between the saber-rattling countries. The World Meteorological Organization, working with the International Civil Aviation Organization, has been able to achieve international agreement on a very effective system to make the data flow possible because if you are trying to forecast the weather, nothing is worse than spending money on old data. It still takes over an hour for some of the data to come from the other side of the globe to Washington, D.C. Once the data arrive at the central computer systems in the centers, they are automatically sorted into their computer files, and they are ready to be used in the various computer programs.

When sufficient data are available, they are scanned for errors. The programs use the last run's forecast as a starting point and those which are outside of normal criteria are thrown out or displayed for a human analyst to make a decision. For the familiar surface weather map, the familiar contour lines are drawn by the computer but the fronts, highs and lows are drawn on the map by people. Analyses of the upper air, where we fly, are done as a starting point. When the analyses are complete, the simulation begins.

The analyses and simulations aren't stored in the computer as weather maps. They are interpolated, using sophisticated statistical techniques, to grid points which are evenly spaced in some coordinate system. Most of the calculations involve the distance between the grid points. If that is a constant, it saves much computer time. Figure 4-1 shows the contiguous United States in the upper left. Follow the arrow from the circled area to see an expanded view centered on Maryland. The lines across Maryland are drawn every half degree of latitude and longitude apart. Each place these lines cross is a location for a set of grid points for the model. The one close to EMI VOR, which is circled, is blown up again showing a number of vertical grid points where the analyses calculate the wind, temperature, pressure, and humidity of the flowing air. Once the values at the grid points are determined, the model runs begin.

All of the present day models simply use the data and make a forecast for about 10 minutes, using the laws of physics at each grid point in the horizontal and vertical. The forecast values are then used as data to make a new forecast, which in turn is used as data to make a new forecast, and so on until some time when it has been determined that the process has no skill in forecasting further. A good example of the methodology evolved out of an evening at home. It was a day not fit for man nor beast. The wind howled around the corner drifting snow into every crevice along the street. I had just come in from shoveling out the fire hydrant in front of the house when the telephone rang. It was George, a flying partner.

"Are we still on for tonight?" he inquired.

"We aren't going anywhere so if you want to come over, fine. But don't you think the weather is a little much?" I asked.

"My son has the chains on his new four wheeler and he says 'no problem', so I guess we're coming."

"Fine. We'll throw another log on the fire. And, we've been looking forward to meeting Jim's new wife."

The wind died down early in the afternoon so by the time they arrived, the drifting had nearly stopped. Jim, their youngest, was torn between pride in Sally, his new wife, the new four wheel drive, and the new job he had landed just out of graduate school. IBC, the mammoth computer company, had hired him as an analyst. George and Linda were pretty happy too.

After supper, I put a log on the fire and the talk ranged. Eventually, as it always does, the conversation mentioned weather, with the usual grousing about forecasts.

"A while ago you said something about using computer models to help predict the weather. I mentioned it to Jim. He said he knew the meteorology graduate students were some of the biggest users of computer time at the computer center," George said.

"What are they up to?" Jim asked.

"At a university, they probably are either doing statistical studies or simulating some part of the atmospheric flows," I said.

"You actually simulate the weather?" Jim asked. "I thought you simply looked at old cases and used these to make the predictions."

"No, our computer models simulate the atmospheric flows, temperatures, moisture, and, can calculate a rough amount of precipitation at various times." I explained. "The National Weather Service system is set up so the forecasters receive the simulation results from the computer runs before the weather occurs."

"How can you simulate the atmosphere on a computer?" Linda asked with a puzzled look.

I took a deep breath as my eye landed on her coffee cup. "Suppose you were interested in forecasting the temperature of that cup of coffee as it sat on the table, how would you do it?"

"Well, it starts at the boiling point and then cools rapidly at first and then more slowly."

"Ok, now suppose you wanted to use the computer to forecast the temperature exactly. You would have to know a way to calculate the temperature." I continued.

"Newton's law of cooling." Jim hopped in. "The temperature change is proportional to the difference between the coffee temperature and the environmental temperature."

"OK, what does that mean?" Linda asked, frowning at her husband.

"It just means that the temperature of the coffee adjusts to that of the room, and the bigger the difference, the faster the temperature changes." Jim answered.


I reached over and scribbled this equation on the pad

and said, "If the coffee started at the boiling point, and the room temperature is 20, then the difference is 80 degrees [100-20 = 80]. Just for pencil and paper purposes, let's suppose that the insulation of the cup "&alpha" can be represented by 0.1 per minute. After one minute, the temperature will drop some, say 6 degrees. Then we use that datum to start a new forecast, " I continued. "Then the temperature 'T' can be forecast by subtracting the change in temperature from the starting temperature. 100-6 is 94 degrees. The change is represented by the thing on the right which is made up of alpha, the insulation factor, the difference in temperature between the coffee and the room temperature, and the forecast time step 't' in minutes."

"That's simple enough to program on a spreadsheet. Can I use that computer over there?" Jim asked, pointing to our terminal.

"Sure, go ahead."

While Jim was entering the equation in the spreadsheet, Linda asked. "I seem to remember from my physics class that this problem had an exact solution."

"It does," I said walking over to the bookshelf and pulling off a physics text. "Here it is. But it is one of the few equations we use that does. Perhaps we can ask Jim to put that in as well."

"OK, what values should I use for alpha and the time interval?"

"Try 0.1 for alpha and five minutes for the time interval," I said.

After putting them in the cells Jim said, "OK, after five minutes the temperature of the coffee should be at 42 degrees. I wonder what it would be at ten minutes?"

"Just copy that column to the next column. Then suppose the coffee starts cooling at the five minute value."

"So you assume the predicted value is data and just repeat the process," Jim mused as he was busy copying.

"Right, and you can carry out the process for as long as you like or the results are reasonable," I added taking the physics text over to him. "By the way, would you program in this equation as well. It's the analytic solution to the problem. The time step approach is called the finite difference approach."

As Jim was busy copying and programming, Linda went over and looked over his shoulder. Coffee was served and after awhile, the printer started up and Jim proudly showed her the graph in Figure 4-2.

"Hey, that makes sense," Linda exclaimed, looking over the graph. "It even seems reasonable. If I leave the coffee on the table for 20 minutes, I know I have to reheat it. But the finite difference solution isn't the same as the equation."

"It really can't be unless the time step is very tiny." I said. "And, since we don't have analytic solutions for the other equations, we just have to live with a little error and try to minimize what errors we know about. It has kept two generations of meteorologists scratching their heads and making the techniques better each year."

"Hey, what's going on?" Jim exclaimed. "I changed the time step to 21 minutes just to get a longer time and I got garbage."

"Do a graph," I suggested.

After a few minutes the printer started again and he showed us figure 4-3.

"What you have there is a forecast gone awry," I said. "The math said you overstepped your time step and a little instability broke out."

"So all the forecast simulations have errors built in," mused Tom who was watching this procedure. "Evidently they aren't mathematically pure."

"You're right, but the alternative, an analytic solution, is beyond the best mathematics that exist," I said. "Meteorologists started studying the problem for the same reason Jim tried extending the time step, so they could do more with limited computer time. After they found a solution to the problem of making the simulations stable by making the system so the variables in phase space are conserved, they began wondering about predictability in general and have started a whole new branch of physics called Chaos. There are about four different types of instabilities or similar effects of this mathematical approach. The programmers and meteorologists have worked out ways of minimizing these problems and they rarely occur these days in the weather simulations. " I continued, "The alternative, the analytic solution, is well beyond our capabilities at this time."

The ideas we talked about that cold windy evening are a simple one-dimensional example of how meteorologists simulate the atmosphere. In the operational simulations of the atmosphere, the calculations are done, not just for temperature, but for wind direction and speed, pressure, temperature, water vapor content and air density. And they must be done at each grid point and at each level. After all, the pressure changes over a horizontal distance causes the winds to blow with the Coriolis force affecting their direction. Once the winds have blown for a little while, the winds move the cold air and the moisture to a new location. This causes a change in the original pressure patterns which, in turn, changes the winds. And so the weather patterns evolve. It reminds you of a kitten biting its own tail. The harder it bites, the madder it gets.

In the operational simulations, we use all the physics we can. The names of the formulas used in the models read like an introductory physics text table of contents:

These equations all can be put into a form which gives the change in the variable we are interested over a time interval. Newton's Second Law, F = ma, is one of the first laws learned in the physical science class as well as driver training. It says that by applying a force 'F' (usually the pedal on the right), the car with mass 'm' accelerates 'a.' Use of the brake pedal usually results in negative acceleration of the mass. Acceleration is simply the change of velocity with respect to time, the final velocity minus the initial velocity. Change the word "final" to "future" and "initial" to "data" and you have a forecast equation. If you know the force per unit mass of air and measure the wind velocity you can predict the future using this equation:




(The idea might occur to you that it might be applicable to money. It is. There are some very sophisticated econometric models which calculate the velocity of money among other things.)

The value of t is dependent on the horizontal grid spacing and the fastest velocity to be encountered; a typical value is around 10 minutes. If you know what the force per unit mass of air is, then everything on the right-hand side is known or specified. So, you can figure the velocity 10 minutes from the time you took the data. Then you can use that set of data to recalculate the pressure contours, the highs and lows which provide the force for the next forecast.

Once the values of the grid points are determined for 6 hr, 12 hr, 18 hr, 24 hr, and so forth, weather maps are contoured and forecast products such as the FD winds, as seen on DUAT, are packaged and shipped electronically to users, and some are placed on the World Wide Web. The Web versions can't be considered operational because of the sporadic outages on the Web. So, the operational results are sent to the private sector and other governmental agencies, including DUAT, through dedicated lines and value-added contractors. Some of these offer custom briefing services to pilots and small companies which have aircraft. Most of the major airlines have their own meteorological staff.

The results of these simulations are untouched by human hands until they arrive at the forecasters. The results are quality controlled by the forecasters who are faced with the job of determining the likelihood of the model being correct under that particular type of weather. At present, four different simulations of the general weather run each day. Three of them are produced at the National Weather Service's National Center for Environmental Prediction. Each has slightly different approximations, purposes and data sets. The other model in common use in the U.S. is the one from the European Center for Medium-range Weather Forecasts (ECMWF) at Bracknell, England. As the data come in at different times, the models which are available first often don't have as much data to work from as other models may have. Even with modern global communications, some data may take two hours to arrive at the center. One model may be run with only 90% of the complete data set from North America simply because the results are needed fast. Another, more sophisticated model will run later and include more data. Each model is constructed from the basic physics equations but each has some differences in resolution or length of the simulation. Other countries have their own models because the time to get data transferred around the world causes operational hiccups with their national goals. If you are using the models to self-brief, you should be aware that there are differences. You don't need to know the differences, but the forecasts will differ. How much they differ appears to be useful information in itself, for the difference appears to be a measure of the difficulty of the forecast.

It may sound like there is a duplication of effort, but there is considerable competition between the various modeling development groups. There is a need for three models in the United States. One of these will contain the latest developments in short term modeling, incorporating all of the lessons learned. Improvements will be made every so often to this model. The second model is a stripped down version which is run out for a much longer term to forecast the longer term weather. The third is the old model which has been "frozen," a backup that the forecasters can rely on. They already know its quirks and stall characteristics of this model and can do a decent job of landing the forecast using that model. Also, there is a need to collect and determine statistics from the model for one of the most useful techniques in the forecaster's tool bag, the Model Output Statistics.

A number of years ago meteorologists realized that the values of wind, temperature, dew point, and pressure at the grid points weren't the weather at the airports or cities. People want to know if it will rain, snow, be foggy, or a host of other things. The output of the models are values or map of the wind speed and direction, temperature, pressure, density, and humidity of the atmosphere at the grid points. Model Output Statistics are statistical interpolations between these values at the grid points and the weather which occurs in town or at the airport - those places for which data are taken. And the place where you and I take off and land. The relationships are not complicated; they're the same type of equations you have on your business or scientific calculators called linear regression. The MOS equations relate the values of the temperatures, dew points, winds, and pressures at the grid points to the visibility, probability of precipitation, ceiling height, probability of freezing precipitation and other weather phenomena for each city and airport. These are the equations which give the first cut percentage of precipitation you hear on the radio. The forecasters adjust them when the results don't look reasonable.

Both government and the private sector receive the results a few hours after data time. Private sector meteorologists get the information through one of three companies who have been awarded contracts for distribution of weather information. These and other companies provide access for pilots through a number of services. DUAT (which stands for Direct User Access Terminal) is one of these services. The upper air winds (in knots and degrees) and temperatures (in degrees Celsius) which you as a pilot get out of the DUAT service are just as it comes out of the model. These are also the wind forecasts used in the flight planning software. Thus, if the model is going awry, there are no forecasters or meteorologists looking at the results to protect us from model errors. Tread carefully.

If the models were all there were to it, we could generate a computer program which would write out the forecast, insert the numbers, ring the telephones, and distribute the forecast by computer generated voice, computer bulletin board, or whatever. While the atmosphere is behaving itself, the computer can handle the workload and does fine. But when the atmosphere has hiccups, the models produce conflicting forecasts. And, it is awfully difficult to make the computer models responsible for the forecasts. When a particular model is not responding well, how do you discipline it? So, when the rubber meets the tarmac, it is the forecaster who is responsible for the forecast. It is his or her job to sort out the different model guidance and use the best parts to compose a forecast which meets the requirements of the user.

We do it by hiring people who have the appropriate college educational background, give them experience as interns, additional training, develop them as forecasters for a number of years, and give them the tools and information they need to do the job. The job is not over with then because research and development comes up with new ideas and technology. Sometimes the forecasters themselves are actively involved with the research and development. Then, additional education and training are needed. The result of the combination is that accuracy and precision of weather forecasts have doubled each decade since World War II.

The man-machine mix relies on the ability of the human brain to process information in terms of a conceptual model of the atmosphere. This is the same conceptual model that most other people use. However, it is usually much more highly developed because forecasters spend most of their working career looking at, reading about, studying, and analyzing mistakes made when forecasting the weather.

One forecaster, in a round table discussion of the forecasters role, commented that "A true measure of a good forecaster is being able to make an accurate forecast in the initial 12 to 24 hours based on data alone....No models....Models are tools! The forecast is a product of a human meteorologist."

Each forecaster has his or her own specialty. Some forecasters are exceptionally good when it comes to forecasting the onset of snow. Others specialize in tropical cyclones or hurricanes. Still, others are best with aviation related weather problems. The local NWS forecast office has a mix of people. And it is that experience and expertise which frequently save the forecast. In a sense, the system is the state of the art in "artificial intelligence." Decisions are made based on nonlinear mathematics, fed by real data, and the models can produce numbers which are then used to make forecasts. One thing we found in doing it this way is that we can't substitute machines for people.

The conceptual model has grown over the years but the daily forecasting job still begins with the old traditional analysis features, highs, lows, and fronts. Calculating the center of a high or low from the computer model output is relatively easy and computer programs are used to save time and money. The computer models do not know about fronts. Although programs have been written to take the output and calculate where a front should be, none of these are completely reliable. A front is an analysis feature, a line drawn on a chart which helps the analyst and others who will be using the chart to resolve a complex weather pattern into simpler and more basic concepts. In a simplistic way, a cold is the leading edge of the cold air mass; in the more realistic way to pilots, the cold front means beware of thunderstorms, icing and strong winds. So the analyst will try to draw the front in such a way that the single line draws attention to the hazards. Since it is not unusual for surface temperatures in the sunny air behind a cold front to be higher than those under a cloud deck ahead of it, the actual temperatures can only provide a first approximation to the location of the front.

In fact, two analysts may draw the fronts quite differently from each other, based on the problem they are trying to solve. One analyst's problem may be restricted to large scale motions of storms and the big waves which move around the hemisphere. In that case, a front he or she will draw will be very smooth. Another analyst who is concentrating on severe thunderstorms may need to incorporate small scale radar information into the analysis and draw a cold front with bulges to represent outflow boundaries. They both may be right even if the analyses are quite different.

There are other kinds of analysis features beyond the fronts. All of them are used to help the meteorologist in forecasting the types of weather associated with storms. My particular favorite is the winter snow storm, and to see how these features are related to the storms, it is helpful to look at the storms themselves.

If you would like to know some more about the atmospheric models you might like this appendice.

Onward to Fronts, Lows and Highs or
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