v is simply the final
velocity minus the initial velocity, A Little More About Computer Simulations of the Atmosphere
The ideas we talked about during that cold windy evening are a simple one dimensional example of how meteorologists simulate the atmosphere. The people designing the simulations then set up a mathematical three dimensional grid over a mathematical sphere roughened to simulate the mountains and plains. Figure 1 shows the globe with lines of latitude and longitude every ten degrees.
Each point where the lines cross defines a grid point. In the National
Center for Environmental Prediction (NCEP), one of the older simulations uses
grid points which are set up for every half of a degree of latitude and
longitude. Where the grid points cross represent places where wind,
temperature, dew point, density, cloudiness, and a number of other things are
calculated using the equations in the list. And at each intersection of
latitude and longitude, there may be as many as 50 points in the vertical above
the ground where calculations are done. As computers get larger and faster, the
spacing has decreased and a model is expected in the near future which divides
the area over North America into a grid with 12 km spacing.
Figure 2 is a closeup of the area around the grid point at the VORTAC EMI. The latitude of EMI is almost 39 deg 30 min and the longitude is almost exactly 77 deg West. So it's easy to interpolate between the grid points at 38 and 39 degrees. Each grid point at the intersection of the latitude and longitude lines has a number of levels. As you very well know, the temperature, pressure, and winds change as you go up. The models recognize this by having different levels which are hopefully close enough in the vertical to catch the layers which may be present. A modern model will have between 30 and 100 levels.
The first step is to interpolate the real data to the grid points. The radiosonde
measurements from Sterling, Virginia (right next to Dulles Airport, at
Philadelphia, and the others nearby are interpolated to the appropriate
elevations at the grid points. In some models, all of the radiosondes and other
upper air data are used statistically to calculate the value at each grid
point. The surface observations, satellite observations, and other
measurements, some from commercial aircraft, are also used. And, in a real
sense, the topography and ground cover are data as well. We don't get direct
measurements of the upper air over the oceans. Satellites with multichannel
instruments fill in these areas but the data are less accurate and precise than
the radiosondes. Clouds also get in the way of the satellite measurements
because satellites using visible and infrared light can't see in and under
clouds. The few microwave instruments available are very coarse and useful only
to detect large patches of rain or snow. But, they are getting better every
year.
The way modelers partially solved the problem of no data out over the oceans is to hope the last model forecasts were reasonably accurate and to use these as data. When new data come in, they adjust the model forecasts to fit the data and use the whole works to start a new model run. We actually keep a running analysis going this way and it has helped improve the simulations. But as new sources of data become available, they are put into the models. Once the major job of determining the atmosphere's temperature, pressure, dew point, wind direction and speed, and cloudiness at each grid point have been determined, the simulation calculations can begin.
In the operational simulations, we use all the laws of physics we can. The names read like an introductory physics text table of contents:
The equations in the list must be put in finite difference form to be used on this grid. Once they are in that form, they are ideal for computers to crank out. 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 to the high school student that by applying a force (usually the pedal on the right), the car (actually the car's mass m) accelerates "a". Use of the other pedal (on an automatic) results in negative acceleration of the mass. Now, as back in driver's ed., acceleration is simply the change of velocity with respect to time.
Expressed in equation form, the change of velocity v is simply the final
velocity minus the initial velocity,
The symbol
represents the change of anything. For me $, the
final checkbook balance minus the initial balance, is usually a slow and
painful negative process involving my checkbook and my bills; however, every
two weeks $
becomes positive, at payday. Unfortunately, it is seldom enough. A change in
time t is simply the final time minus the initial time.
Putting Newton's second law (F = ma or a = F/m) into the definition of acceleration gives
We can specify t, which we usually do as around 5 minutes,
and the initial velocity is the wind speed and direction now (the data) and IF
we know what the forces 'F' are, then everything on the right hand side is
known or specified. Notice that in the equation the velocity on the left of the
equal signs has a subscript of future while the one on the right is the present
velocity. That's the final velocity after the time change 't' from the time we
took the data. Then we have the velocity in the future.
All of the other equations in the list are algebraically put into similar forms.
Of course the forces change as the air blows around the country, but that's what the other equations are for. Each time the winds are calculated, the new pressures, temperatures, densities, humidities, clouds, and ice need to be calculated for each grid point and each level above the grid point. If the technique is valid, we can then simply take the five minute forecast value, call it data and stick it in the right hand side and redo the calculation for the velocity at ten minutes, then repeat for 15 minutes, and so forth for 24 hours. The technique is a reasonable way of solving the equations of physics for in a reasonable time. A 24 hour forecast which takes 35 hours to calculate is fine for research but it isn't practical for people to use. So, the modelers continue to refine the techniques in models of various sizes, applying the results of research to the operational models we pilots use.
If you work out how many calculations a single forecast makes, 720x720 grid points times 50 levels times 7 equations, all for a five minute forecast, your head might swim. Suffice it to say, these models tax the biggest computers available.
So every day at Midnight and Noon Greenwich Mean Time (Z time) the new data are taken. After an hour or so, most of the data have arrived from all over the world and the continuously running model is adjusted for the new data. Once adjusted, the equations are applied at each grid point in the horizontal and at each level for a time step. The results are then used as data for the next time step and so forth to make the 12-hour, 24-hour, 36-hour out to 360-hours, forecasts which are then available to all in grid point values or as charts which you pick up on the web. That's a lot of calculations.
There are different models available for your use. These models differ in the amount of data they collect. Some data take longer than an hour to be transmitted around the world and one modeling group will wait longer for more data. Other centers cut off the data stream after one hour to try to get the results to users faster. Models differ in the techniques used to do the calculations. Also, the way they simulate the growth of clouds differ. As a consequence, much of forecasting today involves knowing the kinks of each of the models and what each is best for.
There is one more stage which the computer can do well. The weather we see where we happen to be is different from that at the grid points which the computer simulations produce. Much of the weather data are taken at airports but rarely does a grid point happen to be at the runway. So statistical equations are used to relate what the models produce and the actual weather at the data boxes. Called Model Output Statistics, these equations give a probability of the actual weather given the best correlated values at the nearby grid points. If you've heard "The probability of precipitation is 30%." the forecaster has used the Model Output Statistics for points at, say, Dulles Airport and Baltimore Washington International, and modified it somewhat to be what he or she expects, to be the best value for the area in between.
Back to Chapter 4,Last modified 12/10/03