A new and advanced weather forecasting model is receiving its finishing touches up at the Weather Forecasting Center of Space Research (Inpe). With it, Brazil will place itself in the group of countries most advanced in weather forecasting, in the company of countries such as the United States, Canada, Australia and nine Europeans. The quality jump that will allow for a more detailed forecast on a regional scale was brought about by the Eta model (Eta being the name of a letter in the Greek alphabet) developed at the University of Belgrade, Yugoslavia, and perfected in the United States.

In Brazil, the adaptations to the system were coordinated by the physicist Prakki Satyamurty, chief of the Meteorology and Oceanography Laboratory of CPTEC and president of the Brazilian Meteorology Society. The installation of Eta is an advance in terms of trustworthiness and above all in resolution, with more detailed forecasts for all of South America. The CPTEC is already feeding all of the country with short term forecasts (72 hours), medium term (seven to ten days) and long term (up to a quarter of a year).

As well, it has a clients portfolio that includes Petrobras, Eletrobrás, Eletropaulo, Operador Nacional de Sistemas Elétricos, Cargill, Nova Dutra, Folha de S. Paulo, TV Record, TV Vanguarda and Band-Vale. “Directly or indirectly, all of the weather forecasting done in Brazil passes through the CPTEC”, says Satyamurty. “Our homepage – www.cptec.inpe.br – updates every twelve hours more than 600 pages of meteorological forecasting and has 25,000 pages hits per month.”

Besides forecasting the weather, the team monitors forest fires and the risk of forest fires – especially on the large arc of deforesting land that includes Rondônia, Mato Grosso, East Pará, Tocantins and Maranhão. However, the main focus of attention of the group is the development of the Eta model itself.

**Six parameters
**The objective of the mathematical models used in meteorology is to calculate the evolution of six parameters: temperature, pressure, relative humidity of the air and wind – this last one with three components, one for each Cartesian spatial axis. Knowing the values of these parameters at any determined instant, it is possible to forecast, by way of mathematical extrapolation, their future values.For the calculation of the so called global model, the surface of the planet is divided into squares of 100 kilometers (km) per side – that means a level of resolution of 100 km x 100 km. Or that is to say, localities that have up to this distance between them, receive the same forecast. In this manner, the maximum that is managed in forecasting the weather is to estimate average values for relatively extensive areas.

However, with the Eta regional model, it will be possible to obtain, for all of South America and the adjacent oceans, a resolution of 40 km x 40 km – which, in practice, is equivalent to an amplification of more than six times, or that is to say, a meteorological map six times more detailed than the current maps. The professionals involved in the project were trained in the United States, where the first version of Eta was produced that went into operation in 1997, at that time somewhat precariously. Since then, the team has been making the effort to improve the regional model, adapting more and more their parameters to the Brazilian reality.

“With this, we have arrived at the current version, whose main novelty is the incorporation of the meteorological effects produced by vegetation, which didn’t play a part in the original model”, informs the meteorologist Chou Sin Chan, chief of the operations division of the CPTEC. The new Eta also gained a more detailed description of the topography and a more sophisticated evaluation of the mechanism for the formation of rain.

The model covers an area that runs from latitude 55 degrees south (southern tip of the continent) until a latitude of 15 degrees north (Antilles Sea) and of longitude 30 degrees west (Atlantic Ocean, just beyond the island of Fernando de Noronha) until longitude of 90 degrees west (Pacific Ocean, just after the Galapagos Islands). Consequently, it extends well beyond the country’s frontiers, which helps to detect and to incorporate the interference of external factors, such as the temperature of the oceans.

**Calculations and fluids
**On this continental scale, the model allows for forecasts hour by hour for time scales of 12, 24, 36, 48, 60 and 72 hours. “This final time interval” emphasizes professor Satyamurty, “is the maximum limit, because, in meteorology, the price that is paid for the greater detail is the shortening of the forecast time period. Long term forecasts are necessity generic – something along the lines of saying that in the month of September, in the region of the Paraiba Valley the climate will be drier than normal. It is not possible to quantify the idea of “dry”, one can only qualify it with words such as “little”, “considerable” or “more or less”. When one wants more than this – and it is this that the regional model wants -, then you have to sacrifice the time scale.”

Two decades ago, weather forecasting still had a lot of interpretation and depended critically on the ability of the meteorologist in interpreting the available data. Now modern meteorology bases itself essentially on a study of the dynamics of fluids, which combine the knowledge of the laws of physics with techniques of numerical calculus and computer analysis. In Brazil, it began in fact in January of 1995, with the arrival at the CPTEC of the supercomputer NEC SX-3, capable of processing daily the global model on a resolution of 200 km x 200 km.

The current computer, an SX-4, increased the resolution to 100 km x 100 km and the new regional model will allow the CPTEC to reach the mark of 40 km x 40 km. “Already there are tests being done with squares of 20 km x 20 km. And the expectation is that in two years time, it will get down to a resolution of 15 km x 15 km”, estimates Satyamurty. “However, for this to happen, it is indispensable to construct a denser network of meteorological observation stations, and more important, to increase the capacity of data processing.”

The country can already count upon close to 400 meteorological observation stations, automatic or controlled by technicians. They are maintained by the National Meteorological Institute (Inmet), which also has available 22 stations for launching meteorological balloons: there are close to 15 launches per day at a cost of around US$ 300 each. To the Inmet stations are added to the 200 automatic stations of Inpe and of the National Electrical Energy Agency. The data collected from all of these observation stations ends up arriving via satellite at the same destination: the supercomputer SX-4 of the CPTEC laboratory in the town of Cachoeira Paulista.

Capable of carrying out 16 billion arithmetical operations per second at peak time, this machine that cost US$ 5 million is already close to its limit: twice a day it runs through the global model, twice the regional model and is further used in perfecting those models. To reach the resolution of 15 km x 15 km – and greater horizontal detailing, will imply greater vertical detailing -, it is necessary to have an even more powerful piece of equipment.

The machine is now the SX-6, which attains, at its peak, a performance of 800 billion operations per second. Together with all of its other accessories, this supercomputer costs around US$ 20 million. Its purchase was authorized by the Ministry of Science and Technology, but it has as yet to be carried out. If everything goes to plan, the SX-6 should be entering into operation in February of 2002.

**The chaos of weather
**It is amazing that a computer of 16 gigaflops (16 billion operations per second) is becoming insufficient for the demands of the CPTEC. It so happens that the atmospheric processes make up part of the category of chaotic phenomena – or that is to say, not totally predictable, such as periodic phenomena, not totally unpredictable, such as the random ones. Located between one extreme and another, its evolution can be estimated, but only for a restricted time range. From that point onwards, the high sensibility of a chaos system to small disturbances makes any forecast impossible (see in

*Pesquisa FAPESP*nº 65).

In other words, the atmospheric processes can be changed into equations, something that doesn’t happen with random phenomena, but not into linear equations, only possible for periodic phenomena. The meteorology equations are highly non-linear. Everything comes down to an exercise of mathematical extrapolation: knowledge of the parameters at the present moment allows the determination of future values. The problem is that, in order to extrapolate one variable, it is necessary to carry out close to one thousand calculations. Also, due to the non-linearity of the equations, or that is the amount of chaos within the phenomena, these extrapolations can only be done for very short time intervals.

In the regional model, time intervals of two minutes are used. This means that for the one-hour forecasts, it is necessary to carry out 30 x 1,000 calculations. For one day the number of calculations jumps to 24 x 30 x 1,000. For the maximum limit of three days, it would be: 3 x 24 x 30 x 1,000. This is for one variable only. Since there are six variables, the number has to grow a little more: 6 x 3 x 24 x 30 x 1,000. And still we are far from the final number since this sum regards one only atmospheric research unit.

And how many units are there? The regional model divides the South American territory and surrounding seas into 40,000 squares of 40 x 40 km. Each square is the base of an atmospheric column, which must be subdivided into layers of 250 meters in height – which gives roughly 50 vertical levels. Multiplying the number of squares by the number of levels, we get 40,000 x 50 parallelepipeds or atmospheric units. Then we have to multiply the number of units by the quantity of operations necessary in each unit, which gives us: 40,000 x 50 x 6 x 3 x 24 x 30 x 1,000. Doing the calculation we arrive at the final total of 25,920,000,000,000 or almost 26 trillion calculations.

Also, these calculations can’t be done for the period of a year, a month, even a day. For the forecast to be of any practical use, they need to be done in the maximum of one hour. Hence the need for a machine capable of billions of operations per second. “No other science depends so much on a high performance computer than meteorology”, sums up Satyamurty.

**Integrated team
**As well as the supercomputer, the Center needs to have available highly qualified people to operate it. A weather forecasting chart generally is made up from 200,000 lines of instructions. In order to master the various types of knowledge at this level, a group of specialists must be put together, their importance being more evident when one takes into account that the meteorological models are in permanent evolution – not only in ever increasing resolution, but with a more and more complete representation of the physical processes.

The change from the global model to the regional model was a revolution in Brazilian meteorology. “We can better estimate the influence of the topography, of the vegetation and of the water resources”, explains the meteorologist Chou Sin Chan, who gave an example: “That which under a vision of 100 by 100 appeared to be a continuous forest, was revealed to be areas of pasture, with lakes, rivers etc.”

He then went on: “Under low resolution we could speak about rain between Cachoeira Paulista and Rio de Janeiro. When we increased the resolution, we could see that the rain, in reality, extended only up to Resende and would not hit Rio. Under low resolution, we are capable of predicting that a cold front will cross the country tomorrow. In high, we can get to a time scale which is closer to real time.”

“In the global vision there isn’t, for example, the Paraíba Valley”, says Chou. The 100 by 100 model only considered an average between the influences of the Paraiba Valley, the Mantiqueira Ridge and the Mar Ridge. Therefore information on a phenomenon typical of the region was lost, which is “circulation within the valley itself” and responsible for the formation of mists. “This process is contemplated by Eta, which also permits phenomena such a hailstorms, very difficult, if not impossible to determine using the global model. The same is true for the influence of mountains in blocking the entrance of sea winds.”

**Advanced specialists
**“The greater resolution is more a question of engineering, related to the development of supercomputers”, says Chou. “Something quite different is the representation of the physical processes that possess a much smaller scale and for this reason escape in the global model.” They are phenomena such as turbulence and the exchange of energy between the earth, the biosphere and the atmosphere. “Consequently we have a group who specialize in convection currents – transmission of heat in the atmosphere -, and another dealing with the surface and vegetation and a third in orography for the study of mountains. Besides the acquisition of more powerful super computers, our challenge is to improve our understanding of the physical processes – and this depends on research and staff training.”

**The project**

Physical Processes in Regional Models and Improvement in Quality of Weather Forecasting in South America (nº 97/11007-1); **Modality **Regular line of research assistance; **Coordinator **Prakki Satyamurty – CPTEC-Inpe; **Investment **R$ 65,876.21 and US$ 163,344.79