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For example, Rossby, Kelvin, Poincare waves are all analytical solutions for a certain reduced set of linearized momentum or vorticity equations. It is important to identify that we need to have the non-linear advection term if we hope to produce accurate forecasts. Thus we solve the equations numerically.

How to solve these PDEs? Processors are not capable of doing derivatives - they know how to add and multiply numbers. All other operations are derived from these two. We need to somehow approximate partial derivatives using basic arithmetic operations. The domain of interest say, the globe is discretized on a grid.

Each grid cell will have a value for each of the state variables. For example, take the pressure gradient term in x-direction:. This example used finite differences , centered in space. There are many other methods to discretize partial derivatives, and the ones that are in use in modern models are typically much more sophisticated than this example. If the grid spacing is not uniform, finite volume methods must be used if the predicted quantitity is to be conserved.

Finite element methods are more common for computational fluid dynamics problems defined on unstructured meshes in engineering, but can be used for atmosphere and ocean solvers as well. Parameterized processes may include turbulence and boundary layer mixing, cumulus convection, cloud microphysics, radiation, soil physics, chemical composition etc. Parameterization schemes are still a hot research topic and they keep improving. There are many different schemes for all of the physical processes listed above. Some work better than the others in different meteorological scenarios.

Once all the terms in all the equations have been discretized on paper, the discrete equations are written in the form of a computer code. Most atmosphere, ocean circulation, and ocean wave models are written in Fortran. This is mostly for historical reasons - having long history, Fortran had the luxury of having very mature compilers and very optimized linear algebra libraries. However, Fortran code is still most prevalent in atmosphere and ocean modeling, even in recently started projects.

Finally, an example code line for the above pressure gradient term would look like this:.

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The whole code is compiled into machine language that is then loaded on the processor s. The model program is typically not user friendly with a fancy graphical interface - it is most commonly run from dumb terminals on high-performance multiprocessor clusters. Once started, the program discretely steps through time into the future. The calculated values for state variables at every grid point are stored in an output file, typically every hour simulation time. The output files can then be read by visualization and graphics software to produce pretty images of model forecast.

These are then used as guidance to forecasters to provide a meaningful and reasonable forecast.

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This is not a complete answer. One aspect of weather models consists of Data assimilation or 4D-var. I agree that they are amazing, and the question how do they work is too broad to be answered. So I recommend you read up on data assimilation and in particular 4D-Var. Concepts are somewhat similar in inverse theory, but of much higher dimensionality. In a tiny nutshell:. Weather models and forecasts are governed by systems of differential equations. One starts with the current levels or values of causal variables: temperature, humidity, atmospheric pressure etc.

One also has to factor in the "derivatives," or rates of change of these variables. Hence the need for differential equations, which incorporate both variables and their derivatives to explain various "wave" phenomena such as heat, light, and sound, etc. Even with the current large body of raw knowledge over large parts of the earth, forecasting the weather is still a dicey business, because of the apparent "randomness" of various variables.

Some of them are truly random, others get explained better over time. By "slicing and dicing" variables, and benefiting from past experience, weather forecasts have slowly but surely gotten more accurate over time over larger spaces.

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Increased computational power has also helped. Extending the length of time for more accurate forecasts is trickier, because there are still too many moving parts. For now, it seems that the tools that we have are a "drop in the bucket" compared to the size of the earth and universe some weather patterns may be caused by things happening in interplanetary space , so it is truly amazing that we can often come up with weather forecasts that are more or less accurate.

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How do weather models work? Ask Question. Asked 5 years, 5 months ago. Active 4 years, 6 months ago. Viewed 4k times. Numerical models have been improving over time for several reasons: More and better input data, Tighter grids, and Better approximations. If you'd be willing to suggest an edit, I'd be happy to approve it.

It's concise but also complete. As the cost of supercomputing declined in the s, more businesses began to use supercomputers for market research and other business-related models. Supercomputers have certain distinguishing features. Unlike conventional computers, they usually have more than one CPU central processing unit , which contains circuits for interpreting program instructions and executing arithmetic and logic operations in proper sequence.

The use of several CPUs to achieve high computational rates is necessitated by the physical limits of circuit technology.

Historical development

Electronic signals cannot travel faster than the speed of light , which thus constitutes a fundamental speed limit for signal transmission and circuit switching. This limit has almost been reached, owing to miniaturization of circuit components, dramatic reduction in the length of wires connecting circuit boards, and innovation in cooling techniques e.

Rapid retrieval of stored data and instructions is required to support the extremely high computational speed of CPUs. Still another distinguishing characteristic of supercomputers is their use of vector arithmetic—i. For example, a typical supercomputer can multiply a list of hourly wage rates for a group of factory workers by a list of hours worked by members of that group to produce a list of dollars earned by each worker in roughly the same time that it takes a regular computer to calculate the amount earned by just one worker.

Supercomputers were originally used in applications related to national security, including nuclear weapons design and cryptography. Today they are also routinely employed by the aerospace, petroleum, and automotive industries. In addition, supercomputers have found wide application in areas involving engineering or scientific research, as, for example, in studies of the structure of subatomic particles and of the origin and nature of the universe.

Supercomputers have become an indispensable tool in weather forecasting: predictions are now based on numerical models. As the cost of supercomputers declined, their use spread to the world of online gaming. In particular, the 5th through 10th fastest Chinese supercomputers in were owned by a company with online rights in China to the electronic game World of Warcraft , which sometimes had more than a million people playing together in the same gaming world. Although early supercomputers were built by various companies, one individual, Seymour Cray , really defined the product almost from the start.

The Cray-designed CDC was one of the first computers to replace vacuum tubes with transistors and was quite popular in scientific laboratories. Each time he moved on, his former company continued producing supercomputers based on his designs. Cray was deeply involved in every aspect of creating the computers that his companies built. In particular, he was a genius at the dense packaging of the electronic components that make up a computer. By clever design he cut the distances signals had to travel, thereby speeding up the machines.

He always strove to create the fastest possible computer for the scientific market, always programmed in the scientific programming language of choice FORTRAN , and always optimized the machines for demanding scientific applications—e. While Cray used expensive state-of-the-art custom processors and liquid immersion cooling systems to achieve his speed records, a revolutionary new approach was about to emerge.

Daniel Hillis , a graduate student at the Massachusetts Institute of Technology , had a remarkable new idea about how to overcome the bottleneck imposed by having the CPU direct the computations between all the processors. Hillis saw that he could eliminate the bottleneck by eliminating the all-controlling CPU in favour of decentralized, or distributed, controls. In Hillis cofounded the Thinking Machines Corporation to design, build, and market such multiprocessor computers.

In the first of his Connection Machines, the CM-1 quickly replaced by its more commercial successor, the CM-2 , was introduced. Hillis had originally been inspired by the way that the brain uses a complex network of simple neurons a neural network to achieve high-level computations. In fact, an early goal of these machines involved solving a problem in artificial intelligence , face-pattern recognition.

Multiprocessing in Python: Introduction (Part 1)

By assigning each pixel of a picture to a separate processor, Hillis spread the computational load, but this introduced the problem of communication between the processors. These machines quickly became known as massively parallel computers. Another common artificial intelligence application for multiprocessing was chess. It was then assigned to predict the weather in Atlanta, Ga.