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Introduction

When computers of reasonable size began to appear in the 1950's, meteorologists were some of the first users to simulate the weather on computers. The idea was to use the laws of physics to calculate the weather of the future. At first, it was pure research and many uncertainties existed in the equations describing the different components contributing to the weather. The attraction of simulations is that scientists could change parameters such as the energy of water vapor concentration by changing a few numbers on a computer card. Scientists could make two runs (one with and one without the change) in a matter of minutes to hours. After a decade of improvements in both computers and the simulations, the results were no longer interesting science experiments, but "practicing" weather forecasters wanted to see the results each day. Today, the results of these simulations are an integral part of the weather forecasting process.

Modern simulations, sometimes called models, take data directly from monitoring stations (e.g. satellites and ground stations) via communications lines, perform an analysis of the data, and then integrate the meteorological values with the model algorithms (based on the laws of physics) to simulate the current weather and make predictions of future weather. Computer contouring programs calculate the familiar weather maps for people to interpret for near-term weather conditions (meteorology). The models can also be used to calculate long-term weather conditions (climates or climatology).  Since the model results are a big part of the present forecast process, let’s look at how a simple model is constructed.

Although the laws of physics can be written as relatively simple mathematical relationships, solving these equations can be problematic. Two major issues face the modeler: the initial weather conditions and the amount of computer resources. The first is caused by a limited amount of information being available to describe the initial conditions in the simulated system. The second major difficulty is the solving the mathematical equations describing the system. If the system is small (e.g. a few particles), exact or analytical solutions can be calculated. But as the system gets larger, the complexity of the solutions increases dramatically. Simulated environments are often millions of cubic meters in size. An exact analytical solution to the equations does not exist so numerical analysis methods are used to generate approximate solutions. With the limited computer resources available at present, a choice must often be made between a timely calculation versus an accurate solution.

Modeling a simple process (e.g. the temperature of a cup of a hot liquid versus time as it cools) offers an insight into how the more complicated weather simulations work and the type of decisions which are made in order to get a timely and economical result. In this lab, the physics of cooling of a hot body (often referred to as Newton's Law of Cooling) will simulated. One advantage to this approach is that Newton's Law of Cooling has an easy analytical (exact) solution so differences can be observed in the accuracy of the calculation method.

Feedback Mechanisms  and Atmospheric Models

Description of the Sample Problem