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# Modeling (computer applications)

Computer modeling is a mathematical tool used to analyze complicated systems or to predict events such as floods, climate changes, or population changes. Computer models are applied in many disciplines, from engineering (predicting the strength of a bridge or dam) to economics (predicting inflation rates) to ecology (describing a food chain/web or projecting the survival chances of an endangered species ). A model may consist of a few simple calculations on a spreadsheet, or it may involve millions of calculations on hundreds of thousands of input parameters, as in the case of general circulation models used to describe and predict climate conditions. Both simple and complex models involve quantifying input variables and the relationships between them, in order to produce numeric output that can describe or predict some real world phenomenon or condition. Models are often criticized because they can generalize real-world phenomena unrealistically, or because any errors in initial assumptions are expanded as assumptions are added and multiplied together. However, modeling remains a common tool because it is often the only available method to find answers to important research questions.

Models let researchers "experiment" with systems that do not allow manipulative experimentation. You cannot actually build a power plant just to test its effect on a population, and you cannot deliberately change the temperature of the atmosphere in order to see what happens to plant populations and sea levels. Instead a model can be used to predict probable outcomes of known conditions. Different variables can also be easily introduced in a model, for example, on the computer a programmer can easily add pollution control equipment to the power plant and observe its effect on lung disease rates in the surrounding population, or a modeler can easily reduce worldwide carbon dioxide emissions and calculate the impact on atmospheric temperatures.

Computer models have many applications. Some aid in assessing or visualizing a phenomenon. Three-dimensional geological models are used to help visualize or approximate the volume and dimensions of an aquifer , an oil reserve, or a magma chamber beneath a volcano . A simple ecosystem model can help identify general relationships between populations and resources, by letting the modeler adjust variables and see which arrangements most closely approximate observed data. Other models are used to predict the outcome of known conditions: a demographic model representing known rates of population growth , reproduction, and death can reasonably predict a country's population a century from now. Still other models are used to test "what if" questions. A pollution dispersion model showing how much pollution could spread from a power plant to a town can be used to test different scenarios: What if there were a northwest wind for an entire week? What if the power plant needed to double its energy production? What if the town expanded in the direction of the power plant? Models used to describe or visualize a system are known as descriptive models. Models that project or predict the results of input conditions are known as predictive models.

Anything that approximates or simulates a real-world phenomenon could be considered a model. A plaster replica of a landform, a diagram drawn on paper to describe links in a food web, or a verbal description of a storm could be considered models, because each of these describes or simulates a real phenomenon. Computer models approximate phenomena in the real world by performing calculations on input variables. These calculations produce numeric output that predicts the outcome of the variables in the model. For example, a wolf population model might multiply the number of breeding adults (A) by the average number of pups per litter (P) to produce the expected number of young wolves in a year (N): A x P= N.

This is a very simple, and not very realistic, mathematical model. A computer model can produce a more realistic representation of a wolf population, by incorporating more variables, by using randomized variables, by performing more complicated mathematical functions, and by repeating calculations many times in order to produce a statistically significant number of "experiments."

Models can be composed of variables, parameters, and constants. A variable is any factor that is changeable. The number of breeding adults in a wolf population might change from year to year, as might the number of pups per adult. Parameters are sometimes distinguished from variables as input factors that are unlikely to change: the number of litters in a wolf pack is unlikely to be more than one per year, or the month in which pups are born might reasonably be expected not to change from one year to the next. Constants are input factors that are assumed to be unchanging. In a model of a dam's structure and strength, the force of gravity on the water behind the dam would be a constant. In addition, randomized (stochastic), values can also be used to introduce an element of chance into the model. For example, in a simulation of population change in wolves a realistic birth rate may be somewhere between 4-9 pups per breeding female per year. A computer model can randomly select a number between 4-9, for this variable each time the model is run. In addition there might be a 70% chance that each pup would survive its first year. This stochastic variable could be added to increase the precision of the model's prediction of population at the end of the year. As the computer processes the model it arbitrarily picks a value for the stochastic variable. Stochastic variables can improve a model by making it better represent real events that are somewhat random, or at least unpredictable.

## Deterministic and Stochastic Models

A deterministic model produces a single answer for each set of variables; that is, the input variables determine the outcome. Different results can be produced only by entering different values for the input variables. Deterministic models are useful where the values of input variables are reliably known. For example, if an engineer knows with reasonable certainty the strength of a concrete dam and the force applied by a full reservoir , a deterministic model should be used to calculate the water level that would cause the dam to break. A stochastic model, in contrast, includes an element of randomness, so that there will probably be a different result each time the model is run. For example, a population model might include a slightly randomized birth rate, or a reservoir model might include a randomized variable for rainfall, which in fact varies unpredictably from year to year. An advantage of using a stochastic (random) variable is that it helps the model approximate the fluctuations that can occur in a real system: there is no way to predict the actual number of pups a wolf pack will have each year, but it is possible to predict with some precision the minimum and maximum number that is likely. Running a stochastic model repeatedly can produce a statistically significant sample of experimental results. Statistical analysis can be used to assess the probability of various outcomes, such as a 25% probability that a wolf population will rise over the next 100 years.

## Development of Modeling

Although mathematical models and analog models (physical structures such as clay models of landforms or river basins ) have been used in environmental problem solving for a long time, the growth of modern computer modeling began in the 1960s with the development of computers. One of the first publicized computer models was a climate model that calculated climate conditions based on three input parameters: temperature, air pressure, and wind speed. Since then models have been used to predict weather, stream discharge , soil erosion , population growth, pollution impacts, and many other occurrences. The ability to use a computer greatly increased the complexity of models that could be developed, and the widespread availability of computers increased the number of people developing models for a growing number of purposes. Models are used in environmental monitoring and management, physics, engineering, hydrology , economics, demographics, and many other fields. One reason modeling developed more or less simultaneously in many disciplines is that the techniques of programming a computer to simulate real-world variables are highly portable: the structure of a model used to interpret water flow might be modified and applied to magma movement in the earth or to nutrient flows through a landscape. Modeling is now a widespread technique that is used to help explain how natural systems function and to inform public policy concerning the environment , the economy, and many other issues.

## Sensitivity Analysis, Calibration, and Validation

Once a model is developed it is usually tested against observed events or data to indicate how reliable it is or where its weaknesses lie. One of the first tests usually run is sensitivity analysis. A model's outcome may be more sensitive to changes in one variable or process than another: in a beach erosion model, for example, the predicted erosion rate is likely to be influenced more by wave energy than by sand particle size, even though both factors need to be considered. It is essential to know to which factors the model is most sensitive, because error in estimating those factors could introduce significant error into the results. Sensitivity analysis involves adjusting variables or processes and then running the model to see which factors cause the greatest variability in outcomes.

Once the input variables and relationships in a model are established, the model can be calibrated, or tuned, to make it better represent reality. Calibration usually entails adjusting different parameters in order to produce a result similar to some observed results in the real world. Calibrating a model for forest growth, for example, might involve running the model repeatedly with different growth rates until the model approximates observed historic growth rates and densities.

Validation is like calibration, in that it involves comparing a model's results to observed data. The objective of validation, though, is to demonstrate that the model is reliable. The assumption of model validation is that if the model predicts the correct results in a known situation, then it will probably predict correctly in an unknown, experimental situation.

## General Circulation Models

A type of model that has received much attention since the mid-1980s is the general circulation model, or GCM. This is a class of highly complex models designed to predict with reasonable accuracy the behavior of the earth's atmosphere (climate) or oceans. GCMs have been used to predict worldwide global warming as a result of increased concentrations of carbon dioxide in the atmosphere. GCMs are complex because they simulate the behavior of the atmosphere and the oceans, which have complex three-dimensional movements or flows of air masses or water. Predicting how changes in heat input at one location impacts temperatures and flow rates at another location requires thousands of calculations performed on many interrelated variables at thousands of points in space. Because GCMs must keep track of so many variables and so many points in space, they are usually run on supercomputers that can perform (billions) of calculations per second.

The appropriate complexity of a model depends on its intended use. A model designed to describe ocean circulation over space and time to produce realistic results on which to base public policy might incorporate many variables. A model built to test very general relationships between variables, in order to stimulate a researcher's insight into a small aspect of ecosystem functions, may more appropriately be quite simple, with only a few input parameters and equations.

[Mary Ann Cunningham Ph.D. ]

## RESOURCES

### BOOKS

Gordon, S. I. Computer Models in Environmental Planning. New York: Van Nostrand Reinhold, 1985.

Hardisty, J., D. M. Taylor, and S. E. Metcalfe. Computerised Environmental Modelling. New York: Wiley, 1993.

Starfield, A. M., K. A. Smith, and A. L. Bleloch. Model It: Problem Solving for the Computer Age. New York: McGraw-Hill, 1990.