)? Poisson's equation is used to derive an expression that governs the conservation of heat. Other equations used are the conservation of mass, or continuity equation, and the conservation of water equation.
What is numerical modeling? Numerical modeling is simply taking the equations that govern a system and using them to simulate the changes in a system with math. With the right equations and the proper math techniques, scientists can use numbers and variables to create a rather accurate portrayal of atmospheric processes. The equations are solved for specific variables which can be used in visualizations so that we can see how the atmosphere changes with time.
We have already covered several of the equations that are used in numerical modeling. Remember the Equation of Motion from Session 4? It is also known as the conservation of momentum equation, and is one of the primary equations used for simulating the atmosphere. Remember Poisson's Equation and potential temperature ()? Poisson's equation is used to derive an expression that governs the conservation of heat. Other equations used are the conservation of mass, or continuity equation, and the conservation of water equation.
These equations are not all simple. Combining equations and solving for terms can be very difficult. Solutions can be found, but the math involved would take even a supercomputer years to solve accurately. So modelers (those who build models) must simplify the equations. They do this by assuming certain conditions, like a hydrostatic atmosphere, and remove from the equations those terms which seem insignificant. Of course, this also removes term which are needed for solving the equations. So scientists use calculus to approximate remaining terms. By simplifying the equations and using culculus to approximate terms, modelers can develop a set of expressions that, when sent through a computer, can accurately model the atmospheric phenomena of interest.
The goal with numerical modeling is to create the most accurate model with the simplest equations. With each assumption, some accuracy is lost. Modelers must decide how important that accuracy is to the overall goal. And different modelers use different techniques and approximations. A microscale modeler will not use the same set of expressions that a synoptic scale modeler would use -- data on the atmosphere has different levels of importance to each. A synoptic scale modeler who is trying to predict the motion of a cold front is not concerned with the turbulence in the PBL with which a microscale modeler might be concerned. In each case, different approximations and expressions are used.
There are a three types of models on which we will place our focus. First, we will cover some meteorological models, and then some air quality models. Finally, we will talk about plume-in-grid models.
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