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Parameterization in a weather or climate model is a method of replacing processes that are too small-scale or complex to be physically represented in the model by a simplified process. This can be contrasted with other processes—e.g., large-scale flow of the atmosphere—that are explicitly resolved within the models.
Parametrization is a mathematical process consisting of expressing the state of a system, process or model as a function of some independent quantities called parameters. The state of the system is generally determined by a finite set of coordinates, and the parametrization thus consists of one function of several real variables for each ...
See Ronald Fedkiw's academic web page for many pictures and animations showing how the level-set method can be used to model real-life phenomena. Multivac is a C++ library for front tracking in 2D with level-set methods. James Sethian's web page on level-set method. Stanley Osher's homepage. The Level Set Method. MIT 16.920J / 2.097J / 6.339J.
In atmospheric science, an atmospheric model is a mathematical model constructed around the full set of primitive, dynamical equations which govern atmospheric motions. It can supplement these equations with parameterizations for turbulent diffusion, radiation , moist processes ( clouds and precipitation ), heat exchange , soil , vegetation ...
Parametrization, also spelled parameterization, parametrisation or parameterisation, is the process of defining or choosing parameters. Parametrization may refer more specifically to: Parametrization (geometry), the process of finding parametric equations of a curve, surface, etc. Parametrization by arc length, a natural parametrization of a curve
In all cases, the equations are collectively called a parametric representation, [2] or parametric system, [3] or parameterization (also spelled parametrization, parametrisation) of the object. [ 1 ] [ 4 ] [ 5 ]
It can be expressed as: = + where X T is the transformed vector; X is the initial vector; The parameters are: . C – translation vector.Contains the three translations along the coordinate axes
On triangular mesh surfaces, the problem of computing this mapping is called mesh parameterization. The parameter domain is the surface that the mesh is mapped onto. Parameterization was mainly used for mapping textures to surfaces. Recently, it has become a powerful tool for many applications in mesh processing.