138,169 research outputs found
Mixed finite elements for numerical weather prediction
We show how two-dimensional mixed finite element methods that satisfy the
conditions of finite element exterior calculus can be used for the horizontal
discretisation of dynamical cores for numerical weather prediction on
pseudo-uniform grids. This family of mixed finite element methods can be
thought of in the numerical weather prediction context as a generalisation of
the popular polygonal C-grid finite difference methods. There are a few major
advantages: the mixed finite element methods do not require an orthogonal grid,
and they allow a degree of flexibility that can be exploited to ensure an
appropriate ratio between the velocity and pressure degrees of freedom so as to
avoid spurious mode branches in the numerical dispersion relation. These
methods preserve several properties of the C-grid method when applied to linear
barotropic wave propagation, namely: a) energy conservation, b) mass
conservation, c) no spurious pressure modes, and d) steady geostrophic modes on
the -plane. We explain how these properties are preserved, and describe two
examples that can be used on pseudo-uniform grids: the recently-developed
modified RT0-Q0 element pair on quadrilaterals and the BDFM1-\pdg element pair
on triangles. All of these mixed finite element methods have an exact 2:1 ratio
of velocity degrees of freedom to pressure degrees of freedom. Finally we
illustrate the properties with some numerical examples.Comment: Revision after referee comment
Compatible finite element methods for numerical weather prediction
This article takes the form of a tutorial on the use of a particular class of
mixed finite element methods, which can be thought of as the finite element
extension of the C-grid staggered finite difference method. The class is often
referred to as compatible finite elements, mimetic finite elements, discrete
differential forms or finite element exterior calculus. We provide an
elementary introduction in the case of the one-dimensional wave equation,
before summarising recent results in applications to the rotating shallow water
equations on the sphere, before taking an outlook towards applications in
three-dimensional compressible dynamical cores.Comment: To appear in ECMWF Seminar proceedings 201
Description of Atmospheric Conditions at the Pierre Auger Observatory Using Meteorological Measurements and Models
Atmospheric conditions at the site of a cosmic ray observatory must be known
well for reconstructing observed extensive air showers, especially when
measured using the fluorescence technique. For the Pierre Auger Observatory, a
sophisticated network of atmospheric monitoring devices has been conceived.
Part of this monitoring was a weather balloon program to measure atmospheric
state variables above the Observatory. To use the data in reconstructions of
air showers, monthly models have been constructed. Scheduled balloon launches
were abandoned and replaced with launches triggered by high-energetic air
showers as part of a rapid monitoring system. Currently, the balloon launch
program is halted and atmospheric data from numerical weather prediction models
are used. A description of the balloon measurements, the monthly models as well
as the data from the numerical weather prediction are presented
Utilization of satellite data and regional scale numerical models in short range weather forecasting
Overwhelming evidence was developed in a number of studies of satellite data impact on numerical weather prediction that it is unrealistic to expect satellite temperature soundings to improve detailed regional numerical weather prediction. It is likely that satellite data over the United States would substantially impact mesoscale dynamical predictions if the effort were made to develop a composite moisture analysis system. The horizontal variability of moisture, most clearly depicited in images from satellite water vapor channels, would not be determined from conventional rawinsondes even if that network were increased by a doubling of both the number of sites and the time frequency
Mathematical algorithms to maximize performance in numerical weather prediction
Numerical weather prediction models, which involve the solution of non-linear partial differential equations at points on an extensive three dimensional grid, are ideally suited for processing on vector machines. It was logical therefore that the new global forecast model to be implemented at the Meteorological Office should be written in vector code for the CYBER 205. In order to achieve full efficiency and to reduce storage requirements the model used 32-bit arithmetic which was found to provide high enough precision. Unfortunately, however, the trigonometrical and logarithmic functions provided by CDC could only handle 64-bit vectors and, although written in efficient scalar code, did not take advantage of the special facilities of a vector processor. It was therefore necessary to rewrite the functions in vector code to handle both 32 and 64-bit vectors. There was also no half-precision compiler available for the Cyber 205 at that time and so the functions, like the model, had to make extensive use of the special call syntax. This made the code more difficult to write but it allowed much greater flexibility in that it became possible to access the exponent of a floating-point number independently of its coefficient. A description is given of the technique and the results which were achieved are summarized
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