Nuñez, M. A. (2003) Domain of validity of some atmospheric mesoscale models. Il nuovo cimento C, 26 (5). pp. 469491. ISSN 18269885

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Abstract
The usual coordinate system in the mesoscale literature is a Cartesian system xyz with its origin at a point on a spherical earth model with the zaxis normal and exterior to the earth. The main form of the momentum equation for theoretical analysis has been dv/dt = −ρ−1∇ p + g−2Ω × v + f r where g is approximated by −gˆz. Several computational models use a version of this equation where z is replaced by a σtype coordinate, and applications of such models have used a horizontal domain D(L) = 2L × 2L with L 650 km but the results of this paper suggest that the equation is valid with L 100 km. However, the necessity of including the effects of synoptic disturbances and reducing the errors from lateral boundaries impose the use of a large(L). This conflict is solved with the use of the correct gravitational acceleration g = −ga2Rr−3 which provides a momentum equation valid on any domain D(L). This is confirmed with an example which shows that the resulting momentum equation can yield the correct pressure field on the whole earth surface. Practical problems limit the use of the coordinate system xyz to L � 500 km. In this case, it is shown that the approximation g ∼ −g(xˆx + yˆy + aˆz)/a can be applied. Some mesoscale models incorporate map projections into model equations to consider the earth curvature. This has motivated the use of such models on a domain with L ∼ 882, 1665 km. Formally, the governing equations from map projections are written in terms of a curvilinear coordinate system xpypzp but it is shown that if xp, yp, zp are taken as x, y, z the resulting momentum equation is valid on a region with L � 100 km.
Item Type:  Article 

Uncontrolled Keywords:  Weather analysis and prediction ; Air quality and air pollution 
Subjects:  300 Scienze sociali > 360 Problemi e servizi sociali; associazioni > 363 Altri problemi e servizi sociali > 363.7 Problemi ambientali (classificare qui la tutela ambientale; l’effetto dei rifiuti, dell’inquinamento, delle iniziative per controllarli) > 363.73 Inquinamento > 363.739 Inquinamento di specifici ambienti > 363.7392 Inquinamento atmosferico 
Depositing User:  Marina Spanti 
Date Deposited:  13 Mar 2020 16:26 
Last Modified:  13 Mar 2020 16:26 
URI:  http://eprints.bice.rm.cnr.it/id/eprint/15157 
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