Map projections and topography in atmospheric mesoscale modeling

Nútildenez, M.A. (2002) Map projections and topography in atmospheric mesoscale modeling. Il nuovo cimento C, 25 (1). pp. 13-34. ISSN 1826-9885

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Digital Elevation Models (DEMs) of the Earth surface are given by a data set {λk, φk, hk}Kk=1, where hk denotesthe terrain height on a point (λk, φk) of an ellipsoidal Earth model E. Map projections have been widely used in mesoscale modeling to get a DEM on a model domain D of a plane surface P. The procedure consists in applying a map projection to each point (λk, φk) to get a point (Xp k, Y p k ) on D for which the correct terrain height Zp k istak en as hk. Thisimpliesthat P coincides with the tangent plane T to E at a point (λc, φc) which can be located at the centre of D. In thisw ork a method isprop osed to get a DEM {Xk, Yk, Zk}Kk=1 on T whose accuracy is similar to that of the original DEM {λk, φk, hk}Kk=1; the method is extended to get a DEM on a spherical Earth model. The method is based on the transformation T that yieldsthe point (Xk, Yk) on T projected by a point Pλφh in the tridimesional space defined by the data λk, φk, hk, T also yields the correct height Zk of Pλφh with respect to the plane T . By construction (Xk, Yk) is the unique point in T for which the correct terrain height can be computed with the data λk, φk, hk alone. It iss hown that the points( Xpk, Y p k ) from map projections do not coincide with the corresponding one (Xk, Yk), hence the correct height Zp k on each (Xp k, Y p k ) cannot be computed with the data λk, φk, hk alone. The two immediate approximations Zp k ∼ Zk and Zp k ∼ hk are studied. The uncertainty Δhk = ±30 m reported for a DEM is used to show that the estimations Zp k ∼ Zk and Zp k ∼ hk are valid on regionsof 500 × 500 and 60 × 60 km2, respectively. It is shown that if the point (Xp k, Y p k ) isnear the boundary of a model domain of 1300 × 1300 km2 the estimation Zp k ∼ hk hasan error of approximately 30 km, and for a domain of 3300 × 3300 km2 the corresponding error may be 200 km. It is shown by means of analytic solutions of mesoscale meteorological equations that the innacuracy of the DEM {Xp k, Y p k , hk}Kk =1 can yield a wrong wind field.

Item Type: Article
Uncontrolled Keywords: Meteorology ; Weather analysis and prediction ; Reference systems ; Topography; geometric observations
Subjects: 500 Scienze naturali e Matematica > 550 Scienze della Terra > 551 Geologia, Idrologia, Meteorologia
Depositing User: Marina Spanti
Date Deposited: 11 Mar 2020 15:57
Last Modified: 11 Mar 2020 15:57

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