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Alan Shapiro
,
Katherine M. Willingham
, and
Corey K. Potvin

1. Introduction A longstanding problem in radar meteorology and hydrology is the sensitivity of radar data–based analysis products to the temporal sampling interval 1 (volume scan time). Successive volume scans of radar data are used to generate accumulated rainfall maps (e.g., Austin 1987 ; Fabry et al. 1994 ; Liu and Krajewski 1996 ; Fulton et al. 1998 ; Anagnostou and Krajewski 1999 ; Tabary 2007 ; Gerstner and Heinemann 2008 ; Islam and Rasmussen 2008 ; Villarini and Krajewski

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H. G. Houghton
and
J. M. Austin

the most striking features of thesurface map. Many of these areas move with the samespeed and in the same direction as the surface cyclonesand anticyclones.10. Cyclostrophic component of the accelerational fieldA comparison of the observed deviations from thegeostrophic wind with the cyclostrophic component ofthe gradient wind may be undertaken by consideringtwo examples. If the isobars at 43"N are spaced so asto give a geostrophic wind of 25 mph, and if the radiusof curvature of the trajectory of

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Leon Sherman

. Furthermore, use of such componentsand derivatives facilitates comparison with the oftenmore well-known expressions appropriate for a "flat"earth. Primarily for this last reason, the u, v, w andx, y, z notation is used in this paper.If we compute -6/6y + 6D/6x from (1) and (2),taking into account the identity62 1 ala- =6x 6yr cos cp ah r acpla 1 a tan9 1 ar acprcos cp ax r rcos (0 ax_____--~a2 tan cp 66y ax r 6x'=---360 JOURNAL OF METEOROLOGY VOLUME 9we obtain6% 6% 3 tan Q 6u6x2 6y2 r 6Y2sin2 Q

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François Lott
,
Andrew W. Robertson
, and
Michael Ghil

Rockies torque being 75% of the Himalayas. The Himalayas and Rockies torques evolve quite independently of each other: the correlation between the two is 0.1 for the 3d series and 0.05 for the IS series. In January 1988, for instance, they reinforce each other to give a pronounced algebraic minimum, while in February 1988 the substantial minimum in the Rockies torque is largely compensated by the maximum in the Himalayas torque. The atmospheric patterns associated with the IS mountain torque

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S. Lakshmivarahan
,
J. M. Lewis
, and
D. Phan

). The first operational numerical weather map analysis or objective analysis as it was then called came from the work of Bergthórsson and Döös (1955) —the B–D scheme. The pragmatic and utilitarian B–D scheme established the following guidelines that became central to development of meteorological data assimilation: 1) use of a background field that, in their case, was a combination of a forecast from an earlier time (12 h earlier) and climatology; and 2) interpolation of an “increment” field, the

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Mouris Neiburger
and
James K. Angell

, flight 1039, was tooshort to be useful for computations. The 4-hr averagevelocity was computed from the trajectories for every2-hr position, and is shown by centered arrows withthe speed in knots given numerically above each position. For comparison, the rawin and radiosonde datain the vicinity of the trajectory, as well as the contoursand isotherms taken from the National WeatherAnalysis Center maps, are shown for every 12-hr maptime. In addition to the usual data, the vertical windshear is shown by

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C. E. Leith

by comparison that Eq. (2.8~) is an approximation to the second-order, nonlinear balancecondition and that the Baer-Tribbia formulation isrelated to the bounded derivative balancing formulation described by Kreiss (1979) for a general systemwith widely different time scales.The principal analysis of this paper is based on theresult of the first iteration only, and this is the samein the Machenhauer and the Baer formulations whenstarting from a linearly balanced state with %xo = 0.The nonlinear

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Y. Martinez
,
G. Brunet
,
M. K. Yau
, and
X. Wang

transformed as A conservation law for the isentropic PV, q , is obtained by taking (1/ σ ) × (6) and η × (7) and adding the results: The terms of the right-hand side of (8) are the sink and the source of PV, which are related to diabatic heating and friction, respectively. Another very useful equation can be obtained by taking rσ × (2) and r v × (3) and adding the results. After some algebraic manipulation, the conservation of angular momentum about the rotation axis is given by where ê

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Robert M. Haberle
,
Howard C. Houben
,
Rolf Hertenstein
, and
Tomas Herdtle

, momentumfluxes are diffusive, and the exchange coefficients arecalculated from simple algebraic expressions .involvingthe local Richardson number. The pressure-gradientc 1993 American Meteorological SocietyI JUNE 1993 HABERLE ET AL. 1545force can be specified (constant or time varying) orcomputed from a slope model. In this paper, we calculate it from a slope modelsince the observations used for comparison

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James H. Curry
and
Douglas Winsand

2373 REFERENCESCollet, P. and J.~P. Eckmann, 1980: Iterated maps on the interval as dynamical systems. Progress in Physics, Birkhauser.Curry, J. H., L. Garnett and D. Sullivan, 1983: On the iteration of a rational function: Computer experiments w~th Newton's method. Commun. Math. Phys., 91, 267-277.Gear, C. W., 1971: Simultaneous numerical solution of differential- algebraic equations. IEEE Trans. Circuit Theory. CT-18, 89 95.Gent, P. R., and J. C. McWilliams, 1982: Intermediate

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