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Thomas Spengler and Joseph Egger

1. Introduction In this study we test the concept of a causal linkage between a potential vorticity (PV) anomaly and the balanced flow that is attributed to it via PV inversion. Attribution seeks to associate to a “feature on a weather chart, such as a vorticity anomaly, a unique influence on the rest of the atmosphere” ( Bishop and Thorpe 1994 , henceforth BT ). The concept of this attribution is encapsulated in the so-called electrostatics analogy ( BT ; Hoskins et al. 1985 , hereafter HMR

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Daniel Gombos and James A. Hansen

piecewise potential vorticity (PV) inversion. The current paper reinterprets Hakim and Torn’s (HT) statistical piecewise PV “inversion” technique as being a PV regression and compares HT08 ’s PV regression results to those from the established dynamical inversion technique of Davis and Emanuel (1991 , hereafter DE91 ) in an effort to explore the applicability of the approach. Section 2 introduces PV, presents the theory of piecewise PV inversion, and describes Davis and Emmanuel’s (DE) piecewise PV

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Timothy J. Dunkerton

1. Introduction Prograde jets are ubiquitous in planetary fluid dynamics ( Baldwin et al. 2007 ). These rotating stratified systems support Rossby waves, quasi-2D turbulent eddies, and their associated lateral transports of angular momentum and potential vorticity (PV), with overturning meridional circulations required to maintain large-scale balance. Various kinds of positive feedbacks exist between the waves, eddies, and mean flow, such that the prograde jets become self-reinforcing. The

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Cristiana Stan and David A. Randall

coordinate surfaces whether heating occurs or not. A detailed analysis of the advantages and disadvantages of using potential temperature as vertical coordinate is given by Hsu and Arakawa (1990) . In this paper, we propose a system of coordinates (PVPT coordinates) that consists of longitude, potential vorticity (PV), and potential temperature (PT). The general definition of potential vorticity, as introduced by Ertel (1942) for the adiabatic atmosphere is where ρ is the fluid density, ζ a is the

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Joseph Egger, Klaus-Peter Hoinka, and Thomas Spengler

1. Introduction Potential vorticity (PV) is an important variable in dynamic meteorology and oceanography and is widely used for the simulation and interpretation of a broad range of flow phenomena (e.g., Vallis 2006 ), where potential vorticity is and is absolute vorticity, η is a function of space and time, and ρ is density ( Ertel 1942 ). Use of is not widespread except for ( θ is potential temperature) where is conserved in adiabatic and inviscid flow. The explicit expression

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Joseph Egger and Klaus-Peter Hoinka

1. Introduction Many aspects of large-scale fluid dynamics can be understood within the framework of “potential vorticity (PV) thinking” ( Hoskins et al. 1985 , hereafter HMR ), where PV plays a central role as a materially conserved quantity in the absence of friction and heating. It is sufficient according to this concept to know the distribution of PV at a certain moment as well as balance and boundary conditions to derive most other variables by PV inversion (PVI) (e.g., Vallis 1996

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Joseph Egger and Klaus-Peter Hoinka

of the wave amplitudes upstream and downstream. This pattern is normally moving eastward, intensifies with increasing negative lag, and becomes weaker for positive increasing lag. An example is presented in Fig. 1 where potential vorticity (PV) is selected as a variable with density ρ , vorticity ζ , potential temperature θ , and Coriolis parameter f . The data evaluation is based on the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) data (see section

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Bjørn Røsting and Jón Egill Kristjánsson

1. Introduction Hoskins et al. (1985) provided a theoretical survey of the concept of potential vorticity (PV), along with applications of PV and low-level boundary temperature anomalies to the interpretation of atmospheric dynamics. Although the PV aspect of atmospheric dynamics had been well known for several decades, having been described by Rossby (1940) , Ertel (1942) , and Charney (1947) , the paper by Hoskins et al. introduced, most likely for the first time, the concept of “PV

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Joseph Egger and Thomas Spengler

1. Introduction Potential vorticity (PV) has been rarely used in diagnostics before the 1970s and 1980s even though its usefulness was demonstrated in a series of papers (e.g., Kleinschmidt 1955 ; Danielsen 1968 ). It was presumably the complicated structure of PV that precluded widespread use of this quantity, where PV is a nonlinear function with absolute vorticity ω a , potential temperature θ , and density ρ . As a matter of fact, lack of data led Kleinschmidt (1955 , p. 96) to

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Steven M. Cavallo and Gregory J. Hakim

1. Introduction Tropopause vortices are extratropical, cold-core cyclones or warm-core anticyclones, defined by closed material contours. On the dynamic tropopause, taken to be a potential vorticity (PV) surface, cyclones are characterized by relatively high pressure (lowered tropopause) and low potential temperature while anticyclones are characterized by relatively low pressure (raised tropopause) and high potential temperature. The Arctic is particularly favorable for these features, with

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