## 1. Introduction

[2] The tropopause separates the well-mixed troposphere from the stratified stratosphere. The increase of static stability across the tropopause demonstrates that the troposphere and the stratosphere are air volumes with different thermal stratification [*Holton et al.*, 1995]. Different definitions for the tropopause exist which are based on different concepts [*Hoinka*, 1997]. The conventional definition is the thermal tropopause, which is based on the vertical temperature lapse rate [*World Meteorological Organization* (*WMO*), 1957]. The original concept of the dynamical tropopause was based on the isentropic gradient of potential vorticity (PV) [*Reed*, 1955], but it has been most often represented by a particular PV surface to simplify matters [e.g., *Hoskins et al.*, 1985; *WMO*, 1986; *Holton et al.*, 1995].

[3] PV contains both dynamic (absolute vorticity) and thermodynamic (potential temperature) properties and is a conserved quantity in the absence of diabatic heating or cooling and frictional forces [*Ertel*, 1942]. The PV threshold between the troposphere and the stratosphere, which defines the dynamical tropopause, is positive in the Northern Hemisphere and negative in the Southern Hemisphere. PV does not provide a well-defined dynamical tropopause for the tropics and is only used in the extratropics [see, e.g., *Holton et al.*, 1995].

[4] There is no universally used PV threshold for the dynamical tropopause, but the most common choice is the 2 PVU surface (1 PVU = 10^{−6} K m^{2} kg^{−1} s^{−1}, standard potential vorticity unit) [e.g., *Holton et al.*, 1995]. *Hoerling et al.* [1991] found that the 3.5 PVU isoline is the optimal value for tropopause analysis, because it statistically agrees with the thermal tropopause. The selection of the PV threshold is often based on the thermal tropopause. However, a particular PV value may not be appropriate for all isentropes and seasons. Figure 1 shows the zonal and meridional variability of PV at the thermal tropopause, TP_{th}, on 27 April 2003 using European Centre for Medium-Range Weather Forecasts (ECMWF) operational data. Here, PV varies roughly between 0.5 and 7 PVU at the thermal tropopause between the equator and the pole. The typical values of PV at the thermal tropopause increase toward the equator and are larger than 2 PVU at lower latitudes (e.g., 30°N, black dots). As an alternative, *Randel et al.* [2007] used a series of PV isolines (1–4 PVU) in their studies to indicate the approximate location of the dynamical tropopause. *Kunz et al.* [2009] deduced the mean PV at all thermal tropopause heights at the measurement locations during the SPURT (trace gas transport in the tropopause region) campaigns as ≈ 4 PVU. This mean value is greater than the often used value of TP_{dyn} = 2 PVU.

[5] The dynamical tropopause as well as the tropopause region have been analyzed in various ways using properties of the PV field on isentropic surfaces. For example, *Reed* [1955] studied upper level frontogenesis and found a near-discontinuous field of PV which separates high values of PV in the stratosphere from low values in the troposphere. *Shapiro et al.* [1998] introduced the mean potential vorticity (MPV) to describe the PV distribution in the vicinity of the tropopause and to analyze interactions between jet streams at different latitudes. MPV represents a vertical average of PV within a layer bounded by the two isentropic surfaces θ = 280 K and θ = 340 K to capture the tropopause characteristics between the subtropics and the Arctic.

[6] Another method to generalize the dynamical tropopause is the calculation of the isentropic PV gradient [*Hoskins et al.*, 1985]. The distribution of the extratropical PV on each middle world isentropic surface is of interest. The isentropic PV gradient has been used as an indicator for the tropopause in idealized life-cycle experiments when analyzing the transport and mixing of distinct air masses across the tropopause [*Polvani and Esler*, 2007]. Here the quasi-latitudinal PV gradient on isentropic surfaces is sharpest across the jet streams. The pattern of PV takes the form of a narrow band of enhanced PV gradient following the position of the meandering jet stream including perturbations or double jet stream structures [*Schwierz et al.*, 2004; *Martius et al.*, 2010]. These PV gradients are maximized near the jet cores and reflect the existence of barriers to eddy transport across the jet stream [*McIntyre and Palmer*, 1984; *Juckes and McIntyre*, 1987; *Holton et al.*, 1995]. There have been studies concerning the strength of the transport barrier in the tropopause region. *Haynes and Shuckburgh* [2000] used the minimum value of effective diffusivity on each isentropic surface as a measure of the tropopause barrier and as an alternative definition of the tropopause. Also, *Berthet et al.* [2007] defined a “Lagrangian tropopause” based on the number of backward trajectories crossing the tropopause during a fixed time period of 30 days. In their study, only few trajectories cross such a surface, highlighting the transport barrier associated with the tropopause.

[7] Although the importance of PV gradients for the determination of the dynamical tropopause has been discussed, no global determination of the dynamical tropopause based on this concept has been performed. The goal of this work is to present a general method to determine the PV isoline on isentropes that is most appropriate for the dynamical tropopause. On the basis of the isentropic gradient, the method follows a previously developed diagnostic to determine the edge of the polar vortex [*Nash et al.*, 1996; *Steinhorst et al.*, 2005]. *Nash et al.* [1996] calculated the product of isentropic PV gradient and zonal wind speed with equivalent latitude to determine the edge of the polar vortex. A method similar to the Nash criterion is developed in this work to determine the dynamical tropopause. We consider this method to be conceptually more fundamental than using an ad hoc value of PV for the dynamical tropopause. Therefore, the location of the jet streams near the tropopause is of interest, because the isentropic PV gradients maximize in their vicinity [*Martius et al.*, 2010].

[8] The generalized dynamical tropopause on a given isentrope is defined as the PV isoline, where the isentropic PV gradient in equivalent latitude space, constrained by the horizontal wind field, is maximized. The method to define the generalized dynamical tropopause, including a description of equivalent latitude, is presented in section 2. We also introduce an additional parameter to characterize the width of the transition region, indicated by enhanced PV gradients around the dynamical tropopause. This parameter is similar to the boundary parameter of the polar vortex defined by *Nash et al.* [1996]. The spatial and temporal behavior of the PV gradient–based tropopause is examined in section 3 using a daily time series of ECMWF analyses for 2002. A zonal and time mean distribution of the PV at the dynamical tropopause is presented for this time period to provide statistical information for understanding the use of selected PV values as the dynamical tropopause. The implication of the PV distribution at the dynamical tropopause, and the potential application of the boundary parameter, are discussed in section 4.