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NOVEMBER 2017 B Ü ELER AND PFAHL 3567 Potential Vorticity Diagnostics to Quantify Effects of Latent Heating in Extratropical Cyclones. Part I: Methodology DOMINIK BÜELER AND STEPHAN PFAHL Institute for Atmospheric and Climate Science, ETH Zurich,€ Zurich, Switzerland (Manuscript received 9 February 2017, in final form 31 July 2017) ABSTRACT Extratropical cyclones develop because of baroclinic instability, but their intensification is often sub- stantially amplified by diabatic processes, most importantly, latent heating (LH) through cloud formation. Although this amplification is well understood for individual cyclones, there is still need for a systematic and quantitative investigation of how LH affects cyclone intensification in different, particularly warmer and moister, climates. For this purpose, the authors introduce a simple diagnostic to quantify the contribution of LH to cyclone intensification within the potential vorticity (PV) framework. The two leading terms in the PV tendency equation, diabatic PV modification and vertical advection, are used to derive a diagnostic equation to explicitly calculate the fraction of a cyclone’s positive lower-tropospheric PV anomaly caused by LH. The strength of this anomaly is strongly coupled to cyclone intensity and the associated impacts in terms of surface weather. To evaluate the performance of the diagnostic, sensitivity simulations of 12 Northern Hemisphere cyclones with artificially modified LH are carried out with a numerical weather prediction model. Based on these simulations, it is demonstrated that the PV diagnostic captures the mean sensitivity of the cyclones’ PV structure to LH as well as parts of the strong case-to-case variability. The simple and versatile PV diagnostic will be the basis for future climatological studies of LH effects on cyclone intensification. 1. Introduction baroclinic instability as the adiabatic energy source re- quired for cyclone development (Charney 1947; Eady Extratropical cyclones are a key component of the 1949), latent heating (LH) due to the formation of global atmospheric circulation because of their transport clouds and precipitation can be an important diabatic of heat, moisture, and angular momentum (Held 1975; contribution affecting mainly cyclone intensification Chang et al. 2002). They contribute substantially to the (e.g., Kuo et al. 1991; Davis and Emanuel 1991; Davis synoptic weather variability in the midlatitudes on a daily 1992; Reed et al. 1993; Stoelinga 1996; Ahmadi-Givi to weekly time scale. When reaching high intensities, they et al. 2004; Marciano et al. 2015; Martínez-Alvarado can cause extreme winds and heavy precipitation with a et al. 2016). In the various studies investigating this huge impact on society, which makes them the third- contribution, potential vorticity (PV) has been estab- costliest natural disasters after tropical cyclones and lished as a key variable (Hoskins et al. 1985). Ertel’s PV earthquakes (e.g., Sigma Research 2016). A large fraction in Cartesian coordinates is defined as of wind extremes in Europe are due to extratropical cy- clones, particularly during winter (e.g., Roberts et al. h Á =u 5 2014). Over 80% of precipitation extremes in the mid- Q r , (1) latitude storm-track regions, in the Mediterranean, and in parts of eastern Asia are associated with extratropical where h 5 = 3 u 1 2 V is the three-dimensional abso- cyclones (Pfahl and Wernli 2012). lute vorticity vector (with u denoting three-dimensional The intensity and, ultimately, impact of extratropical wind and 2 V Earth’s angular velocity), u is the potential cyclones depend on the strength of and interaction be- temperature, and r is density. The change of PV over tween their dynamical driving mechanisms: beside time can be derived from Eq. (1): DQ 1 1 Corresponding author: Dominik Büeler, dominik.bueeler@env. 5 (h Á =u_) 1 (=u Á = 3 F). (2) ethz.ch Dt r r DOI: 10.1175/JAS-D-17-0041.1 Ó 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). Unauthenticated | Downloaded 10/05/21 02:25 PM UTC 3568 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 74 Here, D/Dt 5 ›/›t 1 u Á = is the material derivative op- three anomalous components to be systematically stron- erator, u_ denotes the time derivative of the potential ger for cyclones with lower minimum sea level pressure temperature, and F is the three-dimensional frictional (SLP). Using a similar historical dataset, Binder et al. force per unit mass. The two terms on the right-hand (2016) showed that cyclones with stronger warm con- side of Eq. (2) reveal that PV is conserved (DQ/Dt 5 0) veyor belts (cf. Browning et al. 1973; Madonna et al. in adiabatic, frictionless flows but can be modified by 2014) near their center, and thus stronger diabatic diabatic (u_ 6¼ 0) and frictional processes (F 6¼ 0). The heating associated with more pronounced positive diabatic term of Eq. (2) thus allows for an explicit lower-tropospheric PV anomalies, often intensify more quantification of the contribution of LH (reflected in the strongly in terms of SLP deepening. These two findings potential temperature tendency u_) to the PV distribu- complement the various case studies by indicating the tion in a cyclone. PV distribution to be a good metric for both cyclone The link between the PV distribution in and the dy- intensification and intensity. Consequently, they prove namics of extratropical cyclones as well as the role of the PV concept to be beneficial also for investigating the embedded LH are well understood in a qualitative effect of LH on cyclone dynamics in a climatological sense. The cyclonic circulation is typically associated framework. Considering the importance of LH for present-day with three anomalous components: a positive upper- extratropical cyclones, the question of its role in a tropospheric PV anomaly, a positive potential temperature changing climate arises. Global warming and its associ- anomaly at the surface, and a positive lower-tropospheric ated increase of the atmospheric moisture content (e.g., PV anomaly (Davis and Emanuel 1991; Reed et al. 1992; Schneider et al. 2010) is going to increase the potential Campa and Wernli 2012). By applying PV inversion for LH. Predicting how this will change cyclone intensity techniques, the relative contributions of these anomalies in a future climate, however, remains a challenge for to the wind field and thus the intensity of the cyclone can general circulation models (GCMs). Many of them ex- be determined (Davis and Emanuel 1991). LH due to hibit problems in representing present-day storm tracks cloud and precipitation formation in the lower and (Chang et al. 2013), and there are large intermodel dif- middle troposphere is a crucial process influencing these ferences and thus uncertainties when projecting them anomalies. It mainly forms and maintains the lower- into the future (e.g., Ulbrich et al. 2009; Woollings 2010; tropospheric PV anomaly by diabatic PV generation as Chang et al. 2013; Shaw et al. 2016). This is partly due to expressed in Eq. (2). In addition, it can affect the upper- LH processes, which occur on rather small spatial scales tropospheric PV anomaly, which itself originates from and are thus difficult to capture by the coarse-resolution adiabatic PV advection from the stratosphere, in two GCMs (e.g., Willison et al. 2013; Colle et al. 2015; opposing ways: it can intensify the anomaly via the cy- Trzeciak et al. 2016). In particular, Willison et al. (2015) clonic wind field induced by the lower-tropospheric PV showed a strong amplification of the storm-track re- anomaly (e.g., Wernli et al. 2002) and at the same time sponse to global warming over the northeastern Atlantic weaken the anomaly slightly downstream via diabatic in regional climate simulations with higher-than-usual PV erosion (e.g., Grams et al. 2011). These two op- horizontal resolutions, which they attribute to diabatic posing mechanisms contribute to the typical westward processes. For understanding these diabatic processes tilt between the upper- and lower-tropospheric PV in a warmer and moister climate, the PV framework anomalies, which fosters strong cyclone intensification again provides a useful basis: Pfahl et al. (2015) and (e.g., Stoelinga 1996; Ahmadi-Givi et al. 2004). The- Marciano et al. (2015) found larger lower-tropospheric oretical underpinning for the importance of moist PV anomalies in intense cyclones in a warmer climate, processes for cyclone dynamics can also be obtained which they suggest result from enhanced LH. within the counterpropagating Rossby wave frame- Despite considerable progress in understanding LH work (Bretherton 1966; Heifetz et al. 2004): De Vries effects on extratropical cyclones and in demonstrating et al. (2010) showed that including moist processes in their increasing importance in a warming climate, there life cycle studies of baroclinic waves leads to additional is still a need for a more systematic and quantitative growth regimes that can be described as the interactions description: systematic in the sense that versatile di- of moist and dry Rossby waves. Thereby, the moist agnostic methods should be developed to investigate LH waves are defined based on diabatic PV. More recent effects on individual cyclones in various datasets [output studies applied the PV concept in a climatological of numerical weather prediction (NWP) and climate framework: Campa and Wernli (2012) analyzed the ver- models, as well as reanalysis data] and quantitative in tical PV distribution of a set of historical cyclones in the the sense that these methods need to be able to quantify Northern Hemisphere. They found the aforementioned the contribution of LH to cyclone dynamics, which in Unauthenticated | Downloaded 10/05/21 02:25 PM UTC NOVEMBER 2017 B Ü ELER AND PFAHL 3569 turn allows for comparison between the different data- main assumptions and technical details of the PV sets and model simulations of different climates and diagnostic.

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