1. Introduction
Intense precipitation in summer over western Europe is largely associated with the passage of extratropical cyclones. Using data from the Global Precipitation Climatology Project daily precipitation dataset (Huffman et al. 2001; Adler et al. 2003) and the ERA-Interim product (Simmons et al. 2007; Dee et al. 2011), Hawcroft et al. (2012) determined that more than 65% of total precipitation during June–August is associated with extratropical cyclones over the United Kingdom, northern Europe, and Scandinavia. Heavy precipitation can have an important societal impact, as it can lead to extreme weather events, such as flash flooding. Water vapor condensation in the rising air also releases latent heat, which typically intensifies the ascending motion and the cyclone near the surface (e.g., Tracton 1973; Davis 1992; Stoelinga 1996; Ahmadi-Givi et al. 2004; Grams et al. 2011). For example, studying a cyclone that reached its maximum intensity (based on mean sea level pressure) on 24 February 1987, Stoelinga (1996) showed that its intensity was 70% stronger as a result of coupling between baroclinic wave growth and latent heat release. Until now, studies on latent heat release and cyclone intensification have focused on Northern Hemisphere extratropical cyclones occurring mostly during wintertime (December–February), but also during spring (March–May) and autumn (September–November). On the other hand, the importance of latent heat release, and diabatic processes in general, for the development of summer extratropical cyclones has received much less attention.
Summer extratropical cyclones are generally less frequent and weaker than their winter counterparts. In an analysis of the ERA-Interim dataset between 1989 and 2009, Čampa and Wernli (2012) showed that the central mean sea level pressure of winter cyclones in the Northern Hemisphere can be found in the range between 930 and 1030 hPa, with around 45% occurring in the band between 990 and 1010 hPa and 15% occurring in the lowest band between 930 and 970 hPa. In contrast, Northern Hemisphere summer cyclones can be found within the same range, but 83% occur in the band between 990 and 1010 hPa, and only 0.2% in the lowest band between 930 and 970 hPa. These differences are arguably due to differences in the environmental conditions between summer and winter. The environmental differences include different background state flows as well as higher temperature and saturation humidity, reduced ice phase, and increased insolation during summer. Despite these differences it can be hypothesized that diabatic processes contribute to the intensification of summer cyclones as much as they contribute to the intensification of cyclones in winter and other seasons. Indeed, Dearden et al. (2016) showed that ice processes, such as depositional growth, sublimation, and melting, are important in determining a summer cyclone’s minimum central pressure and track. However, more work is needed to fully understand the importance of diabatic processes in general for cyclone intensification in summer.
This article has two objectives. The first objective is to quantify the heating (calculated as the change in potential temperature following an air parcel) produced during the occurrence of two contrasting summer extratropical cyclones and assess the effects of this heating in terms of changes to the circulation around the cyclones. In contrast to Dearden et al. (2016), the analysis is not restricted to ice processes. Instead, all the diabatic processes represented in the model by parameterization schemes are included. The second objective is to determine the contribution that each relevant parameterization scheme made to the total heating and its effects in these two cyclones. These objectives are pursued through simulations with a numerical model that requires the parameterization of convection. The model includes tracers of diabatic effects on potential temperature (e.g., Martínez-Alvarado and Plant 2014) and potential vorticity (PV) (e.g., Stoelinga 1996; Gray 2006).
The two cyclones occurred during the last field campaign of the Diabatic Influences on Mesoscale Structures in Extratropical Storms (DIAMET) project (Vaughan et al. 2015), which took place in the summer of 2012. Dearden et al. (2016) use the same two cases to examine the effect of ice phase microphysical processes on summer extratropical cyclones dynamics. Both cyclones developed bent-back fronts and exhibited prolonged periods of heavy frontal precipitation (Figs. 1a,b). Despite these similarities, the two cyclones represent two very different intensity scenarios for summer. The first cyclone reached a central pressure minimum of 995 hPa on 19 July 2012. Its central pressure places it in the most frequent cyclone category for summer cyclones over western Europe (Čampa and Wernli 2012): five out of an average of seven annual summer cyclones that reach maximum intensity over western Europe have a minimum sea level pressure between 990 and 1010 hPa (Table 1). In contrast, the second cyclone reached a central pressure minimum of 978 hPa on 15 August 2012. Only 0.8 summer cyclones per year on average have a minimum sea level pressure between 970 and 990 hPa (Table 1). Given its minimum sea level pressure, this cyclone would be more typical of winter than summer.
(a),(b) Radar rainfall rates (courtesy Met Office ©2012 Crown Copyright) and (c),(d) model-derived rainfall rates at (a),(c) 0900 UTC 18 Jul 2012 and (b),(d) 1600 UTC 15 Aug 2012. The color bar on the right of (d) is also valid for (a)–(c). In (c),(d), thin lines represent contours of 850-hPa equivalent potential temperature(K, with a separation of 5 K), and the bold × represents the position of the low pressure center, while the segments A–B and C–D indicate the approximate position of dropsonde curtains. Synoptic charts at (e) 0600 UTC 18 Jul 2012 and (f) 1200 UTC 15 Aug 2012 (courtesy Met Office ©2012 Crown Copyright).
Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0395.1
Number of cyclones over western Europe in summer (Jun–Aug) and winter (Dec–Feb) in the ERA-Interim dataset for the period between 1989 and 2009. The definition of western Europe and the frequency columns were taken from Čampa and Wernli (2012).
The rest of the article is organized as follows. The available aircraft observations, numerical model, and diabatic tracers are described in section 2; section 3 is devoted to the comparison of the simulations with the available observations; the results are presented and discussed in sections 4 and 5, which deal with the July and August cases, respectively, and in section 6, which makes a comparison in terms of diabatic processes between the two cyclones; conclusions are given in section 7.
2. Data and methods
a. Available aircraft observations
The cyclone on 18 July 2012 was the subject of the DIAMET Intensive Observation Period (IOP) 13, while the cyclone on 15 August 2012 was the subject of the DIAMET IOP14. Both cyclones were observed with the instruments on board the Facility for Airborne Atmospheric Measurements (FAAM) BAe 146 research aircraft (Vaughan 2011). See Vaughan et al. (2015) for a summary of the instruments, their sampling frequency, and uncertainty on output parameters.
The dropsonde system is essentially the same as that described by Martínez-Alvarado et al. (2014b). In the flights discussed in this work, the average sonde spacing was limited to a minimum of 4 min along the flight track or 24 km at the aircraft science speed (i.e., the aircraft speed that ensures consistent instrument performance) of 
b. Hindcast simulations
The simulations have been performed using the Met Office Unified Model (MetUM) version 7.3, which is based on the so-called New Dynamics dynamical core (Davies et al. 2005). The model configuration, vertical and horizontal resolutions, and the domain used here are the same as in Martínez-Alvarado et al. (2014b). The model description follows Martínez-Alvarado et al. (2014b), with minor modifications to accommodate details relevant to this work. The simulations have been performed on a limited-area domain corresponding to the Met Office’s recently operational North Atlantic–European domain with 600 × 300 grid points. The horizontal grid spacing is 0.11° (~12 km) in both longitude and latitude on a rotated grid centered around 52.5°N, 2.5°W. The North Atlantic–European domain extends approximately from 30° to 70°N in latitude and from 60°W to 40°E in longitude. The vertical coordinate is discretized in 70 vertical levels with the lid around 80 km. The initial conditions were given by Met Office operational analyses valid at 1200 UTC 17 July 2012 for IOP13 and at 1800 UTC 14 August 2012 for IOP14. The lateral boundary conditions (LBCs) consisted of the Met Office operational 3-hourly LBCs valid from 0900 UTC 17 July 2012 for 72 h for IOP13 and from 1500 UTC 14 August 2012 for 72 h for IOP14.
c. Diabatic tracers
The MetUM has been enhanced by the inclusion of diabatic tracers of potential temperature θ and PV (Martínez-Alvarado et al. 2015). The description of diabatic tracers in this section is derived from Martínez-Alvarado and Plant (2014) and Martínez-Alvarado et al. (2015) with updates and additional details relevant to this work.
Diabatic tracers of θ and PV track θ and PV changes due to diabatic processes. Diabatic potential temperature tracers enable identification of the processes (including turbulent mixing and resolved advection) that bring air parcels to their current isentropic level through cross-isentropic motion. Cross-isentropic motion is interpreted as vertical motion in isentropic coordinates so that a positive change in θ indicates mean cross-isentropic ascent, while a negative change in θ indicates mean cross-isentropic descent. Notice that cross-isentropic ascent does not imply an increase in height, as an air parcel can experience an increase in θ while conserving its geopotential height. Similarly, an increase in height does not imply cross-isentropic ascent, as an air parcel can ascend adiabatically. Diabatic PV tracers enable identification of modifications to the circulation and stability and the diabatic processes responsible for such modifications. Diabatic θ tracers have been previously described in Martínez-Alvarado and Plant (2014) and Martínez-Alvarado et al. (2014b), while the diabatic PV tracer technique has been developed in Stoelinga (1996), Gray (2006), Chagnon and Gray (2009), Chagnon et al. (2013), Chagnon and Gray (2015), and Saffin et al. (2015). The diabatic tracers described here are conceptually related to those described by Cavallo and Hakim (2009) and Joos and Wernli (2012). However, those methods analyze Lagrangian tendencies, whereas diabatic tracers can be interpreted as time integrals of diabatic tendencies along trajectories. Diabatic tracers of θ and PV have been used together in the analysis of forecast errors in upper-level Rossby waves (Martínez-Alvarado et al. 2015).
Equations (2), (3), and (5) are solved using the same numerical methods implemented in the MetUM to solve the evolution equations of the model’s prognostic variables (velocity components, θ, and moisture variables) (cf. Davies et al. 2005). However, there are details in the numerical representation of the equations of motion that have been specifically designed for the prognostic variables. These details include the staggered distribution of the variables on the Arakawa C grid, which implies differences in the advection of PV computed from prognostic variables and as a tracer (Whitehead et al. 2014) or the treatment of the advection of θ (Davies et al. 2005). These details lead to an unavoidable mismatch between the advection of φ and that of the sum 
d. Integral interpretation of θ tracers: Cross-isentropic mass transport
Given that the 
e. Integral interpretation of PV tracers: Circulation
3. Comparison between simulations and observations
The two extratropical cyclones in this study exhibited similarities. The IOP13 cyclone traveled around 600 km during 18 July 2012; the IOP14 cyclone traveled around 700 km during 15 August 2012. Furthermore, both cyclones produced precipitation for prolonged periods. Precipitation associated with the IOP13 cyclone started around 1800 UTC 17 July 2012 over Northern Ireland and ended at around 0100 UTC 19 July 2012 across northern England. Radar rainfall rates at 0900 UTC 18 July 2012 show heavy precipitation on a band over Scotland, corresponding to the detached warm front, and scattered precipitation over the southwest of England, corresponding to weak precipitation at the cold front (Fig. 1a). Precipitation associated with the IOP14 cyclone started before 0000 UTC 15 August 2012 and continued until the end of the day, passing over the United Kingdom and Ireland from south to north (Fig. 1b). These features were well represented by the simulations. Figure 1c shows the rainfall rate for IOP13 derived from the simulation corresponding to the time shown in Fig. 1a (i.e., T + 21). Figure 1d shows the corresponding rainfall rate for IOP14 for the time shown in Fig. 1b (i.e., T + 22). In both cases, the simulations compare well with radar observations in terms of location and intensity of precipitating features, bar differences in the resolutions of both datasets. However, one feature that the model fails to represent is the clear split into two precipitation bands over the east of England in IOP14 due to the gap between the system’s cold and warm fronts (Fig. 1b), even though the model is able to represent the gap in the equivalent potential temperature 
Despite the similarities in speed and precipitation, the cyclones represent very different synoptic conditions. The synoptic chart for IOP13 at 0600 UTC 19 July 2012 shows a T-bone structure (Shapiro and Keyser 1990) (Fig. 1e). The IOP13 cyclone was a shallow system that deepened slightly after the time shown, reaching 995 hPa at 0600 UTC 19 July 2012. However, its structure remained largely the same from 0600 UTC 18 July 2012 until the end of its life cycle. In contrast, the IOP14 cyclone was a relatively deep system for a summer cyclone. Figure 1f shows the IOP14 cyclone at 1200 UTC 15 August 2012 with its bent-back front (analyzed as an occluded front) wrapped up around the system’s low pressure center. These features were also well represented by the simulations as indicated by the 850-hPa 
Several quantities derived from the dropsonde observations during the first IOP13 leg are shown in a vertical cross section in Figs. 2a and 2c. Figure 2a shows zonal velocity u, θ, and relative humidity with respect to ice 
Vertical section along segment A–B in Fig. 1c showing in color shading (a),(b) zonal velocity (
Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0395.1
Figures 2b and 2d show vertical sections through segment A–B (Fig. 1c) for the same quantities as in Figs. 2a and 2c, but derived from the simulation at 0900 UTC 18 July 2012 (T + 21). Segment A–B approximately corresponds to the aircraft’s track during the first IOP13 dropsonde leg. Zonal velocity has similar magnitude in model and observations (Fig. 2b). However, the system’s CCB extends farther up in the model than in observations, reaching 850 hPa. The column with 
Now we compare the dropsonde observations obtained during IOP14 with the simulation at 1600 UTC 15 July 2012 (T + 22). The vertical structure of dropsonde-derived u, θ, and 
As in Fig. 2, but for the vertical section along segment C–D in Fig. 1d at 1600 UTC 15 Aug 2012 (IOP14). The model output in (b),(d) corresponds to the output of 22-h integration. The position of a low-level jet (LLJ) is shown. Notice that the color bars in Fig. 2 and here are different.
Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0395.1
4. Diabatic effects in IOP13
Figure 4 shows 
Maps of 
Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0395.1
Figure 5 shows 
Vertical section along segment E–F in Fig. 4 showing in color shading (a) 
Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0395.1
Vertical section along segment E–F in Fig. 4 showing in color shading contributions to PV modification from (a) BL and turbulent mixing, (b) convection, (c) cloud microphysics, and (d) radiation after 21 h of integration at 0900 UTC 18 Jul 2012 (T + 21; IOP13). Grid points where PV residual error is larger than 1 PVU and relative PV residual error is larger than 50% have been masked out. Thin black lines indicate potential temperature contours (K, with a separation of 2.5 K). Bold black lines indicate 2-PVU contours. Bold red lines indicate the position of the system’s warm (solid) and cold (dashed) fronts.
Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0395.1
A deep column of air originating from the layer 
The low-level positive PV anomaly, which in the 305-K isentropic surface appears as an elongated east–west feature, extends from the surface up to at least the 310-K isentropic level (500-hPa isobaric level) in this section. This low-level PV anomaly has been diabatically generated. Figure 5b shows that the PV within the anomaly has increased by more than 2 PVU as a result of diabatic activity. The lower part of the low-level PV anomaly (below 750 hPa) exhibits negligible θ change (Fig. 5a). Yet it shows strong changes in PV because of BL and turbulent mixing processes (Fig. 6a). This part of the low-level PV anomaly is constituted by air that, moving quasi isentropically, has traveled through the regions of PV production induced by BL heating [since 
There are also shallow low-level regions of positive diabatically generated PV below 800 hPa, particularly visible to the north of 58°N (Fig. 5b). These regions of positive diabatically generated PV are generated by radiative cooling due to low-level clouds at the BL top. Radiative cooling in these regions produces cross-isentropic descent. Moreover, it destabilizes clouds and triggers BL and mixing processes, which tend to increase θ (Fu et al. 1995). The effects on PV induced by radiation have greater magnitude than those induced by BL processes so that the net effect in the final diabatically generated PV is a dipole structure with positive on top of negative diabatically generated PV (see Fig. 5b).
The upper troposphere is characterized by a PV reduction spanning a large section between 52° and 59°N and between 310 and 322 K (Fig. 5b). The region north of 56°N, between 315 and 325 K, exhibits strong θ change in the interval 
5. Diabatic effects in IOP14
Figure 7 shows 
As in Fig. 4, but for IOP14 at 1500 UTC 15 Aug 2012 (T + 21) at the isentropic levels (a) 320 and (b) 305 K. The segment G–H indicates the position of the vertical sections in Figs. 8 and 9. WCB1 and WCB2 indicate the primary and secondary WCB branches, respectively.
Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0395.1
Figure 8 shows 
As in Fig. 5, but for the vertical section along segment G–H in Fig. 7 at 1500 UTC 15 Aug 2012 (T + 21; IOP14). Bold red lines indicate the position of the system’s occluded warm (solid) and surface cold (dashed) fronts. Labels C1, C2, and C3 indicate the positions of columns of cross-isentropic ascent. Label C4 indicates the position of a PV tower.
Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0395.1
As in Fig. 6, but for the vertical section along section G–H in Fig. 7 at 1500 UTC 15 Aug 2012 (T + 21; IOP14). Bold red lines indicate the position of the system’s occluded warm (solid) and surface cold (dashed) fronts. Label C1 represents the position of the strongest column of cross-isentropic ascent.
Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0395.1
The cross-isentropic mass transport in IOP14 is much more complex than that in IOP13 (cf. Fig. 5a). Unlike IOP13, in which there was only one main column of strong cross-isentropic ascent, strong cross-isentropic ascent occurs in at least four columns throughout the cross section in IOP14. A comparison between the intersection of the columns of cross-isentropically ascending air intersecting the 320-K isentropic level and the structures shown in Fig. 7 suggests that these columns are all part of the same airstream. This airstream corresponds to the system’s WCB, the secondary branch of which (WCB2) was tightly wrapped around the cyclone’s center by this time (labeled C1–C3 following the WCB2 spiral). The highest column of cross-isentropic ascent (labeled C1 in Fig. 8) is located around 54°N. Column C1 extends from around 800 hPa (300 K) up to the upper troposphere, which by this time is located around 200 hPa (335 K). The diabatically generated PV within this column is characterized by a core of positive diabatically generated PV along the ascending axis over 54°N, extending from 900 hPa to around 380 hPa (Fig. 8b). The core of positive PV is surrounded by negative diabatically generated PV from 600 hPa to tropopause level (around 200 hPa). Column C1 is part of the WCB before the split; two smaller columns (labeled C2 and C3 in Fig. 8), located south of 54°N, are part of WCB2. The column tops for columns C1 and C2 are also close to the local tropopause and their diabatically generated PV structure resembles that of column C1’s.
The air within the principal ascending branch of the system’s WCB (column C1 in Fig. 8) produces similar PV patterns to those produced by the WCB in IOP13. The parameterization of BL processes and mixing is the main parameterization responsible for the negative diabatically generated PV in the upper troposphere within this airstream (Fig. 9a). However, in this case the negative diabatically generated PV is largely compensated by positive diabatically generated PV because of the cloud microphysics parameterization (Fig. 9c), which indicates stronger heating due to this parameterization in IOP14 than in IOP13. Thus, the core of positive diabatically generated PV over 54°N is formed by BL process at lower levels (below 500 hPa) and by cloud microphysical processes at upper levels (above 500 hPa). Dearden et al. (2016) have found, via independent simulations of this same case, that at these levels the heat released during vapor growth of ice within the WCB is a major factor in the creation of positive PV anomalies. The induction of PV sources and sinks due to the representation of latent heat release in the convection parameterization is a secondary contributor to the negative PV production at upper levels.
A column directly above the cyclone’s center (labeled C4 in Fig. 8) has a different structure to that of C1, C2, and C3 previously described. This column, characterized by high PV values that extend the 2-PVU contour from tropopause level to the surface, constitutes a PV tower (Rossa et al. 2000). The PV tower exhibits intense positive PV modification in its lower part (below 315 K) and negative PV modification in its upper part (Fig. 8b). A PV tower is typically composed of air from three different regions: tropopause-level air, low-level warm-sector air, and low-level cold-conveyor-belt air (Rossa et al. 2000). The air composing each of these sources has a particular heating and diabatic PV evolution (Rossa et al. 2000). The following interpretation is based on the findings by Rossa et al. (2000).
The air from tropopause level entering the PV tower, located above 400 hPa in Fig. 8a, exhibits negligible θ change, which can be inferred by comparing the 
The warm-sector air entering the PV tower, located toward the northern flank of the PV tower between 700 and 450 hPa in Fig. 8a, has undergone cross-isentropic ascent mainly as a result of heating and mixing within the BL, but with contribution from the convection parameterization. As the air ascended cross-isentropically through the BL, the cloud microphysics parameterization produced a small negative contribution to the θ change (not shown). The positive PV change is driven by BL and turbulent mixing processes (Fig. 9a) and heating due to the convection parameterization (Fig. 9b). However, there is also a negative contribution induced by radiative cooling taking place in clouds at BL top level (Fig. 9d).
The air moving within the system’s CCB into the PV tower, being drier and colder than that from the warm sector, also experiences less cross-isentropic ascent than the warm-sector air. This air mass corresponds to the southern flank of the PV tower between 700 and 450 hPa in Fig. 8a. As for the warm-sector air, BL and mixing processes drive cross-isentropic ascent, while cloud microphysics tends to counteract this ascent by cooling the air as it ascends cross-isentropically through the BL. However, the magnitude of BL net heating is weaker in the cold-conveyor-belt air than in the warm-sector air. Another important difference between the warm-sector air and that of the cold-conveyor-belt air is given by the contribution to heating from the convection parameterization, which in the latter is negligible. The PV increased as the CCB air within the PV tower traveled through regions of PV production induced by heating as a result of cloud microphysical processes (Fig. 9c). However, this air also traveled through regions of negative PV production induced by BL and mixing processes (Fig. 9a).
6. Cyclone comparison
The results presented so far are restricted to the selected horizontal and vertical sections. A more thorough comparison is achieved by the integral diagnostics within cylindrical volumes centered on the cyclones under comparison. The results from such integral diagnostics, formulated around the diabatic tracers, are presented in the following two sections.
a. Cross-isentropic mass transport
In this section, 
(a),(b) Cross-isentropic mass transport within a 1000-km spherical cap concentric to the cyclone for (a) IOP13 and (b) IOP14. The lines are colored according to the 
Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0395.1
The minimum θ value in each cyclone illustrates a major difference between the environments of these cyclones: IOP13 evolves in an environment around 10 K colder than does IOP14, which also implies the potential for greater moisture availability near the surface in IOP14, consistent with the findings by Madonna et al. (2014), even though the actual amount of moisture available also depends on surface moisture fluxes and lapse rate. The locations of the 2.5th and 97.5th percentiles essentially determine the range of the 
Figures 10c and 10d show θ changes for the bin 
Figure 11 shows the contributions to the θ changes in Figs. 10c and 10d from the four parameterized processes considered here. The BL and turbulent mixing parameterization is the main contributor in both cases (Figs. 11a,e). The convection parameterization starts contributing about 5 h earlier in IOP14 than in IOP13 (Figs. 11b,f). Furthermore, this parameterization acts on a much wider layer in IOP14 than in IOP13, spanning from the 75th percentile up. This is consistent with the differences between cases in terms of convective activity, as described in sections 4 and 5. The cloud microphysics parameterization in IOP14 starts contributing about 2 h later than the convection parameterization in IOP14, but about 9 h earlier than the cloud microphysics parameterization in IOP13 (Figs. 11c,g). In the atmosphere, like in a numerical model, the main sources of heating are water phase changes. The three parameterization schemes that contribute to total heating do so mainly through latent heat release, including the BL and turbulent mixing parameterization. The latent heat release associated with the latter scheme can be found by tracing the changes in cloud liquid water and associated θ changes due to this parameterization [as in Martínez-Alvarado and Plant (2014)]. In the atmosphere, unlike in a numerical model, phase changes are not distributed among parameterization schemes, and the challenge for numerical models is to achieve the actual heating and induced cross-isentropic mass transport through the interaction between parameterization schemes and between the parameterization schemes and the dynamical core. These aspects are not always well represented by current numerical models (e.g., Martínez-Alvarado et al. 2015).
Heating due to the parameterization of (a),(e) BL and turbulent mixing; (b),(f) convection; (c),(g) cloud microphysics; and (d),(h) radiation for the bin with 
Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0395.1
In general, the 2.5th-percentile lines in Fig. 10 describe slow cross-isentropic subsidence in both cyclones, corresponding to the widespread cross-isentropic subsidence discussed in sections 4 and 5. This subsidence is associated with cooling. Figures 10c and 10d show that the lower part of the band with 
The bin 
b. Circulation
When a large integration region (~1000 km) is used, the cyclones have similar vertical structures, an effect that has been noted in previous studies (e.g., Čampa and Wernli 2012). When this is done for IOP13 and IOP14 at the end of 21-h simulations, the 
When smaller length scales are considered, the differences between cyclones are more apparent. The results corresponding to the last 18 h in each simulation using, as integration regions, 500-km-radius circles concentric to each cyclone are shown in Fig. 12. The cylindrical control volumes move with the cyclone center defined by minimum sea level pressure. These results are not qualitatively sensitive to the choice of radius, which has been confirmed by performing alternative analyses with 400- and 600-km radii (not shown). The figure shows 
Vertical profiles of average isentropic vorticity (black) for a 500-km spherical cap concentric to the cyclone for (a)–(d) IOP13 and (e)–(h) IOP14: (a) 1500 UTC (T + 3) and (b) 2100 UTC 17 Jul 2012 (T + 9); (c) 0300 UTC (T + 15) and (d) 0900 UTC 18 Jul 2012 (T + 21); (e) 2100 UTC 14 Aug 2012 (T + 3); and (f) 0300 UTC (T + 9), (g) 0900 UTC (T + 15), and (h) 1500 UTC 15 Aug 2012 (T + 21). The frames also show contributions from conserved PV (blue) and diabatically generated PV (orange) and the value of planetary vorticity at the position of the cyclone’s center (gray vertical line). The dashed lines represent the conserved and diabatically generated PV contributions with the contribution from the residual added and subtracted as an indication of uncertainty.
Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0395.1
The IOP13 cyclone developed in a weakly cyclonic environment (
In contrast, the IOP14 cyclone developed in an already highly cyclonic environment (
To conclude this section, the contributions from individual diabatic processes to the 
Vertical profiles of contributions of BL and turbulent mixing processes (BL), parameterized convection (Conv), cloud microphysics processes (Microphys), and radiation (Rad) to average isentropic vorticity for a 500-km spherical cap concentric to the cyclone for (a)–(d) IOP13 and (e)–(h) IOP14: (a) 1500 UTC (T + 3) and (b) 2100 UTC 17 Jul 2012 (T + 9); (c) 0300 UTC (T + 15) and (d) 0900 UTC 18 Jul 2012 (T + 21); (e) 2100 UTC 14 Aug 2012 (T + 3); (f) 0300 UTC (T + 9); (g) 0900 UTC (T + 15); and (h) 1500 UTC 15 Aug 2012 (T + 21).
Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0395.1
7. Conclusions
To investigate the importance of diabatic processes in determining the intensity of summer extratropical cyclones, the diabatic contributions to the evolution of two such cyclones have been analyzed. The two cyclones occurred in the vicinity of the United Kingdom during the summer of 2012. Despite similarities in precipitation and cyclone stationarity, the cyclones represented very different synoptic conditions. The first cyclone, observed during the DIAMET IOP13, deepened down to a minimum central sea level pressure of 995 hPa. In contrast, the second cyclone, observed during the IOP14, was a much deeper cyclone, with a minimum central sea level pressure of 978 hPa. The analysis was performed through simulations performed with the MetUM enhanced with diabatic tracers of θ and PV. The simulations were compared with Met Office operational analysis charts, radar rainfall observations, and dropsonde measurements. Although summer extratropical cyclones typically possess much weaker winds than winter cyclones, the observations showed that water vapor mass flow along the warm conveyor belt of the stronger cyclone examined here was over half the magnitude of water vapor mass flow reported by other authors (e.g., Zhu and Newell 1998) in wintertime atmospheric river cases where the cyclone and its warm conveyor belt move slowly. The large-scale environment was represented well by the model in both cases. However, when the water vapor mass flow rearward relative to the motion of the cyclone is calculated for the weakest cyclone, the model overestimates the mass flow by approximately a factor of 2. This is because of a greater flow and humidity extending above the boundary layer and deeper into the lower troposphere than observed. Despite these differences, consistent with a systematic wet bias in the model, the simulations provided a good representation of the mesoscale structure for at least 21 h for IOP13 and 22 h for IOP14.
The environment during IOP13 was colder and, therefore, had a lower saturation mixing ratio than the environment during IOP14. These contrasting environmental conditions led to weaker diabatic effects during IOP13 than during IOP14. The cyclone during IOP13 was characterized by a single column of large-scale ascent, corresponding to the system’s WCB, and weak low-level positive PV anomalies. In contrast, the cyclone during IOP14 was characterized by a powerful WCB that wrapped in a spiral around and toward the cyclone’s center, forming several columns of large-scale ascent. Furthermore, this cyclone exhibited very strong positive PV anomalies, extending throughout the troposphere and constituting a PV tower.
In both cases, the low-level positive PV anomalies were diabatically produced. However, the amount of diabatic activity and the contribution from different parameterized processes were different in each case. In IOP13 the processes that contributed the most to the production of the low-level positive PV anomaly were the BL and turbulent mixing and cloud microphysics parameterization schemes. The convection parameterization also contributed to the production of the low-level positive PV anomaly in IOP14. The microphysics scheme gave rise to more positive PV within the WCB in both cases in the mid to upper troposphere and negative PV anomalies above this near the tropopause in the ridge wrapping above the bent-back surface front. These anomalies are hypothesized to arise from latent heat release within upper-tropospheric clouds. It is likely that condensation associated with saturated ascent dominates the PV anomalies associated with both the BL and turbulent mixing and cloud microphysics parameterizations.
Under the integral interpretation of diabatic θ tracers, the materially conserved tracer 
The use of the integral interpretation of diabatically generated PV tracers in terms of area-averaged isentropic vorticity 
The explanation for both effects was found by applying the PV impermeability theorem (Haynes and McIntyre 1987) to diabatic PV tracers. It was deduced that the ratio of the along-isentropic nonadvective flux term to the cross-isentropic flux term in the equation of diabatically generated circulation scales as 
The analysis of these two contrasting summer cyclones has shown the suitability of diabatic tracers for the analysis of diabatic effects. Moreover, it has led to advances in the theory of diabatic tracers under the form of an integral interpretation. The integral interpretation of diabatic θ and PV tracers establishes a new framework for a systematic comparison of diabatic processes and their importance for the evolution of extratropical cyclones. This interpretation provides a quantitative way of measuring the effects of different diabatic processes (e.g., BL processes and mixing, convection, and cloud microphysics) in a region rather than at a single point. Furthermore, the integral interpretation makes the tracers effectively independent of model resolution. A potential use of this property is the assessment of consistency between simulations at different resolutions, which is essential if truly seamless numerical weather and climate models are to be developed. Together with new observational techniques, including airborne measurements and satellite observations, the methods presented here can prove useful in answering questions, such as what isentropic levels WCB outflows should reach (e.g., Martínez-Alvarado et al. 2014b), which is important in determining the effects on PV anomalies due to WCB outflows (Methven 2015). Another related question is whether some modifiers of isentropic vorticity due to parameterized processes are missing in current numerical weather and climate models. The answers to these questions have implications for the development of new parameterizations of diabatic processes in numerical weather and climate models.
Acknowledgments
This work was initiated by the MSc dissertation of Ms. Na Zhou, supervised by Professors Gray and Methven at the Department of Meteorology, University of Reading, and was funded by the UK’s Natural Environment Research Council (NERC) as part of the DIAMET project (NE/I005234/1). The authors thank the following persons and organizations: Dr. Jeffrey Chagnon, for useful discussion during the initial development of this work and, together with Mr. Leo Saffin, for the implementation of PV tracers into the MetUM; Dr. Christopher Dearden, for useful comments on the initial manuscript; two anonymous reviewers, for interesting and insightful comments that led to the improvement of the manuscript; the Met Office, for making the MetUM and associated initial and lateral boundary condition files available, and the NERC-funded National Centre for Atmospheric Science (NCAS)–Computational Modelling Services, for providing computing and technical support. The BAe 146 aircraft was flown by Directflight Ltd. and managed by FAAM on behalf of NERC and the Met Office. Model output from the simulations of IOP13 and IOP14 is available through the NCAS British Atmospheric Data Centre (badc.nerc.ac.uk). The MetUM branches used are /dev/oma/vn7.3_thetra_residual/ revision number 15717 and /dev/LSaffin/vn7.3_PV_tracers_budget/ revision number 16506.
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