1. Introduction
Midlatitude cyclones form during all four seasons, and over a wide range of latitudes, in both maritime and continental regions. Thus, the mean environmental temperatures in which they develop (here denoted T0) can vary widely. Moreover, owing to anthropogenic emissions of greenhouse gases, the distributions of T0 experienced by these cyclones may gradually change in coming decades (IPCC 2013), although likely to a smaller degree than seasonal and latitudinal variations in the current climate. To interpret the behavior of such cyclones over different seasons, latitudes, and climates, it is useful to conceptually understand their sensitivities to T0. This sensitivity has not received extensive attention from a dynamical perspective, in part because it is secondary in classic quasigeostrophic theories of dry baroclinic instability (Eady 1949; Charney 1947). In these theories, the linear growth rate of baroclinic instabilities depends on the meridional baroclinicity and static stability, neither of which depends strongly on T0.
Midlatitude cyclones may still be regulated by T0 through its indirect control over diabatic processes like latent heat release. At a fixed relative humidity, the atmospheric water vapor content increases by around 7% K−1 and, hence, nearly doubles with every 10 K of warming. This increased moisture content supports enhanced latent heat release, which influences the parent baroclinic wave by destabilizing ascending motions and generating diabatic potential vorticity (PV) anomalies that interact with dry baroclinic PV anomalies (e.g., Hoskins et al. 1985; Davis and Emanuel 1991; De Vries et al. 2010). In the vertical, a diabatically generated PV tendency dipole straddles the active cloud layer, with cyclonic tendencies below and anticyclonic tendencies above.
Using the semigeostrophic equations with parameterized condensational heating, Emanuel et al. (1987) found that such heating led to faster wave growth, at a reduced horizontal scale. However, in subsequent studies that modified the parameterization of cloud latent heating for added realism, the positive impacts on cyclone growth weakened or even reversed (Whitaker and Davis 1994; Mak 1994). Lapeyre and Held (2004) evaluated the dynamics of moist baroclinic eddies using a two-layer quasigeostrophic model, also with parameterized cloud diabatic heating. As the heating rate was increased, the eddies transitioned from baroclinic wave structures analogous to dry cyclones to intense, vortex-dominated structures with no dry analog.
Case studies mostly support Emanuel et al. (1987)’s finding that latent heat release contributes to parent-cyclone intensification. For example, using real-case numerical simulations and piecewise PV inversion, Stoelinga (1996) found that diabatically generated PV anomalies within an intense Atlantic cyclone greatly amplified the low-level cyclonic circulation and the phase locking between lower- and upper-level PV anomalies. Similarly, Ahmadi-Givi et al. (2004) found that a diabatically generated low-level cyclonic PV anomaly dominated the spinup of an Atlantic cyclone at low levels. The cyclone growth was aided by the corresponding anticyclonic PV anomaly aloft, which eroded the downstream flank of the upper trough to reinforce an upstream phase tilt. While other case studies have reached similar conclusions (e.g., Reed et al. 1988; Willison et al. 2013), some have also found the opposite. Notably, in a case study of a winter cyclone over the central United States, Davis (1992) found that differential eastward propagation of the upper-level dry baroclinic PV anomaly and a lower-level diabatic PV anomaly led to cyclolysis.
Further insights into the dynamics and sensitivities of moist baroclinic waves have been gained from idealized initial-value experiments in periodic limited-area domains. Such experiments should be interpreted with caution, because their prescribed domain size constrains the wave dynamics and their periodicity promotes unphysical self-interactions, as disturbances shed downwind may recirculate to the upstream side. Nonetheless, most such simulations suggest an amplification of the waves due to moist processes (e.g., Whitaker and Davis 1994; Balasubramanian and Yau 1994; Fantini 2004; Boutle et al. 2011; Booth et al. 2013). Only a few such studies have explored the sensitivities of the waves to T0, including Whitaker and Davis (1994) and Boutle et al. (2011, hereafter BBP11), who both found a modest but systematic wave intensification in warmer atmospheres. Because these findings reinforced the expectation that stronger diabatic heating intensifies baroclinic waves, they were not analyzed in detail. Importantly, given the small sampling of initial jets, initial wave perturbations, and other factors in these studies, their findings may not generalize to all baroclinic waves.
By contrast, climate studies have shown mixed sensitivities of cyclone intensity to T0 (e.g., O’Gorman 2011; Pfahl et al. 2015; Büehler and Pfahl 2017). Using an idealized global climate model (GCM), Pfahl et al. (2015) found that, on average, these cyclones tend to amplify with increasing T0 in cooler atmospheres but weaken with increasing T0 in warmer atmospheres. This nonmonotonic sensitivity tracked that of the zonal-mean available potential energy Pm, implying that Pm serves to broadly regulate it. However, the strongest 10% of cyclones defied this trend by exhibiting a nearly monotonic intensification as T0 was increased. In GCM climate projections, no consensus has been reached on whether midlatitude cyclones will intensify in warmer future climates (e.g., Bengtsson et al. 2009; Catto et al. 2011; Zappa et al. 2013; Colle et al. 2013). Also, using the “pseudo global warming” approach of Schär et al. (1996) over the East Coast of the United States, Marciano et al. (2015) found that most, but not all, simulated cyclones strengthened when the environment was warmed in a fashion consistent with GCM projections.
Given the contrasting sensitivities of midlatitude cyclones to T0 found previously, and the possibility that the nature of this sensitivity may depend on numerous factors, this problem remains unresolved and merits further investigation. Of particular interest herein are the dynamical feedbacks of enhanced diabatic PV anomalies in warmer atmospheres on their parent waves. To address this question, we conduct idealized initial-value experiments of moist baroclinic waves, including both isolated waves in an otherwise undisturbed flow and periodic wave trains, where T0 is systematically varied. Section 2 describes the numerical configuration, with the isolated- and periodic-wave simulations presented in sections 3 and 4, respectively. Further discussion is provided in section 5, followed by the conclusions in section 6.
2. Model setup
a. Model configuration
The Advanced Research version of the Weather Research and Forecasting (WRF) Model, version 3.7 (Skamarock et al. 2008), an Eulerian finite-difference model that integrates the nonhydrostatic and nonlinear atmospheric equations using third-order Runge–Kutta time differencing and a split time step for stability of sound waves, is used for the numerical experiments. All aspects of the simulation design are geared toward isolating the problem of interest in the simplest possible framework. Thus, some physical processes that may impact baroclinic waves, but do not bear directly on our main scientific question, are deliberately omitted and deferred to future work.
A single domain is used with dimensions of Lx = 16 000 km (zonal) by Ly = 12 000 km (meridional) by Lz = 20 km (vertical). The nominal horizontal grid spacing is Δh = 100 km, which is relatively coarse by modern numerical weather prediction (NWP) standards but still sufficient to capture the key sensitivities of the waves to T0 (as found by selected experiments reducing Δh down to 25 km; not shown). A stretched hydrostatic-mass vertical coordinate with 101 unstaggered levels is used, with a grid spacing ranging from ~90 m near the surface to ~400 m at the model top. The uppermost 4 km uses a Rayleigh damping layer to minimize wave reflections off the rigid model top. The lateral boundaries are periodic in x and rigid in y. In keeping with previous initial-value experiments in limited-area domains, an f-plane approximation is used with f = f0 = 2Ωsinϕ0, where Ω is Earth’s angular velocity and ϕ0 = 45°N. Because WRF uses a Cartesian horizontal grid, its neglect of spherical metric terms—which promotes cyclonic over anticyclonic Rossby wave breaking (e.g., Govindasamy and Garner 1997)—may limit the real-world applicability of the experimental findings.
Default physical parameterizations include the WRF single-moment 6-class cloud microphysics scheme (Hong and Lim 2006), the Kain–Fritsch cumulus parameterization scheme (Kain 2004), the Yonsei University planetary boundary layer scheme with Monin–Obukhov similarity theory in the surface layer (Hong et al. 2006), and horizontal mixing along coordinate surfaces using a Smagorinsky–Lilly scheme. The lower boundary is a no-slip land surface with zero sensible and latent heat fluxes. Thus, flows that are initially dry stay dry over time. This simplification, as well as the neglect of both short- and longwave radiation, is enforced to ensure that the vast majority of diabatic heating is owing to phase changes of water substance. While these simplifications limit the realism of the simulations, they also facilitate physical understanding.
b. Initialization
Details of the model initialization for the T290-moist ISO case: (a) water vapor mixing ratio (filled contours), virtual potential temperature (thin lines, interval: 8 K), zonal winds (thick lines, interval: 6 m s−1), tropopause height (thick dashed line) of initial jet profile; (b) PV′ (filled) and meridional winds [m s−1; positive values (solid lines) indicate flow into the page and negative values (dashed lines) indicate flow out of the page].
Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0188.1
The initial jet is defined using the full moist equations and is thus perfectly balanced. However, because the surface winds are nonzero and the model lower boundary is no slip, a zonally symmetric Ekman layer develops over the first 24 h of model integration. Thereafter, the jet remains in a steady state if left unperturbed (not shown).
To create growing wave disturbances, an initial perturbation is added to the jet. While normal-mode perturbations can be defined for any baroclinically unstable environment (e.g., Simmons and Hoskins 1976; Merlis and Schneider 2009), such perturbations do not generally explain transient cyclogenesis (Farrell 1985). Modal calculations with a saturated atmosphere can capture some of the destabilizing effects of latent heat release (e.g., Emanuel et al. 1987) but have collapsing updraft area for warm basic states that are not reproduced in finite-amplitude baroclinic life cycle simulations (O’Gorman et al. 2017). Last, optimal transient perturbations can also be obtained (Farrell 1989), but their derivation assumes zonal periodicity and does not naturally account for nonlinear diabatic heating.
Eight initial baroclinic jets are defined using different combinations of T0, RH1, and RH2, the details of which are summarized in Table 1. These cases span a range of T0 (275–290 K, in 5-K increments) that roughly represents the variation in T0 between the midlatitude winter and spring/autumn seasons. They also incorporate two RH profiles, one moist with RH1 = 0.8 and RH2 = 0.1 and the other dry with RH1 = RH2 = 0. By using fixed meridional and vertical Tυ gradients and tropopause heights, the experiments neglect changes in midlatitude storm tracks that might accompany global climate change (e.g., Schneider et al. 2010). Thus, some factors that may affect baroclinic waves in future climates are omitted.
Details of the eight simulations with varying T0 and RH, including prescriptions of varying parameters (all of which are defined in the text).
The simulations are named according to their T0 and RH; for example, the moist case with T0 = 290 K in Fig. 1a is named T290-moist (Table 1). Two sets of eight simulations are considered, each set with different initial perturbations to initiate baroclinic waves. The first (“ISO”) uses an isolated PV perturbation centered at xp = xc, where xc = Lx/2. To help bridge the gap between the ISO simulations and the periodic waves simulated in related studies (Whitaker and Davis 1994; BBP11), the second (“PER”) superposes three of the same PV perturbations, equally spaced over the zonal domain, to initiate a periodic wave train. The spacing between these perturbations (5333 km) is set to roughly match the natural zonal wavelengths that develop in the ISO simulations (~5400 km, as will be seen).
The value of Pm of the moist simulations exceeds that in the dry simulations and also exhibits the opposite sensitivity to T0: rather than decreasing over the range of T0, it increases from 4.3 to 5.3 MJ m−2. This trend is owing to increased latent heat release, and consequent static destabilization, in the process of rearranging air parcels to obtain the reference state for the Pm calculation. Also, the maximum initial convective available potential energy at the southern end of the domain (CAPEmax) increases dramatically with T0, from 112 J kg−1 (T275-moist) to 3180 J kg−1 (T290-moist), with nonzero values shifting northward from around 2000 to 500 km equatorward of yc (not shown). Except for a similar northward shift in nonzero values at larger T0, the convective inhibition (CIN) exhibits minimal sensitivity to T0, with mean values of around 50 J kg−1 in areas of nonzero CAPE (not shown).
3. Isolated waves
a. Overview
Snapshots of surface equivalent potential temperature θe, cloud hydrometeor path, surface pressure, and surface winds for four ISO simulations (T275-dry, T290-dry, T275-moist, and T290-moist) are shown in Fig. 2. These are taken at 0 h on day 6, within 24 h of the cyclones reaching their minimum surface pressure. Over this range of parameter space, the simulated waves exhibit only subtle qualitative differences—notably that the magnitude of the surface low increases slightly in the moist cyclones and decreases slightly as T0 is increased (Figs. 2b,d). The most noticeable structural difference between the two moist simulations is an eastward extension of the warm-frontal cloud band in T290-moist. The colder simulations also exhibit larger ps, which follows directly from (1) and (2): with a fixed pressure distribution at zref = 4 km across all simulations, the mean ps increases with the density of the underlying layer, which is larger in the colder flows.
Snapshots of surface 
Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0188.1
Quantitative differences in simulated wave growth are evaluated within a cyclone-centered reference frame, which occupies the full domain in y and z but is limited to a zonal length of lx = 5400 km to roughly encompass one zonal wavelength (e.g., Fig. 2). The cyclone position is tracked using an algorithm that steps chronologically through each model output time, calculating (ΔSLP)min, the minimum surface pressure perturbation relative to the zonally averaged initial value, and the maximum horizontal Laplacian of surface pressure, over the entire domain. Once these two extrema are zonally separated by less than lx/2 and (ΔSLP)min ≤ −5 hPa, the cyclone center (xc, yc) is assigned to the location of (ΔSLP)min. The algorithm then tracks this feature at subsequent times by restricting the search area to x ± lx/2 of the previous cyclone position, thus preventing it from jumping to developing cyclones elsewhere in the domain.
As the ISO cyclones mature, they undergo a cyclonic wrapping process that ultimately results in the base of the upper-level trough impinging upon the downstream boundary of the control volume by around day 8. Nonetheless, analyses with the reference frame shifted eastward by up to 1000 km yielded similar results to those for a cyclone-centered frame. Hence, the analyses below (which focus on the cyclone growth over days 1–7) are not strongly sensitive to the precise reference-frame position.
Because of the increased atmospheric moisture content in warmer environments, the cumulative precipitation within the analysis region 〈Rtot〉 increases monotonically with T0 in the moist ISO simulations and more than doubles over the range of T0 (Table 2). This trend stems primarily from increased parameterized convective precipitation 〈Rcu〉 driven by the rapid increase in moist instability at larger T0 (Table 1). By contrast, the explicit precipitation from the cloud-microphysics scheme 〈Rmic〉 increases by only ~50% over the range of T0.
Horizontally averaged cumulative precipitation (mm) at 0 h on day 10 from the cloud microphysics 〈Rmic〉 and cumulus 〈Rcu〉 schemes, along with the sum of the two 〈Rtot〉, for all moist simulations. All averages are taken over the limited-area cyclone-tracking analysis domain.
Time series of (a),(b) Ke, (c),(d) conversion efficiency (the ratio of Ke to initial Pm), and (e),(f) 
Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0188.1
In the dry ISO simulations, Ke of the tracked wave increases until about day 7 and then decays (Fig. 3a). Averaged over the growth phase, Ke and |(ΔSLP)min| decrease by ~15% as T0 is increased from 275 to 290 K. This negative sensitivity stems, at least in part, from the negative sensitivity of Pm to T0 (Table 1). Thus, when Ke is normalized by Pm to give the conversion efficiency, the gap between the different simulations is narrowed (Fig. 3c). An additional contribution to this negative sensitivity is the decreased air density in the warmer cases, which causes the tropospheric mass, and hence the wave Ke, to decrease by ~5% over the range of T0.
Compared to their dry counterparts, the moist ISO waves intensify faster and exhibit less sensitivity to T0, during their early growth phase (days 2–3.5; Figs. 3b,f). This amplification stems from cloud diabatic heating, which commences early on day 2 (as will be shown). During this period, the reduced dry growth of the warmer waves (as evident from Figs. 3a and 3e) is offset by increased diabatic heating to leave minimal residual sensitivity to T0.
The moist waves reach maturity over days 3.5–7, attaining a ~30% larger peak Ke and a ~10-hPa smaller (ΔSLP)min than the corresponding dry ISO waves. Thus, cloud diabatic heating clearly intensifies the parent cyclone. However, consistent with Schemm et al. (2013), the degree of diabatic enhancement for this configuration is small compared to that in some other studies (e.g., BBP11; Stoelinga 1996). During this phase of development, the warmer waves intensify less rapidly than the colder waves, leading to a monotonic decrease in maximum Ke and |(ΔSLP)min| with increasing T0 (Figs. 3b,f). Although the percentage decrease in Ke over the simulated range of T0 is similar to that in the corresponding dry cases, the conversion efficiency declines much faster with increasing T0 (Figs. 3c,d). Thus, as the environment warms, the moist cyclones become increasingly inefficient at converting environmental Pm into wave Ke.
b. Energetics
Consistent with the Ke time series in Fig. 3a, the Ke tendency of the dry ISO simulations is positive until ~day 7 and weakens slightly at larger T0 (Fig. 4a). The latter effect is driven by reduced C(Pe, Ke) and yields a consequent weakening of 
Time series of Ke budget terms from (12), for the dry ISO simulations. Both the rate of change of the model-diagnosed Ke and the sum of the Ke-budget source terms [the lhs and rhs of (12), respectively] are respectively shown by solid and dotted lines in (a).
Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0188.1
Time series of the differences of three terms of the Ke budget between the T275-dry and T290-dry ISO simulations.
Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0188.1
The moist cases develop larger C(Pe, Ke) and Ke tendencies than the corresponding dry cases, and these terms do not noticeably depend on T0 until the onset of the maturation phase (day 3.5; Figs. 6a,b). Thereafter, the Ke tendency weakens with increasing T0. Unlike in the dry cases, this decrease is not driven by C(Pe, Ke); it instead stems from a more negative AGEO term (Fig. 6e), related to the aforementioned structural differences in the warm-frontal cloud band (Figs. 2c,d). As this cloud band shifts eastward at larger T0, so does the low-level warm advection, which approaches the downwind boundary of the analysis volume (Fig. 7). Because both the diabatic heating and the warm advection contribute to upper-level ridge building and divergence (e.g., Holton 1992), the ageostrophic geopotential fluxes across the downwind boundary increase.
As in Fig. 4, but for the moist ISO simulations.
Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0188.1
Mean 200–400-hPa geopotential height perturbation 
Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0188.1
The increased AGEO magnitude at larger T0 is partially offset by a corresponding reduction in the magnitudes of 
The fact that Ke does not increase with T0 in the maturing moist cyclones suggests that increased latent heat release, which is supported in warmer environments with larger moisture content, does not necessarily energize the baroclinic waves. If, for all else equal, increased latent heat release occurred in warm and ascending portions of the cyclone, it would directly enhance 
c. QG ω analysis
Figures 8a and 8b compare C(Pe, Ke) diagnosed directly from the simulations against 
QG analysis of C(Pe, Ke) in the ISO simulations. See section 3c for definitions of terms.
Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0188.1
In the dry cases, the diabatic component (term D) is negligible, so the dry baroclinic component (term B) fully accounts for the time evolution of 
Analysis of PV and baroclinic vertical motion in the (left) T275-dry, (center) T275-moist, and (right) T290-moist ISO simulations at 0 h on day 5. (a)–(c) Mean 100–1000-hPa diabatic heating rate (filled) along with mean 700–900-hPa Ertel PV (contours, PVU) and wind vectors. (d)–(f) Mean 700–900-hPa dry-baroclinic rhs forcing term of (16) [filled, with warm (cold) colors indicating forcing for ascent (descent)], geostrophic absolute vorticity 
Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0188.1
In the T275-dry case, a low-level mesoscale cyclonic PV anomaly, associated with frictional wind turning in baroclinic zones (e.g., Stoelinga 1996; Adamson et al. 2006), wraps cyclonically around the surface low (Fig. 9a). In the moist cases, this PV anomaly is enhanced by diabatic PV generation along the frontal cloud band and shifts progressively eastward as T0 is increased (Figs. 9b,c). This eastward shift becomes prominent during the transition from the early growth phase to the maturation phase (Fig. 10). On day 3, the frontal cloud bands in the T275-moist and T290-moist cases are similarly located, but increased diabatic PV generation in the latter extends the PV anomaly slightly eastward (Figs. 10a,b). As a result, the southerly branch of the induced cyclonic circulation, carrying high-
Evolution over days 3–4 of mean 700–900-hPa PV (solid black lines, contours of 1, 1.5, and 2 PVU) and wind vectors, along with CAPE (based on lifting the parcel in each column with the maximum 
Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0188.1
Similar to the PV, the low-level geostrophic absolute vorticity 
In the T275-moist simulation, diabatic PV generation in the warm-frontal cloud band increases 
Because of approximations in (16) and the inversion of the 3D Laplacian operator, the retrieved 
Based on the above analysis, we propose a physical hypothesis for the reduced Ke and conversion efficiency with increasing T0 in the moist ISO simulations: diabatic heating along the warm-frontal cloud band locally enhances the low-level PV and 
A similar mechanism was cited in the aforementioned case study by Davis (1992). In that case, which also involved a type-B cyclone over land (the central United States), the diabatically forced eastward shift in the cyclone’s warm-frontal PV anomaly caused it to propagate faster than the corresponding upper-level PV anomaly. The resulting disruption of the phase-locking process ultimately led to cyclolysis.
4. Periodic waves
The ISO simulations represented one idealization of baroclinic life cycles—isolated cyclones developing within otherwise undisturbed flows. Another meaningful, and commonly studied, idealization is that of a periodic Rossby wave train, where repeated instances of the same wave can interact with each other (e.g., Whitaker and Davis 1994; BBP11; Booth et al. 2013). To evaluate the sensitivities of such waves to T0, and to compare their behavior to that of the ISO waves, we briefly analyze the PER simulations.
a. Overview
The baroclinic waves in the PER simulations differ subtly from those in the ISO simulations in that (i) the high-pressure regions flanking the cyclone are stronger, (ii) the cold front exhibits a noticeable forward tilt in the horizontal, and (iii) the cold front extends farther to the south (cf. Figs. 11 and 2). Both the dry and moist versions of the PER simulations attain 30%–50% larger Ke than the corresponding ISO simulations (cf. Figs. 12a,b and 3a,b). This generally increased Ke does not result from a deepening of the cyclone, as the magnitude of 
As in Fig. 2, but for four corresponding PER simulations.
Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0188.1
As in Fig. 3, but for the PER simulations.
Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0188.1
The cyclones in the moist PER simulations again exhibit minimal sensitivity to T0 during their early growth phase, as the positive effects of increased diabatic heating at larger T0 offset the slower dry growth. They subsequently exhibit a stronger negative sensitivity to T0 than that in the corresponding moist ISO simulations, with the maximum Ke decreasing more prominently (~40%) over the range of T0. This negative sensitivity is even more pronounced in the conversion efficiency, which is largely insensitive to T0 in the dry cases but decreases strongly in the moist cases, by as much as 50% (cf. Figs. 12c,d and 3c,d). While the positive sensitivity of precipitation to T0 found in the moist ISO simulations persists in these simulations, the rate of increase of 
b. Energetics
The Ke budget of the PER simulations is computed identically to that of the ISO simulations, over a cyclone-following, limited-area zonal region (5400 km) that approximately matches the cyclone zonal wavelength. Most of the trends in this budget from the dry ISO simulations carry over to the dry PER simulations (Fig. 13), including a slight decrease in the Ke tendency during the cyclone growth phase at larger T0, stemming primarily from decreased C(Pe, Ke). Similarly, consistent with a slight weakening of the cyclone from T275-dry to T290-dry, both 
As in Figs. 4a–d, but for the dry PER simulations.
Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0188.1
The pronounced decrease of Ke with increasing T0 in the moist PER simulations is caused primarily by a sharp increase in 
As in Figs. 4a–d, but for the moist PER simulations.
Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0188.1
The increase of 
Vertical integral over 400–800 hPa of 
Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0188.1
To explain the horizontal forward wave tilt in the moist PER simulations, we compare the evolution of upper-level (200–400 hPa) PV and difference wind vectors between the ISO and PER versions of the T290-moist case in Fig. 16. At 0 h on day 3, the two waves exhibit similar structures and diabatic heating distributions, with generally small differences in their wind fields (Figs. 16a,b). By the next day, an upper-level PV anomaly in the PER case, generated by diabatic heating along the warm front and carried downwind by the westerly jet, recirculates through the system to interact with the upper-level trough. Its anticyclonic flow is northerly along the upstream (western) flank of the trough, which tends to elongate the trough meridionally (Figs. 16c,d). Meanwhile, the zonally elongated warm-frontal diabatic PV anomaly at lower levels advects the surface thermal wave eastward (as seen in Figs. 9a–c). As a result of the differential propagation of the northern and southern ends of the wave, the wave develops a horizontal forward tilt over time, which increases with T0 as a result of increased diabatic PV generation.
Vertically averaged PV over 200–400 hPa (filled contours), along with 500–1000-hPa thickness (thin black lines, interval: 10 dam) and mean 100–1000-hPa diabatic heating rate (thick black line, contour 10−5 K s−1) for the (a),(c),(e) ISO and (b),(d),(f) PER versions of the T290-moist simulation. The difference mean 200–400-hPa wind vectors between the two simulations (PER minus ISO) are also shown in (b),(d),(f).
Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0188.1
The meridional elongation of the upper-level trough explains the increased Ke in the PER simulations relative to the ISO simulations. However, in terms of surface pressure perturbations, the PER cyclones are relatively weak. This is because the phase-locking between lower- and upper-level PV anomalies in the ISO cyclones is not disrupted by the recirculating diabatic PV anomaly. Rather than being stretched meridionally, the upper trough wraps cyclonically around the low center, creating a downstream bulge in the trough that limits the horizontal wave tilt (Figs. 16e,f).
5. Discussion
a. Pe budget
As before, the integration operator in (11) is used to transform specific energy conversions in (18) into full energy conversions. The resulting Pe budget, shown for the T275-moist and T290-moist ISO simulations in Fig. 17, reveals clear parallels to the previous Ke analysis. The Pe tendencies in Fig. 17a are similar in magnitude to the corresponding Ke tendencies in Fig. 6a and again exhibit very weak dependence on T0 during the cyclone growth phase. This insensitivity reflects offsetting effects: a substantial increase in 
As in Fig. 4, but for Pe budget terms in (18) in the moist ISO simulations.
Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0188.1
b. On the generalizability of the results
The above simulations correspond to a particular cyclogenesis configuration over land, where a large-amplitude upper-level PV anomaly propagates over a low-level baroclinic zone. This configuration, loosely based on the Petterssen type-B paradigm of cyclone development, is not representative of all midlatitude cyclones, which develop under widely different environmental conditions, with varying configurations of PV anomalies and low-level diabatic processes (e.g., Graf et al. 2017). Among the important environmental parameters neglected in these experiments is the basic-state barotropic horizontal wind shear, which can modify the strength of the warm front and its associated diabatic heating (e.g., Thorncroft et al. 1993). Because the feedbacks of diabatic heating on the parent cyclone depend on this and other parameters (e.g., Davis 1992; Davis et al. 1993), the broader applicability of our findings are uncertain.
While the increase in wave Ke due to moist processes in the ISO and PER simulations is consistent with many past studies (e.g., Balasubramanian and Yau 1994; Stoelinga 1996; Booth et al. 2013), the monotonic decrease in Ke with increasing T0 during the cyclone maturation phase is not. Although a nonmonotonic sensitivity to T0 has been found in GCMs (O’Gorman 2011; Pfahl et al. 2015), our simulations are more comparable to the NWP experiments of BBP11, where Ke monotonically increased with T0. BBP11’s setup differs from ours in terms of its (i) baroclinic jet, which was based on Polvani and Esler (2007) rather than Olson and Colle (2007); (ii) inclusion of weak meridional variation in initial RH, (iii) smaller domain size (Lx ≈ 4000 km); (iv) periodic initial perturbation, a small-amplitude thermal wave of wavelength 
To reconcile the differences between our results and those of BBP11, we perform various experiments to bridge the gaps between the two experimental configurations. Starting with the moist ISO setup, we first replace the land surface with ocean, both with and without surface heat fluxes. For the latter, the sea surface temperature is set to the local surface air temperature minus 1 K. Compared to the reference case over land, Ke and 
Time series of Ke and (ΔSLP)min for various moist simulations, including (a),(b) ISO configuration with varied surface types; (c),(d) periodic waves in a small domain with an initial sinusoidal thermal perturbation (SIN); (e),(f) as in (c) and (d), but replacing the Olson and Colle (2007) jet with the Polvani and Esler (2007, or PE07) jet used in BBP11; and (g),(h) the ISO configuration with the Olson and Colle (2007) jet replaced with the PE07 jet. As shown in (a), blue and red lines correspond to T0 = 275 and 290 K, respectively, and solid, dashed, and dotted lines correspond to land, ocean, and ocean with interactive surface heat fluxes, respectively.
Citation: Journal of the Atmospheric Sciences 75, 1; 10.1175/JAS-D-17-0188.1
Keeping the small-domain configuration, we then replaced our initial jet with that of BBP11, with a similar maximum speed (45 m s−1) but a higher Z (nominally 12 km) and a stronger meridional gradient in both dry and moist static stability. Before day 6 of these simulations, both Ke and 
As a final experiment, we return to the large-domain ISO setup but again replace our initial jet with that of BBP11. The isolated initial PV perturbation eliminates the negative feedbacks of recirculating PV anomalies, leading to a positive sensitivity of Ke and 
6. Conclusions
To evaluate the sensitivities of moist baroclinic waves to environmental temperature and moisture content, a series of idealized initial-value simulations of both moist and dry waves were conducted. These simulations used a configuration representative of Petterssen’s type-B cyclogenesis (Petterssen and Smebye 1971), where an isolated and strong upper-level PV anomaly propagates over a low-level baroclinic zone. With horizontal and vertical virtual-temperature gradients held fixed, the surface temperature at 45°N T0 was varied from 275 to 290 K. Relative to corresponding dry waves, the moist waves exhibited faster growth [based on eddy kinetic energy Ke and minimum surface pressure perturbation 
The feedbacks of diabatic heating on moist wave intensity depended on the phase of the wave life cycle. During the early growth phase (days 2–3.5), increased cloud diabatic heating compensated for slightly reduced dry baroclinic instability in the warmer waves, allowing them to grow at a similar pace as the colder waves. However, during the maturation phase (days 3.5–7), the warmer waves grew more slowly than the colder waves, causing the peak Ke and 
The reduced conversion efficiency of the warmer moist waves was owing to an eastward shift in the low-level warm-frontal PV anomaly, driven by increased diabatic heating and moist convection along the frontal cloud band. It induced a corresponding eastward shift in the upper-level ridge, thereby increasing the downstream export of wave energy by ageostrophic geopotential fluxes. It also degraded the phasing between the buoyancy and the baroclinically forced vertical motion within the warm sector by shifting the latter progressively downstream of the former. The resulting indirect suppression of baroclinic conversion (from eddy potential energy to eddy kinetic energy) offset the direct enhancement of baroclinic conversion arising from diabatic heating.
Compared to isolated moist waves, periodic moist waves exhibited an even faster decrease in intensity and conversion efficiency at larger T0. This enhanced weakening was linked to the interaction of the upper-level trough with a recirculating anticyclonic upper-level diabatic PV anomaly originally generated along the warm front. As this PV anomaly caused the upper-level trough to elongate southward, the low-level diabatic cyclonic PV anomaly along the warm front advected the surface thermal wave eastward, causing the cyclone to develop a horizontal forward tilt. This tilt led to an increased conversion from wave Ke to mean kinetic energy, which strengthened the zonal jet at the expense of the cyclone. To our knowledge, such strong modifications of moist baroclinic wave growth by wave periodicity have not previously been documented and should be considered in future idealized modeling studies.
The finding that enhanced diabatic heating may feed back negatively on its parent cyclone is reminiscent of a case study by Davis (1992) over the central United States, where low-level cyclogenesis occurred in a similar type-B configuration to that used here. However, it differs from other case studies where diabatic heating led to major amplifications in cyclone development (e.g., Stoelinga 1996) and from previous initial-value experiments that found a monotonically positive sensitivity of wave Ke with T0 (Whitaker and Davis 1994; BBP11). Further experiments revealed that the simulated sensitivity can be substantially modified or even reversed by changing some combination of the initial jet structure, initial perturbation, and/or surface type. Thus, the sensitivities found herein likely only apply within a limited subset of parameter space. Given that no universal sensitivity of wave growth to T0 likely exists, experiments that sweep through the full parameter space, using a wide range of initial configurations of varying realism, are recommended to further examine this sensitivity.
Acknowledgments
The first author acknowledges funding from the Natural Sciences and Engineering Research Council (NSERC) Grant NSERC/RGPIN 418372-12. The numerical simulations were performed on the Guillimin supercomputer at McGill University, under the auspices of Calcul Québec and Compute Canada. We are grateful for insightful comments on this work from Paul O’Gorman [who also shared code for the efficient Pm calculation in Stansifer et al. (2017)], Bob Plant, Heini Wernli, John Methven, James Booth, and one anonymous reviewer.
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