Dry and Semidry Tropical Cyclones

a. Simulation design

In this paper, we focus on two sets of simulations that shift the surface turbulent heat transfer from dominantly latent to sensible heat fluxes, smoothly varying from moist to dry radiative–convective equilibrium.

1. Our first set of 16 simulations directly reduces the surface wetness at constant $T_S=300\hspace{0.17em}\text{K}$ and $T_T=210\hspace{0.17em}\text{K}$ by using values of β of 0, 0.001, 0.003, 0.01, 0.03, 0.1, 0.15, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0. Because β is a multiplier on the surface specific humidity rather than the difference between the surface and atmospheric specific humidities, low values of β can result in a downward transfer of latent heat from the moist atmosphere into the surface.

2. Our second set of 7 simulations holds $\beta =1$, but uses surface temperatures $T_S$ of 300, 290, 280, 270, 260, 250, and 240 K. For values of T_S ≲ 260 K, the surface sensible heat flux dominates the latent heat flux, and the stratification of the troposphere is nearly dry adiabatic. In these simulations, we use $T_T=0.7T_S$, which maintains a constant thermodynamic efficiency in the absence of dissipative heating, and also ensures that the tropopause remains at nearly the same pressure across a range of surface temperatures. Because the radiative cooling scheme described in Eq. (1) gives an integrated tropospheric radiative cooling proportional to the mass of the troposphere, the condition of nearly fixed tropopause pressure with colder surface temperatures also ensures that in radiative–convective equilibrium, the total surface enthalpy flux varies little with surface temperature. This is an unfamiliar limit, because we normally assume tropospheric radiative cooling increases with surface warming (e.g., Allen and Ingram 2002).

All simulations in these two main sets used a domain 1152 km × 1152 km in the horizontal, with 2-km horizontal grid spacing, and a Coriolis parameter $f=3\times {10}^{-4}{\hspace{0.17em}\text{s}}^{-1}$. A stretched grid was used in the vertical, with 64 levels in the lowest kilometer and a spacing of 500 m above 3.5 km, and the model top at 28 km. Simulations were run for 70 days, and each was initialized using a sounding from the last 20 days of a 100-day simulation of nonrotating RCE in a small domain 192 km × 192 km (with the same resolution), to which a small amount of random thermal noise was added in the lowest model levels to initiate convection. These initialization simulations were each performed with the matching value of β (for the first set of simulations) or of $T_S$ and $T_T$ (for the second set). Below (section 3a) we present thermodynamic profiles from these initialization simulations.

We conducted two further simulations after finding that the $\beta =1$ and $\beta =0.9$ simulations culminated with only a single vortex in the domain. This state of only a single simulated vortex in the domain was termed “lattice” equilibrium by Zhou et al. (2014) in contrast to the “turbulent” equilibrium obtained with multiple storms in the domain. They found that that lattice equilibria resulted in storms that were strongly influenced by the domain size, being either too weak or intermittent for small domains, or too large for large domains, relative to turbulent equilibrium. Sharing this view that the turbulent multistorm TC-world provides a more faithful simulation of the statistical properties of vortices (should they form), we reran the $\beta =1$ and $\beta =0.9$ simulations with larger domain sizes of 1728 km × 1728 km, which led to turbulent multistorm TC-worlds for all times following genesis. Thus, in our results and discussion below we focus exclusively on these larger-domain simulations; we designate them with an asterisk as the $\beta ={1.0}^{*}$ (equivalently $T_S=300{\hspace{0.17em}\text{K}}^{*}$) and $\beta ={0.9}^{*}$ simulations, to remind the reader that they were conducted with a domain size different from the rest. We touch on a few differences between simulations with large and normal domain sizes in section 3d.

Snapshots at day 43 of a subset of the simulations with varied β show that the surface wind field is dominated in most simulations (including moist and dry limits) by multiple cyclones, but that one nearly dry simulation with $\beta =0.1$ has little large-scale flow (Fig. 1). Figure 1 immediately gives several preliminary answers to the motivating questions in the introduction: the moist–dry transition appears to have both continuous and discontinuous aspects, and storm size and intensity appear to decrease with surface drying. Less glib answers, however, require us to automate vortex identification; we proceed to describe that process.

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Snapshots at day 43 of the surface wind speed V (m s⁻¹) for several simulations with varied surface wetness: (a) $\beta =1^{*}$, (b) $\beta =0.7$, (c) $\beta =0.5$, (d) $\beta =0.1$, and (e) $\beta =0$.

Citation: Journal of the Atmospheric Sciences 76, 8; 10.1175/JAS-D-18-0357.1

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b. Storm tracking and analysis

Tropical cyclones are identified at each time step as follows. First, the surface pressure perturbation $p^{\prime }$ is calculated from the surface pressure field by subtracting the domain-mean value: $p^{\prime }\left(x,y\right)=p\left(x,y\right)-\overline{p}$. Grid points with $p^{\prime }\ge -5\hspace{0.17em}\text{hPa}$ are masked out to isolate regions of relatively low pressure. This field is then replicated in a 3 × 3 x–y grid to allow for identification of regions that cross horizontal boundaries of the doubly periodic domain. Contiguous low pressure objects are created using an eight-connected component labeling algorithm, and objects containing at least 13 grid points are retained. For each object, the storm center is defined as the pressure-weighted centroid of the 13 grid points with the lowest $p^{\prime }$ values, such that the center will be located in the vicinity of the local minimum pressure while minimizing noise due to small scale variability at one or two grid points. The storm central pressure is defined by bilinearly interpolating the pressure field to the storm center. Finally, for each storm center, radius–height cross sections of relevant azimuthally averaged quantities are extracted from the data, including the decomposition of the total wind field into its radial and tangential components. Azimuthal averages are calculated in $\mathrm{\Delta }r=2\hspace{0.17em}\text{km}$ radial bins moving outwards beginning at r = 1 km in 2-km steps. Examples of this process for $\beta =1^{*}$, $\beta =0.5$, and $\beta =0$ are shown later (see Fig. 4) and will be discussed in detail in section 3b.

When discussing winds in the context of cyclones, we will use a cylindrical-polar decomposition, with u as the outward radial wind component, υ the counterclockwise (here, cyclonic) tangential wind component, and w the vertical wind component. We will use ${\upsilon }_m$ to denote the maximum azimuthally averaged tangential wind speed, $r_m$ as the radius of maximum winds, and capital V to indicate horizontal wind speed $\left[{\left(u^2+{\upsilon }^2\right)}^{1/2}\right]$. Unless otherwise stated, values refer to winds at the lowest model level (z = 37.5 m).

c. Potential intensity

d. Storm size

We use three metrics of storm size. The first two, $r_0$ and $r_8$, indicate the radius for a given storm where the lowest-level azimuthal mean tangential wind $\upsilon \left(r\right)$ first passes below 0 or 8 m s⁻¹, respectively. To find these, we opt for the simplest method of selecting the first radius greater than $r_m$ where $\upsilon \left(r\right)<0$ or $\upsilon \left(r\right)<8{\hspace{0.17em}\text{m s}}^{-1}$ for each storm. If a storm has no radius where the circulation first reverses (becoming anticyclonic), we set $r_0$ to the maximum attainable radius in the domain ($L\sqrt{2}/2$; this occurs for fewer than 0.04% of identified vortices). This simple method has limitations, because radial decay of winds outside $r_m$ is nonmonotonic for many storms, especially those involved in strong cyclone–cyclone interaction pairs or triads. More sophisticated methods that involve fitting the outer wind profile with a theoretical curve, however, are still subject to errors from vortex–vortex interactions, and require additional assumptions.

a. Nonrotating RCE from moist to dry limits

Temperature and humidity profiles from the varied-β initialization simulations show that as the surface becomes drier, the dry adiabatic subcloud layer at the bottom of the troposphere grows upward. The moist-adiabatic cloud layer, which occupies most of the troposphere for T_S = 300 K and $\beta =1$, shrinks with surface drying, vanishing entirely for $\beta =0$ (Fig. 2).

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Profiles from nonrotating initialization simulations with varied surface wetness β for (a) temperature, (b) specific humidity (note logarithmic horizontal axis), (c) cloud fraction, and (d) precipitation flux. The surface temperature $T_S=300\hspace{0.17em}\text{K}$ in all simulations, and the radiative tropopause temperature $T_T=210\hspace{0.17em}\text{K}$, indicated with a vertical dashed line in (a). The depth of the well-mixed dry adiabatic subcloud layer can be inferred from the portion of the troposphere in each simulation where the specific humidity is constant with height in (b); lowest cloud bases in (c) coincide with the top of the subcloud layer. Note that specific humidity, cloud fraction, and precipitation flux are 0 at all heights in the $\beta =0$ simulation.

Citation: Journal of the Atmospheric Sciences 76, 8; 10.1175/JAS-D-18-0357.1

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Surprisingly, the cloud fraction increases as the surface is dried (Fig. 2c); for surfaces with $\beta >0.2$ the effects of surface moistening are reminiscent of the decrease and upward shift in high cloud amount with atmospheric warming noted by Bony et al. (2016) in climate models and in SAM by Cronin and Wing (2017). For very dry surfaces, the entire troposphere resembles a boundary layer topped with broken nonprecipitating clouds. For $\beta =0.001$ and $\beta =0.003$, the autoconversion threshold for ice clouds (0.1 g kg⁻¹) exceeds specific humidities in the subcloud layer, so precipitation cannot form even if surface parcels are lifted high enough that saturation specific humidity is zero. In these simulations, we speculate that the entire layer above the lifted condensation level would fill with cloud were it not for ice cloud sedimentation. Two other notable features of dry and semidry RCE are the sharp tropopause inversion in the dry limit (Fig. 2a), and the vigorous internal moisture recycling for moderately dry surfaces implied by precipitation fluxes which have lower-tropospheric values several times as large as those at the surface (Fig. 2d). Upper-tropospheric temperatures well below the radiative tropopause temperature (T_T = 210 K) indicate the presence of an “overshooting layer” that is convectively cooled and radiatively heated (similar to Pauluis and Held 2002).

The warm–cold transition is not marked by a similar increase in the depth of the subcloud layer or decrease in precipitation efficiency (Fig. 3). Instead the cold limit is marked by convection that is energetically dry—with dry adiabatic stratification and dominantly sensible heat transport—but which carries water vapor and cloud ice with it as a nearly passive tracer. For surface temperatures of 240–260 K, the bulk thermal stratification of the troposphere is less than 1 K, the troposphere is saturated and overcast over a deep layer, and the tropopause inversion is sharp—as in the small-β limit (Figs. 3a,c). In the cold limit, the subcloud layer seems to vanish, as clouds exist all the way down to the surface, and the distinction between dry and moist adiabatic stratification disappears. The behavior of cloud and relative humidity fields in the cold limit is undoubtedly sensitive to the treatment of ice microphysics, but with energetically dry convection and prescribed radiative cooling, it is unclear whether this alters convective dynamics.

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As in Fig. 2, but for nonrotating initialization simulations with varied surface temperature. Black solid lines in (a) indicate dry adiabats starting at the surface pressure and average surface air temperature of each of the seven simulations.

Citation: Journal of the Atmospheric Sciences 76, 8; 10.1175/JAS-D-18-0357.1

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The transition from moist to dry nonrotating RCE appears to be rich territory for further study, particularly for understanding controls on tropopause temperature structure, cloud fraction, and how precipitation evaporation affects rainfall rates over land. Deeper analysis of the nonrotating moist–dry transition, however, is deferred to future work: rotating RCE will be the focus of the remainder of this paper.

b. Storm basics: Moist, half-dry, dry

As a primary concern of our study is the transition between moist and dry rotating RCE, we begin with a detailed comparison of simulations with $\beta =1^{*}$, $\beta =0.5$, and $\beta =0$ (all with $T_S=300\hspace{0.17em}\text{K}$ and $T_T=210\hspace{0.17em}\text{K}$; see Figs. 1a,c,e). For brevity, we refer to these as “moist,” “half-dry,” and “dry” simulations, respectively.

In all three simulations, cyclones spontaneously emerge from initially random convection; we compare cyclone structure from an illustrative snapshot 43 days into each simulation (see supplemental videos S1–S3 for time evolution of surface wind speeds). As previously noted (Figs. 1a,c,e), Figs. 4a–c show that cyclones appear to fill the domain in the three simulations, as in previous work on moist rotating RCE (e.g., Zhou et al. 2014). The dry simulation achieves this result with a larger density of smaller cyclones (~7.5 per 1 million km²) than either the half-dry (~3 per 1 million km²) or moist (~1.3 per 1 million km²) simulations.

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Snapshots of tropical cyclones on day 43 for (top) moist $\left(\beta ={1.000}^{*}\right)$, (middle) half-dry $\left(\beta =0.500\right)$, and (bottom) dry $\left(\beta =0.000\right)$ simulations. (a)–(c) Plan view of wind speed V (colors, m s⁻¹) and negative pressure perturbation $-p^{\prime }$ (contours; interval = 3 hPa, dashed = 0) at the lowest model level (z = 37.5 m) with storm centers (×). (d)–(f) Radius–height cross section of tangential wind speed υ (colors, m s⁻¹; red positive, blue negative, gray line = 0) and temperature perturbation from horizontal domain mean $T^{\prime }$ (contours; interval = 1 K, solid positive, dashed = 0) for storms marked with the magenta × in (a)–(c). (g)–(i) Azimuthal-mean radial profiles of horizontal wind speed V (black line), tangential (υ, blue line) and radial (−u, green line) velocity components at z = 37.5 m, and midlevel (z = 4.96 km) vertical velocity w (red line), with maximum 2D near-surface tangential velocity υ (blue dot) and total horizontal wind speed V (black dot) for storms shown in (d)–(f). (j)–(l) Radial profile of tangential wind for all storms in (a)–(c) for five consecutive 6-hourly time steps. Profiles in (l) are shown only for the initial time step for clarity.

Citation: Journal of the Atmospheric Sciences 76, 8; 10.1175/JAS-D-18-0357.1

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Radius–height cross sections of the tangential wind and temperature perturbation for example storms from moist (Fig. 4d), half-dry (Fig. 4e) and dry (Fig. 4f) simulations show typical characteristics of a tropical cyclone in all cases. These characteristics include an upper-level warm core at the storm center and a tangential wind speed that peaks near the surface at small finite radius and decays with both radius and height. The dry storm circulation varies weakly with height through the troposphere, and by association (thermal wind balance) its warm core is confined to a relatively thin layer below the tropopause. The moist simulation shows storms with a deeper warm core and a more gradual decay in tangential winds with height. The half-dry simulation lies between the two, but unlike either limiting case has a low-level cold patch coincident with the region of maximum surface winds, likely associated with evaporation of rainfall. The contrasting vertical extent of the warm core seems consistent with the dry simulation having a well-mixed boundary layer that spans the entire depth of the troposphere, in which it is difficult to support strong horizontal temperature gradients.

Though the dry case (Fig. 4f) appears to lack a warm core over much of the depth of the troposphere, its core is still positively buoyant due to its relatively low pressure (i.e., a deep warm core exists on isobaric surfaces). A buoyant core is essential, as it indicates the existence of available potential energy in the system (Yanai 1964) and the production of available potential energy by covariance between heating and buoyancy. To plot the buoyant core, we define a buoyancy temperature $T_b$ that is analogous to a density temperature but includes the effects of pressure perturbations at constant z. SAM defines the buoyancy B as (Khairoutdinov and Randall 2003, p. 622)

$B=g\left({\displaystyle \frac{T^{\prime }}{\overline{T}}}+0.608q_{\upsilon }^{\prime }-q_n-q_p-{\displaystyle \frac{p^{\prime }}{\overline{p}}}\right),$(7)

where g is the gravitational acceleration, T is temperature, $q_{\upsilon }$ is water vapor mixing ratio, $q_n$ is nonprecipitating condensate, $q_p$ is precipitating condensate, p is pressure, bars denote horizontal means, and primes denote perturbations from the horizontal mean. We can express the buoyancy as

$B\equiv g\left({\displaystyle \frac{T_b^{\prime }}{\overline{T_b}}}\right),$(8)

where $\overline{T_b}$ is the horizontal-mean virtual temperature (for buoyancy SAM assumes $\overline{q_n}=\overline{q_p}=0$), and $T_b^{\prime }$ is given by combining Eqs. (7) and (8):

$T_b^{\prime }=\overline{T_b}\left({\displaystyle \frac{T^{\prime }}{\overline{T}}}+0.608q_{\upsilon }^{\prime }-q_n-q_p-{\displaystyle \frac{p^{\prime }}{\overline{p}}}\right).$(9)

The radius–height structure of $T_b^{\prime }$ (Fig. 5) is similar to that for $T^{\prime }$ (Figs. 4d–f), but the inclusion of pressure perturbations greatly strengthens the buoyant core near the surface and in the lower troposphere. In both the moist and dry limits, $T_b^{\prime }$ is positive and nearly uniform with height through the depth of the troposphere. This is not true of the half-dry case, though the vertical distribution of $T_b^{\prime }$ is more uniform than that of $T^{\prime }$. In particular, the low-level cold anomaly $T^{\prime }$ appears as a warm anomaly in $T_b^{\prime }$, indicating that the low-level core of the storm is still positively buoyant but less buoyant than air at mid- to upper levels. Understanding the processes that act to reduce the buoyancy of the low-level core in the half-dry case is beyond the scope of this work, but it could yield insight into why no storms form at low-intermediate β.

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As in Figs. 4d–f, but for $T_b^{\prime }$ in lieu of $T^{\prime }$.

Citation: Journal of the Atmospheric Sciences 76, 8; 10.1175/JAS-D-18-0357.1

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Radial profiles of azimuthally averaged near-surface horizontal winds and midlevel vertical winds for each example storm show low-level inflow at all radii within each cyclone’s circulation, and upward motion concentrated near the radius of maximum wind (Figs. 4g–i). The inflow in each storm is maximized just beyond the radius of maximum wind, with progressively less smoothness for the half-dry and dry cyclones relative to the moist one. In the moist and half-dry storms, convective updrafts are largely confined to a narrow annulus in the inner core of the storm, whereas in the dry storm convective updrafts occur at all radii. All storms exhibit anticyclonic flow beyond some finite outer radius $r_0$ (i.e., υ decreases below zero), with oscillations in υ in the dry case due to sampling the winds from near and far sides of the surrounding ring of cyclones.

Finally, radial profiles of the tangential wind for all identified storms (on day 43) reveal that radial profiles vary across storms in the moist case (Fig. 4j), but share a common radial structure across storms in the half-dry and dry cases (Figs. 4k,l). This behavior mirrors the wide variance of storm size seen in the real world (Merrill 1984; Chavas et al. 2016), as well as the consistent radial structure of the wind field for a given storm size noted in observations and models and predicted by theory (C15; Chavas and Lin 2016; Reed and Chavas 2015). We speculate that the much slower temporal variation of storm size in the moist case relative to the dry or even half-dry case may be tied to the longer time scales for radiatively induced subsidence in the environment outside of the storm inner cores; this topic is addressed in section 3f.

c. Statistical relationships among moist and dry storm parameters

We next examine the relationships among structural parameters $\left(r_8,r_m,{\upsilon }_m\right)$ for moist, half-dry, and dry cyclones for simulation days 40–70 (Fig. 6; corresponding statistics in Table 1). We use $r_8$ here as a measure of outer storm size because it is less variable in time than $r_0$, in line with previous work (Schenkel et al. 2017; Chavas et al. 2017); we discuss $r_0$ in subsequent sections. Moist storms are larger and more intense than either half-dry or dry storms, and more variable in both size $r_8$ and intensity ${\upsilon }_m$ (Fig. 6a). The coefficient of variation for $r_8$ is largest in the moist simulation (0.24), reflecting the persistent variability in size across storms displayed in Fig. 4j. This quantity is much smaller for the half-dry simulation (0.09), indicating storms have a tight distribution of sizes, but only slightly below the moist case for the dry simulation (0.19), perhaps indicating an increase in turbulent variability in the dry system. Outer size and intensity show a slight positive correlation for dry storms, but little correlation for half-dry and moist storms, as is found in nature (Merrill 1984; Chavas et al. 2016) and permitted by theory (Chavas and Lin 2016). In association with their greater intensities, moist storms have smaller and less variable radii of maximum winds than either half-dry or dry storms (Fig. 6b). Storms for all three surface wetness values show a positive correlation between radius of maximum winds and outer size, but $r_m$ depends more strongly on $r_8$ for dry and half-dry simulations (Fig. 6c). Overall, the cluster of half-dry storms in $\left(r_8,r_m,{\upsilon }_m\right)$ space falls between those for moist and dry storms, but lies closer to the dry storm cluster due to the low intensities of dry and half-dry storms.

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Statistical covariability among ${\upsilon }_m$, $r_m$, and $r_8$ across moist $\left(\beta ={1.000}^{*}\right)$, half-dry $\left(\beta =0.500\right)$, and dry $\left(\beta =0.000\right)$ simulations for days 40–70: (a) ${\upsilon }_m$ and $r_8$, (b) ${\upsilon }_m$ and $r_m$, and (c) $r_m$ and $r_0$. Median, interquartile range (thick line), and 5th–95th-percentile range (thin line) of individual variables plotted on their respective axes. Storms with ${\upsilon }_m<10{\hspace{0.17em}\text{m s}}^{-1}$ have been excluded.

Citation: Journal of the Atmospheric Sciences 76, 8; 10.1175/JAS-D-18-0357.1

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Table 1.

Statistics of quantities for each simulation displayed in Fig. 6, including the median, first quartile (25%), third quartile (75%), mean μ, standard deviation σ, and coefficient of variation c_υ.

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The joint dependences of the radius of maximum tangential wind $r_m$ and the central pressure deficit, $\mathrm{\Delta }p=p_c-\overline{p}$, on outer storm size and intensity ($r_8$ and ${\upsilon }_m$) differ slightly between moist, half-dry, and dry cyclones (Fig. 7). Each value of surface moisture gives rise to storms that occupy a distinct region of $\left(r_8,{\upsilon }_m\right)$ space, but in all three simulations, $r_m$ is greatest for large and weak storms in accordance with theory (Emanuel 1986; Emanuel and Rotunno 2011; Chavas and Lin 2016). Large dry storms show only a weak anticorrelation between intensity and $r_m$, unlike moist and half-dry storms (Figs. 7a,c,e). The central pressure deficit is larger for storms with higher maximum wind speeds and larger size (Figs. 7b,d,f), in accordance with recent work (Chavas et al. 2017).

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Joint variability of cyclone structure parameters for days 40–70. (a) $r_m$ as function of ${\upsilon }_m$ and $r_8$ for the moist simulation $\left(\beta ={1.000}^{*}\right)$. (b) As in (a), but for the central pressure deficit. (c),(d) As in (a) and (b), but for the half-dry simulation $\left(\beta =0.500\right)$. (e),(f) As in (a) and (b), but for the dry simulation $\left(\beta =0.000\right)$. Note that color scales differ for each panel and that storms with ${\upsilon }_m<10{\hspace{0.17em}\text{m s}}^{-1}$ have been excluded.

Citation: Journal of the Atmospheric Sciences 76, 8; 10.1175/JAS-D-18-0357.1

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d. Rotating RCE from moist to dry limits

Although cyclones form readily in both moist and dry limits, spontaneous genesis is strikingly absent for intermediate values of surface wetness, from $\beta =0.01–0.3$ (Fig. 8). All simulations that form cyclones ($\beta =0–0.003$ and $\beta =0.4–1^{*}$) have surface kinetic energy dissipation $\left(\rho c_D\overline{V^3}\right)$ values of 1–4 W m⁻² (though up to 10 W m⁻² immediately following genesis for moist storms), mean surface wind speeds of about 8 m s⁻¹, and maximum surface wind speeds of 35–75 m s⁻¹. In between these two clusters of simulations with dry and moist storms is a “no-storms-land” where spontaneous genesis does not occur, marked by smaller surface kinetic energy dissipation of 0.2–0.5 W m⁻², average surface wind speeds of less than 5 m s⁻¹, and maximum surface wind speeds of 20–30 m s⁻¹.

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(left) Time series of domain-averaged surface kinetic energy dissipation for (a) simulations with varied surface wetness β and (c) simulations with varied surface temperature $T_S$ (note the logarithmic vertical axes). (right) Median values over time from days 40–70 are shown for the domain-averaged surface wind speed $\overline{V}$ (dots), maximum tangential winds associated with tracked cyclones ${\upsilon }_m$ (circles), and domain-maximum surface wind speeds $\max \left(V\right)$ (×) with (b) varied β and (d) varied $T_S$. Horizontal lines in (b) and (d) around markers for domain-mean and maximum cyclone azimuthal winds indicate the 5th–95th percentiles of each value (across time for the domain-mean wind and across time and cyclones for the azimuthal winds). Vertical black lines in (b) and (d) indicate potential intensity ${\upsilon }_p$ averaged from days 40–70 of each simulation and calculated from the domain-average surface enthalpy disequilibrium [Eq. (5)].

Citation: Journal of the Atmospheric Sciences 76, 8; 10.1175/JAS-D-18-0357.1

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It would be tempting to conclude that this no-storms-land acts as a divider between moist $\left(\beta =0.4–1^{*}\right)$ and dry $\left(\beta =0–0.003\right)$ blocs of storms. But based on the analysis above, and the vortex statistics described here, this conclusion would be misleading: the storms with $\beta =0.4–0.6$ are truly intermediate states between the fully moist and dry limits, sharing features of both. The $\beta =0.4$ and $\beta =0.5$ cases have median tangential winds in tracked cyclones of 15–20 m s⁻¹—similar to the fully dry and the nearly dry storms with $\beta =0.001$ and $\beta =0.003$—yet the convective dynamics and ambient stratification in these simulations remain fundamentally moist. These storms are also intermediate in structure between the moist and dry limits, with large radii of maximum winds as compared to the very moist storms from $\beta =0.8–1^{*}$, and more eyewall asymmetry than the moist storms, but less than the dry ones (Figs. 1a,c,e).

Potential intensity ${\upsilon }_p$, shown by black vertical lines in Fig. 8b, acts as a strong upper bound for ${\upsilon }_m$ of moist cyclones, but semidry and dry cyclones have much lower values of ${\upsilon }_m$ relative to ${\upsilon }_p$. Note that the absolute maximum of V in the domain exceeds ${\upsilon }_p$ for moist storms, because potential intensity theory does not include azimuthal asymmetries or small-scale convective gusts. In simulations with $\beta =0–0.003$, the combination of convective gusts and asymmetric eyewall structure leads to maximum surface wind speeds that are roughly twice ${\upsilon }_m$. The upward jump in potential intensity in no-storms-land arises from the constraint in RCE that surface enthalpy disequilibrium vary inversely with the domain-average wind speed, for fixed column-integrated radiative cooling. Thus, the weaker mean winds that occur for simulations without any cyclones allow for greater surface enthalpy disequilibrium and potentially stronger storms, but if storms were to form, the average surface wind speed would increase and the potential intensity would fall. This negative feedback between cyclone activity and global ${\upsilon }_p$ also causes surface dissipation to overshoot its equilibrium value before stabilizing in simulations that experience cyclogenesis (Fig. 8), and is likely relevant for predicting the properties of cyclones in a turbulent TC-world from the initial sounding.

Simulations across a range of surface temperatures show a similar transition from moist to dry as the surface is cooled (Figs. 8c,d). Simulations that form cyclones ($T_S=240$ and $T_S=280–300\hspace{0.17em}\text{K}$) show kinetic energy dissipation and wind speeds close to those from the varied-β simulations (note that the T_S = 300 K* simulation with $\beta =1^{*}$ is shared between these groups). Genesis is delayed and maximum wind speeds weaken as $T_S$ is reduced from 300 K* to 280 K, akin to the effects of reduced β from 1* to 0.4. A no-storms-land is found for simulations with $T_S$ from 250 to 270 K, with slightly weaker convective turbulence than the semidry simulations that lack cyclones. One simulation with T_S = 240 K parallels the set of dry TC-world simulations from $\beta =0–0.003$, showing near-immediate genesis, surface kinetic energy dissipation ~2 W m⁻², average surface wind speeds of ~8 m s⁻¹, and maximum surface wind speeds ~35 m s⁻¹. The $T_S=280-\text{K}$ simulation strongly resembles the $\beta =0.400$ simulation in terms of the delayed genesis of cyclones (Figs. 8a,c), suggesting a similar process gradually impedes cyclogenesis as the surface is dried or cooled, but this similarity may be a coincidence.

As found by Zhou et al. (2014), as well as Chavas and Emanuel (2014) in axisymmetric geometry, the outer size of our simulated cyclones does not appear to scale cleanly with either the deformation radius $NH/f$ or a potential intensity radius ${\upsilon }_p/f$ (Fig. 9). The radius of vanishing azimuthal winds $r_0$ decreases by about a factor of two going from moist to dry or warm to cold limits, but $NH/f$ decreases by a factor of roughly six, whereas ${\upsilon }_p/f$ decreases by only 30%–40%. Instead, ${\upsilon }_p/f$ appears to more closely follow the convective vortex size $r_C$, which varies only weakly as surface moisture or temperature is decreased; $r_C$ shows a hint of smaller values for intermediate β or $T_S$ than for either warm/moist or dry/cold storms. Moreover, the convective vortex size appears approximately bounded from above by ${\upsilon }_p/f$, as suggested by Emanuel (2004), with dry storms bumping up more closely against this upper bound, suggesting that the intensities of dry storms might be limited by the storms becoming too large. Thus, our results indicate that ${\upsilon }_p/f$ is a more relevant length scale for the inner convective core of a tropical cyclone, while the overall size of the storm may further depend on a length scale associated with the structure of the nonconvecting outer circulation, in line with the axisymmetric results of Chavas and Emanuel (2014). The circulation structure is analyzed in section 3f.

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Metrics of storm size, for simulations with (a) varied surface moisture and (b) varied surface temperature. The medians for all cyclones from days 40–70 of fully convective vortex extent $r_C$ [Eq. (6)] are shown with × symbols, and the larger radius of vanishing winds $r_0$ with open circles. Thin horizontal lines indicate 5th–95th percentiles of each value, and thicker lines indicate interquartile range. For each simulation, vertical black bars denote the length scale given by the time-average of ${\upsilon }_p/f$ [Eq. (5) defines the simplified potential intensity], and asterisks denote the deformation radius $NH/f$, where N is the density-weighted buoyancy frequency of the troposphere and H is the tropopause height (defined as the height of the last model level where the lapse rate exceeds 2 K km⁻¹), both taken from a time-mean domain-average temperature profile.

Citation: Journal of the Atmospheric Sciences 76, 8; 10.1175/JAS-D-18-0357.1

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Cyclone properties in both sets of simulations can also be compared using nondimensional intensity ${\upsilon }_m/{\upsilon }_p$ and the inner-core Rossby number $\text{Ro}={\upsilon }_m/f{r}_m$ (Fig. 10). Median ${\upsilon }_m/{\upsilon }_p$ lies between 0.75 and 1 for surfaces with $\beta =0.7–1^{*}$ and with T_S = 290 K to 300 K*, but decreases rapidly with further surface drying to about 0.3 for $\beta =0.4$—with similar values for the nearly dry and fully dry $\beta =0–0.003$ simulations (Figs. 10a,c). Although increased asymmetry and convective gustiness in the dry limit makes ${\upsilon }_m/{\upsilon }_p$ an imperfect measure of intensity, Fig. 8 shows that $V/{\upsilon }_p$ also decreases with surface drying (albeit nonmonotonically for varied β). We note as an aside that our 1152 km × 1152 km simulation with a fully moist surface $\left(\beta =1\right)$, which eventually collapsed to one storm, showed much smaller normalized median intensity of ${\upsilon }_m/{\upsilon }_p=0.7$ and much greater variability in time (5th–95th percentiles of ${\upsilon }_m/{\upsilon }_p$ ranging from 0.38 to 1.06), consistent with Zhou et al. (2014), who found that cyclone intensity varies intermittently in time in lattice TC-worlds with only one storm. The inner-core Rossby number, $\text{Ro}={\upsilon }_m/f{r}_m$, shows a similar gradual transition between cyclostrophic vortices with Ro ≫ 1 for warm/moist surfaces, and gradient-balance vortices with Ro ~ 1 for dry/cold surfaces (Figs. 10b,d). Overall, Fig. 10 reinforces our impression that the no-storms-land is not a divider between regimes of moist and dry cyclones, but rather serves to interrupt a gradual transition from moist to dry vortex dynamics.

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(a),(c) Dimensionless cyclone intensity ${\upsilon }_m/{\upsilon }_p$ and (b),(d) inner-core Rossby number $\text{Ro}={\upsilon }_m/f{r}_m$. Dots indicate median values for all tracked cyclones from days 40–70, thin horizontal lines indicate 5th–95th percentiles, and thick horizontal lines indicate interquartile range (25th–75th percentiles). (a), (b) Simulations with varied β and (c),(d) simulations with varied $T_S$. Thin vertical gray lines indicate values of unity for each dimensionless parameter.

Citation: Journal of the Atmospheric Sciences 76, 8; 10.1175/JAS-D-18-0357.1

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e. Transient variations in surface properties

To test whether the no-storms-land can destroy established storms, or merely prevents spontaneous genesis, we conducted four additional simulations where the surface wetness or temperature were ramped up or down in time from initial values that allow spontaneous genesis. We refer to these as “β-sweep” and “$T_S$-sweep” simulations. For the downward β-sweep simulation we used $\beta \left(t\right)={\exp }^{-0.034\hspace{0.17em}54t}$ and for the upward β-sweep simulation we used $\beta \left(t\right)=0.001\hspace{0.17em}{\exp }^{0.034\hspace{0.17em}54t}$ (with t as time in days), giving transitions between $\beta =1$ and $\beta =0.001$ over each 200-day simulation. For the downward T_S-sweep simulation we used $T_S\left(t\right)=300-0.25t$ and for the upward T_S-sweep simulation we used $T_S\left(t\right)=240+0.25t$; these simulations were run for 240 days each. In the T_S-sweep simulations, two additional modifications were made in an attempt to limit variations in ${\upsilon }_p$ over the course of each simulation and across the two simulations. First, the tropopause temperature was increased or decreased in time at 0.7 times the rate of the surface temperature [i.e., $T_T\left(t\right)=210-0.175t$ and $T_T\left(t\right)=168+0.175t$], maintaining a similar thermodynamic efficiency and tropospheric mass across surface temperatures. Second, the radiative cooling rate relative to the surface temperature was held fixed at 1 K day⁻¹ (i.e., modifying $\dot{Q}$ to 0.75 K day⁻¹ in the upward sweep and to 1.25 K day⁻¹ in the downward sweep). This choice was made because a surface that warms in time will have a greater enthalpy flux than a surface of constant temperature or one that cools in time; varying $\dot{Q}$ is an attempt to offset this.

In all of the four temperature and moisture sweep simulations, cyclones form in moist/warm or dry/cold limits before the boundary conditions transit through no-storms-land, and partially disrupted cyclones persist for tens of days as the simulation passes through the no-storms-land. Therefore, we conclude that the regions of parameter space from $\beta =0.01–0.3$ and T_S = 250–270 K are barriers to spontaneous cyclogenesis, but not to the existence of cyclones.

To present simulations across both β and $T_S$ on the same axes, we examine whether the surface kinetic energy dissipation $\rho c_D\overline{V^3}$ normalized by the surface enthalpy flux $F_k=E+H$, depends similarly on the surface latent heat flux fraction, $E/F_k$, across both suites of simulations. The normalized dissipation $\rho c_D\overline{V^3}/F_k$ is a measure of the global conversion efficiency of convective heat transport into surface frictional dissipation, whereas $E/F_k$ is a dimensionless measure of surface evaporation, and should tend to 0 in both cold and dry limits. In this nondimensional parameter space, the no-storms-land appears as a common region from $E/F_k$ of about 0.1–0.4, and $\rho c_D\overline{V^3}/F_k<0.005$ (Fig. 11), and dry to nearly dry TC-worlds are disjoint from semidry and moist TC-worlds. All four of the sweep simulations, however, connect the dry and moist regions, and can be clearly distinguished from simulations without cyclogenesis because they maintain dissipation efficiencies greater than 0.01 after cyclones have initially formed. Note that the β-sweep and T_S-sweep simulations show considerable spread in dissipation efficiency at any given value of $E/F_k$, except in the dry limit. The downward β-sweep simulation is an oddity because of its numerous points with $E/F_k<0$; this occurs because Eq. (3) allows a moist atmosphere to transfer latent heat into the surface if $\beta q_S^{*}<q_1$, and β decreases rapidly enough in time that this condition is satisfied for much of the simulation. Cyclones generally have a different ratio of $E/F_k$ than the domain as a whole; for example, cyclones from simulations with $\beta =0.4$ and $\beta =0.5$ have negative latent heat fluxes but very large positive sensible heat fluxes near their eyewalls. Whether the cyclone-scale ratio of evaporation to total enthalpy flux might be used to characterize the transition from moist to dry vortex dynamics is a question left for future work.

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Plot of domain-averaged normalized surface dissipation, $\rho c_D\overline{V^3}/F_k$, against the fraction of surface enthalpy flux carried by evaporation, $E/F_k$, for the two main sets of simulations with varied values of β (filled circles) and $T_S$ (filled squares), as well as simulations where β or $T_S$ is swept upward (upward-pointing triangles) or downward (downward-pointing triangles) in time. For the main sets of simulations, daily averages are shown for days 40–70; for the β-sweep and T_S-sweep simulations, 5-day averages are shown from day 10 onward.

Citation: Journal of the Atmospheric Sciences 76, 8; 10.1175/JAS-D-18-0357.1

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