Tropical cyclogenesis in warm climates simulated by a cloud-system resolving model

Abstract

Here we investigate tropical cyclogenesis in warm climates, focusing on the effect of reduced equator-to-pole temperature gradient relevant to past equable climates and, potentially, to future climate change. Using a cloud-system resolving model that explicitly represents moist convection, we conduct idealized experiments on a zonally periodic equatorial β-plane stretching from nearly pole-to-pole and covering roughly one-fifth of Earth’s circumference. To improve the representation of tropical cyclogenesis and mean climate at a horizontal resolution that would otherwise be too coarse for a cloud-system resolving model (15 km), we use the hypohydrostatic rescaling of the equations of motion, also called reduced acceleration in the vertical. The simulations simultaneously represent the Hadley circulation and the intertropical convergence zone, baroclinic waves in mid-latitudes, and a realistic distribution of tropical cyclones (TCs), all without use of a convective parameterization. Using this model, we study the dependence of TCs on the meridional sea surface temperature gradient. When this gradient is significantly reduced, we find a substantial increase in the number of TCs, including a several-fold increase in the strongest storms of Saffir–Simpson categories 4 and 5. This increase occurs as the mid-latitudes become a new active region of TC formation and growth. When the climate warms we also see convergence between the physical properties and genesis locations of tropical and warm-core extra-tropical cyclones. While end-members of these types of storms remain very distinct, a large distribution of cyclones forming in the subtropics and mid-latitudes share properties of the two.

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Notes

  1. 1.

    The dependence of PI on relative SST (local SST minus a tropical mean SST) requires horizontal temperature gradients in the free-troposphere to be weak. Although the mid-latitude region in which PI increases lies outside the tropical domain in which weak temperature gradient theories are strictly valid, we still expect upper-tropospheric temperature gradients to be weaker than low-level gradients in equivalent potential temperature, so that relative SST will behave at least qualitatively like PI.

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Acknowledgements

We thank two anonymous reviewers for their constructive comments on the paper. Financial support was provided by grants to AVF from the David and Lucile Packard Foundation, NSF (AGS-0163807), and NOAA (NA14OAR4310277). WRB was supported by Office of Naval Research award N00014­15­1­2531. JS was supported by the Russian Foundation for Basic Research (grant #17-05-00509) and the Russian Science Foundation (grant #14-50-00095). Support from the Yale University Faculty of Arts and Sciences High Performance Computing facility is acknowledged.

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Correspondence to Alexey V. Fedorov.

Appendices

Appendix 1: RAVE rescaling

To improve the simulation of tropical cyclogenesis, and also to achieve a mean tropical state more closely resembling observations, we use the Reduced Acceleration in the Vertical (RAVE) rescaling, which reduces the vertical velocities and increases the horizontal length scales of convective motions, in effect making them closer in size to those of the unaltered large-scale, nearly hydrostatic flow (e.g. Kuang et al. 2005; Pauluis and Garner 2006; Garner et al. 2007; Boos et al. 2016). RAVE is also referred to as the hypohydrostatic rescaling because it increases the inertia of vertical motion, and is implemented by multiplying the acceleration term in the vertical momentum equation by a factor γ > 1:

$${\gamma ^2}\frac{{Dw}}{{Dt}}= - \frac{1}{\rho }\frac{{\partial p}}{{\partial z}} - g+{F_z}$$

Here, \(\frac{{Dw}}{{Dt}}\) is the material derivative of vertical velocity, \(- \frac{1}{\rho }\frac{{\partial p}}{{\partial z}}\) the acceleration due to the vertical pressure gradient, g the acceleration due to gravity, \({F_z}\) the acceleration due to vertical diffusion, and γ is the RAVE factor. Choosing γ = 1 corresponds to the standard vertical momentum equation (no rescaling), while γ = 0 corresponds to the hydrostatic approximation.

The RAVE rescaling is mathematically equivalent to the Diabatic Acceleration and Rescaling (DARE), in which the planetary rotation rate and diabatic processes, such as radiative fluxes and surface enthalpy fluxes, are increased by the factor γ, while the planetary radius is decreased by γ. The DARE approach shrinks the time and space scales of the large-scale dynamics (e.g. the Rossby radius of deformation), bringing them closer to the scales of convective motions. Another related approach is known as the Deep Earth rescaling, in which the gravitational acceleration is decreased and the vertical coordinate is increased in scale by γ (Pauluis and Garner 2006). The same modification of the equations of motion was also used years earlier in numerical weather prediction in so-called quasi-nonhydrostatic models (Browning and Kreiss 1986; MacDonald et al. 2000). Although all of these treatments are mathematically identical, RAVE has the simplest physical interpretation and can be easily implemented in numerical models.

Kuang et al. (2005) conducted RAVE simulations of the atmospheric circulation on an equatorial β-plane with an ocean mixed-layer lower boundary, with emphasis on convectively coupled equatorial waves. Garner et al. (2007) conducted global aqua-planet simulations with large RAVE factors (γ ≥ 100) and found that the extra-tropical circulation was largely unaltered by such extreme rescaling; they noted that use of RAVE with γ ≈ 3 and horizontal resolutions on the order of 10 km may provide a promising alternative to convective parameterization. Ma et al. (2014) produced a remarkably accurate climatology of South Asian monsoon precipitation using RAVE in a global model (on a sphere) without convection parameterization, with a horizontal resolution of 40 km and γ = 10. Boos and Kuang (2010) used RAVE on an equatorial β-plane to examine the mechanisms involved in tropical intraseasonal variability in a model with horizontal resolution of about 30 km and γ ≈ 15.

Realistic simulation of TCs typically requires model horizontal resolution on the order of 1 km in models without convective parameterization. Recently, Boos et al. (2016) studied convective self-aggregation and tropical cyclogenesis in doubly-periodic domains on an f-plane and showed that the RAVE approach could improve simulation of TCs in cloud-system resolving models with relatively coarse resolutions, on the order of 10 km. For the simulation of TCs, RAVE thus provides an attractive alternative to convective parameterization at resolutions in the so-called “gray zone”.

The conclusions of Boos et al. (2016) contradicted the earlier work of Pauluis and Garner (2006), who argued that RAVE worsened the dry bias in coarse resolution models; however, the authors of that earlier study did not consider that, since they were increasing their domain size as horizontal resolution was coarsened, convective self-aggregation and an associated domain-mean drying would occur at the coarser resolutions (e.g. Bretherton et al. 2005; Muller and Held 2012). Boos et al. (2016) showed that instead of increasing the humidity bias, RAVE actually reduces a dry bias caused by use of coarse resolution in simulations of radiative-convective equilibrium.

The present study builds on the results of Boos et al. (2016) but goes one step further and simulates both the atmospheric general circulation and tropical cyclogenesis on a global scale. Throughout the integrations described in the main text we used γ = 15, which, given the explicit grid spacing of 15 km, provides an “equivalent” rescaled horizontal resolution of 1 km (e.g. Pauluis and Garner 2006). Use of γ = 15 allowed our control integration (TM0) to produce a somewhat realistic representation of the modern zonal mean tropical climate state and tropical cyclones up to category 5. Here, we describe the differences between several simulations for our idealization of modern climate, using the same boundary conditions as in TM0, but increasing the value of γ from 1 to 5 and then to 15.

Without RAVE or with small RAVE factors the simulations exhibit a “double-ITCZ” problem—the ITCZ splits into two convergence zones, with the stronger one located on the southern flank of the SST maximum (Fig. 11b). This feature is not unlike the much discussed double-ITCZ problem in GCM simulations that produce two local maxima in precipitation in the eastern Pacific on opposite sides of the equator (e.g. Li and Xie 2014). For γ = 1, the stronger ITCZ sits 0.5° south of the equator, and is geographically well-separated from most tropical cyclogenesis events (Fig. 12a, b). A second, weaker convergence zone is located as far north as 20°N. As we increase γ to 5, the stronger ITCZ moves north of the equator while the secondary convergence zone weakens and shifts southward. Only for γ = 15 does the model simulate a single ITCZ, roughly at 5°N, not too far from the observed mean ITCZ position in the central Pacific in July (e.g. Schneider et al. 2014).

Fig. 11
figure11

Meridional distribution of a prescribed sea surface temperature (°C), and the simulated zonal means of b precipitation (mm/day) and (c) precipitable water (mm) for simulations using different RAVE numbers γ = 1 (light gray), γ = 5 (gray) and γ = 15 (black). Note that the ITCZ moves to a more northerly position, several degrees of latitude away from the equator, for higher RAVE numbers

Fig. 12
figure12

Composites of (left) category 2 and (right) category 4 tropical cyclones, shed from the ITCZ and evident in the precipitable water field, for simulations using different RAVE numbers: γ = 1 (top), γ = 5 (middle), and γ = 15 (bottom). Note the environmental moistening over the cyclogenesis region (discussed by Boos et al. 2016) and a better representation of the hurricane eye for higher RAVE numbers

Why does using RAVE shift the ITCZ with respect to the SST maximum? This is a difficult question as it requires understanding the mechanisms that set the latitude of the ITCZ, given the SST distribution, and those mechanisms are not well understood (e.g. Back and Bretherton 2009; Schneider et al. 2014; Faulk et al. 2017). Boos et al. (2016) argued that RAVE increases the free-tropospheric humidity of the environment surrounding aggregated convection, and there is indeed an increase in precipitable water near and just north of the ITCZ, which is a type of aggregated convection, as γ is increased (Fig. 11c). Perhaps this increase in precipitable water allows convection near the SST maximum to be less inhibited by the entrainment of dry air, so that the ITCZ latitude is controlled more by thermodynamics (e.g. the latitude of maximum CAPE) than by boundary layer dynamics (e.g. Pauluis 2004). Other studies have shown that ITCZ latitude simulated in a GCM can be greatly influenced by the amount of entrainment required to occur in parameterized deep convection (Kang et al. 2008); although that sensitivity was demonstrated to be mediated by cloud radiative effects in a model with interactive SST, our results show that ITCZ latitude can be greatly influenced by the details of moist convection even when SST is prescribed.

Unsurprisingly, increasing γ to 15 also affects tropical cyclogenesis. In particular, as γ is increased from 1 to 15, the number of tropical cyclones increases by roughly a factor of two, with the frequency of strong cyclones also increasing (Fig. 13). This increase in TC activity for sufficiently high RAVE numbers might occur because of three main factors. The first is the ITCZ shift to its northerly position where it can play a more active role in cyclogenesis (e.g. Merlis et al. 2013; Figs. 11, 12). The second is the general moistening of the environment around tropical cyclones (Figs. 12, 11), especially in the region of active cyclogenesis, consistent with the argument of Boos et al. (2016). The third factor is a better representation of the core of the cyclones, specifically the hurricane eye and eyewall, and more coherent convective bands (Fig. 12).

Fig. 13
figure13

Scatterplots of maximum surface wind speed (m/s) versus minimum central surface pressure (hPa) for warm-core cyclones in perpetual July simulations using different RAVE numbers: a γ = 1, b γ = 5, and c γ = 15. Each point is colored according to the cyclone’s genesis latitude; the Saffir–Simpson categories are also shown. Note the significant increase in the number of tropical cyclones, including strong storms, for γ = 15. The numbers at the top of each panel refer to the total number of tropical (TC) and extra-tropical (ETC) cyclones in the simulations. The bottom panel is identical to Fig. 7a. Each simulation lasts 20 boreal summers

Appendix 2: Tracking algorithm and cyclone clustering

To track warm-core cyclones we follow the algorithm of Scoccimarro et al. (2011), closely related to that of Walsh et al. (2007). We first identify all cyclonic vortices above a given vorticity threshold at 850 hPa. Then we find the sea level pressure (SLP) minimum within a 350 km radius of the vorticity maximum. This location is now a candidate for a cyclone, which we subject to several key tests:

Test 1:

Vorticity maximum at 850 hPa is above the threshold ηmin.

Here we use ηmin = 10−5s−1.

Test 2:

SLP minimum is 2 hPa lower than SLP averaged within a 350 km radius from the vorticity maximum.

Test 3:

Surface wind speed maximum is greater than 15.5 ms−1 (within a 350 km radius).

Test 4:

Average wind speed over inner 50 km is greater at 850 hPa than at 300 hPa

Test 5:

The cyclone has a warm core. That is, the temperature anomaly, in the location of the maximum vorticity, estimated as T′ = T′300 hPa + T′500 hPa +T′700 hPa, is positive and T′ > 1 °C

Test 6:

The core temperature is warmer than temperature averaged within a 350 km radius from the vorticity maximum

Finally, to obtain the cyclone tracks we connect locations of each vortex at different time steps separated by 6 h, as long as the vortex has persisted for a minimum of 24 h and its center has not moved more than 350 km in 6 h. The cyclone tracks shown in Fig. 6 are obtained through this procedure. For the distributions shown in Figs. 7 and 13 we pick up the strongest values of surface wind speed along the tracks and the corresponding values of SLP.

To further investigate how the distributions of tropical and warm-core extra-tropical cyclones change with SST gradient we use a formal clustering technique to separate storms of different origin according to their physical characteristics. In particular, separation based on the 200 and 800 hPa geopotential heights works especially well for the modern climate since ETCs are typically too shallow to produce large fractional changes in upper tropospheric heights (Fig. 14). The computation of the clusters follows Studholme et al. (2015) and uses the k-means algorithm (e.g. Lloyd 1982, here k = 2). It involves grouping cyclones into k clusters by minimizing the sum of squares of Euclidean distances to each cluster’s centroid within the 200 and 800 hPa geopotential height phase space for all identified warm-core cyclones.

Fig. 14
figure14

Scatterplots of simulated warm-core cyclones in terms of 200 and 800 hPa geopotential heights in different simulations: a TM0, b TM6, and c TM15. Two distinct clusters of storms are identified—Tropical (red) and Extra-tropical (blue-green). These two clusters merge in the TM15 simulation. Even though the clustering analysis draws a boundary between the two clusters in the last simulation, the properties of storms change gradually across this boundary

Reducing the meridional SST gradient acts to reduce the “distance” between the clusters in the TM6 simulation and eventually to merge the two clusters in TM15 (Fig. 14c). In terms of core temperature anomalies, extra-tropical cyclones are typically a little colder than tropical cyclones, as they originate farther north (Fig. 15). Nevertheless, where the two distributions overlap in mid-latitudes in TM15, their properties become quite similar.

Fig. 15
figure15

The same two clusters as in Fig. 14, Tropical (red) and Extra-tropical (blue–green), but shown in terms of core temperature anomaly and genesis latitude for a TM0, b TM6, and c TM15. The plot further illustrates that the two clusters in TM15 overlap as tropical cyclones can develop much farther north in this simulation

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Fedorov, A.V., Muir, L., Boos, W.R. et al. Tropical cyclogenesis in warm climates simulated by a cloud-system resolving model. Clim Dyn 52, 107–127 (2019). https://doi.org/10.1007/s00382-018-4134-2

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Keywords

  • Tropical cyclones
  • Climate change
  • Atmospheric modeling
  • Paleoclimate