Geophysical Research Letters
RESEARCH LETTER
10.1002/2016GL067730
Key Points:
• SST dependence of TCs assessed with
uniform SST GCM simulations
• Spherical geometry allows TC
poleward drift
• Results are broadly similar to rotating
radiative convective equilibrium
Supporting Information:
• Figures S1 and S2
Correspondence to:
T. M. Merlis,
[email protected]
Citation:
Merlis, T. M., W. Zhou, I. M. Held,
and M. Zhao (2016), Surface
temperature dependence of tropical
cyclone-permitting simulations in
a spherical model with uniform
thermal forcing, Geophys. Res. Lett.,
43, doi:10.1002/2016GL067730.
Received 8 JAN 2016
Accepted 19 FEB 2016
Accepted article online 23 FEB 2016
Surface temperature dependence of tropical
cyclone-permitting simulations in a spherical
model with uniform thermal forcing
Timothy M. Merlis1 , Wenyu Zhou2 , Isaac M. Held3 , and Ming Zhao4
1 Department of Atmospheric and Oceanic Sciences, McGill University, Montreal, Quebec, Canada, 2 Scripps Institution of
Oceanography, University of California, San Diego, La Jolla, California, USA, 3 NOAA/Geophysical Fluid Dynamics
Laboratory, Princeton, New Jersey, USA, 4 UCAR/Geophysical Fluid Dynamics Laboratory, Princeton, New Jersey, USA
Abstract
Tropical cyclone (TC)-permitting general circulation model simulations are performed with
spherical geometry and uniform thermal forcing, including uniform sea surface temperature (SST) and
insolation. The dependence of the TC number and TC intensity on SST is examined in a series of
simulations with varied SST. The results are compared to corresponding simulations with doubly periodic
f -plane geometry, rotating radiative convective equilibrium. The turbulent equilibria in simulations with
spherical geometry have an inhomogenous distribution of TCs with the density of TCs increasing from
low to high latitudes. The preferred region of TC genesis is the subtropics, but genesis shifts poleward and
becomes less frequent with increasing SST. Both rotating radiative convective equilibrium and spherical
geometry simulations have decreasing TC number and increasing TC intensity as SST is increased.
1. Introduction
Simulations of rotating radiative convective equilibrium (RCE) in small [e.g., Nolan et al., 2007] and large [e.g.,
Held and Zhao, 2008] doubly periodic f -plane (constant Coriolis parameter f ) domains have revealed important sensitivities governing tropical cyclones (TCs). In addition to highlighting the role that the planetary
vorticity plays in TC development, this idealized geometry emphasizes thermodynamic factors (e.g., surface
temperature) that influence the genesis, intensification, and turbulent equilibria of TCs.
Here we present the results of TC-permitting atmospheric general circulation model (GCM) simulations with
uniform thermal forcing, as is typical of rotating RCE, but retain Earth’s spherical geometry and the concomitant 𝛽 effect. Introducing differential rotation allows for poleward propagation of TCs, “𝛽 drift” [Chan, 2005].
Shi and Bretherton [2014] demonstrated the importance of 𝛽 drift for TCs in this configuration. The storm
motion introduces a TC-loss mechanism, when viewed from a fixed latitude frame, that is not present in f
plane simulations. Previous research has emphasized the importance of the spatial inhomogeneity of deep
convection and the associated time-mean divergent circulation in determining TC frequency [Held and Zhao,
2011; Merlis et al., 2013; Ballinger et al., 2015], and simulations with uniform thermal forcing have weak spatial
inhomogeneity of convection and weak mean circulations [Kirtman and Schneider, 2000; Shi and Bretherton,
2014]. Thus, this configuration provides an interesting step in model hierarchy by introducing the 𝛽 -drift
dynamics not present in rotating RCE that are critical for storm propagation but suppressing other dynamical
factors associated with the large-scale environment (such as strong divergent mean circulations and vertical
wind shear).
Here we present 50 km horizontal resolution, spherical geometry simulations with uniform thermal forcing
and perform the first examination of the sea surface temperature (SST) dependence of TC characteristics.
These spherical geometry simulations are compared to the results of corresponding f -plane rotating RCE
simulations with the same GCM at 25 km horizontal resolution [Zhou et al., 2014].
2. General Circulation Model
©2016. American Geophysical Union.
All Rights Reserved.
MERLIS ET AL.
The Geophysical Fluid Dynamics Laboratory’s High-Resolution Atmospheric Model (HiRAM) simulates the
climatology and interannual variability of TC frequency well with comprehensive boundary conditions and
observed SSTs [Zhao et al., 2009]. HiRAM has been used to examine the response of TC frequency to climate
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change in comprehensive [Zhao et al., 2009; Zhao and Held, 2012] and idealized aquaplanet simulations with
Earth-like insolation [Merlis et al., 2013]. The quality of the TC climatology in the comprehensive configuration
has been compared favorably to that in other global models by Shaevitz et al. [2014]. We note that while the
simulation of the distribution of TCs is of high quality in the comprehensive HiRAM model, TCs of intensity
category 3 and higher are nearly absent. The model quality helps motivate close study of the TC climate in
idealized configurations of this model in that it provides circumstantial evidence that we are creating building blocks for an understanding of TC statistics in reality and not only in the model itself. We examine the SST
dependence of TCs in spherical geometry simulations with uniform thermal forcing and in rotating RCE [Zhou
et al., 2014].
2.1. Spherical Geometry With Uniform Thermal Forcing
The simulations presented here have spatially uniform and time-independent boundary conditions (SST, insolation, greenhouse gas, and ozone concentrations). A complete description of the radiative parameters, which
we follow exactly in the simulations presented here, can be found in Zhou et al. [2014]. The SST is varied over
the range of 280 K to 307 K.
The primitive equations’ variation of the Coriolis parameter in latitude is the exclusive inhomogeneity.
Because mean meridional circulations can form in this configuration [Kirtman and Schneider, 2000; Barsugli
et al., 2005; Horinouchi, 2012; Shi and Bretherton, 2014, Figure S1], we avoid using the terminology “rotating
RCE” for this configuration (differing from the convention of Shi and Bretherton [2014]). This configuration supports convectively coupled waves including the Madden-Julian Oscillation [Arnold and Randall, 2015], though
we focus exclusively on tropical cyclones here.
We follow the methodology for assessing TC statistics described in Zhou et al. [2014]. Instantaneous local minima in sea level pressure (SLP) exceeding 5 hPa relative to the time-mean and zonal-mean SLP for spherical
geometry simulations are identified over a region of about 350 km × 350 km (a search region of 7 × 7 on a uniformly spaced 360 × 576 latitude-longitude grid to which the GCM’s cubed sphere geometry is interpolated).
Using a more stringent 10 hPa criterion has a minimal (∼10%) effect for all but the coldest simulations. The SLP
minima in this configuration coincide with high near-surface relative vorticity, and nearly all have warm core
thermal anomalies in the upper troposphere. We evaluate the maximum surface (10 m height) wind speed
within a 350 km × 350 km search region centered on the location of the SLP minimum. In addition, we present
results from the tracking algorithm described in Zhao et al. [2009] applied within 35∘ of the equator, where
there are minimal vortex-vortex interactions and mergers, so TC genesis events are well defined.
The simulations are integrated for 3 years, and TC statistics are computed using 6-hourly instantaneous output
from the last 2 years of the simulations. The TC statistics in the final 2 years of the simulations do not differ
substantially. This time sampling is much shorter than that used for Earth-like GCM configurations, due to the
homogeneity of the climate in longitude and in time and the much greater number of TCs.
2.2. Rotating Radiative Convective Equilibria (f -Plane)
We show results from the rotating RCE simulations presented in Zhou et al. [2014] as a point of comparison.
We use the series of simulations with Coriolis parameter f (𝜙 = 20∘ ) and varied SST and the series of simulations with SST of 301 K and varied Coriolis parameter f (𝜙) with 𝜙 = 5∘ , 10∘ , 15∘ , and 20∘ . These simulations
have 25 km horizontal resolution and a domain of 20,000 km by 20,000 km (≈80% of Earth’s surface area). TC
statistics are taken from 3-hourly output from the last 6 months of 2.5 year simulations. Large-domain rotating RCE has also been examined by Held and Zhao [2008], Khairoutdinov and Emanuel [2013], and Reed and
Chavas [2015], who use a GCM with spherical geometry but constant Coriolis parameter like an f -plane. All
develop a turbulent equilibrium in which TCs are densely, though irregularly, packed into the domain.
TCs in the rotating RCE simulations are defined with SLP lower than 990 hPa, which corresponds to a 5 hPa
anomaly relative to the domain-mean SLP for the coldest simulation. The domain-mean SLP increases with
temperature (5 hPa over the range of simulations) because the mass of atmospheric water vapor is accounted
for in the dynamical core, while the magnitude of SLP anomalies of the weakest TCs [Zhou et al., 2014, Figure 2]
(Figure 1) has a stronger temperature dependence. Therefore, the 990 hPa threshold does not influence the
results and the comparison between spherical geometry and f -plane simulations is consistent across the
range of simulated temperatures.
While the f -plane simulations have higher horizontal resolution (25 km) compared to the spherical geometry
simulations (50 km), we have checked that the f -plane simulation results are similar with 50 km horizontal
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Figure 1. Polar projection of instantaneous surface wind speed for uniform thermal forcing spherical geometry
simulations with (left) SST = 297 K and (right) SST = 305 K. The region shown extends to the equator, and black dashed
lines indicate 30∘ and 60∘ of latitude.
resolution for SST between 297 K and 305 K. There are ∼15% more TCs, and the maximum surface wind speed
is ∼15% lower with 50 km horizontal resolution (Figure S2). Other aspects of the intensity distribution and the
temperature dependence of the TC statistics are insensitive to this change in resolution (Figure S2).
3. Simulation Results
The spherical geometry simulations feature long-duration TCs that develop primarily in subtropical latitudes
and migrate poleward, consistent with nonlinear vortex self-advection or 𝛽 drift (the track of a typical TC is
similar to that of Shi and Bretherton [2014, Figure 3]). Figure 2 shows an example of the instantaneous surface
Figure 2. (a) Global number of tropical cyclones versus SST for spherical geometry (gray circles) and f -plane RCE
(black diamonds) with dotted lines showing SST sensitivities. f -plane RCE have been multiplied by the ratio of the
domain size to Earth’s surface area to account for difference in domain size. (b) Time-mean and zonal-mean number of
tropical cyclones per unit area for spherical geometry simulations with SST indicated in legend. (c) Time-mean and
zonal-mean number of tropical cyclones genesis events per unit area for spherical geometry simulations with legend as
in Figure 3b. (d) Number of tropical cyclones per unit area in f -plane RCE with varying latitude 𝜙 of Coriolis parameter
f (𝜙) (diamonds), linear fit of RCE density in latitude (dashed line), and the time-mean and zonal-mean number of
tropical cyclones per unit area in the spherical geometry simulation with the corresponding SST of 301 K.
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Figure 3. Intensity measures versus SST for (a, b) spherical geometry simulations and (c, d) f -plane RCE simulations. The
median (gray circles), first and third quartiles (gray dashed lines), and time mean of strongest in each instantaneous field
(red circles) of the TC surface pressure lows (Figures 1a and 1c) and TC maximum surface wind speed (Figures 1b and
1d) are shown. The global-mean potential intensity (black lines) and tropical cyclone density-weighted potential
intensity (blue lines) are shown.
wind speed of the resulting turbulent equilibrium, where the peak number of TCs occurs in extratropical latitudes (poleward of 30∘ ) and there is a relative minima in TCs in low latitudes. We continue to use the term
“tropical cyclone” to describe these warm core vortices, despite their geographic distribution being weighted
toward extratropical latitudes. While 50 km resolution is not adequate to resolve aspects of TC structure that
affect the tail of the intensity distribution, TC eyewalls are apparent in these simulations (Figure 2).
The range of latitudes dominated by TCs depends on the SST: as the SST is increased, the region of persistent TC activity shifts poleward (Figure 2). This is one factor that contributes to an SST sensitivity of the global
number of TCs. In addition to the geographic changes with SST, there is an indication from the instantaneous surface wind speed that the TCs intensify as SST is increased. We quantify the simulated changes in the
frequency and intensity in detail in what follows.
3.1. Number
The global number of TCs ⟨N⟩ is shown in Figure 3a. Specifically, this is the time average of the global number
of TCs in the instantaneous simulation fields. The number of TCs decreases with increasing SST in the spherical geometry simulations. These simulations have a rate of decrease of ∼7.5% K −1 (dotted line in Figure 3a).
We estimate this sensitivity using a least squares estimate between the logarithm of ⟨N⟩ and SST. The logarithmic dependence better captures the wide range of ⟨N⟩, which varies by more than a factor of 5 over the
range of SSTs simulated, though a similar sensitivity is obtained from a linear regression of ⟨N⟩ on SST for the
simulations with SST ≥295 K.
Figure 3b shows the time-mean and zonal-mean number of TCs per unit area. The reduction in the global
number of TCs as SST is increased arises both from a decrease in TC frequency in the extratropical region of
peak TC density, which changes by a factor of ≳3 over the range of SSTs, and from a contraction toward the
poles of the range of latitudes with substantial TC activity, as is clear in Figure 2.
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Figure 3c shows the time-mean and zonal-mean number of TC genesis events per year per (1000 km)2 area,
obtained from the tracking algorithm described in Zhao et al. [2009]. The parameters in the tracking algorithm
are fixed, independent of SST, to values developed for Earth’s tropical cyclones. There is some sensitivity to the
tracking parameters, though the results discussed here do not critically depend on them. The rate of genesis
is largest in subtropical latitudes, where there is weak subsiding vertical velocity in the time mean of most
simulations (Figure S1 in the supporting information).
There is a reduction in the rate of low-latitude TC genesis as SST is increased, which contributes to the decreasing global number with warming. The region of genesis shifts poleward as the SST is increased. Beyond the
factor of ∼4 variation in genesis frequency, the rate of meridional TC propagation in low latitudes increases
with warming by ∼2 over the range of simulated SSTs. This is consistent with the expectation that TC size
increases with SST [Held and Zhao, 2008; Khairoutdinov and Emanuel, 2013; Zhou et al., 2014; Chavas and
Emanuel, 2014] and 𝛽 drift’s sensitivity to storm size: nonlinear self-advection has a greater propagation speed
for larger TCs because they experience a wider range of planetary vorticity from the poleward to the equatorward side of the TC. The TC intensity also increases with SST (discussed next), which will increase 𝛽 drift’s
meridional propagation speed. Taken together, the decreasing rate of genesis, poleward shift in genesis, and
increased meridional propagation rate with SST are sufficient to account for the factor of ∼10 variation in
number of TCs within the tropics.
The series of rotating RCE (f -plane simulations) with varying Coriolis parameter have TC density that increases
approximately linearly in the latitude of the Coriolis parameter (Figure 3d, diamonds). The TC density of the
rotating RCE is greater than that of the spherical geometry simulation at the corresponding latitude (Figure 3d,
solid line). This lower density in the spherical model is consistent with TCs drifting poleward into environments
where their size is larger than the local equilibrium size, which decreases with increasing Coriolis parameter
[Held and Zhao, 2008; Khairoutdinov and Emanuel, 2013; Chavas and Emanuel, 2014; Zhou et al., 2014].
The rotating RCE, f -plane simulations also have a decreasing number of TCs as the SST is increased [Zhou et al.,
2014]. The rate of decrease is ∼12% K−1 in the rotating RCE simulations (dotted line in Figure 3a), which is an
∼50% higher sensitivity to SST than found in spherical geometry. The Coriolis parameter in the rotating RCE
simulations is that of 20∘ , which contributes to a larger TC size and lower global number than the spherical
geometry simulations where the peak TC density is substantially poleward of 20∘ (Figures 3b and 3d). If only
the densely packed extratropical regions are considered in the spherical geometry simulations, the rate of
decrease is somewhat lower than 7% K−1 because part of the temperature dependence of the number of
TCs arises from changes in the geographic distribution of TCs (Figure 3b). Therefore, the difference between
the temperature sensitivity of the TC number in the spherical and f -plane geometry does not depend on the
spatial averaging conventions.
3.2. Intensity
The TC intensity increases with SST in the spherical geometry simulations, as measured by SLP anomalies and
surface wind speed (Figures 1a and 1b). The median intensity, considering all TCs, increases by ∼1 hPa K−1
or ∼0.35 m s−1 K−1 (gray circles in Figures 1a and 1b). The time mean of the strongest instantaneous TC has
approximately twice the rate of SST dependence as the median TC (red circles in Figures 1a and 1b). This
measure of intensity behaves similarly to the 99th percentile of all TCs, which is an intensity measure that is
independent of frequency changes.
The potential intensity (PI) is calculated from the simulations’ time-mean fields using the algorithm described
in Bister and Emanuel [2002] (obtained from ftp://texmex.mit.edu/pub/emanuel/TCMAX/ using the pseudoadiabatic ascent option, including dissipative heating, surface wind speed reduction factor of 0.9, and the ratio
of the surface exchange coefficients for enthalpy and momentum Ck to CD of 0.6, as in Zhou et al. [2014]). The
potential intensity is inhomogeneous in the simulations with spherical geometry, in spite of the spatially uniform boundary conditions. There is ∼10 m s−1 or ∼10 hPa greater PI within ∼20∘ of the equator. PI’s spatial
structure arises both from subtle meridional variations in the atmospheric stratification and humidity, which
alter the TC outflow temperature in the PI calculation [Bister and Emanuel, 2002], and from meridional variations in the surface enthalpy disequilibrium, which decreases toward the pole from an increase in the surface
relative humidity. In Figures 1a and 1b, we present both the global-mean and TC density-weighted PI.
The sensitivity of the mean of the strongest surface wind speed to SST is consistent with PI theory when
it is evaluated with the TC density weighting (blue line in Figure 1b), but this agreement appears to be,
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in part, fortuitous. The simulations’ SLP minima are lower than the density-weighted PI for all but the coldest
simulation; the SLP minima also decrease more rapidly than the density-weighted PI (blue line in Figure 1a).
The global-mean PI has a more sensitive SST dependence (black line in Figure 1a) that better matches the simulated changes in the TCs’ SLP minima, but this includes a contribution from the low-latitude region where
TCs are not simulated or are much less frequent (Figures 2 and 3).
The TCs in rotating RCE simulations also intensify when the SST is increased. The median intensity increases by
∼2 hPa K−1 or ∼0.7 m s−1 K−1 , and the time mean of the strongest is more sensitive to SST changes (gray and
red circles in Figures 1c and 1d). The f plane simulations intensify more than spherical geometry simulations,
and this result does not change in rotating RCE simulations with 50 km horizontal resolution.
As found in the spherical geometry simulations, PI captures the variation in maximum surface wind speed but
underestimates the minimum simulated SLP in the rotating RCE simulations (see Zhou et al. [2014] for further
discussion). In both cases, we find that the PI calculations are sensitive to the assumption that the surface
relative humidity in the TC eyewall, which is nearly saturated in the simulations, is equal to the surface relative
humidity of the environment.
4. Discussion and Conclusions
We have conducted a series of simulations with spherical geometry (thereby including poleward TC propagation from 𝛽 drift) with all boundary conditions spatially uniform (e.g., SST and insolation) over a wide range
of SST values. Examining this configuration is motivated by our desire to bridge the gap in model simulations
between Earth-like configurations, where anthropogenic climate change and idealized globally uniform SST
perturbations have been examined, and large-domain rotating RCE, where SST sensitivity has been examined.
The results are qualitatively consistent with aspects of these other simulation types: there is a decrease in number of TCs and an intensification with warming. (While future climate change scenarios often have reduced
global TC frequency as reviewed by Knutson et al. [2010], we note that Merlis et al. [2013] and Emanuel [2013]
simulate more TCs globally in warmed climates.)
The spherical geometry simulations with uniform thermal forcing are a step toward the Earth-like regime from
rotating RCE: the inclusion of the 𝛽 drift allows important dynamics on the TC scale while preserving the simplicity of a nearly homogeneous thermodynamic environment. In the aquaplanet framework of Merlis et al.
[2013] with Earth-like insolation and an off-equatorial Intertropical Convergence Zone (ITCZ), the movement
of the ITCZ dominates the TC response. There is no sharp ITCZ in these simulations, and in any case, the tropical
precipitation maximum is on the equator for all but the coldest of the simulations. This difference in sensitivities within aquaplanet configurations as well as additional factors in comprehensive simulations of Earth,
where seasonality plays an important role and additional loss mechanisms from TC dissipation over land and
mean vertical wind shear are included, suggests that there is value in carefully examining each intermediate
step in the model hierarchy.
The spherical geometry simulations presented here have inhomogeneous TC statistics, and the SST sensitivity of TC number occurs from both changes in the region containing tropical cyclones and changes in the
peak density of TCs (Figure 3). The TC genesis occurs primarily in subtropical latitudes, and the density of TCs
generally increases toward the pole. This is consistent with rotating RCE simulations that have an increasing
TC density as the Coriolis parameter is increased. However, the spherical geometry simulations have a lower
density at a given latitude than rotating RCE with that latitude’s Coriolis parameter (Figure 3d). This potentially
results from lower latitude TCs with larger equilibrium size [Held and Zhao, 2008; Khairoutdinov and Emanuel,
2013; Chavas and Emanuel, 2014; Zhou et al., 2014] propagating poleward to environments where their size
is larger than the local equilibrium size. The flow regime of the spherical geometry simulations in higher latitudes is one with vortex mergers and vortex-vortex interactions (the “Fujiwhara effect” of mutually interacting
TCs is ubiquitous) that also potentially results in wider TC spacing than rotating RCE.
In homogeneous rotating RCE simulations, TCs effectively fill the domain and there is very little turnover, with
genesis and merger/decay both rare. So comparisons of statistically steady rotating RCE do not provide a
convenient framework for studying the differences in genesis as parameters are varied in a particular model or
across models. In this spherical framework with homogeneous thermal forcing, the presence of 𝛽 drift allows
for more spacing between TCs and a steady genesis rate. Studies of this genesis rate in different models could
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be valuable in understanding overall differences in genesis across comprehensive global models. In addition,
an examination of the factors governing the preference for low-latitude TC genesis found in the spherical
geometry simulations with uniform thermal forcing presented here and in Shi and Bretherton [2014], as well
as the poleward shift in genesis with warming, is warranted.
Acknowledgments
We acknowledge two anonymous
reviewers for their constructive
comments and are grateful for the
support of DOE grant DE-SC0006841,
Compute Canada, and Natural Science
and Engineering Research Council
grant RGPIN-2014-05416. T.M. thanks
Ian Eisenman for his encouragement
and Morgan O’Neill for her helpful
discussions. The model source code
and simulation results are available
upon request.
MERLIS ET AL.
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