Response to Reviewer #2’s Comments
We would like to thank Reviewer 2 for his/her many detailed and constructive comments.
In addressing the concerns of all 3 reviewers, we have made a number of improvements
to our manuscript. These include the addition of a new subsection, with an additional
figure, comparing CTL and NFUS vertical motion profiles in the eye region, as well as an
additional discussion in Section 7 comparing our findings to several recent TC rapid
intensification studies. We also added emphasis on the fact that the results that we show
come from a specific case study and that further work on fusion heating impacts in the
context of weaker storms and less favorable environments is needed. Our point-by-point
responses are given below in black.
(1) The work is focusing on the impact of the fusion heating and conclusions are obtained
for a very special case of extremely small and uniquely strong storm Hurricane Wilma.
How do the authors anticipate this can be applied for other similar RI cases? i.e., is it true
that fusion heating is important for all cases?
This is a valid point, and we acknowledge that Wilma’s record-breaking intensification
rate and near-ideal environmental conditions make this somewhat of a special case
among TCs. At the end of Section 7, we have added a statement addressing this point,
and highlighting the need for future studies of ice process latent heat release (LHR) for
weaker storms and for those in less favorable environments. Nevertheless, we believe that
our analysis provides a valuable contribution to the current understanding of inner-core
processes in TC rapid intensification by examining the impacts of ice process LHR in this
case study of an intense storm that develops an upper-level warm core.
Recent work (Braun 2002; Eastin et al. 2005; Guimond et al. 2010) has argued that even
though the eyewall may be characterized by slantwise neutral ascent in an axisymmetric
sense per the Emanuel (1986) WISHE hypothesis, buoyant updrafts may provide a
significant contribution to eyewall upward mass flux. Since the warming upper-level
environments in TCs should inhibit positive buoyancy, we believe that ice processes,
which have been shown to reinvigorate updrafts in ordinary tropical convection (Romps
and Kuang 2010; Fierro et al. 2012), may be in important contributor to buoyancy in TC
eyewalls across a variety of cases.
Other recent studies have speculated on (but have not directly tested) fusion heating
impacts on the intensification of sheared TCs. Molinari and Vollaro (2010) hypothesized
that fusion heating may have aided the development of intense updrafts within a
convective burst (CB) in the rapidly intensifying Tropical Storm Gabrielle, which
featured frequent lightning as well as exceptionally strong upper-level reflectivity and 85GHz scattering. This storm, unlike Wilma, was embedded in a high-shear environment
associated with an approaching upper-level trough. A brief but intense period of RI
coincided with the lifetime of this inner-core CB, with 22 hPa of pressure falls in less
than 3 hours and intense subsidence warming adjacent to the cell, accompanied by a rapid
spinup of the low level wind and vorticity fields. These authors argued that since the CB
developed in the downshear side of the storm where inflow and CAPE were maximized,
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the ambient shear aided in Gabrielle’s RI. However, unlike for storms embedded in
weaker shear, the RI could not be sustained for more than a few hours. Similarly, Rogers
et al. (2015) speculated that convective instability (toward which fusion heating
undoubtedly contributes positively) could be a characteristic of intensifying storms by
allowing the downshear side updraft cores to remain more upright and thus reside in
regions of higher inertial stability.
2) I understand that there are two experiments conducted in this study. By reducing the
impact of fusion heating, I see NFUS is more like a modified Thompson scheme. It has
been well-known that different microphysics schemes would give different intensity
forecasts and we don’t know what is the best scheme (or which scheme accurately
represents the inner core processes related to hydrometeors and their dynamical and
thermodynamical responses to deep convection.) As such, I would interpret this study as
a sensitivity study, and the conclusion obtained appears to be too strong to be inferred
from a single case simulation.
Agree. We have added a statement in Section 7 underscoring the need for further testing
of fusion heating using other microphysics schemes. We added extra emphasis that our
results come from a single case study using the Thompson microphysics.
3) I can see the reason why the authors used the Thompson scheme in their experiments,
but this scheme on the other hand has many issues. It could provide you with the
expected fusion heating but could deteriorate the result due to its other negative impacts.
This needs to be discussed so that readers can distinguish what results are the physical
processes, and what could be artifact of the model.
Good point. In Section 7 we have added mention of the possible problems with the
Thompson scheme, and cited McFarquhar et al. (2012), who found that the scheme
overpredicted upper-level reflectivity relative to observations in their WRF simulation of
Hurricane Dennis. We also mentioned that the Thompson scheme produced a fictitious
secondary eyewall merger in CTL that briefly halted the RI process (Chen and Zhang
2011).
4) Since this work mainly focuses on the role of latent heat of fusion within the latent
heat of deposition, some straightforward question are: How important is the total amount
latent heat release in maintaining Hurricane Wilma’s intensity and in its rapid
intensification? What is the relative role of other latent heat release (e.g. latent heat of
condensation, latent heat of deposition, latent heat of fusion) in Wilma’s rapid
intensification? This will lead to several additional sensitivity experiments by turning off
these specific latent heat release term in the microphysics scheme. I strongly recommend
the authors to conduct more comprehensive analysis by conducting additional
experiments to make the results more convincing and applicable to understanding the role
of convective bursts on RI of TCs in a broader sense.
We do not believe that additional sensitivity runs examining other sources of latent
heating (condensation, for example) are needed for this particular study. Our objectives
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here are quite specific: to study the impacts of the latent heat of deposition (by removing
the fusion component Lf) on Wilma’s structure and intensification rate through
convective burst (CB) activity, in addition to analyzing the thermodynamic
characteristics of CBs. We would expect that the removal of condensational heating Lv in
condensation processes would have a more drastic impact on Wilma’s structure since it
would affect warm rain processes in updrafts at lower altitudes, and thus have a more
direct impact on the evolution of the background secondary circulation. This would be an
interesting experiment, but given these expected impacts, we feel that it should be left for
a future study. Our focus here is on the upper levels. Testing the removal of the entire
heat of deposition (Lf + Lv) would be another interesting experiment, and for this case we
would expect the effects to be more drastic than for NFUS due to the much larger amount
of latent heating involved. As we mention in our concluding remarks, future work is also
needed in understanding the relative importance of surface heat fluxes and upper-level ice
process LHR to the generation of deep convection in the eyewall.
5) It is equally possible that the sensitivity of results could be completely different when
a different microphysics scheme is used – authors may comment on what makes
Thompson scheme special for such study.
We agree with you that TC simulation results can be dependent on the microphysics
scheme used. After testing several microphysics schemes with WRF, we found that the
Thompson scheme performed best in reproducing observations, including the timing of
the first eyewall replacement cycle (Chen and Zhang 2011), and the simulation of the
upper-level warm core (Chen and Zhang 2013). One possible reason why the Thompson
scheme performs well with Wilma, a storm with extensive CB activity, is that it uses a
mixing ratio-dependent intercept parameter in its graupel size distribution, such that for
regions like deep convective updrafts where the mixing ratios are high, the distribution
shifts toward larger sizes, increasing the mass-weighted graupel mean fall speed
(Thompson et al. 2008). This might possibly give it a better handle on hydrometeor
loading effects in deep convective updrafts. It uses gamma distributions for other
hydrometeor species as well, allowing it to perform more like a bin scheme without the
heavy computational cost. Most bulk microphysics schemes, to our understanding, use
simpler exponential hydrometeor size distributions where such an adjustment cannot be
made. We added a brief discussion of this aspect of the Thompson scheme to Section 2.
In short, we agree that the CTL simulation results could differ when a different
microphysics scheme is used. But we do not think the sensitivity due to the treatment of
fusion would differ much.
6) Recent studies have shown that the extreme RI cases in the Western Pacific have
completely different vertical structures of temperature anomalies, with distinct formation
of double warm cores separated from each other. I don’t see such mechanism noted in
these experiments. Could the subsidence of warmer stratospheric air be responsible for
the enhancement of the upper level warm core in the CTL?
This is a good observation. We have noted this interesting feature, too; and our Fig. 2
does show a lower-level warm core. But the upper-level warm core becomes more
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dominant because of the RI during the earlier period of the model integration. We
attribute the upper-level warm core enhancement in Wilma to the subsidence of
stratospheric air. We believe that the high altitude of CB updrafts makes them key to the
upper-level warm core formation because their compensating subsidence originates
above the tropopause. That is why we show, in the manuscript Figure 2, descending
isentropic surfaces coincident with the development of the upper-level temperature
anomaly.
Interestingly, Ohno and Satoh (2015) also simulated an upper-level warm core in an
idealized TC, but for their case the upper-level warm core developed only after a
midlevel warm core had already formed. They hypothesized that it was the expansion of
the vortex circulation into the higher static stability region above the tropopause, causing
an increased local Rossby depth, that extended the diabatically-forced secondary
circulation to the upper levels and caused the upper-level warm core to develop. A
reference to this study was added to the manuscript.
6) Could you elaborate on the storm size differences (both symmetric and asymmetric)
between CTL and NFUS and potential causes for such differences?
It appears that the NFUS eyewall does not contract quite as fast as that of CTL, especially
during the early portion of RI (compare (a,e) to (b,f) in Fig. 3, reproduced here as Fig. A
below). This appears to support the theoretical findings of Shapiro and Willoughby
(1982), who showed that diabatic heating sources placed near the radius of maximum
wind (RMW) caused peak positive tangential wind tendencies inside of the RMW where
the radial gradient of absolute angular momentum peaked. Therefore, eyewall contraction
could be driven by LHR.
The other main storm size difference that we found was a dramatic widening of the CTL
eyewall in the 27:00-29:00 timeframe, as a result of the merging of a secondary eyewall
(Chen and Zhang 2011, Figs. 11 and 12). This briefly halted the CTL RI, but the effects
on the intensification process were minimal because unlike for true “eyewall replacement
cycles,” the inner-core convection maintained itself and absorbed the secondary eyewall.
NFUS, on the other hand, did not develop a secondary eyewall during RI. As a result, at
time of peak intensity (32:30 CTL/39:00 NFUS) CTL has a significantly wider eyewall.
When calculating our CCFAD probabilities in the eyewall (Section 5/subsection a), we
calculated them over the same area for CTL and NFUS. The larger area of w > 0 for CTL
within the 15-km wide annulus used to calculate probabilities at time of peak intensity
(manuscript Fig. 8c) may be partially responsible for the dramatic increase in the
moderate-strength (50-70th percentile) updrafts in CTL from the previous time (Fig. 8a),
versus the lack of such an increase for NFUS. We address this briefly in the manuscript.
Figure 8 from the manuscript is reproduced below as Figure B.
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Figure A. Radar reflectivity (shaded, dBz) and storm-relative flow vectors (m s-1) at z = 1 km level with CB
elements (orange crosses) and azimuthally-dependent z = 1-km RMW (blue dots) and z = 11-km RMW
(black dots). Left panel shows CTL for (a) 15:00, (b) 20:00, (c) 32:30, and (d) 39:00. Right panel shows
NFUS for (e) 19:00, (f) 24:00, (g) 39:00, and (h) 45:00. For (a),(b),(e), and (f), an 80 × 80 km subdomain
is used (scale ticks mark 10-km intervals) while for (c),(d),(g), and (h), a 160 km × 160 km subdomain is
used (scale ticks mark 20-km intervals). Upper right label boxes display total number of CB elements in the
subdomain.
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Figure B. Left panels: CCFAD of vertical motion for the eyewall, showing the percentage of gridpoints in
the horizontal plane with vertical motion magnitudes greater than the abscissa-marked scale. Updrafts are
shaded in orange for CTL and contoured in black for NFUS. Downdrafts are shaded in blue for CTL and
contoured in green for NFUS, following the same percentage intervals but with only the outer three lines
labeled. Right panels: eyewall area-averaged upward (w > 0 m s-1, red) and downward (w < 0 m s-1, blue)
vertical motion profiles with areal fraction of updraft core elements (w ≥ 1 m s -1, black) and downdraft core
elements (w ≤ -1 m s-1, gray); CTL/solid, NFUS/dotted. Top row shows 20:00 CTL/24:00 NFUS, and
bottom row shows 32:30 CTL/39:00 NFUS.
*Note that for Fig. B, faint negative signs might appear near the downdraft labels in the
color bar for some magnification settings of this document. This is an artifact of the fact
that the downdraft percentiles were recorded as negative numbers in the data file, and
when plotting the data using GrADS, the negative signs were manually blanked out.
These lines do no appear in the corresponding .eps file which we are uploading as a NonRendered figure.
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