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\
\vskip 0.5truein
\centerline{\bf HYPERCANES:  A POSSIBLE LINK IN }
\centerline{\bf  GLOBAL EXTINCTION SCENARIOS}
\vskip 0.2truein
\centerline{by}
\vskip 0.2truein
\centerline{Kerry A. Emanuel\footnote{$^1$}
{Center for Meteorology and Physical Oceanography, Massachusetts Institute
 of Technology, Cambridge, MA USA}, Kevin Speer\footnote{$^2$}{Institut
 Fran\c cais pour la Recherche et l'Exploitation de la Mer (IFREMER),
 Brest, France}, Richard Rotunno\footnote{$^3$}{National Center for
 Atmospheric Research, Boulder, CO}, }
\centerline{Ramesh Srivastava\footnote{$^4$}{Department of Geophysical
Sciences, The University of Chicago, Chicago, IL}
and Mario Molina$^1$}

\centerline{ Second draft,\ \ July, 1994}



\vfill\eject

\centerline{ABSTRACT}

Bolide impacts and large--scale volcanic eruptions have been proposed as
possible causes of the massive extinction of life that has occurred
episodically in earth's history. In spite of the catastrophic disruption of
the local environment that accompanies bolide impacts and volcanic
eruptions, it has been difficult to explain why these events sometimes lead
to {\it global} extinction of species.  We propose that in some cases, the
missing link may be provided by hypercanes, runaway hurricanes that are
capable of injecting massive amounts of water and aerosols into the middle
and upper stratosphere, where they may have profound effects on atmospheric
chemistry and radiative transfer. Hypercanes are theorized to occur when
the sea surface temperature exceeds a critical threshold, which may occur
when sea water is locally heated by bolide impact, shallow-sea volcanism
or, possibly, by overturning of superheated brine pools formed by
underwater volcanic activity. Simulations using a convection--resolving
nonhydrostatic, axisymmetric numerical model show that hypercanes can
indeed develop when the sea surface temperature is high, and that they
inject large amounts of mass into the stratosphere.

\parindent=15pt
\vfill\eject

\beginsection  1.\  Introduction

Evolution of life has been punctuated by events during which large numbers
of species have become extinct. Largest among the known events was the Late
Permian extinction, about 245 million years ago, during which about 96\% of
all species disappeared.  The most recent major extinction occurred at the
end of the Cretaceous, between 64 and 66 million years ago, and was marked
by the disappearance of about 3/4 of all species that existed at that
time. Two hypotheses have emerged to explain the end-Cretaceous
extinction. Alverez et al. (1980) proposed that the impact of a large
asteroid led to the massive extinction, while Officer and Drake (1983) and
others argue that the extinction was related to massive volcanic eruptions
that resulted in the formation of the Deccan Traps. It has also been
suggested that these two geophysical events are related (Alt et al.,
1988).

\footline={\hss\folio\hss}\pageno=3

Considerable evidence has accumulated in recent years in support of the
idea that the earth was struck by one or more bolides at the end of the
Cretaceous. Foremost among such evidence is the finding by Alvarez et
al. (1980) that iridium and other platinum-group metals known to be more
concentrated in extraterrestrial bodies than on earth, are enriched in a
thin clay layer at the Cretaceous/Tertiary boundary worldwide. Other
evidence includes the finding that this clay layer contains
extraterrestrial amino acids (Zahnle and Grinspoon, 1990), soot attributed
to global wildfires (Wolbach et al., 1985), and an Osmium isotopic ratio
with a distinctly extraterrestrial signal (Luck and Turekian, 1983). Many
K/T boundary sequences also contain abundant shocked mineral grains that
suggest an impact, although it has also been proposed that this may result
from explosive volcanism. Recent attention has focused on the Chixslub
feature on the northern Yucatan coast as a possible impact crater, though
several other craters can also be dated to the K/T transition, suggesting
that multiple impacts may have occurred in a short time.  There is also
evidence in K/T sediments for a large tsunami event in the Caribbean
region.

Although the evidence for the impact of at least one large bolide at the
end of the Cretaceous is mounting, there remains considerable controversy
about just how such an event might lead to massive extinction of life.  The
original Alvarez et al. paper suggested that the hypothesized asteroid
impact would have thrown up a large quantity of dust into the stratosphere,
where it would have reduced substantially the incoming solar radiation,
leading to a dramatic decrease of photosynthesis and concomitant disruption
of the food chain.

Other means by which the impact might have led to mass extinctions 
include:

\item{1.} Dramatic, direct warming of the atmosphere and/or ocean by 
the impact (Hs\"u, 1980)

\item{2.} Global cooling owing to soot produced by global wildfires 
(Wolbach et al., 1985)

\item{3.} Chemical contamination of the atmosphere and/or upper ocean 
(Hs\"u, 1980)

\item{4.} Global warming by large increases in atmospheric $CO_2$ 
owing to impact on carbonate terrain (O'Keefe and Ahrens, 1989)

\item{5.} Global acid rain owing to large increases in atmospheric sulfur 
and nitrates (Prinn and Fegley, 1987)

As an alternative to the bolide impact hypothesis, large--scale volcanism
has also been cited as a possible cause of mass extinctions. Of particular
interest are flood basalt fissure eruptions, which are capable of producing
individual lava flows with volumes greater than $100\ km^3$ at very high
eruption rates. It is speculated that such large eruptions would inject
massive amounts of debris into the stratosphere where it might lead to
reduced sunlight and depletion of ozone, and that immense quantities of
acid rain would reduce the alkalinity and {\it p}H of the upper ocean.

The mass extinctions were evidently selective.  The weight of evidence
suggests that the most dramatic extinctions occurred amongst the planktonic
foraminifers (D'Hondt and Keller, 1991) and calcareous nannoplankton
(Thierstein, 1981), and a major mollusk group disappeared entirely (Ward,
1988).  But diatoms, dinoflagellates and other dwellers of the upper ocean
suffered only modest reductions. The planktonic flora and fauna appeared to
undergo a rather sudden decline. There were also large reductions in land
animals, particularly among the larger species (e.g.  dinosaurs), but
considerable controversy surrounds the question of the timing of such
reductions, and many smaller animals survived the K/T transition.

Many, although not all, of the proposed mechanisms by which bolide impacts
and/or large--scale volcanism lead to mass extinctions rely on massive
injections of material into the stratosphere, where it may remain for many
years. By contrast, injections of large quantities of aerosols into the
troposphere should have only transient and local effects, since excess
material is washed out of the troposphere on a time scale of weeks. The
original Alverez et al. thesis contends that large amounts of material from
the colliding bolide and from the crust would find its way to the
stratosphere, perhaps by being mechanically injected through the ``hole"
punched in the atmosphere by the incoming bolide. To our knowledge, this
conjecture has never been subject to rigorous tests.

Another conjecture holds that significant amounts of mass entered the
stratosphere through hot plumes generated directly through the heat of
impact or the combustion of surface material. The volcanic hypothesis also
relies heavily on thermal plumes to loft material into the stratosphere,
where it can have long term effects.  But the altitude to which thermal
plumes from areally limited surface sources ascend in the stratosphere
increases only as the 1/4 power of the surface heat flux (Morton et al,
1956). It is thus highly unlikely that global wildfires could affect the
stratosphere in a significant way, even if there were many of them, since
the surface heat flux {\it per unit area} is vastly insufficient to achieve
stratospheric altitudes. Moreover, even the very largest of historical
eruptions (e.g. Krakatoa in 1883) managed to achieve only limited
penetration into the stratosphere, such that the material settles out in a
matter of a few years (e.g. see Budyko et al., 1988).  Moreover, the
settling time of aerosols in the stratosphere may have an upper bound owing
to the fact that the very smallest particles have diameters comparable to
or smaller than the mean free path at those altitudes (Reitmeijer, 1993).
It is not obvious that either large--scale volcanism or bolide impacts
could loft enough material into the stratosphere for long enough periods to
have global effects of a magnitude necessary to explain mass extinctions.

Our present purpose is to suggest that in at least some cases of oceanic
massive volcanism or bolide impact, hypothetical atmospheric storms known
as {\it hypercanes} may have played an essential role in injecting material
into the stratosphere. Hypercanes are extraordinarily intense hurricanes
whose energy production is so large that it cannot be balanced by surface
dissipation, resulting in storms that are so intense that internal
dissipation becomes important. These storms are hypothesized to occur when
the degree of air--sea thermodynamic equilibrium exceeds a theoretically
defined threshold value. Their circulations would penetrate to large
altitudes in the stratosphere where they could deposit large quantities of
mass, including water vapor, condensed water and volcanic ash.

After reviewing the theory of hypercanes, we present the first numerical
simulations of these storms using a fully nonhydrostatic model, lending
credence to the idea that hypercanes are physically possible. We then
discuss plausible scenarios under which hypercanes might have occurred as a
result of bolide impact or undersea volcanism. We conclude by speculating
about the effects of hypercanes on the stratosphere and how these effects
may have helped cause mass extinctions.

\beginsection 2. \  Hypercanes

{\it a. Theory}

The energy cycle of a mature hurricane can be characterized as that of a
Carnot heat engine (Emanuel, 1986), as illustrated in Figure 1.

In its normal state, the tropical atmosphere is quite far from being in
thermodynamic equilibrium with the underlying ocean. This disequilibrium is
necessary to support the large rates of heat loss by evaporation needed to
balance the incoming solar radiation. (Little heat is lost directly by
infrared radiation, owing to the opacity of the moist atmosphere above,
leaving evaporation as the principal means of disposing of heat.) The
disequilibrium is reflected in the subsaturation of air just above the sea
surface; typical relative humidities are about 80\%.

As the ambient air spirals into the storm center in a thin boundary layer,
the wind speed increases and so too does the rate of evaporation. In the
strongest hurricanes, the air near the core comes close to a state of
thermodynamic equilibrium with the ocean, reflecting a large heat gain on
its inward journey. This heat gain is observed to occur at nearly constant
temperature. Having reached the core, the air spirals upward in a ring of
convection known as the ``eyewall", which surrounds a circular region of
nearly cloud--free air known as the ``eye". This upward motion represents a
nearly adiabatic expansion of the working fluid, which is a mixture of
moist air and suspended condensed water droplets. These droplets ultimately
combine into particles large enough to fall out of the system as
precipitation. The air then flows out at high altitude to large distances
from the storm center, after which it loses the heat it gained from the
ocean by radiating it to space, or, in an open cycle system, by exporting
it to other atmospheric circulation systems. Finally, the air descends back
to the surface, losing more heat by electromagnetic radiation. But since
the vertical profile of air temperature in the environment of the storm is
nearly that of adiabatic ascent of moist air with suspended water droplets,
this additional heat loss is almost exactly that which would have occurred
if the condensed water had been retained and was now reevaporating.

If the working fluid is considered to consist of a mixture of dry air,
water vapor and condensed water, the energy cycle may be closely
approximated by isothermal expansion of air spiraling inward along the
ocean surface, followed by adiabatic expansion of air ascending in the
eyewall, followed by isothermal compression of air losing heat at the storm
top, and finally by adiabatic compression to the starting point. The
thermodynamic efficiency of the engine is proportional to the temperature
drop from the sea surface to the lower stratosphere, where the outflow
occurs. For typical conditions, this temperature drop is of order $100\ K$,
while the inflow temperature is roughly $300\ K$, giving an efficiency of
about $1/3$.

The total increase in enthalpy of the inflowing air is limited by the
degree of air--sea thermodynamic disequilibrium of the ambient air: When
this air reaches thermodynamic equilibrium, no further heat input is
possible. (Such an equilibrium is characterized by equal sea and air
temperatures and air relative humidity of 100\%.) This provides an upper
bound on the energy input to the system.

In the mature hurricane, the energy input balances dissipation. Most of
this dissipation occurs in the thin, turbulent boundary layer above the sea
surface, and is proportional to the total pressure drop from the ambient
environment to the storm center. A smaller amount of energy is lost at
large radii in the outflow, where the low angular momentum of the outflow
(which has been previously lost to the sea in the inflow) must be restored
to environmental values by turbulence. A yet much smaller, but poorly known
amount of energy is lost in turbulence in the interior of the system.

Neglecting this last sink, the energy balance may be written as an equation
for the central surface pressure of the storm, which is a direct measure of
its intensity. Given the aforementioned bound on the heat input, there is a
corresponding bound on the surface pressure drop from the ambient
environment to the center.  Emanuel (1988) developed an implicit equation
for this drop, in the form

$$
ln(x)=-{A\over x}+B, \eqno(1)
$$

\noindent where $x$ is the ratio of the central value of the partial pressure
of dry air to its ambient value, and $A$ and $B$ are coefficients that
depend on the ambient degree of air--sea thermodynamic disequilibrium, the
thermodynamic efficiency, and the storm radius, which determines how much
energy is dissipated in the outflow.

Solutions to (1) are graphed in Figure 2 as a function of the sea surface
temperature and the outflow temperature, assuming a fixed environmental
surface relative humidity of 75\%. (The surface relative humidity is
observed to vary little with local climate conditions over the ocean; then
the sea surface temperature determines the degree of air--sea thermodynamic
disequilibrium.) The asterisk indicates conditions typical of the warmest
regions of the tropics. Computations of this same bound for
climatologically normal conditions (e.g. see Emanuel, 1986) show that a
small fraction of real hurricanes come very close to their energy bound. On
the other hand, accurate numerical simulations of hurricanes (e.g. see
Rotunno and Emanuel, 1987) seem to always produce storms at the theoretical
limit of intensity. Non-axisymmetric interactions of real storms with their
environments, and local reduction of sea surface temperature owing to
turbulent mixing of surface waters with deeper, colder water, limit most,
but not all, storms to intensities well below the theoretical limit.

Figure 2 also shows that there are no solutions to (1) for certain values
of the coefficients $A$ and $B$. Close analysis of the system shows that in
the supercritical regime where no solutions to (1) are possible, the Carnot
cycle is unstable owing to the the component of heat input by isothermal
expansion. The lower the central surface pressure, the more heat is added
to the inflow by isothermal expansion; this added heat intensifies the
vortex, leading to further reduction of the central surface pressure, more
heat input by isothermal expansion, and so on. This effect is so strong in
the supercritical regime that the additional surface dissipation cannot
balance it, and the vortex intensifies until internal dissipation becomes
sufficient to balance the energy input.  The resulting system is what we
have called a hypercane.

To date, the only numerical simulation of a hypercane was that of Emanuel
(1989), who used a very simple model consisting of only three layers of
atmosphere and which made several restricting assumptions about the force
balances in the flow. This nevertheless showed that in the hypercane regime
of parameter space, the vortex continues to intensify until numerical
stability criteria are exceeded and the integration had to be stopped. Here
we present results of integrations in the hypercane regime using a much
more sophisticated model.

{\it b. Numerical simulations}

We performed several integrations of the numerical hurricane model
developed by Rotunno and Emanuel (1987).  It is designed to simulate the
axisymmetric circulation of hurricanes, including the circulation within
convective clouds, though the latter are forced to be axisymmetric
rings. This model integrates the fully nonhydrostatic, compressible
equations on an axisymmetric domain $1000\ km$ in radius and $45\ km$ in
altitude, with radial and vertical resolutions of $5
\ km$ and
$1.25\ km$, respectively. The model also integrates conservation equations
for heat and water, but condensed water is represented by only one
category, the total liquid water mixing ratio. The terminal velocity of the
falling liquid water is taken to be $7\  m\ s^{-1}$ if the water content
exceeds $1\ g\ kg^{-1}$ and zero otherwise; this is the crudest way of
handling rain while retaining only one category of condensate. One drawback
to this approach is that evaporation of falling rain must proceed at a pace
sufficient to keep the air saturated; this exaggerates the rate of
evaporation. A sponge layer occupying the top $5\ km$ of the domain serves
to partially absorb internal wave activity, which in nature would radiate
into the high atmosphere without much back reflection.
 
All turbulence in the model is represented by an eddy viscosity that
depends on the local rate of deformation and the local Richardson number,
the latter of which is defined with a dry or moist static stability,
depending on whether the air is unsaturated or saturated. Surface fluxes of
heat, moisture and momentum are represented using the classical bulk
aerodynamic formulae, but with wind--dependent exchange coefficients (all
of which are equal).  Radiative cooling is crudely mimicked by a Newtonian
relaxation back to the initial condition, with maximum values limited 
to $2\ K\ day^{-1}$.

A few approximations to the equations that are considered minor for
simulations of ordinary hurricanes may prove to be problematic in the
hypercane regime. In the construction of the model equations, the pressure
and potential temperature are separated into parts representing the
background state and deviations from it; the former being functions of
altitude alone. The full pressure gradient acceleration, given by

$$
-c_p\theta_v\nabla\pi
$$

\noindent is replaced in the model by

$$
-c_p\overline{\theta_v}\nabla\pi,
$$ 

\noindent where $c_p$ is the heat capacity at constant pressure,
$\theta_v$ is the virtual potential temperature, and $\pi$ is the
nondimensional pressure perturbation. The overbar indicates the background
state value. This approximation neglects the quadratic terms in the
pressure and buoyancy perturbations. In normal hurricanes, these
perturbations are of order 10\% of the mean values, so the neglect of the
quadratic terms is justified. In hypercanes, however, the perturbations are
of the same order as the mean values, and so this approximation breaks
down.

Although sound waves are meteorologically unimportant, they are explicitly
calculated in the model. The terms in the equations that govern the
propagation of sound are integrated on a smaller time step than the other
terms. This may be considered a special way of calculating mass continuity
that avoids the solution of an elliptic equation at the expense of
integrating some of the terms on a smaller time step. In the present case,
the {\it effective} mass continuity equation is the standard anelastic
equation, in which the background density, rather than full density, is
employed. This can be shown to be a good approximation as long as the Mach
number of the flow is small. In the case of hypercanes, however, the Mach
number is of order unity and the anelastic approximation breaks down.

The two approximations discussed above are probably not serious problems
before and just after the transition of the model storm to the hypercane
regime, in which the central surface pressure is lower than the critical
transition value, but they become problematic as the hypercane approaches
full intensity. Thus, while we feel that the model in its present form
shows that the transition to the hypercane is indeed a physical
possibility, the characteristics of the mature storm should be viewed as
preliminary.

With one exception, the initial condition is identical to that used by
Rotunno and Emanuel (1987), consisting of a tropical atmosphere and sea
surface temperature that has been adjusted so that the atmosphere is
effectively neutral to moist convection. This mimics the real state of the
atmosphere in which moist convection is in statistical equilibrium with
large--scale processes, such as radiative cooling of the atmosphere and
surface heat fluxes, that act to destabilize the flow to convection. Such a
state is nearly, but not exactly neutral to convection. It is an example of
self--organized criticality. The stratosphere in the initial state is
isothermal.

Onto this state we superimpose a bell-shaped axisymmetric sea surface
temperature anomaly with a decay scale of $100\ km$. The maximum sea
surface temperature at the center is $50\ C$, decaying to the ambient value
of $27\ C$ at large radii. This anomaly is intended to represent the result
of local ocean warming by bolide impact or undersea volcanism; since its
scale is assumed to be much smaller than an atmospheric deformation radius,
the ambient atmosphere as a whole will not adjust appreciably to the
anomaly.

As in Rotunno and Emanuel (1987), an initial vortex with maximum wind
speeds of $12\ m\ s^{-1}$ is used to initiate the finite amplitude
instability that results in tropical cyclones. (Later we shall see that the
large temperature gradients generated by the sea surface temperature
anomaly are sufficient to initiate a storm from very small amplitude
initial conditions.)

Figure 3 shows the evolution of the central surface pressure and maximum
azimuthal wind with time. After a short time, the initial vortex undergoes
rapid intensification, with central pressures lower than $300\ mb$ at
around $25 - 40\ hrs$. Afterward, the vortex weakens somewhat and
approaches a slowly decaying state with very strong winds. Experiments in
which the cap on radiative cooling rate was removed show that the resulting
storms reach a nearly steady state. The slow decay in the control
experiment at long time is a result of the inability of the system to lose
heat at a sufficient rate.

The spatial distributions of various quantities in the mature hypercane at
$50\ hrs$ into the simulation are shown in Figure 4. These fields have been
averaged over a $5\ hr$ period. Surface radial inflow in the boundary layer
reaches peak values in excess of $50\ m\ s^{-1}$, while outflow near the
tropopause has a maximum value of $60\ m\ s^{-1}$. Although most of the
outflow occurs near the tropopause, some convection in the eyewall reaches
altitudes greater than $30\ km$, and weak outflow can be detected there. The
large penetration depths are achieved because of the very high specific
entropy contents reached by air spiraling into the core. Figure 4d shows
that the equivalent potential temperature (a quantity whose natural
logarithm is proportional to the total specific entropy) of air rising in
the eyewall has values in excess of $700\ K$. Such large values result from
the nearly isothermal expansion of air flowing into regions of very low
pressure in the eye.

The azimuthal wind component is shown in Figure 4b. The maximum value of
$220\ m\ s^{-1}$ occurs at the surface at a radius of $6\ km$, and the
cyclonic circulation extends up to about $35\ km$ altitude.

At 50 hrs., the vertical velocity (Fig. 4c) reaches peak values in excess
of $35\ m\ s^{- 1}$, though at other times values greater than $70\ m\
s^{-1}$ occurred.  These are comparable to vertical velocities achieved in
the most severe middle latitude thunderstorms, and are about an order of
magnitude greater than are typical in normal hurricanes. Descent occurs at
the inner most grid point (the ``eye"), and weak descent characterizes most
of the outer region of the simulated storm.

The water vapor mixing ratio (Fig. 4e) shows extreme values of over $50\
g\ kg^{-1}$ in the core, reflecting the low partial pressure of dry air
there. Condensed water mixing ratios well over $10\ g\ kg^{-1}$ extend well
up into the stratosphere (Fig. 4f).

Several experiments were performed to test the sensitivity of the hypercane
evolution to the size and magnitude of the sea surface temperature anomaly;
these are summarized in Figure 5. As the geometric size of the sea surface
temperature anomaly decreases, the maximum wind speed decreases, but is
still very substantial when the decay scale is only $25\ km$. The mature
circulation is somewhat steadier when the scale of the sea surface
temperature anomaly is small. When the peak value of the ocean temperature
is reduced, the maximum wind speed falls, but is still substantial when the
peak sea surface temperature is $42\ C$.

Although the approximations in the model physics render suspect some
features of the mature hypercane circulation, these approximations should
not be of great importance near the transition from hurricane to hypercane,
suggesting that hypercanes are physically possible. The experiments suggest
that sea surface temperatures of greater than about $45\ C$ occurring on
scales greater than about $50\ km$ may be capable of supporting
hypercanes.  It remains to be seen whether sea surface temperature
anomalies of this size and magnitude are capable of {\it spontaneous}
ignition of hypercanes, or whether an independent disturbance of ``trigger"
is necessary, as is certainly the case with ordinary hurricanes. To help
answer this question, we ran an experiment identical to the control but
beginning with a warm core vortex with maximum winds of only $2
ms^{-1}$. This initial vortex amplified to the same intensity as the
control simulation with only a minor delay, showing that the atmospheric
temperature gradients associated with the sea surface temperature anomaly
are sufficient for spontaneous generation of storms.

We have assumed that the ambient atmosphere is calm and that it has the
thermodynamic characteristics of the present tropical atmosphere. But
significant vertical wind shear is known to inhibit or prevent the
development of hurricanes, and there is no reason to suspect that this is
not the case with hypercanes, whose early evolution is similar to that of
hurricanes. At the very least, the presence of mean wind, even if it is
does not vary with altitude, will move the storm across the ocean
surface. In order for hypercanes to develop, the mean wind would have to be
small enough relative to the size of the sea surface temperature anomaly to
permit the storm to develop in the time it takes to cross the
anomaly. Given a development time of $40\ hrs$, mean winds would have to be
less than about $1\ m\ s^{-1}$ to allow hypercane development over a $100\
km$--scale sea surface temperature anomaly. Such conditions are unusual,
but not unknown in the deep tropics.  But it is unlikely that hypercanes
would develop over localized sea surface temperature anomalies of the kind
likely to have been produced by bolide impact or volcanism if the mean
winds are much stronger than this. Given weak but nonvanishing tropospheric
winds, we conjecture that a sequence of hypercanes would develop, with each
member developing rapidly over the sea surface warm anomaly, moving away,
ands decaying while another forms.
 
\beginsection 3. \ Environmental effects of hypercanes

The most significant characteristic of hypercanes, from the standpoint of
environmental impact, is their ability to inject large amounts of mass into
the middle stratosphere, where it may remain for many years. If we assume,
on the basis of the numerical simulations, that a ring of air between $5\
km$ and $35\ km$ radius is ascending at a rate of $5\ m\ s^{-1}$ at an
altitude of $20\ km$ (see Figure 4c), then the net mass flux into the
middle stratosphere is about $10^{10}\ kg\ s^{-1}$. This is enough to
replace the entire mass of the atmosphere between the $100\ mb$ and $50\
mb$ pressure surfaces in about 6 months. Two aspects of this mass transport
are of particular interest: the flux of water substance, which has the
potential of radically altering radiative transfer through the stratosphere
and of affecting atmospheric chemistry; and the flux of aerosols, which
also may alter radiative transfer.

{\it a. Stratospheric water}

The critical issue here is how much water ascends in the main hypercane
updraft without precipitating out of the system. The minimum absolute
temperature in the updraft occurs near the altitude of the outflow; this is
about $-70\ C$. At the tropopause, where outflow in normal hurricanes is
concentrated, this temperature corresponds to a saturation water vapor
mixing ratio of about 30 ppm, but at $26\ km$ altitude, the saturation
mixing ratio is closer to 100 ppm, owing to the lower total pressure. Thus,
assuming that the updraft is saturated, somewhat more water vapor is
present in the hypercane updraft. One peculiarity of the hypercane
environment is that the saturation mixing ratio actually increases with
altitude in the nearly isothermal stratosphere; thus any hypercane effluent
that begins to sink isothermally through the lower stratosphere under the
influence of radiative cooling will experience a {\it decrease} of
saturation mixing ratio with time. Thus, further condensation of water may
occur in the descending air.

Of potentially far greater importance is the flux of condensed phase water
at high altitudes in the hypercane updraft. At the low temperatures of the
outflow region, all of the condensed water would be in the ice phase; a
critical issue is how much of the ice would be in the form of very small
crystals that might remain in the stratosphere long enough to affect the
global heat balance.

In an air parcel undergoing rapid vertical lifting (say, greater than $30
m\ s^{-1}$), the condensate does not have time to grow to precipitation
sizes; therefore, almost all the water vapor present at the cloud base will
be deposited in the stratosphere in the form of small ice particles.
Also, in a strong updraft, the air may remain supersaturated
with respect to water preventing water drops from evaporating and
depositing on to ice particles, a process characteristic of the
Bergeron-Findeisen mechanism of precipitation initiation.  In an
air parcel undergoing a slower rate of lifting, some of the condensate may
have time to grow big enough to fall out of the parcel; therefore, only a
fraction of the water vapor present at the cloud base may be deposited at
high levels in the form of small ice particles.

What happens to small ice crystals depositied in the middle stratosphere?
Let us begin by estimating the average size of the ice particles deposited
in the stratosphere. Cloud microphysical calculations show that when an
unmixed air parcel is lifted beyond the saturation level, the air becomes
supersaturated; the supersaturation reaches a maximum at a short height
above and thereafter it decreases slowly with continued lifting of the
parcel (see, for example, Rogers and Yau, 1989). In an unmixed air parcel,
in which condensation is the only process operating, the concentration of
cloud drops (expressed as number of particles per unit mass of air) is
determined at the point of the maximum supersaturation and thereafter it
remains constant with height; furthermore, with continued condensation, the
size distribution of the cloud drops tends to be monodisperse. In this
approximation, the particle radius ($r$), the mixing ratio ($M$), and the
particle concentration ($n$) are related by:

$$ M={4\pi\rho_i\over 3} nr^3,
\eqno(2)
$$

\noindent where $\rho_i$ is the density of the ice particles. For a rapidly
lifted parcel, the ice mixing ratio may be taken equal to the saturation
water vapor mixing ratio at the cloud base level (considering that there is
no fall out and that the saturation mixing ratio is small in the
stratosphere); for a slowly lifted parcel, the ``average'' radius may be
calculated from (2) provided that $M$ is taken to be the actual mixing
ratio of the condensate in the stratosphere, and that we have an estimate
of the particle concentration.

Twomey (1959) derived the following approximate equation for
the concentration ($N$) of cloud drops:

$$
N=\alpha^{{2\over (\beta+2)}} f_1
f_2(\beta)w^{{3\beta\over 2(\beta +2)}},
\eqno(3)
$$

\noindent where $w$ is the vertical velocity of the air.  Twomey assumed a
power-law
spectrum of the critical supersaturation of condensation nuclei, that is,
he assumed that the concentration of nuclei activated at supersaturation
$\sigma$ is $\alpha\sigma^\beta$, where $\alpha$ and $\beta$ are constants
that depend on the characteristics of the cloud condensation nucleii.  In
(3),\ $f_1$ depends upon the cloud base temperature and pressure while
$f_2$ is a function of $\beta$.  The power-law is in fair agreement with
observations; $\alpha$ and $\beta$ are found to range from about 20 to 3000
cm$^{-3}$ and 0.4 to 1.2 respectively when $\sigma$ is expressed in percent
(Braham, 1976).  Maritime aerosols have smaller values of $\alpha$ while
continental and polluted aerosols have higher values.  There is also a
tendency for $\beta$ to be larger for maritime aerosols. For our purposes,
the predominant effect is the dependence of $N$ on $\alpha$ and the
vertical air velocity $w$.  Figure 6 shows the cloud particle concentration
as a function of the vertical air velocity for three nuclei spectra. We see
that the cloud particle concentration varies from about $10^6\hbox{
g}^{-1}$ to $10^7\hbox{ g}^{-1}$.  Once the particles are deposited in the
stratosphere they can settle slowly and if the ambient air is unsaturated
with respect to the particle they can evaporate while settling.

We now consider the settling time of the particles. First let us consider
the settling time in the absence of vertical air motion and particle
evaporation.  Except for the very largest particles considered above, the
particle terminal fall speed $v$ is given by the Stokes formula:

$$
v={2\rho_ig\over 9\eta}r^2,
\eqno(4)
$$

\noindent where $g$ is the gravitational acceleration and $\eta$ the dynamic
viscosity of air.  Calculations show that particles of radii $3\mu m$, $10\
\mu m$, $30\ \mu m$, and $60\ \mu m$ will take about 2216 h (92 days),
199.4 h (8.3 days), 22.16 h (0.92 days) and 5.55 (0.23 days) to settle
through 10 kilometers. Thus these particles can reside in the stratosphere
for time periods ranging from a day to months if sedimentation is the only
process operating to remove the particles.

However, as updraft air comes to rest in the stratosphere and mixes with
the ambient air, or as the particles settle out of the parcel into the
ambient air, they will tend to evaporate if the ambient air is
unsaturated. The rate of change of particle mass is ($m$) given by:

$$
{dm\over dt} = {4\pi rD\rho_s\over 1+\gamma}S,\ \  \gamma \equiv {LD\over
k} \rho'_s,
\eqno(5)
$$

\noindent where $D$ is the diffusivity of water vapor in air, $\rho_s$ is the
saturation vapor density in the ambient air (with respect to ice), $L$ is
the latent heat of sublimation, $k$ is the thermal conductivity of air,
$\rho'_s$ is the derivative of $\rho_s$ with respect to the temperature,
and $S$ is the supersaturation with respect to the particle.  (Equation 5
involves certain approximations; it is accurate only for small magnitudes
of $S$.  However, for our purposes, it should be adequate even for
considerable subsaturations.)  For an approximate calculation, we assume
constant $S$ and constant $D$, $\rho_s$, and $\gamma$; for the isothermal
stratosphere, the latter is a good approximation except for $D$, which is
inversely proportional to the pressure. With these approximations, equation
(5) gives:

$$ r^2=r^2_0 +{2D\rho_s\over (1+\gamma)\rho_i} St,
\eqno(6)
$$

\noindent where $r_0$ is the initial radius. For subsaturated conditions the
time ($\tau_e$) to completely evaporate a particle of radius $r_0$ is
given by:

$$
\tau_e = {(1+\gamma)\rho_i\over 2D\rho_s}
{r^2_0\over 1-{\cal H}_i}
\eqno(7)
$$

\noindent where ${\cal H}_i$ is the ambient relative humidity with respect to
ice.  A
particle of initial radius less than $60\ \mu m$ will evaporate completely
in less than 5.6 hours in an ambient relative humidity of 99\%, assuming
$T=220$\ K and $p=25$ mb. Since the diffusion coefficient is inversely
proportional to the pressure the times to complete evaporation would be
doubled (quadrupled) if we had used the value of $D$ for $p=50$ mb ($100$
mb) keeping $T=220$\ K. The time to complete evaporation is also inversely
proportional to $\rho_s$; therefore, using a temperature lower than $220$\
K will tend to increase the evaporation time not only because of a decrease
in $\rho_s$ but also because, with pressure fixed, $D$ decreases with
decreasing temperature.

If we consider sedimentation and evaporation simultaneously, equations (4)
and (6) can be used to derive the following expression for the distance of
fall in which the particle evaporates completely (assuming no vertical air
motion):

$$
h_f = {\rho_ig\over 18\eta}
{(1+\gamma)\rho_i\over D\rho_s}
{r^4_0\over 1-{\cal H}_i}.
\eqno(8)
$$

Figure 7 shows the evaporation distance as a function of the initial radius
for three selected relative humidities.  (Again, we have used $T=220$\ K,
$p=25$ mb; the above remarks on the effects of changing pressure and
temperature on $\tau_e$ apply to $h_f$ as well.)  It should be noted that
the Stokes fall velocity law on which (8) is based breaks down for particle
radii exceeding about $50\ \mu m$.  We see that a particle of initial
radius $50\ \mu m$ can evaporate completely in a fall through $2$ km in a
relative humidity of 99\%.  Thus we see that most of the condensate lofted
high into the stratosphere is likely to evaporate in the stratosphere and
increase its vapor content, until and unless the stratosphere becomes
saturated.

Assuming that $1\ g\ kg^{-1}$ of water substance exists in the ring of
convection as it enters the middle stratosphere, and that the updraft
characteristics are those described above, then the flux of water into the
middle stratosphere is about $10^7\ kg\ s^{-1}$. This is sufficient to
completely saturate the layer between $100\ mb$ and $50\ mb$ in about 20
days. Were this to happen, the lower and middle stratosphere might become
cloudy, with profound consequences for global climate. Even if the
condensed water were removed from the stratosphere on fairly short time
scales, the saturated air would remain.

The injection of large amounts of water into the stratosphere may have
significant consequences for the chemistry of that region.  Water vapor is
the source of the free radicals OH and HO$_2$, which contribute to
stratospheric ozone depletion through the following catalytic cycle:

\medskip
\settabs 6\columns
\+&OH $+$ O$_3 \rightarrow$  HO$_2$ $+$ O$_2$&&&&\cr
\+&HO$_2$ $+$ O$_3 \rightarrow$ OH $+$ 2 O$_2$&&&&\cr
\+&\hbox to 2in{\hrulefill}&&&&\cr
\+&Net: 2 O$_3 \rightarrow 3$ O$_2$&&&&\cr
\medskip

\noindent This is the reaction couplet that contributes most to ozone
destruction in the lower stratosphere; it is followed in importance by
catalytic cycles involving nitrogen oxides and halogen free radicals.  The
OH radical plays also another important role: it activates chlorine (by
converting the relatively stable HCl species to Cl atoms) and deactivates
nitrogen (by converting nitrogen dioxide to nitric acid, a more stable
species), the net effect being enhanced ozone depletion by chlorine free
radicals.

An important separate effect of water on stratospheric chemistry could
result from the formation of clouds: chemical reactions on cloud droplets
activate chlorine and deactivate nitrogen oxides, in a manner analogous to
that described above for the OH radical.  Such a mechanism explains the
formation of the Antarctic ozone hole.  Furthermore, over Antarctica
precipitation of the cloud particles leads to the irreversible removal of
nitrogen oxides, because they scavenge nitric acid.  This removal sets the
stage for efficient ozone destruction by halogen free radicals, a process
that slows down in the presence of nitrogen oxides.

Stratospheric clouds are, however, rather scarce, and are normally present
only over the poles in the winter or spring months, which is where ozone
depletion has taken place in recent years.  These observations indicate
that the presence of stratospheric clouds at low latitudes could have
profound consequences for ozone depletion.  The main natural source for
chlorine in the stratosphere is methyl chloride, produced in the biosphere;
if additional amounts of chlorine were to be injected---e.g., from sea
salt---the effects on stratospheric ozone could be dramatic.

{\it b. Aerosol injection}

The large vertical velocities and mass flux rates sustained in hypercanes
are capable of injecting large amounts of aerosol into the middle
stratosphere. Bolide impact might generate large amounts of fine dust by
excavation, while undersea volcanism produces ash. The injection of
volcanic ash or terrestrial material excavated by bolide impact into the
middle stratosphere can be expected to influence climate for several years
to a decade, given the observed presence of volcanic material in the
stratosphere for several years following major historical eruptions. The
largest of historical eruptions have led to measurable global cooling
(Budyko et al., 1988).

\beginsection 4.  \ Bolide impact, undersea volcanism and hypercane formation

The numerical simulations described in Section 3 suggest that hypercanes
might occur over localized regions of water heated to peak temperatures in
excess of about $45\ C$ on scales greater than about $50\ km$. Such regions
could only initiate hypercanes if the ambient atmospheric conditions were
otherwise favorable for hurricane formation; i.e., the atmosphere would
have to have nearly moist adiabatic lapse rates through most of the
troposphere and could not contain much vertical wind shear. In addition,
the mean wind speed would have to be small, particularly in the case of
small--scale sea surface temperature anomalies, so that the developing
storm would not move rapidly away from the sea surface temperature
anomaly.

All of these conditions suggest that hypercanes would be extremely rare,
occurring only when the ocean surface is heated to an extraordinary degree
somewhere in the tropics, and then only under ideal conditions.  In the
open ocean, warm SST anomalies tend to generate winds which erase the
anomaly. According to monthly climatological data (COADS), which sets the
base value of the SST distribution, the highest climatological values are
not in the open ocean but in the Persian Gulf, where maxima attain 32
C. Mean values only a degree or so cooler are found in the Red Sea, the
next warmest region. However, even starting from these values, it is
implausible for solar heating to raise the upper few tens of meters of the
marginal sea by 10 C because of the high net daily heating required
(e.g. 1000 W/m2 for two weeks in a layer 30 m thick). Thus solar heating is
unlikely to be capable of initiating hypercanes, and other heat sources
must be considered.

  In the hypothetical impact scenario envisioned by Emiliani et al. (1981),
a 14 km diameter body of mass $2.5 \times 10^{15}$kg hits the earth with a
speed $2\times 10^4$m/s. Only a tiny fraction (0.1\%) of the initial
kinetic energy, $5\times 10^{23}$J, is lost as the bolide moves through
the atmosphere; the principal transfer to the atmosphere occurs via the
plume thrown up by the impact, estimated at 25\% of initial K.E.. The
remaining 75\% is available to excavate the impact crater in the ocean and
solid earth, and to heat the rock and seawater. It is thought that such an
impact would create a crater roughly 100km in diameter and 35 km deep at
its center, exposing underlying mantle. As the ocean rushes back over the
rim to fill in the crater over a period of hours, it is heated mainly by
contact with hot or molten rock. This direct heating depends crucially on
the degree of heat exchange between the hot debris, upwelling magma, and
seawater.

  Subtracting the energy going into the plume, the total energy available
from the collision is $4\times 10^{23}$J, including that liberated from the
warm crust and mantle (Emiliani et al., 1981). Using this energy to heat
seawater in a layer 4km thick (4$\times 10^{13}$m$^3$) the ocean
temperature in the crater 100 km in diameter could rise by 1000 C, that is,
create a column of boiling water, with sea-surface temperature near 100 C
(higher at depth owing to pressure).

 Emiliani et al. (1981) note that direct heating of the ocean by lava
outflow is attenuated because of the tendency for molten rock to be
insulated from seawater by a thin solid crust, effectively reducing the
heat transfer rate. However, they also describe the probable intimate
mixing of hot debris with seawater as the ocean rushes back into the
crater. Furthermore, although they discount a large-scale, ocean-wide
heating, because of the tendency for rotational constraints to confine the
hot column locally, it is precisely this confinement which encourages the
high SST needed for hypercane formation.

To investigate the nature of this rotational confinement with strong
heating, we consider a less dramatic event: a volcanic eruption within the
deep Red Sea hot brine pools. This provides us with a real, existing
natural laboratory for testing ideas about the mixing and confinement of
superheated seawater.

 The brine pools are reservoirs of hot, salty fluid which accumulate around
geothermal sources at the floor of the Red Sea. Their extreme saltiness
turns them into huge heat storage devices in which temperature can build
up, since the density remains high enough for them to rest on the
bottom. Typically, the observed temperature is above 60\degs C and salinity is
above 250psu (Ross, 1983), giving a density of about 1200kg/m$^3$.  The
overlying deep water, at 22\degs C and 40.5psu, has a density close to
1030 kg/m$^3$.  To make the dense brine buoyant, its temperature must be
raised above 300\degs C by volcanic activity. An estimate of brine volume
in the Atlantis Deep, Chain Basin, Discovery Basin, and nearby smaller
basins is 7 km$^3$ (Blanc et al., 1990; J.-L. Charlou, data personally
communicated).  The possibility for a substantial volume of water to become
superheated before becoming buoyant suggests that even after dilution with
the surrounding seawater in the rising plume the final temperature anomaly
may still be very high.

 To explore the dynamical possibility that this hot brine reaches the
surface in some diluted form, we adapted a 3-d nonhydrostatic numerical
model. This model has been described and applied to convection in the
Mediterranean Sea by Jones and Marshall (1993), and to hydrothermal plumes
(Speer and Marshall, 1995). A nonhydrostatic model is necessary in our case
to resolve explicitly the processes which produce dilution and mixing with
strong vertical motion, and avoid making assumptions about
entrainment. Earth's rotation constrains the lateral expansion of the plume
in the sea and is expected to influence the long term evolution of the
volcanic plume.

 The domain is a periodic box 32km x 32 km x 2000 m, with heating
distributed over a disk 8km in diameter at the bottom, representing a
volcanic eruption in the basins. The grid is 132 x 132 x 20, for a grid
size of 250 m in the horizontal and 100 m in the vertical. Initially there
is a layer of hot brine one gridbox thick on the bottom with neutral
buoyancy, that is, it is assumed that heating has already raised the
temperature of the brine to the point of convective overturning.  The
horizontal mixing coefficients are all set to 5m$^2$/s, and the vertical
coefficients are 0.2m$^2$/s. These small values ensure that mixing occurs
mainly by advection.

 To estimate the forcing strength, an eruption documented on the Juan de
Fuca Ridge Cleft Segment is used as a reference (Fox et al., 1992). In this
case, 0.05 km$^3$ of magma erupted covering approximately 2.1 km$^2$ of
seafloor. A total heat transfer of about 1.5$\times 10^{11}$J m$^{-2}$
occurred as this lava flow cooled to ambient temperature. For a thickness
of order $d= 10$ m, the time scale for cooling is of order $d^2/4\kappa$,
giving 10$^7$ s for a conductivity $\kappa = 10^{-6}$m$^2$/s. Then the heat
flux into the ocean is of order 10$^4$ W m$^2$ on average. To represent a
strong eruption a heat flux value of $H=50$ kW m$^{-2}$ was chosen. The
equivalent buoyancy flux $B=g\alpha H/\rho c_p = 4.5 \times 10^{-5}$m$^2$
s$^{-3}$, and the total buoyancy input integrated over the source area is
$F=2700$ m$^4$ s$^{-3}$.

 The stratification of the Red Sea is relatively weak below 500 m depth,
where the buoyancy frequency $N_{deep} = 7\times 10^{-4}$s$^{-1}$, but
there is a strong thermocline in the upper 500 m, where $N_{therm} =
7\times 10^{-3}$s$^{-1}$. Using a Coriolis parameter appropriate for
mid-basin (latitude 20$^{\circ}$ N), $f=5\times 10^{-5}$s$^{-1}$, the large
ratio $N_{therm}/f= 140$ or $N_{deep}/f = 14$ shows that stratification and
not rotation controls the height of penetration. The penetration height is
therefore $Z_N = 3.8(F/N^3)^{1/4}$ above a virtual source several km below
the real seafloor.  For the above forcing and $N_{deep}$, $Z_N=6400$m,
sufficient to reach the base of the thermocline. At the base of the
thermocline a point source approximation is no longer appropriate for
scaling purposes.

 The results of a numerical simulation of an eruption into the brine pools
shows the generation of a hot brine plume at intermediate depths in the Red
Sea (Figure 8). Numerical constraints precluded the use of realistic brine
temperature and salinity, so salinity was used as a proxy tracer for
mixing; the final temperature of the equilibrium plume as determined by
salinities of 40-100psu is roughly in the range 25-50\degs C. Over the
rising and spreading period most of the heat in the plume comes from the
brine pools and not the source. This situation is similar to that of the
megaplumes which have been observed above the mid-ocean ridge in the
Pacific Ocean (Baker et al. 1989).  After one day of integration the
radial motion of water toward the source at depth and away from the source
at the spreading level has generated a vortex, anticyclonic at intermediate
depths and cyclonic in deep water, owing to rotation. The vortex holds
together a lens of warm brine above the source.  Despite this confinement
and recirculation of the plume, it still does not reach the surface after
several days of integration. Runs with similar stratification and source
geometry showed similar behavior.

 The buoyancy flux from the source, though large compared to inactive
ridge-crest fluxes, is simply too weak to to drive the plume across the
thermocline.  \footnote*{Note that the largest volcanic
plumes in the atmosphere easily penetrate the stratosphere (Sparks,
1986). The analogous thermocline, the tropopause, is only roughly double
the stratification in the troposphere, and does not appear to form much of
a barrier.}  A penetration scale based on buoyancy flux is
$(B/N_{therm}^3)^{1/2}$, which is only 12 m. A source 1000 times stronger
would appear to be strong enough to penetrate the thermocline; the total
source strength would then be 3.2$\times 10^{15}$W, placing it among the
largest eruptions observed on land (Settle, 1978; Wilson  et al.,
1978). In the present model configuration such large forcing is impossible
to simulate as it leads to numerical instabilities. We conclude that the
dynamical constraint of rotation is important to form a strong anomaly, and
that these anomalies can attain the surface in the case of very powerful,
but not unprecedented, volcanic sources.

  We note parenthetically that isopycnals at intermediate depths outcrop at
the northern end of the Red Sea, so if the subsurface hot plume is carried
north in the general circulation it is conceivable that it may eventually
reach the surface following isopycnals.  It is interesting that even modest
eruptions are capable of forming a hot brine plume at intermediate depths.

 On the other hand, a straightforward way for volcanism to heat the surface
layer of the ocean is for it to occur in shallow water, as in the first
stages of island formation.  To raise the temperature of an ocean surface
layer 50 m thick and 50 km on a side (125 km$^3$) from 25\degs C to 50\degs
C requires 1.3$\times 10^{19}$J. To supply this heat over an eruption time
scale of 10 hours (Wilson et al., 1978) implies a thermal source of
3.4$\times 10^{14}$W. At 100\% efficiency of heat transfer from magma to
seawater, the corresponding magma flow rate is about
6$\times10^4$m$^3$s$^{-1}$ (assuming $\rho c_p = 3\times 10^6$ J m$^3$
\degs C, an initial temperature of 1000\degs C, and an equal heating
contribution from latent heat of freezing). Lower efficiencies imply higher
flow rates, but even higher flow rates are not unknown in existing
volcanoes (Settle, 1978).

 The nature of the eruption will determine whether or not the heat transfer
efficiency is high. Explosive eruptions are more effective at mixing
pyroclast with surrounding fluid; slower eruptions have to cover a large
area with thin layers of lava in order to generate fluxes of the order
10$^4 W m^{-2}$, capable of adequately heating the overlying water column
tens of meters deep in a period of days. Thus high efficiency is not
necessary for a strong anomaly, but the quicker the anomaly is formed the
less chance that it is dissipated into the background before a storm
develops.  The above estimates show only the plausibility of a volcanically
produced SST anomaly adequate to generate a hypercane. The actual
probability of satisfying the various conditions is difficult to
determine.

 Finally, it should be emphasized that even the large air-sea heat fluxes
induced by hypercane generation are nevertheless far too small to erase the
sea-surface temperature anomaly in a short time. The maximum surface fluxes
produced by the
numerical simulation would cool a $100 m$ column of sea water at the rate
of no more than $1\ C$ per day. The average fluxes over the warm pool would
cool the same column by about $0.1\ C$ per day. Thus it would take several
weeks to reduce the sea water temperature to below the hypercane threshold,
even if there were no continuing heat fluxes into the ocean from the
volcanic or bolide impact-induced source. 

\beginsection 5. \ Summary

The two principal scenarios for rapid global extinctions, bolide impact and
extensive volcanism, both rely to some degree on stratospheric effects to
produce worldwide ecosystem stress. We regard with skepticism claims that
the mechanical effects of bolide impact would directly lead to large--scale
contamination of the stratosphere, or that the heating effects of such an
impact or the wildfires that result from it, could lead to significant
injection of mass into the stratosphere. Similarly, the weak dependence of
the maximum penetration altitude of turbulent convective plumes on the
surface heat flux casts doubt on whether even unusually large volcanic
events could disrupt climate much beyond what has been observed in
historical eruptions. We propose instead that some instances of undersea
volcanism or oceanic bolide impact could lead to the formation of
hypercanes capable of injecting large amounts of material into the middle
stratosphere. The contamination of the normally dry stratosphere with water
may have large transient effects on climate through the direct absorption
of infrared radiation by water vapor and through the radiative effects of
large--scale stratospheric cloudiness, and may lead to serious depletion of
ozone and thus to increased ultraviolet radiation at the surface. The
injection of large quantities of aerosol into the middle stratosphere may
also have strong effects on climate.

The necessary conditions for the formation of normal hurricanes lead us to
conclude that hypercane formation would be limited to the tropics, even in
the case of very large anomalies of sea surface temperature. If our
hypothesis has any merit, it suggests that global extinctions will be
somewhat more frequent in the case of oceanic bolide impact or undersea
volcanism in the tropics. This prediction may provide some means of
empirically testing the theory.

\vfill\eject

\def\ref{\leftskip 20pt\parindent -20pt\parskip 12pt plus 1pt}


\beginsection 5.\ References


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}

\beginsection 6.\ Figure captions

{\parskip=10pt \parindent=0pt

Figure 1: The Carnot cycle of a mature tropical cyclone. Air spirals inward
from the environment ({\it a}) to near the center ({c}), while acquiring
entropy from the sea surface. Air then ascends adiabatically and flows out
to large radius, where it eventually loses heat by radiation to space along
legs 3 and 4.

Figure 2: Minimum central pressure (mb) of tropical cyclones calculated
from eq. (1), with ambient surface relative humidity of 75\%. The asterisk
denotes conditions typical of the tropical Pacific. Normal sea level
pressure is 1013 mb, while the lowest pressure ever recorded in a tropical
cyclone is 870 mb.

Figure 3: Evolution of the maximum azimuthal velocity (solid) and minimum
pressure (dashed) in the main experiment.

Figure 4: Distributions of variables at 50 hours into the main experiment,
in a domain extending radially to 300 km and vertically to 30 km. {\bf
(a)}: radial velocity in $m\ s^{-1}$ with contour interval of 10 $m\
s^{-1}$; {\bf (b)}: azimuthal velocity in $m\ s^{-1}$ with contour interval
of 10 $m\ s^{-1}$; {\bf (c)}: vertical velocity with contour interval of 2
$m\ s^{-1}$; {\bf (d)} Equivalent potential temperature with contour
interval of 25 $K$; {\bf (e)}: water vapor mixing ratio in $g\ kg^{-1}$,
with contour interval of 3 $g\ kg^{-1}$; {\bf (f)} liquid water mixing
ratio in $g\ kg^{-1}$, with contour interval of 3 $g\ kg^{-1}$.

Figure 5: Evolution of the maximum azimuthal velocity in 5
experiments. {\bf A}: The main experiment with a maximum temperature of 50
C and decay scale of 100 km; {\bf B}: maximum temperature of 47 C and decay
scale of 100 km; {\bf C}: maximum temperature of 42 C and decay scale of
100 km; {\bf D}: maximum temperature of 47 C and decay scale of 50 km; and
{\bf E}: maximum temperature of 47 C and decay scale of 25 km.

Figure 6: Cloud particle concentration as a function of vertical air
velocity for three nucleus spectra.

Figure 7: Fall distance to complete evaporation as a function of initial
radius for three relative humidities.

Figure 8: Simulation of a Red Sea hot brine plume created by a volcanic
heat source on the bottom. The domain is 32 km on a side and 2 km deep.
Contours of salinity (solid) at an interval of 2.5 psu from 60-70 psu and
density (dashed) at an interval equivalent to 1 degree C.  The
corresponding maximum temperature anomaly is roughly 40 C. The brine rises
off the bottom as a plume up to the base of the thermocline, where it
spreads laterally. After a period of about one day the plume is circulating
anticyclonically (clockwise). After a few days the plume reaches the edge
of the domain.

}

\bye

