Homework Review

All right, so this is the review of the
first homework. So the first question
dealt with why is a negatively tilted
trough more favorable for severe
weather than positively tilted trough,
and so we have this scenario posted up here.
So imagine we have a positively tilted
trough ejecting out over the Plains.
So the part that's going to eject out first
will be the upper portion of this trough
right here, and when that portion ejects,
you can expect a surface flow to develop.
And notice that the surface flow is
pretty far to the north, and in terms of
the Great Plains, that's going to be
really far away from the moisture source,
so it's going to be much more difficult to pull
moisture up from the Gulf to the northern latitudes.
Additionally, your coldest air is going to be back behind
towards the west over the Rockies still,
so you're really getting a displacement
of the best environments. You're seeing
the warm, moist sector further to the
south and to the east and the coldest air
aloft off to the west. Additionally, if you notice,
your boundaries such as the cold front
may be more parallel to your upper-level winds,
which isn't very favorable for storm propagation.
So basically what it comes down to is that this set up
with a positively tilted trough ejecting
out over the Plains leads to less favorable lapse rates
and less favorable shear. Meanwhile, let's take a
look at the negatively tilted trough.
As this ejects out over the Plains, you're going
to have the maximum in positive
cyclonic vorticity advection occurring
right there at the base of that trough.
So you can expect a stronger low to develop.
Additionally, this low will be closer
towards the Gulf, so closer towards your
moisture source, so you're going to have
much more strong moisture return.
Additionally, you're going to have your
coldest air aloft still back out to the west,
but you will have this area where
you're going to have an overlap between
your warm, moist sector and your cold
temperatures aloft. These will lead to
better lapse rates. Additionally, you can
notice that your upper-level wind flow
may be more orthogonal to your surface
boundaries, which is more favorable for
propagation of the storms off those boundaries.
So the key takeaway, you're going to
have better lapse rates in this setup.
You're also going to have better wind shear overall.
Moving on to question two. This question
dealt with if you have two given air
masses, one which is very stable and one
which is more neutral, which one is going
to lead to stronger cyclogenesis.
We can go back to our QG mega equation.
So in the QG omega equation, we have the
static stability times omega is equal to the two
forcing terms. Now let's assume that we have two
forcing terms that are giving you
ascent for cyclogenesis. In this case, the
magnitude of omega is going to be,
the magnitude of omega is going to be
dependent on the static stability parameter.
So in case A where we had the
very high static stability air,
that's going to lead to a lower magnitude of omega.
Meanwhile in the more neutral
buoyant air, we're going to have a lower
value of static stability, so we can have a
higher magnitude of omega. So because of this,
the higher omega is associated with
the more neutral air, so that's going to
be better for cyclogenesis. We can also
think of this in just a mass continuity standpoint.
Over here on air mass A, we have
our high static stability air mass
with cold air at the surface and warm air aloft.
If you tried to displace one of these
parcels from the surface, it's going to
go up, but eventually it's going to become
negatively buoyant and come back down at
the surface. So it's going to be very
hard to lift the parcel and keep it lifted.
Meanwhile in air mass B,
because it's neutrally buoyant, you can
lift that parcel and it'll keep going
until it reaches a more stable boundary.
So therefore, you're not going
to have this issue of lifting a parcel
and have it sinking back down. You can
continuously lift that parcel.
Therefore, it's easier to get convergence at the
surface and easier cyclogenesis.
So question three had to deal with the idea
of vertical velocities on the synoptic scale
versus the mesoscale. So in our
calculations, we found that the synoptic scale
lifting was around centimeters per second.
Meanwhile, the mesoscale lifting
was an order of meters per second to tens of
meters per second. Whenever you convert
these timescales, we see the synoptic
time scale is more on the order of days,
while the mesoscale lifting
is on the order of tens of minutes
to hours. The question was then asked which
of these processes, synoptic scale lifting
or mesoscale lifting, is more likely
responsible for convection. So to answer
this question, we have to go back to what
we observe with thunderstorms. Typically,
we see a thunderstorm begin and initiate and
then grow into a mature storm on the
timescale of one to two maybe three hours,
so it's on the order of hours rather than days.
So if we observe this happening and
we've known by our calculations that
mesoscale lifting is on roughly
the same order magnitude, then we
can be reasonably sure that mesoscale
lifting is responsible for convection.
So question four dealt with rising
motion in a tropical wave. So tropical
waves are going to be much different
than your typical mid-latitude waves,
and the whole reason comes back to in the
upper-levels, you're not going to have
nearly as strong of winds because the
thermal gradient overall is much weaker,
so your thermal wind response won't
be as strong, you won't have the strong
baroclinic waves like we see in the
mid-latitudes. Instead, what's actually
driving these lows in the tropics is
more of a mid to lower-level disturbance.
So therefore, whenever you go back to
your QG omega equation, you have to
think in terms of differential vorticity advection.
So here we have, on the x, a low
that's propagating off towards the west,
so Africa would be up here on the right,
the Americas would be off on the left.
So as the thing is moving off
towards the west, we're going to positive
vorticity advection on the west side at
the surface and negative vorticity
advection on the right side on the east
side at the surface. The trick here is
you have to think of the differential
with height. So as you go up with height,
you're actually decreasing your
vorticity advection. So that leads to an
overall sinking motion, whereas
on the east side, you're actually having
less negative vorticity advection as you go
up with height. That's actually leading to
positive, overall positive vorticity
advection and you're going to get rising motion.

Homework Review

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