A Potpourri of Interesting Research Problems

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A Potpourri of Interesting Research Problems
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TC Effects on El Nino?
This plot shows a measure of El Niño/La Niña
(green) and a measure of the power put into the
far western Pacific Ocean by tropical cyclones
(blue). The blue curve has been shifted rightward
by two years on this graph. There is the
suggestion that powerful cyclones in the western
Pacific can trigger El Niño/La Niña cycles.
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Agukabams(aka Landphoons, Terracanes)From
aboriginal roots agu (land) and kabam (storm)

• Case studies
• Hypothesis
• Simple model

Emanuel, K., J. Callaghan, and P. Otto, 2008 A
hypothesis for the re-development of warm-core
cyclones over northern Australia. Mon. Wea. Rev.,
136, 3863-3872
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Case TC Abigail, Feb-March, 2001
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Best-track winds
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Hypothesis Non-baroclinic rejuvenation of
tropical cyclones over land can be caused by
rapid flux of heat out of hot, sandy soils that
have been moistened by the early rains of the
system
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20 cm Soil Temp at Halls Creek during Passage of
Abigail
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Idealized Experiments Constant translation
velocity and environmental temperature,initializa
tion with a warm core vortex with maximum winds
of 17 ms-1
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Sensitivity to Initial Soil Temperature(translati
on speed 13 km hr-1)
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Sensitivity to thermal diffusivity
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Sensitivity to translation speed
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Effect of depletion of water PBL environmental
RH declines from 80 to 0 over 8 days
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Abigail Hindcast
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Tropical Storm Erin, 2007
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But then, deep in the heart of Oklahoma....
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12 GMT August 18 2007
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18 GMT August 18 2007
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00 GMT August 19 2007
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06 GMT August 19 2007
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12 GMT August 19 2007
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Oklahoma Soils
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Soil temperature record at Hinton, OK
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Estimate of Soil Heat Flux
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Hurricanes in the Persian Gulf?
Annual Frequency0.04
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Back to Norway
A Return to the Concept of Air Masses
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Two Key Concepts from the Norwegian School

• Fronts
• Air masses

Bergeron, 1922 An air mass is a vast body of air
whose physical properties are more or less
uniform in the horizontal, while abrupt changes
are found along its boundaries, i.e. the frontal
zones.
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Bjerknes and Solberg, 1922
The cyclone consists of two essentially
different air-masses, the one of cold and the
other of warm origin. They are separated by a
fairly distinct boundary surface which runs
through the center of the cyclone. This boundary
surface is imagined to continue, more or less
distinctly, through the greater part of the
troposphere. Emphasis mine
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Early Emphasis on Air Mass Formation
Bergeron, 1922, visualized air masses as forming
within semi-permanent circulation systems, such
as wintertime continental highs and subtropical
anticyclones The air that takes part in the
circulation around any such system will become
subject to the prolonged influences of the
underlying surface, with the result that there
will be a tendency for distinct properties to be
acquired. Although the vertical structure of
any air mass may be modified by differential
advection and vertical stretching and shrinking,
the more direct modifications are brought about
by interactions between the atmosphere and the
earths surface. Bergeron, as paraphrased by
Petterssen, 1954
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Sanders, 1955The intense surface frontal zone
attains maximum strength near the ground and
weakens rapidly with altitude.
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The Dynamics Revolution
Carl-Gustav Rossby and Hans Ertel Conservation
and invertibility of potential vorticity
is the fluid velocity,
is the fluid density,
and S is any conserved state variable (usually
the entropy)
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Rossby Waves

• Wherever there are gradients of q on surfaces of
  constant s
• Wherever there are gradients of s on rigid
  boundaries

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Baroclinic Instability and Fronts

• Eadys 1949 model of baroclinic instability No
  interior gradients of potential vorticity
• Hoskins and Brethertons 1972 semi-geostrophic
  model of frontogenesis no interior gradients of
  PV fronts develop only at surface and tropopause

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Contemporary View

• PV dynamics seated mostly in surface and
  tropopause entropy gradients
• Troposphere proper can be approximated as a fluid
  of constant PV or constant PV gradient (ß)
• 5-10 day forecast errors owing to dynamical error
  growth sensitivity can be measured by adiabatic
  error growth
• Fronts are features of surface and (deformed)
  tropopause

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What Ever Happened to Thermodynamics?
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Some basic principles

• Heating of cold air masses from below is a
  relatively rapid process, occurring usually in a
  few days
• Cooling of air masses from below may require many
  tens of days

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Successive temperature soundings at Fairbanks,
Alaska, in December, 1961. Curves labeled with
time in days relative to first sounding.
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J. Curry, 1983

• The rate of cooling is shown to be very
  sensitive to the amount of condensed water in the
  atmosphere
• The model requires two weeks for the formation
  of fully developed continental polar air,
  although after only four days of cooling, the air
  has acquired most of the air mass properties

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Evolution of the vertical profile of temperature
in a single-column radiative-convective model,
beginning with a tropical sounding with 99 of
the water vapor removed at each level. Profile
labeled in days relative to the initial sounding.
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Evolution of the vertical profile of temperature
in a single-column radiative-convective model,
beginning with a subtropical sounding. In this
case, the fraction of water removed decreases
from 90 at the surface to 99 at 100 hPa.
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Time-height plot of the fractional cloudiness in
the simulation
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Evolution of the vertical profile of temperature
in a single-column radiative-convective model,
beginning with a subtropical sounding. In this
case, the fraction of water removed decreases
from 60 at the surface to 99 at 100 hPa. A
smooth vertical profile of is specified,
vanishing at the surface and at 100 hPa and
reaching a peak value of 0.5 hPa hr-1 at 750 hPa
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Re-classification of Air Masses, based on the
Saturated Potential Vorticity
is the saturation value of the equivalent
potential temperature
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Features

• It is always invertible, provided the flow is
  balanced, since is a state variable.
• It is nearly conserved in very cold air (e.g.
  arctic air, stratospheric air), because in the
  cold limit it reduces to the ordinary potential
  vorticity (PV), since at low temperature
• Neutrality to (slantwise) convection is
  characterized by SPV0, which is equivalent to
  having moist adiabatic lapse rates along vortex
  lines (absolute momentum surfaces, in two
  dimensions). Thus in much of the tropical and
  middle latitude free troposphere, where we
  observe convective neutrality, SPV is nearly zero.

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Define Four Basic Air Masses

• Convected Moist adiabatic lapse rates on vortex
  lines. Formation time of 1-2 days. Most of the
  troposphere, most of the time
• Stratosphere High PV reservoir. Long formation
  time scales
• Arctic High PV owing to radiative cooling in
  continental interior in winter. Formation time of
  4-14 days
• PBL Direct surface influence. Formation time of
  1-6 hours

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Cross-section of saturated potential vorticity
(SPV) along 90oW at 00 GMT on 8 March 2003. Value
have been multiplied by 104, and all values
larger than 2 x 104 have been reset to 2 x 104
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Cross-section of saturated potential vorticity
(SPV) along 100oW at 00 GMT 7 July 2003
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Could the Norwegians have been Right About Fronts
Extending Through the Depth of the Troposphere?
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Classical Semi-Geostrophic Frontogenesis Model,
but with Pre-existing Deep Tropospheric PV
Gradient
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Summary

• Discussion of forecast errors usually focuses on
  dynamical problems, e.g. error growth
• Some medium-range forecasts may be compromised by
  errors in model thermodynamics, especially as
  they concern arctic air mass formation
• Re-classification of air masses based on SPV may
  prove beneficial for analyzing tropospheric
  dynamics and thermodynamics

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Data Assimilation by Field Alignment
Ravela, S.,  K. Emanuel and D. McLaughlin, 2007
Data Assimilation by Field Alignment. Physica(D),
230, 127-145
http//dx.doi.org/10.1016/j.physd.2006.09.035
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Forecast Ensemble
Truth and Observations
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Deterministic Analysis
EnKF Analysis
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Aligned Forecast Ensemble
Deterministic Analysis
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Two Dimensions
Truth
Observations
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Forecast Ensemble
First Guess
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3D-Var Analysis
First Guess after Field Alignment
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Some Other Topics

• Winter sea-ice anomalies T anomalies
• Application of game theory to market response to
  seasonal forecasts
• Rossby wave propagation in typical tropopause
  distributions of PV