A Potpourri of Interesting Research Problems

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. TC Effects on El Nino?

Agukabams (aka Landphoons, Terracanes) From aboriginal roots “agu” (land) and “kabam” (storm) Case studies Case studies Hypothesis Hypothesis Simple model 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, A hypothesis for the re- development of warm-core cyclones over northern Australia

Case : TC Abigail, Feb-March, 2001

Best-track winds

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

20 cm Soil Temp at Halls Creek during Passage of Abigail

Idealized Experiments: Constant translation velocity and environmental temperature, initialization with a warm core vortex with maximum winds of 17 ms -1

Sensitivity to Initial Soil Temperature (translation speed = 13 km hr -1 )

Sensitivity to thermal diffusivity

Sensitivity to translation speed

Effect of depletion of water: PBL environmental RH declines from 80% to 0% over 8 days

Abigail Hindcast

Tropical Storm Erin, 2007

But then, deep in the heart of Oklahoma....

12 GMT August

18 GMT August

00 GMT August

06 GMT August

12 GMT August

Oklahoma Soils

Soil temperature record at Hinton, OK

Estimate of Soil Heat Flux

Hurricanes in the Persian Gulf? Annual Frequency=0.04

Back to Norway A Return to the Concept of Air Masses

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.

“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] Bjerknes and Solberg, 1922

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 earth’s surface.” [Bergeron, as paraphrased by Petterssen, 1954]

Sanders, 1955: “The intense surface frontal zone attains maximum strength near the ground and weakens rapidly with altitude.”

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)

Rossby Waves: Wherever there are gradients of q on surfaces of constant s Wherever there are gradients of s on rigid boundaries

Baroclinic Instability and Fronts Eady’s 1949 model of baroclinic instability: No interior gradients of potential vorticity Hoskins and Bretherton’s 1972 semi- geostrophic model of frontogenesis: no interior gradients of PV; fronts develop only at surface and tropopause

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 (β) 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

What Ever Happened to Thermodynamics?

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

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

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”

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.

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.

Time-height plot of the fractional cloudiness in the simulation

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

Re-classification of Air Masses, based on the Saturated Potential Vorticity: is the saturation value of the equivalent potential temperature

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 SPV=0, 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.

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

Cross-section of saturated potential vorticity (SPV) along 90 o W at 00 GMT on 8 March Value have been multiplied by 10 4, and all values larger than 2 x 10 4 have been reset to 2 x 10 4

Cross-section of saturated potential vorticity (SPV) along 100 o W at 00 GMT 7 July 2003

Could the Norwegians have been Right About Fronts Extending Through the Depth of the Troposphere?

Classical Semi-Geostrophic Frontogenesis Model, but with Pre-existing Deep Tropospheric PV Gradient

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

Data Assimilation by Field Alignment Ravela, S., K. Emanuel and D. McLaughlin, 2007: Data Assimilation by Field Alignment. Physica(D), 230, Data Assimilation by Field Alignment

Forecast EnsembleTruth and Observations

Deterministic AnalysisEnKF Analysis

Aligned Forecast EnsembleDeterministic Analysis

Two Dimensions TruthObservations

Forecast EnsembleFirst Guess

3D-Var AnalysisFirst Guess after Field Alignment

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