Baroclinic Instability

1. Baroclinic Instability Trough Ridge Southerlies Northerlies H L Cold Warm H L M. D. Eastin

2. Baroclinic Instability • Baroclinic Instability • Basic Idea • Simple Models • Classic Eady Framework • Contributions from Barotropic Instability • Examples of Observational Evidence M. D. Eastin

3. Concept of Instability • Definition • Spontaneous growth of a small-scale perturbations within a basic-state environment • Energy source for the growth is drawn from the basic-state environment • Different Types of “Instability” • Convective instability → Convective clouds grow • as parcels tap into the • background CAPE • Kelvin-Helmholtz instability → Wave-like clouds grow • (and “break”) as parcels • tap into the background • vertical shear M. D. Eastin

4. Concept of Instability • Definition • Spontaneous growth of a small-scale perturbations within a basic-state environment • Energy source for the growth is drawn from the basic-state environment • Different Types of “Instability” • Barotropic instability → Disturbances grow by • extracting kinetic energy • from the background flow • → suction-vortices in tornadoes • → meso-vortices in hurricanes • → short-waves in jet stream • Baroclinic instability → Disturbances grow by • extracting potential energy • from the background flow • → Synoptic-scale waves M. D. Eastin

5. Baroclinic Instability • Questions: • QG theory and polar-front theory have taught us that the development and intensification • of a surface cyclone requires the interaction of the fledgling surface cyclone or stationary • front with a pre-existing upper-level wave. • What mechanism develops the upper-level waves? • What determines the size, structure, and intensity of the upper-level waves? • What basic-state conditions are required for the waves to develop? • Our Approach: • Your text (Chapter 7) provides a very well-written and thorough explanation of baroclinic • instability via the classic theoretical framework first presented by Eady (1949) • This will be (has been) presented in detail in Advanced Dynamics • Here, we will address the relevant results from a practical perspective M. D. Eastin

6. Baroclinic Instability Review of Potential and Kinetic Energy: “Growth” of Wiley’s fall speed due to extraction of potential energy from the basic-state environment (conversion of potential energy to kinetic energy) “Available” Potential Energy No kinetic energy Unstable Situation M. D. Eastin

7. Baroclinic Instability • The Basic Idea: “Coin Model” • Consider a coin resting on its edge • (an “unstable” situation) • Its center of gravity (or mass) is located • some distance (h) above the surface • As long as h > 0, the coin has some • “available potential energy” • If the coin is given a small push to one side, • it will fall over and come to rest on its side • (a “stable” situation) • The instability was “released” and “removed” • Its center of gravity was lowered and thus its • potential energy was decreased • The coin’s motion represents kinetic energy • that was converted from the available • potential energy Center of Gravity h h ≈ 0 M. D. Eastin

8. Baroclinic Instability • The Basic Idea: “Simple Atmosphere” • Consider a stratified four-layer atmosphere with the • most dense air near the surface at the pole and the • least dense near the tropopause above the equator • (an “unstable” situation) • Each layer has a center of gravity ( ) located some • distance above the surface • Each layer has some available potential energy • The entire atmosphere also has a center of gravity ( ) • and some available potential energy • If the atmosphere is given a small “push” (e.g. a weak cyclone) then the layers will move until they have adjusted their centers of gravity to the configuration that provides lowest possible center of gravity for the atmosphere (the most “stable” situation) • The baroclinic instability was released and removed • Each layer’s motion represents a portion of the total • atmospheric kinetic energy that was converted from • the atmosphere’s available potential energy Tropopause Light P Surface Heavy Equator T Pole Light Heavy Equator Pole M. D. Eastin

9. Baroclinic Instability • The Basic Idea: “Simple Atmosphere” • Several “events” occurred during this process • in our simple atmosphere that are commonly • observed in the real atmosphere: • Kinetic energy (or wind) was generated • similar to the increase in winds as a • weak low pressure system intensifies • Warm (less dense) air was lifted over • cold (more dense) air in a manner very • similar to fronts • There is a poleward transport of warm air • and an equatorward transport of cold air • similar to the typical temperature advection • pattern around a low pressure system. Tropopause Light P Surface Heavy Equator T Pole Light Heavy Equator Pole M. D. Eastin

10. Baroclinic Instability • Eady Framework: Energy Conversion Processes • Basic-state environment consists of a strong north-south temperature gradient with • an upper-level zonal jet stream (atmosphere in thermal wind balance) • Basic-state environment contains both available potential energy and kinetic energy • Instability is initiated by (1) perturbation flow inducing weak localized WAA and CAA • across the thermal gradient → warm and cold air parcels (or eddy potential energy) • Eddy kinetic energy is then generated (2) as warm parcels rise and cold parcels sink • Acceleration of initial parcels away from their origin creates (via mass continuity) more • WAA and CAA [or creates more eddy potential energy (3)] System continues to intensify (increase its eddy kinetic energy) until is can no longer generate eddy potential energy (becomes a closed occluded system) 1 2 3 M. D. Eastin

11. Baroclinic Instability • Eady Framework: Idealized Situation • Maximum growth rate occurs for waves • with wavelengths of 3000-6000 km • Synoptic scale • Maximum growth rate occurs for waves • tilting west with height (21º phase shift) • Greater tilt → no intensification • Less tilt → no intensification • We look for westward tilt • Stacked systems are mature • Eddy kinetic energy develops from • an upward heat flux • Warm air rising poleward • Cold air sinking equatorward • Similar to warm/cold fronts Trough Ridge Southerlies Northerlies H L Cold Warm H L M. D. Eastin

12. Contributions from Barotropic Instability • Production of Eddy Kinetic Energy • Our analysis of baroclinic instability showed that the synoptic waves/cyclones are essentially • systems of eddy kinetic energy → What else can create eddy kinetic energy? • Term A: Eddy Kinetic Energy (EKE) Production • Term B: Baroclinic Generation → Upward heat flux produces EKE • → Warm air rising / cold air sinking • Term C: Barotropic Generation → Function of location relative to zonal mean jet stream • → Function of mean momentum flux • → Let’s examine a few scenarios… See your text (Section 2.7) For full derivation Term A Term B Term C M. D. Eastin

13. Contributions from Barotropic Instability Barotropic Production of Eddy Kinetic Energy: Term C: Perfectly Circular Eddy Term A Term B Term C Average of u’gv’g over entire eddy is zero Circular systems do NOT intensify from barotropic processes (but they can from) (baroclinic processes) M. D. Eastin

14. Contributions from Barotropic Instability Barotropic Production of Eddy Kinetic Energy: Term C: Asymmetric Eddy with Negative Tilt Term A Term B Term C Average of u’gv’g over entire eddy is negative “Negatively tilted” systems CAN intensify from barotropic processes IF located south of the ͞u maximum M. D. Eastin

15. Contributions from Barotropic Instability Barotropic Production of Eddy Kinetic Energy: t = 0 t = 0 t = +6 hrs t = 0 M. D. Eastin

16. Baroclinic/Barotropic Instability Observational Evidence for Possible Cyclogenesis? Answer #1: When a jet core is upstream of a trough axis that is above and west of a weak surface low Upstream jet streaks have large positive vorticity on their poleward flank with PVA downstream near the trough axis and over the weak surface low PVA → ascent → Psfc decreases → ΔP increases → EKE increases → enhances WAA / CAA → maintains any ongoing baroclinic instability process Example of a Trough with an Upstream Jet Streak + L M. D. Eastin

17. Baroclinic/Barotropic Instability Observational Evidence for Possible Cyclogenesis? Answer #2: When a diffluent trough is above and west of a weak surface low Diffluent upper-level troughs induce deep-layer ascent Ascent → Psfc decreases → ΔP increases → EKE increases → enhances WAA / CAA → maintains any ongoing baroclinic instability process Example of a Diffluent Trough L Note how the distance between the 6 height contours increases downstream of the trough axis M. D. Eastin

18. Baroclinic/Barotropic Instability Observational Evidence for Possible Cyclogenesis? Answer #3: When a negatively-tilted trough is above and west of a weak surface low and south of the zonal mean jet core Negative tilts permit barotropic processes to generate a net increase in eddy kinetic energy ↑ EKE → enhances WAA / CAA → maintains any ongoing baroclinic instability process Example of a Negatively-tilted Trough Y L Note how the slope of the trough axis is negative in the X-Y coordinate system X M. D. Eastin

19. Baroclinic/Barotropic Instability • Observational Analysis Tips: • Not all negatively-tilted troughs intensify • Not all diffluent troughs intensify • Not all troughs with upstream jet cores intensify • Must evaluate the vertical tilt of the system • Westward – may intensify(21º optimal) • Stacked – should not intensify much • Eastward – should not intensify • Must evaluate the latitude of the zonal mean jet core • Negatively-tilted systems south of the jet core may intensify • Positively-tilted systems north of the jet core may intensify • Negatively-tilted systems north of the jet core should not intensify • Positively-tilted systems south of the jet core should not intensify • Should evaluate all forcing terms in modified QG Omega equation • Should evaluate all forcing terms in modified QG Height Tendency equation M. D. Eastin

20. References Bluestein, H. B, 1993: Synoptic-Dynamic Meteorology in Midlatitudes. Volume II: Observations and Theory of Weather Systems. Oxford University Press, New York, 594 pp. Bretherton, F. P., 1966: Critical layer instability in baroclinic flows, Quart. J. Roy. Meteor. Soc., 92, 325-334. Charney, J. G., 1947: the dynamics of long waves in a baroclinic westerly current. J. Meteor., 6, 56-60. Eady, E. T., 1949: Long waves and cyclone waves. Tellus, 1, 33-52. Lackmann, G., 2011: Mid-latitude Synoptic Meteorology – Dynamics, Analysis and Forecasting, AMS, 343 pp. Orlanski, I., 1968; Instability of frontal waves. J. Atmos. Sci., 25, 178-200. M. D. Eastin