Why do we have storms in atmosphere?

Mid-atmosphere (500 hPa) DJF temperature map What are the features of the mean state on which storms grow?

Zonal thermal winds, and zonal mean cross sections

The DJF Atlantic Jet 10 m/s 20 m/s 30 m/s 0 m/s 40 m/s Sector zonal mean cross section Thermal wind map (250 hPa – 850 hPa)

Are atmospheric jets stable? Will perturbations to the jet immediately decay? Does the jet support instabilities? Analogy: Ball on top of a hill Answer #1: Perturbations to the jet seem to grow in magnitude; The jet is unstable. Answer #2: The jets are the time mean of the atmospheric flow; Something most kill the instability and return the flow to the time mean.

Velocity Shear The velocity shear between the two layers leads to an instability

Consider two different mean states with different velocity shears 5 m/s - 5 m/s - 10 m/s 10 m/s The systems have the same linear momentum But the system with more shear has more kinetic energy x y

Can the perturbations extract energy from the flow? Key concept: If the perturbations can decrease the velocity shear in the flow, the flow will have less energy This energy will go to the perturbations Therefore, in order for the perturbations to grow in shear flow, they must transport momentum against the shear of the flow

Lets put this in mathematical terms dU dy > 0 x y MEAN STATE Which perturbation stream function will grow? A B C

Which way do perturbations transport momentum When v’ is positive, u’ is zero When u’ is negative, u’ is zero u’v’ = 0 When v’ is positive, u’ is negative When v’ is negative, u’ is positive u’v’ < 0 u’v’ > 0 When v’ is positive, u’ is positive When v’ is negative, u’ is negative No momentum transport Negative momentum transport In the y direction Positive momentum transport In the y direction

Barotropic Conversion Mean State Shear Perturbation Stream Function Energy flow from mean state to the perturbation if : u’v’ dU dy < 0 And the initial perturbation will grow

Simple analogy: If we perturb a ball, lying on top topography from its resting position, will it continue to move away or will it return to the original position StableNeutrally stable

Ideal Flow and most unstable mode

Barotropic Normal Modes Linearize about a basic state with zonally invariant zonal velocity The equation becomes In the spatial domain, we require that the solution at each grid point grows linearly We assume a sinusoidal structure in x and discrete structure in y

Is this the form of instability which is most pronounced in the atmosphere 10 m/s 20 m/s 30 m/s 0 m/s 40 m/s Sector zonal mean cross section Thermal wind map (250 hPa – 850 hPa) There is much more vertical sheer than horizontal sheer in the jet This is a different form of instability because it is in hydrostatic and geostophic balance

Mid-atmosphere (500 hPa) DJF temperature map Can we extract energy from this?

How do Storms Grow? Perturbations (Storms) extract energy from the mean state via two different mechanisms Meridional Temperature Gradient (Baroclinic) Velocity Shear (Barotropic) High Energy Low Energy High Energy Low Energy Wind Vectors Isotherms Hot Cold Not too hot Not too cold

Atmospheric available potential energy- energy decrease by flattening isotherms Temperature Potential Temperature Equator Pole Height cold hot More Energy Less Energy

Simple model of baroclinic instability x y z Top layer Bottom layer MEAN STATE 2 layer model Uniform meridional temperature gradient No zonal variations warm cold FASTEST GROWING PERTURBATION Contours = perturbation stream function Colors = tendency in stream function Peturbations slant against the vertical shear This causes the energy to be converted to the eddies

The maximum growth of perturbations is:.31 f N -1 Eady Growth Rate Using values for the mid-latitude atmosphere, the perturbations will double in magnitude every 2 days, ocean = 20 days The horizontal spatial scale of the perturbations is 4000 km in the atmosphere, 400 km in the ocean Results of the simple model dU dz

Tilt of baroclinic modes

What happens to eddies as they are advected by the mean flow T=0, u’v’ dU =0 dY u’v’ dU >0 dY T=1

Layered eddy advection Upper Level mean flow Lower Level mean flow T= 0 days T= 2 daysT= 4 days v’t’ < 0 u’v’ = 0 v’t’ = 0 u’v’ > 0 dT dy dU dy dT dy dU dy

Atmospheric Energy Reservoirs Mean State Potential Energy Equator to Pole Temperature Gradient Mean State Kinetic Energy Large Scale Circulation Transient Eddy Potential Energy Transient thermal anomalies Transient Eddy Kinetic Energy Transient Circulations 10X > -v’t’ dT dy w’α’ N 2 u’v’ dU dy Baroclinic Growth Barotropic Decay

Lifecycles in simple models Chang and Orlanski, 1993

Baroclinic Instability explains the Locations of storm tracks Storm activity High pass height variance at 250 hPa 75 m m 2 Baroclinicity Eady Growth Rate.6 /day Hoskins, Valdes, 1989

Different Ways of defining a storm-track High Pass Eulerian variances High pass filter a field and take the variance z’ 2 (250 hPa) v’ 2 (300 hPa) slp’ 2 v’t’ (850 hPa) u’v’ (250 hPa) Chang, 2002

Alternative approach, Lagrangian tracking Dotted red lines = tracks Colored boxes = size

Defining a storm track, continued Track features (Lagrangian) and keep track of where they pass and how strong their central value is Sea level pressure features- track density.

The picture in 1888 Hinman, 1888

What seeds storms? Cyclogenesis density at 850 hPa. Courtesy of Sandra Penny

Seasonality of storminess Pacific Storminess V’ 2 (300 hPa) Atlantic Storminess V’ 2 (300 hPa) Pacific Baroclinicity U(500 hPa) – U(925 hPa) Atlantic storm activity follows the baroclinicity, but Pacific does not Chang, 2002

Mid-winter suppression of the Pacific storm track Courtesy Camille Li

Ideas on Midwinter Suppression DJF SON Weaker seeding in winter? From Sandra, again

Last Glacial Maximum Storm Tracks V’T’ throughout the troposphere (colors) and upper level jet (contours) during the winter LGM has less storm activity LGM - MODERN MODERN LGM

LGM baroclinicity LGM Modern LGM - MODERN LGM has more baroclinicity

Do faster growing storms mean bigger storms? Composite Storm size (m) Composite storm growth Rate (per day) LGM MODERN

Do faster growing storms mean bigger storms? LGM MODERN Probability distribution function of initial size, growth rate, and growth period for LGM and Modern

Predicted and observed storm size distribution for LGM and modern LGM MODERN Predicted from initial size and growth PDF Observed in model Bottom line, storm size not proportional to growth rate/instability in mean state

Baroclinic instability in the ocean