Linearly Stable Localized Atmospheric Features Inserted

Into Nonlinear Cyclogenesis

Richard Grotjahn,

Daniel Hodyss, and Sheri ImmelAtmospheric Science Program,

Dept. of LAWR, Univ. of California

Davis, CA 95616, USA

Linearly Stable Localized Atmospheric Features Inserted Into Nonlinear

Cyclogenesis

• Linearly Stable:Structure composed of neutral modes from a linear version of the model

• Localized:Structure has appreciable amplitude only in a small region of 3 dimensional space

• Nonlinear CyclogenesisAdvection term includes linear part from a basic state flow plus nonlinear velocities

Context of Study

• Observed precursors to midlatitude cyclogenesis are typically individual, coherent features of finite amplitude and not a wavetrain.

• Various linear instability studies exist using the QG system but most use wavetrains.

• We construct localized, linearly coherent, features and test effect of adding nonlinear advection

• Model: QGPV conservation eqn + Bndy. Conds. Eigenvalue and IVP numerical solutions.

Our Work with Localized Structures

• Introduced Localized, linearly stable structures & test calculations (linear and nonlinear) at 12th AOFD (New York) Grotjahn & Hodyss (1999)

• Interpretation, including modal decompositions just published: Grotjahn, Hodyss, and Immel, 2003: Dyn. Atmos. Ocn, 55-87, (June)

• Today will briefly review some Grotjahn et al. 2003 results and show current work in progress: 1. “type B” cyclogenesis and 2. “downstream development”

Example initial condition (I.C.) in Grotjahn et al. (2003)

Bickley jet + eddy

E-W Cross section

Upper level

Lower level

Single trough in stream function

Nonlinear evolution of example I.C.

• Perturbation part of stream function shown at (a) tropopause level, (b) surface level and at times 1.2 – 4.8

• dashed: values <0; solid: values >0. UL1 and SL1 are initial structure.

Growth rates of extrema for example IC

Most unstable normal mode:

MU (dashed line)

Upper features

Surface features

Projections at t=6 for example IC

• growing normal modes (first 114 on left side – red line)

• decaying modes (last 114 on right side – red line)

• remaining 1650 are ‘continuum’ modes

growing normal modes decaying normal modes

Conclusions from Grotjahn et al. (2003)• Global growth rates < normal mode values (not shown) • For Bickley jet, IC are constructed from only a few modes• Relative to IC trough, leading upper high & trailing surface

high develop similar to observations.• Highs and lows have normal mode-like properties:

1. upstream tilts develop, then remain fixed over time2. often extrema grow at rates < or comparable to normal mode rates3. vertical structure: maxima at surface and tropopause

• Projections onto eigenmodes find1. nonlinear advection activates growing normal modes2. most unstable mode inhibited while larger modes favored3. only a few modes present after a few days, most are unstable normal

modes.

Current Work in Progress

• Improved initial condition• “Type B” cyclogenesis:

1. upper trough passing over low level baroclinic zone.

2. upper trough passing over low level warm advection

3. lower structure made from surface trapped linearly stable, slowly moving perturbations as elongated dipole oriented perpendicular to mean flow.

• “Downstream development”

Initial condition (IC) with improved stratosphere

Example IC from prior work IC in current work

“Type B” cyclogenesis IC

IC has upper tropospherictrough + shallow surfacebaroclinic zone. (SBZ)

“Type B” cyclogenesis calculation (SBZ)

• Nonlinear calculation with favorable upstream location.

“Type B” (SBZ) cyclogenesis weak in this modelNonlinear development with SBZ

Nonlinear development without SBZ is similar, but less surface & upper amplitude (up to 20%)

Other shifts between SBZ & upper trough same or less interaction.

Linear calculation – no interaction

t = 7.5

“Type B” cyclogenesis for “warm advection” even weaker than for SBZ in this model

Downstream development

• The extrema that develop to either side of the IC trough might be viewed as:

1. emerging modes due to nonlinearity2. phase separation of constituent

modes3. downstream development

• Simple calculation done:1. estimate ageostrophic stream

function flux vectors2. compare linear and nonlinear runs

Nonlinear Animation

Linear Animation

Summary

• Results of nonlinear advection upon linearly stable, localized structures shown.

1. Extrema form near IC trough. All have normal mode-like properties. Upstream tilts develop.

2. Selected, often larger scale normal modes activated

• Current work looks for evidence of “type B” cyclogenesis and “downstream development”. Both effects present, but weak in this model.

• Comments welcome…I’m only here today.

Basic Flows

• Bickley with linear• Linear• Bickley

Figures from Grotjahn et al. (2003)Initial Conditions Building Blocks

Figures from Grotjahn et al. (2003)Initial Conditions Used

Figures from Grotjahn et al. (2003)Time Evolution, no horizontal shear

Figures from Grotjahn et al. (2003)Global growth rates, no horizontal shear

Figures from Grotjahn et al. (2003)Extrema growth rates, no horizontal shear

Figures from Grotjahn et al. (2003)Time Evolution, Bickley jet

Figures from Grotjahn et al. (2003)Time Evolution, upper/lower trough speeds

Bickley jet

Figures from Grotjahn et al. (2003)Global growth rates, Bickley jet

Figures from Grotjahn et al. (2003)Extrema growth rates, Bickley jet

Table 1. from Grotjahn et al. (2003)

Table 2. from Grotjahn et al. (2003)