1. Baroclinic and barotropic annular modes
Lina Boljka, Ted Shepherd and Mike Blackburn
Unified Model Training Course, 12/4/2018

2. Contents Introduction Baroclinic vs barotropic
Barotropic & baroclinic annular modes
Motivation
Unified Model
Held-Suarez Model Configuration
Results
Cross-spectra
Conclusions

3. introduction

4. BAROCLINIC LIFE CYCLES (CYCLONE DEVELOPMENT)
LINKED
Baroclinic vs
Barotropic
Baroclinic instability
Strong meridional temperature gradients
Vertical wind shear important (d[u]/dz)
Heat flux [v*θ*] important
Growth of storm tracks
cyclones
Horizontal wind shear important (d[u]/dy)
Uniform vertical structure
Momentum flux [v*u*] important
Decay of storm tracks
cyclones
Acceleration of zonal mean flow (jet stream)
BAROCLINIC LIFE CYCLES (CYCLONE DEVELOPMENT)

5. Annular ModeS
Name: from “annulus” (“a ring-shaped object - a region bounded by two concentric circles.’’)
Are ‘’hemispheric scale patterns of climate variability’’
Internal mid-latitude dynamics cause them (not air-sea coupling etc.)
Most important modes of variability in mid-high latitudes
Explain 20-30% of variability in field

6. BAROTROPIC Annular Mode
Based on EOF of wind/geopotential/pressure fields
We know Southern (SAM, Antarctic oscillation) and Northern (NAM, Arctic oscillation) annular modes
Represent the jet shift poleward (positive phase)/equatorward (negative phase)
Impact weather
Timescale: 10 days
Linked to
Momentum flux
Thompson and Woodworth (2014)

7. BAROCLINIC ANNULAR MODE
BAM: based on EOF of EKE
Represents pulsing (variations in amplitude) of EKE rather than a shift  impacts to be determined
Related to oscillator model, periods days
Linked to heat flux
EKE
Thompson and Woodworth (2014)

8. (De)coupling of SAM & BAM
SAM & [v*u*]
Thompson & Woodworth (2014)
SAM only affected by momentum fluxes (weak heat flux signal)
BAM only affected by heat fluxes (weak momentum flux signal)
No correlation between SAM and BAM
Baroclinic and barotropic modes of variability decoupled
BAM & [v*θ*]

9. (De)coupling of SAM & BAM
Barotropic and baroclinic parts of the flow decoupled
Counter-intuitive compared to the general perspective from baroclinic life cycles (cyclones)
Baroclinic and barotropic responses linked through eddy growth and decay (momentum and heat fluxes linked)
I aim to understand this paradox theoretically & through modelling/modes of variability

10. Unified Model

11. Held-Suarez (HS) Model
After Held & Suarez (1994) (use: Unified Model vn8.6)
Resolution: 1.25o x 1.875o x 63 levels (32km top level) & daily output
Run for 26 years + 4 years for spin-up
Dry model – no moisture
Very idealised:
Usually perpetual conditions, e.g. equinox
no seasonal cycle
Imposed relaxation to equilibrium temperature
Prescribed bottom friction
No asymmetries (only synoptic eddies/cyclones)
Results robust to more complex configurations

12. Climatology & Forcing FORCING CLIMATOLOGY TEMPERATURE
Height (m)
FORCING
CLIMATOLOGY
Equillibrium Temperature
latitude
ZONAL MEAN WIND
Height (m)
Height (m)
latitude
latitude

13. HELD-Suarez & model hierarchies
Simple model
no moisture, seasonal cycle, asymmetries
Can add complexity (easily)
Shaw et al. (2016)

14. results

15. Simplified EKE budget α, τ : constants
Motivated by decoupling between baroclinic & barotropic modes
Model EKE using heat flux only & represent the rest as dissipation
α, τ : constants
Tendency
Heat Flux
Dissipation
Thompson et al. (2017)

16. Cross-Spectrum ANALYSIS
Follow Lorenz and Hartmann (2001)
Similar simplification for zonal momentum equation
Use spectral analysis to test EKE relationship
FFT
EKE
ω: angular frequency
Heat Flux Im Re
Boljka et al., JAS (2018)

17. Cross-Spectrum ANALYSIS
decoupling
coupling
EKE at 300mb
Heat Flux at 850mb
Average EKE & Heat Flux over a 20o latitude band & take zonal mean
Plot imaginary and real parts of cross spectrum
cross-spectrum
INTERMEDIATE FREQUENCY
SYNOPTIC TIMESCALE
frequency (cycles/day)
Period = 10 days Im Re
Cross Spectrum
Boljka et al., JAS (2018)

18. CONCLUSIONS 2 timescales of annular mode variability
Synoptic timescale baroclinic life cycles (~10 days)
Cyclones; baroclinic & barotropic processes linked
Intermediate frequency oscillator model (~20-30 days)
Baroclinic & barotropic processes decoupled
Implications: better understanding of climate variability
e.g. impacts on precipitation patterns, subseasonal prediction etc.
Unified Model can be used for hierarchies of models studies!
Boljka et al., JAS (2018)

19. THANK YOU for YOUR attention! any Questions?
REFERENCES:
Boljka, L., T. G. Shepherd and M. Blackburn, 2018: On the coupling between barotropic and baroclinic modes of extratropical atmospheric variability. J. Atmos. Sci., in press.