Explicit simulations of convection on an equatorial beta-plane

<strong>Explicit</strong> <strong>simulations</strong> <strong>of</strong> <strong>convection</strong> on
an equatorial beta-plane
Stefan Tulich
CIRES, University <strong>of</strong> Colorado, Boulder CO, USA
Collaborator: George Kiladis (NOAA ESRL)
Funding: NSF ATM-0806553

Historical Background
• The paradigm <strong>of</strong> radiative-convective equilibrium
(RCE) has proven invaluable in studies <strong>of</strong> the tropical
climate system
Manabe and Strickler (1964)

Nearly 30 years later
• Held et al. (1993): RCE with explicit 2D moist
<strong>convection</strong>
• Model setup:
26 km
SST = 303 K
640 km

Nearly 30 years later
• Held et al. (1993): RCE with explicit 2D moist
<strong>convection</strong>
• Simulation with zonal-mean u-wind allowed to vary:
A QBO-like oscillation!

Nearly 30 years later
• Held et al. (1993): RCE with explicit 2D moist
<strong>convection</strong>
• Simulation with zonal-mean u-wind set to zero:

Ten years ago
• Grabowski and Moncrieff, 2001: Large-scale organization
<strong>of</strong> tropical <strong>convection</strong> in 2D explicit <strong>simulations</strong>
• Model Setup:
25 km
SST = 303 K
20,000 km

Ten years ago
• Grabowski and Moncrieff, 2001: Large-scale organization
<strong>of</strong> tropical <strong>convection</strong> in 2D explicit <strong>simulations</strong>
• Model Setup:
25 km Background u-wind nudged to -10 m/s
20,000 km

Ten years ago
• Grabowski and Moncrieff, 2001: Large-scale organization
<strong>of</strong> tropical <strong>convection</strong> in 2D explicit <strong>simulations</strong>
• Model Setup:
25 km Cooling <strong>of</strong> 1.5 K/day
20,000 km

Grabowski and Moncrieff (2001)
Spontaneous large-scale wave organization!

Grabowski and Moncrieff (2001)
18 m/s (flow relative)
Spontaneous large-scale wave organization!

Grabowski and Moncrieff (2001)
Boomerang temperature structures like obs.

Grabowski and Moncrieff (2002)
Standing waves develop with interactive radiation

These papers set the stage for my
own PhD and postdoctoral research
No preferred hor. scale; -5/3 spectrum

Today: Extend these studies to 3D
basin-scale domains
• <strong>Explicit</strong>, nested <strong>simulations</strong> <strong>of</strong> <strong>convection</strong> on
an equatorial beta-plane
• Two types <strong>of</strong> runs:
1) Zonal-mean u-wind relaxed to zero
2) Zonal-mean u-wind relaxed to shear
pr<strong>of</strong>ile

Further details
• Model: WRF (most recent version)
• Forcing: Spatially uniform radiative-like
cooling to drive deep <strong>convection</strong>
• SST: Zonally uniform; peaked at eq.

Further details
• Model: WRF (most recent version)
• Forcing: Spatially uniform radiative-like
cooling to drive deep <strong>convection</strong>
• SST: Zonally uniform; peaked at eq.

45 N
Nesting strategy: 3 grids
9900 km
Grid 1
dx, dy = 36 km
Equator
45 S
5000 km

45 N
Nesting strategy: 3 grids
9900 km
Grid 1
dx, dy = 36 km
Equator
Periodic
Periodic
45 S
5000 km

45 N
Nesting strategy: 3 grids
Rigid wall
9900 km
Grid 1
dx, dy = 36 km
Equator
Periodic
45 S
5000 km
Periodic
Rigid wall

45 N
Nesting strategy: 3 grids
3300 km
Grid 2
dx, dy = 12 km
15 N
15 S
45 S
5000 km

45 N
Nesting strategy: 3 grids
Periodic
Grid 2
dx, dy = 12 km
15 N
Periodic
15 S
45 S
5000 km

45 N
Nesting strategy: 3 grids
Periodic
Grid 2
dx, dy = 12 km
15 N
Periodic
15 S
45 S
5000 km

45 N
Nesting strategy: 3 grids
5 N
5 S
Grid 3
dx, dy = 4 km
15 N
15 S
45 S
5000 km

One last detail
• Coriolis force acts only on perturbation
winds (about the zonal mean)
• Prevents the formation <strong>of</strong> unwanted
zonal jets and tradewinds

Results for uniform background
cooling <strong>of</strong> 1.25 K/day
200 mb
150 mb
Qrad = 1.25 K/day

Quiz time: Does the model
produce a single or double ITCZ?

Quiz time: Does the model
produce a single or double ITCZ?
Perhaps both?

Quiz time: Does the model
produce a single or double ITCZ?

The ITCZ is multilayered

The ITCZ is multilayered

The ITCZ is also non-stationary

The ITCZ is also non-stationary
5 m/s

Quiz time: What type <strong>of</strong> zonallypropagating
waves develop?

Quiz time: What type <strong>of</strong> zonallypropagating
waves develop?

Space-time spectrum <strong>of</strong> rain

Composite wave structures through
linear regression on filtered index
WIG
EIG

Compute difference through rotation <strong>of</strong>
EIG composite then subtract
WIG
Rotate(EIG)
- =

Compute difference through rotation <strong>of</strong>
EIG composite then subtract
-

Repeat the simulation with a
specified pr<strong>of</strong>ile

Evolution <strong>of</strong> meridionally-averaged rainfall

Space-time spectrum <strong>of</strong> rainfall

This westward bias apparently
impacts the ITCZs structure

Further exploring the
parameter space
• Quiz time: What happens if we
decrease or increase the cooling rate by
10%?

Cooling rate <strong>of</strong> 1.125K/day
Westward bias develops even with U = 0

Cooling rate <strong>of</strong> 1.125K/day
Also, the ITCZ becomes narrower and more intense

Cooling rate <strong>of</strong> 1.375K/day
The ITCZ becomes broader and less intense

Cooling rate <strong>of</strong> 1.375K/day
Also, some hint <strong>of</strong> eastward bias

Open questions
• Why does easterly shear cause a westward bias?
• Why is a westward bias produced under weak cooling
with no shear?
• Why is rainfall maximized <strong>of</strong>f the equator? Why does
the ITCZ become narrower/broader as the cooling is
made weaker/stronger? What causes the meridional
propagation <strong>of</strong> the ITCZ?
• Why dont low-frequency Kelvin waves develop?

Kelvin waves are obtained in the
presence <strong>of</strong> baroclinic instability