Multiple equilibria in a cloud resolving model
Sharon Sessions1 ,∗ Satomi Sugaya1 ,
David Raymond1 , Adam Sobel2 , Stipo Sentić1
1 New
Mexico Tech
2 Columbia
University
World Climate Research Programme 2011
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∗
This work supported by the National Science Foundation
Sessions Sugaya Raymond Sobel Sentić
Multiple equilibria
(NMT) in a cloud resolving model
WCRP 2011
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Multiple Equilibria
Definition
In limited domain simulations which parameterize the large scale,
Multiple equilibria refers to a steady state which either
supports persistent precipitating deep convection
remains completely dry
under identical forcing and boundary conditions.
Sessions Sugaya Raymond Sobel Sentić
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Multiple equilibria
(NMT) in a cloud resolving model
WCRP 2011
2 / 11
Multiple Equilibria
Definition
In limited domain simulations which parameterize the large scale,
Multiple equilibria refers to a steady state which either
supports persistent precipitating deep convection
remains completely dry
under identical forcing and boundary conditions.
Exists in
single column model (Sobel, Bellon & Bacmeister, 2007)
cloud resolving model (Sessions, Sugaya, Raymond & Sobel, 2010)
Depends on the initial tropospheric moisture
Sessions Sugaya Raymond Sobel Sentić
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Multiple equilibria
(NMT) in a cloud resolving model
WCRP 2011
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Weak temperature gradient (WTG) approximation
Charney (1963) scaling analysis: δθhoriz ∼ 10−3 × θ in the tropics
Sobel & Bretherton (2000) used this to parameterize the large scale
tropical environment in a single column model (SCM)
Raymond & Zeng (2005) adapted WTG to a cloud resolving model
(CRM)
Sessions Sugaya Raymond Sobel Sentić
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Multiple equilibria
(NMT) in a cloud resolving model
WCRP 2011
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Implementing WTG in a cloud resolving model
Radiative-convective equilibrium (RCE) profiles of θ and rt are used to
represent ambient environment
15000
height (m)
12000
WTG: vertical θ profile
approximately horizontally
homogeneous
Average moisture
in immediate
convective vicinity
9000
6000
3000
0
300
Sessions Sugaya Raymond Sobel Sentić
320
θ (K)
340
0
0.005
0.01
rt (g/g)
0.015
0.02
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Multiple equilibria
(NMT) in a cloud resolving model
WCRP 2011
4 / 11
Implementing WTG in a cloud resolving model
Radiative-convective equilibrium (RCE) profiles of θ and rt are used to
represent ambient environment
15000
height (m)
12000
WTG: vertical θ profile
approximately horizontally
homogeneous
Average moisture
in immediate
convective vicinity
9000
6000
3000
0
300
320
θ (K)
340
0
0.005
0.01
rt (g/g)
0.015
0.02
Constrain θ profile to ambient profile by generating WTG vertical
velocity, wWTG , to exactly balance diabatic heating
Moisture horizontally advected from immediate vicinity via mass
continuity
Sessions Sugaya Raymond Sobel Sentić
Multiple equilibria
(NMT) in a cloud resolving model
WCRP 2011
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Multiple equilibria experiments
Run parallel WTG experiments with
identical boundary conditions
identical ambient environments (WTG reference profiles)
initialize domain with ambient moisture or completely dry
Sessions Sugaya Raymond Sobel Sentić
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Multiple equilibria
(NMT) in a cloud resolving model
WCRP 2011
5 / 11
Multiple equilibria experiments
Run parallel WTG experiments with
identical boundary conditions
identical ambient environments (WTG reference profiles)
initialize domain with ambient moisture or completely dry
2D CRM, periodic boundary conditions
horizontal domain sizes: 50-200 km (0.5-1 km resolution)
20 km vertical dimension (250 m resolution)
statistics averaged over last 30 days of 4 month simulations
Sessions Sugaya Raymond Sobel Sentić
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Multiple equilibria
(NMT) in a cloud resolving model
WCRP 2011
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Multiple equilibria in a cloud resolving model
Sessions, Sugaya, Raymond & Sobel (2010)
rain rate (mm/day)
40
50km domain, tθ=1.85 hours
RCE input
dry initial
30
20
10
0
Sessions Sugaya Raymond Sobel Sentić
5
10
15
horizontal windspeed (m/s)
20
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Multiple equilibria
(NMT) in a cloud resolving model
WCRP 2011
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Connection to self-aggregation
Bretherton, Blossey & Khairoutdinov (2005)
precipitation rate
WVP =
1
g
R
rt dp
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Day 1
Sessions Sugaya Raymond Sobel Sentić
Day 50
Multiple equilibria
(NMT) in a cloud resolving model
WCRP 2011
7 / 11
Connection to self-aggregation
Day 50
Hypothesis:
Multiple equilibria in a small
WTG domain is analogous
to precipitating or dry
regions of the larger RCE
self-aggregated state
Use WTG multiple equilibria
experiments to identify
conditions which permit
self-aggregation
Sessions Sugaya Raymond Sobel Sentić
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Multiple equilibria
(NMT) in a cloud resolving model
WCRP 2011
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Self-aggregation dependence on sea-surface temperature
Khairoutdinov and Emanuel 2010
aggregated
(SST ≥ 298 K)
disaggregated
(SST ≤ 297 K)
Strong nonlinear dependence of self-aggregation on SST
Sessions Sugaya Raymond Sobel Sentić
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Multiple equilibria
(NMT) in a cloud resolving model
WCRP 2011
9 / 11
Multiple equilibria dependence on changes in reference SST
rain rate (mm/day)
40
100km domain, tθ=0.51 hours
WTG reference profile
generated for each SST
SST = 300 K
SST = 302 K
SST = 303 K
SST = 304 K
SST = 305 K
Wet
Dry
30
20
WTG experiments have
same SST as reference
conditions
Existence of multiple
equilibria depends on SST
10
0
5
10
15
horizontal windspeed (m/s)
Sessions Sugaya Raymond Sobel Sentić
20
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Multiple equilibria
(NMT) in a cloud resolving model
WCRP 2011
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Summary
Multiple equilibria in small WTG domains may be a computationally
economic way to investigate self-aggregation
Hypothesis:
Conditions which permit multiple equilibria correlate to conditions
which promote self-aggregation
Sessions Sugaya Raymond Sobel Sentić
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Multiple equilibria
(NMT) in a cloud resolving model
WCRP 2011
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