future modeling?
DESCRIPTION
Future Modeling?. Hann-Ming Henry Juang RSM workshop 2011. Topics. Different IOs? To downscaling from different data? More accurate? Generalized coordinates as GFS Speed up model code Semi-Lagrangian Modulerization Fortran 99 Non dimensional code Others?. - PowerPoint PPT PresentationTRANSCRIPT
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Future Modeling?
Hann-Ming Henry Juang
RSM workshop 2011
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Topics• Different IOs?
– To downscaling from different data?
• More accurate?– Generalized coordinates as GFS
• Speed up model code– Semi-Lagrangian
• Modulerization– Fortran 99– Non dimensional code
• Others?
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A specific form for generalized hybrid
€
ˆ p k = ˆ A k + ˆ B k ps + ˆ C k ˆ T vk / ˆ T 0k( )C p / Rd
For sigma-pressure, let
where
€
ˆ A K +1 = ˆ B K +1 = ˆ C K +1 = 0
ˆ A 1 = ˆ C 1 = 0
ˆ B 1 =1
€
ˆ B k
€
ˆ C k = 0 for all levels
€
ˆ A k
- decrease from 1 to 0 at low layers
- increase from 0 to be pressure where B=0, then decrease to zero.
For sigma-theta, let
€
ˆ A k = 0 for all levels
€
ˆ B k works the same, and
€
ˆ C k works as in sigma-p
€
ˆ A k
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2005 hurricane season
sigma-theta
operational
parallel H
parallel M
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€
∂q
∂t= −u
∂q
∂x
Numerical instability due to advection by the CFL condition
Let
€
q = Q(z)e−(x +wt )i
€
Δx − uΔt > 0
uΔt /Δx <1
i.e u=200m/s dx=1000m dt <5 sec
But if we solve by
€
dq
dt= 0 then unconditional stable
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A
D
M
€
∂q
∂t+ u
∂q
∂x+ v
∂q
∂y= 0
Dq
Dt= 0
qAn +1 = qD
n−1
Traditional-Upstream SL
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A
D
M
Starting from mid-point
No guessing and no iteration
but one 2-D interpolation and one 2-D remapping
NDSL
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AD M€
XD = XM −UM Δt
XA = XM + UM Δt
ρ A*n +1 = ρ D
n−1
Interpolation
remapping
€
ρDn−1
relocation
€
ρA*n +1
€
ρ*n +1
Instead doing following
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€
∂ρ∂t
+∂ρu
∂x+
∂ρv
∂y= 0
∂ρ
∂t
⎛
⎝ ⎜
⎞
⎠ ⎟X −direction
+∂ρu
∂x+
∂ρ
∂t
⎛
⎝ ⎜
⎞
⎠ ⎟Y −direction
+∂ρv
∂y= 0
For mass conservation, let’s start from continuity equation
Consider 1-D and rewrite it in advection form, we have
€
∂ρ∂t
⎛
⎝ ⎜
⎞
⎠ ⎟X −direction
+ u∂ρ
∂x= −ρ
∂u
∂x
Advection form is for semi-Lagrangian, but it is not conserved if divergence is treated as force at mid-point,So divergence term should be treated with advection
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Divergence term in Lagrangian sense is the change of the volume if mass is conserved, so we can write divergence form as
€
∂u
∂x
⎛
⎝ ⎜
⎞
⎠ ⎟Lagrangian _ sense
=1
Δx
dΔx
dt
€
dρΔx
dt
⎛
⎝ ⎜
⎞
⎠ ⎟X −direction
= 0
∂ρΔx
∂t
⎛
⎝ ⎜
⎞
⎠ ⎟X −direction
+ u∂ρΔx
∂x= 0
Put it into the previous continuity equation, we have
which can be seen as
€
ρΔ x( )departure= ρΔx( )arrival
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ALDL M
€
XLD = XL
M −ULM Δt
XRD = XR
M −URM Δt
ΔD = XRD − XL
D
Interpolation
€
ρDn−1
relocation
€
ρA*n +1
We do
X
DRAR
€
ρDn−1ΔD = ρ A
n +1ΔA
€
ΔD
€
ΔA
ML MR€
XLA = XL
M + ULM Δt
XRA = XR
M + URM Δt
ΔA = XRA − XL
A
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06h fcst specific humidity at model layer 40
control
nislfv
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24h fcst specific humidity at model layer 40
control
nislfv
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72h fcst specific humidity at model layer 40
control
nislfv
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6hr fcst cloud water at model layer 35
control
nislfv
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24hr fcst cloud water at model layer 30
control
nislfv
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T574 GC Eulerian
T574 Opr Eulerian
TL878 NDSL
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Day 1
Day 5
Opr T574 EulerianTL878 NDSL
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Day 1
Day 5
Opr T574 EulerianNDSL TL878
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The possible future• More generalized and/or hybrid system will be
built, more accurate thermodynamics will be used.
• Semi-Lagrangian will become more simple, conserving and economical code for time integration.
• Gravity and acoustic waves can be resolved explicitly (show in Riemann solver talks).
• Deep atmosphere or non-approximated system will be introduced for further accuracy in model dynamics.