1 advanced coupled atmosphere-wave-ocean modeling for improving tropical cyclone prediction models...
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Advanced coupled atmosphere-wave-ocean modeling for improving tropical cyclone
prediction models
PI: Isaac GinisUniversity of Rhode Island
Co-PIs: T. Hara (URI), E. Andreas (NWR), R. Lucas (UH), A. Soloviev (NSU),
J.-W. Bao, C. Fairall (NOAA/ESRL)H. Tolman (NOAA/NCEP)
Advanced coupled atmosphere-wave-ocean modeling for improving tropical cyclone
prediction models
PI: Isaac GinisUniversity of Rhode Island
Co-PIs: T. Hara (URI), E. Andreas (NWR), R. Lucas (UH), A. Soloviev (NSU),
J.-W. Bao, C. Fairall (NOAA/ESRL)H. Tolman (NOAA/NCEP) NOPP Review Meeting, 2011, Miami, FL
1) To understand the physical processes that control the air-sea interaction and their impacts on intensity changes in tropical cyclones.
1) To develop a physically based and computationally efficient unified air-sea interface module for use in the next generation of research and operational coupled atmosphere-wave-ocean-land models.
Long-Term GoalsLong-Term Goals
• Initial development of basic model structure for the air-sea interface module.
• Investigation of the effect of wave-current interaction on the momentum fluxes and hurricane prediction.
• Developing physical constrains on the sea-state dependence of the drag coefficient at high wind speeds.
• Exploring new methods of coupling the sea-spray parameterization with the surface wave properties.
Year 1: Work CompletedYear 1: Work Completed
• Investigation the effects of sea spray on the momentum and enthalpy fluxes in high wind conditions.
• Continuing refinements of the ESRL and Andreas’ interfacial flux algorithms and the predicted near-surface distributions of sea spray.
• Implementation and initial testing of the air-sea interface module with URI/ESRL air-sea coupling parameterizations into a research versions of the GFDL coupled hurricane-wave-ocean model.
Year 1: Work Completed (cont’d)Year 1: Work Completed (cont’d)
• Air-sea fluxes in the hurricane model depend on sea state and sea spray and include surface current• Sea spray model depends on wind and sea state (Bao et al. 2011)• Wave model is forced by sea state dependent wind forcing and includes surface current (Fan et al. 2009)• Ocean model is forced by wind stress that is modified by growing or decaying wave fields (air-sea momentum flux budget, Fan et al. 2010)• Ocean model does not yet account for the wave-induced Stokes drift effects. They will be included in Year 2
Coupled Atmosphere-Wave-Ocean FrameworkCoupled Atmosphere-Wave-Ocean Framework
Wind stress calculation (no ocean coupling)Wind stress (or friction velocity ) is estimated iteratively to match wind speed at a specific height (typically lowest mode level ~35 m).
: Obukhov lengthWind Profile: : Stability function
Roughness: bulk parameterization (e.g., a constant Charnock coeff.)
sea state dependent parameterization ( is the phase speed at the spectral peak of a local wind sea)
with sea spray effect
.
€
u (z)
u*
=1
κln
z
zo
⎛
⎝ ⎜
⎞
⎠ ⎟+ψ M
z
L
⎛
⎝ ⎜
⎞
⎠ ⎟
⎡
⎣ ⎢
⎤
⎦ ⎥
Note on sea spray implementation: 1. Sea spray effect itself is a function of and wave parameters (the total wave
energy dissipation rate, significant wave height, wave phase speed at pick frequency)
2. Since sea spray modifies the wind profile, it can be expressed in terms of a modification to the wind profile (like the stability function ). However, since the spray effect is mainly confined below 10~35 m it is more convenient to express it in terms of the modified roughness length.
€
zo = func(u*)
M
L
€
zo = func(u*,c pi)
€
u* u
€
zo = func(u*,c pi,seaspray)
€
M
€
c pi
€
u*
Wind stress (or friction velocity ) is estimated iteratively to match the relative wind speed (wind speed relative to surface current) at a specific height (e.g. 35m).
Wind Profile:
wind speed vector at a specific height
wind speed vector at the surface (= ocean current vector)
Note: The direction of the wind stress is the same as the direction of
€
ru (z) −
r u (0)
u*
=1
κln
z
zo
⎛
⎝ ⎜
⎞
⎠ ⎟+ψ M
z
L
⎛
⎝ ⎜
⎞
⎠ ⎟
⎡
⎣ ⎢
⎤
⎦ ⎥
*u
)(zu
€
ru (0)
)0()( uzu
Wind stress calculation (with ocean coupling)
Coupling between surface waves and ocean currents/turbulence
Recently, several theories of wave-current interaction have been developed (e.g., Mellor, 2003, 2005, 2008; Ardhuin et al., 2008; McWilliams and Restrepo, 1999).
Mellor’s (2008) equation for regional scale models:Traditional ocean current equation
Surface wave effects (linear terms)
Surface wave effects (nonlinear terms) including Langmuir forcing
In regional scale models (including hurricane models) with a horizontal resolution of ~10km and a vertical resolution of ~10m: * Second line (linear surface wave effects) can be integrated across the wave boundary layer and included in the surface boundary condition.
* Third line (nonlinear surface wave effects) is relatively small and negligible.
* However, the Langmuir forcing is significant in smaller (unresolved) scales. This must be parameterized and be included in the turbulence closure model (Langmuir turbulence). from Fan et al. (2010)
scsscss
szsp
tczcccc
Wuz
Uux
uUx
uux
fuSx
utz
zx
PfUWU
zUU
xU
t
1
cU su:(Eulerian) ocean current : Stokes drift :Radiation stress
.
S
Coupling between surface waves and ocean currents/turbulence
Ocean model component in the coupled URI model: Turbulence closure (modified)
Traditional ocean current equation
Surface boundary condition (modified)
zx
PfUWU
zUU
xU
tt
czcccc
1
.
ˆ
zatMFx
Mt sairt
dzuM s
ˆdzSMF
ˆdzfuszs
ˆ
: Air-sea flux budget terms (Fan et al. 2010) – already included in the URI coupled model
: Coriolis-Stokes forcing term (Polton et al. 2005) – being incorporated in the URI coupled model
: Langmuir turbulence effect – will be included in the turbulence closure model of the URI coupled model (in collaboration with Tobias Kukulka, U. Delaware)
Air-sea flux budget (Fan et al. 2010)
Surface stress for ocean model is modified by the air-sea flux budget terms.
Surface boundary condition (modified)
.
ˆ
zatMFx
Mt sairt
dzuM s
ˆ
dzSMF
ˆ
Momentum (in α direction) contained in the wave field (wave momentum)
Horizontal flux (in β direction) of wave momentum (in α direction)
ddM wx cos,
These can be simply calculated from the WAVEWATCH III spectrum alone. No other information is needed.
For example:
,
MFxy wCg , cos sin d d
The calculations of , are insensitive to the spectral tail parameterization.
The accuracy of the flux budget calculation is dependent ONLY on the accuracy of the WAVEWATCH III spectral output.
MFM
diff
diff
Air-sea flux budget under (idealized) hurricanes (Fan et al. 2010)Relative reduction of the
momentum flux to ocean
depends on wind stress , which is not well constrained at high winds.
Uncertainty of drag coefficient
Upper bound: extrapolation of bulk parameterization
Our estimates from coupled wind wave model (blue)
Lower bound: observations by Powell et al. (2007)
Upperbound of wind stress
Our estimate of wind stress
7% loss
Lowerbound of wind stress
15% loss
air
diffair
air
ocean
air
Langmuir turbulence under hurricanes.
Three Lagrangian floats passed on the right side (red), the eye (blue) and the far left edge (green). The VKE (heavy lines) correlate swell with bulk wind stress (light lines) for the 'peak' and 'edge' floats. However, the kinetic energy at the 'eye' float decreases in the eye and does not increase again on the back side of the float. We hypothesize that this is because the wind and waves are misaligned in this region so that the waves' Stokes drift, which usually enhances boundary layer turbulence, instead suppresses it (D’Asaro, personal communication).
Langmuir turbulence
Subsurface turbulent kinetic energy (TKE) budget in the presence of surface waves
Production/consumption due to Stokes drift shear
1.When the direction between wind stress and Stokes drift is less than 90 degrees, surface waves lose energy and subsurface turbulence gains energy.
2.When the direction between wind stress and Stokes drift is more than 90 degrees, subsurface turbulence loses energy and surface waves gain energy.
.
Implications
Best fit is
* N10u 0.0619U 0.267
where both u* and UN10 are in m/s.
Hence, 2 2
*DN10
N10 N10
2
3
N10
u 0.267C 0.0619
U U
4.313.83 10 1
U
Spray Issues• At High Winds Sea Spray Becomes Relevant
– How Much Sea Spray? Source function, Sn(r)
– What does Sn do?
• Direct Heat Qs
• Evaporation Heat Ql
• Effect on momentum flux through buoyancy
2aDa UC
)( asaEeal qqUCLH )( asaHpaas TTUCcH
Droplet Source Functions
P energy wave breaking σ surface tensionr droplet radiusη Kolmogorov microscale in the ocean f fraction of P going into droplet productionUtop wind speed near breaker topUb group speed of breaking waveΛ Unspecified length scale (or, P/ Λ volume dissipation near surface)
Fairall et al. 1994
Fairall-Banner Physical Model:
Balance of energy produced by wave breaking and lost in production of drops and bubbles. Error function describes probability drop trajectory escapes surface.
2/)]/
(1[*])(4
9exp[)(
3
4 3/43
u
fbtopkn
SlopeVUUerf
r
PfrrS
r
)()()( 0 rSUWrS nbn
Sn Surface Source Strength for Sea Spray Droplets
)]TT(T[UCcH aa0Hpaas
)]TT(q)T(q[UCLH dds0sEeal
)]TT(T[FcQ ww0Mpwws
)]TT(q)TT(q[)T(h)U(WSLQ ddsaasaaewl
Parameterization of the Sea-Spray Modification of Heat Fluxes (Fairall et al. 1994; Bao and Fairall et al. 2008)
)Dmf(cc
DmfL)]TT()f1()TT[(DmcT
ievpvdpd
ieewaea0iwa
feedtuneV
h25dtime
dtime*massfluxm
f
i
where Ta is based on the sea-spray enthalpy balance (Andreas and Emanuel 2001)
massfluxL
'Qf
e
le
where the factor of 25 is an adjustment to approximately agree with the previous version of the scheme
spray mediated fluxes
turbulence fluxes
Parameterization of the Sea-Spray Modification of Momentum Flux (e.g., Barenblatt 1996 and Lykossov 2001)
Swz
SKw'S',0Sgwσε
z
uw'u' fsf
m20
*
ψzz
ln
uku
1ωforz
zαln1ln
1ωfor1z
z
ω1
ωα1lnω
ψ-
h
ω1
h
21
s
,)(
,2*
2
u
zSzkg
ku
wω hh
*
f :w f
: :zh
3
a
aw 10
where the mean fall speed of droplets
empirical parameter spray generation height
where S is the spray concentration profile.
turbulent suspension vs freefall
Ck/Cd ratio
10 20 30 40 50 60 700.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
U10
(m/s)
Ck/C
d
Ck includes dissipaton
Ck no dissipation
0 10 20 30 40 50 60 70 800
1
2
3x 10
-3
Ch
Effective Heat Xfer coefs
0 10 20 30 40 50 60 70 800
1
2
3x 10
-3
U10
(m/s)
Ce
0 10 20 30 40 50 60 70 800
1
2
3x 10
-3
U10
(m/s)
Cd
Direct Disruption of the Air-Sea Interface
1/ 42/ /a s w aK u g
A non-dimensional number,
The instability occurs at K > Kcr , where Kcr = 0.26 (corresponding
to U10 ~ 30 m s-1). Due to intermittency, sporadic instabilities can,
however, start from K as low as K = 0.09 (corresponding to U10 ~
10 m s-1).
which we call here as the Koga number, is the criteria for
the KH instability (Soloviev and Lukas 2010).
Model Velocity Profile
The model assumes regime of marginal stability in the transition layer. The change of velocity in the wave-stirred layer water (~Hs) below the transition layer cannot be
resolved in this scale (less than 1% of wind speed U10).
log layer
transition layer
W a
t e
r
A
I r
H
U U10 U(z)
z
h10
0
-Hs
2
2 a acr
w
UH mRi
g
m ~0.8
Equation for the bulk air-sea drag coefficient
U10 – wind speed at h10 = 10 m
k - von Karman constant
c – coeff. connecting surf. roughness with transition layer thickness (c ~ 0.02)
g – acceleration due to gravity
a, w – air, water densities
22 2 210 10
10 10 2
1/ ln 1 / 2 ln 1a
crw
U CC h m Ri c
g c
The model provides constraints on the air-sea drag coefficient in hurricane conditions
After Soloviev and Lukas (2010)
Case Study: Hurricane Earl (2010)
Research version of GFDL model with full wave coupling. Sensitivity experiments: 1.Without current in wind stress calculation, without air-sea interface budget2.With current, without budget3.With current, with budget4.Without current, with budget
30
Surface Roughness and Drag Coefficient (with no sea spray effect)
Zo Cd
Case Study: Hurricane Earl (2010)
Note: Wind/current ratio is not in a proper scale
Wind and Current Vectors Near the Storm Center
Case Study: Hurricane Earl (2010)
U* vs. Wind Speed at 35 m
Case Study: Hurricane Earl (2010)
Wind at 35 m
Drag Coeff. at 35 m
Wave phase speed
SignificantWaveheight
Case Study: Hurricane Earl (2010)
Wind stress
Wave Momentum flux
Momentum flux intoocean
€
ocean
τ air
€
ocean
€
air
€
wave
Case Study: Hurricane Earl (2010)
Effect of Current Effect of Momentum Budget
Input Parameters to Sea Spray ModuleInput Parameters to Sea Spray Module
Sea Spray Effect on uSea Spray Effect on u**
Sea Spray Effect on Drag CoefficientSea Spray Effect on Drag Coefficient
Sea Spray Effect on Drag CoefficientSea Spray Effect on Drag Coefficient
• Completing the initial development and testing of the wind-wave-current coupling and sea spray parameterization.
• Investigating how surface gravity waves modify the momentum flux to subsurface
currents via three mechanisms (the Coriolis-Stokes effect, the air-sea momentum budget, and the wave- current interaction).
• Refinement of the sea spray parameterizations based on available observations and additional theoretical analysis
• Continue work to investigate the impact of the wave-induced form drag on the reduction of the drag coefficient at high wind speeds and the sea-state dependence of the drag coefficient.
• Implementation and testing the new air-sea interface module into COAMPS TC-WAVEWATCH III-NCOM and HWRF-WAVEWATCH III-HYCOM
Year 2 Plans for the URI Co-PIsYear 2 Plans for the URI Co-PIs