Transcript Document

Bulk Parameterizations for Wind Stress
and Heat Fluxes (Chou 1993; Chou et al. 2003)
Outlines:
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Eddy correlation (covariance) method
Surface layer (or Monin-Obukhov) similarity theory
Bulk aerodynamic fomulations
Definition of parameters for bulk flux model:
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Z -- Reference height for wind, temperature, and humidity (can be
different for different variables)
U -- Surface wind speed at Z
qs -- Sea surface temperature (SST)
Qs – Sea surface saturation specific humidity (salinity, cool skin effect)
Q -- Surface air specific humidity at Z
q -- Surface air potential temperature at Z
r -- Air density
Cp -- Isobaric specific heat
Lv -- Latent heat of vaporation
CD, CH, CE – Bulk transfer coefficients for momentum, sensible
and latent heat fluxes
L -- Monin-Obukhov length { = qv u*2/(g k qv*) }
k -- von Karmen constant ( =0.4)
u -- kinematic viscosity of air
Eddy Correlation (Covariance) Method
Wind stress
Sensible heat flux
Latent heat flux
Where
Vertical wind:
Wind speed :
Temperature:
Humidity:
t = - r <w’u’>
FSH = r CP <w’T’>
FLH = r LV <w’q’>
w = <w> + w’
u = <u> + u’
T = <T> + T’
q = <q> + q’
(1a)
(1b)
(1c)
Surface Layer (Monin –Obukhov) Similarity Theory
Profile Scaling Parameters:
Wind:
u* = ( t / r )1/2
Temp. :
q* = – FSH /(r CP u*)
humidity: q* = – FLH /(r Lv u*)
----
----
-----
t =
r
u*2
FSH = – r Cp
FLH = – r Lv
(2a)
u* q *
u*q*
(2b)
(2c)
M-O length: L = qVu*2/(g k qV*) ---- L ~ u(∂u/∂z)/<w’ qV’>
Z/L = 0, <w’ qV’> = 0,
neutral atm sfc layer (mechanical turbulence dominan
Z/L < 0, <w’ qV’> < 0, unstable atm sfc layer (convective turbulence dominan
Z/L > 0, <w’ qV’> > 0, stable atm sfc layer (mechanical turbulence suppressed)
Nondimensional Gradients of Wind, Potential
Temperature, and Humidiy:
(k Z/u*)(∂u/∂Z) = fu(Z/L)
(3a)
(k Z/ q*)(∂ q/∂Z) = fT(Z/L)
(3b)
(k Z/q*)(∂q/∂Z) = fq(Z/L)
(3c)
Z/L = 0, neutral, fu= fT= fq = 1
Z/L < 0, unstable, f u= (1 – 16 Z/L)-1/4 ,
fT= fq= (1 – 16 Z/L )-1/2
Z/L > 0, stable,
fu= fT= fq = 1 + 7 Z/L
von Karman constant: k = 0.40
Vertical Profiles of Wind, Potential Temperature, Humidity
(U – Us)/u* = [ln(Z/Zo) – yu(Z/L)]/k
(q – qs)/q* = [ln(Z/ZoT) – yT(Z/L)]/k
(Q – Qs)/q* = [ln(Z/Zoq) – yq(Z/L)]/k
y =∫(1 – f) d ln(Z/L),
*
(4a)
(4b)
(4c)
L = qv u*2/(g k qv*)
Eq.(4) obtained by adding 1 and subtracting 1 on right
hand side of Eq.(3), dividing Z on Eq.(3), then
integrating Eq.(3) from lower boundary (Zo, ZoT, and
Zoq) to height Z.
Stability Functions: y =∫(1 – f) d ln(Z/L)
Z/L = 0, neutral, yu= yT= yq= 0
Z/L > 0, stable, yu= yT= yq= -7 Z/L
Z/L < 0, unstable,
yu= 2 ln [ (1 + x)/2] + ln[ (1 + x2)/2] – 2 tan-1x +p/2
yT= yq= 2 ln[(1 +y)/2]
x = fu-1
y = f T-1 = fq-1
Bulk Aerodynamic Formulations:
Wind stress
t = r CD (U–Us)2
Sensible heat flux FSH = r CP CH (U–Us) (qs–q)
Latent heat flux
(5a)
(5b)
FLH = r LV CE (U–Us) (Qs–Q) (5c)
*Input parameters: U(Z), qs, q(Z), Qs, Q(Z), and Z
* CD = k2/[ln(Z/ZO) – yu(Z/L)]2
CH = CD1/2 k/[ln(Z/ZOT) – yT(Z/L)]
(6a)
(6b)
CE = CD1/2 k/[ln(Z/ZOq) – yq(Z/L)]
(6c)
* Eq. (6) obtained by combining Eqs. (2), (4), & (5).
Us = 0.55 u* (~0)
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ASTEX: Atlantic Stratocumulus Transition Experiment
COARE: Coupled Ocean-Atmosphere Response Experiment
FASTEX: Fronts and Atlantic Storm Track Experiment
JASMINE: Joint Air-Sea Monsoon Interaction Experiment
KWAJEX: Kwajalein Experiment
NAURU99: Nauru ’99 Experiment
SCOPE: San Clemente Ocean Probing Experiment
TIWE: Tropical Instability Wave Experiment
PACSF99: Pan-American Climate Study in eastern Pacific during 1999
MOORINGS: Buoy service in the North Pacific
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1913-hourly fluxes
calculated from ship
data using GSSTF2
bulk flux model vs
observed (a) wind
stresses determined by
ID method, (b) latent
and (c) sensible heat
fluxes determined by
covariance method of
10 field experiments.
C: COARE
F: FASTEX
X: other experiments
Conclusions:
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GSSTF2 bulk flux model for turbulent fluxes validated
well by comparing hourly turbulent fluxes computed from
research ship data with those of 10 field experiments
conducted by the NOAA/ETL scientists over tropical and
northern midlatitude oceans during 1991-1999 (Chou et al.
2003)
GSSTF2 bulk flux model for latent heat flux validated
well by comparing hourly latent heat fluxes computed
from research ship data with those of 12 field experiments
conducted by NOAA/ETL and French scientists over
tropical and northern midlatitude oceans during 19911999 (Curry et al. 2004)