Transcript Slide 1

TUBULENT FLUXES OF HEAT, MOISTURE AND
MOMENTUM: PRACTICE OF PARAMETERIZATIONS
  zu 

2


Cd   ln    m 
  z0 

Bulk formulae:
   Cd u z2 ,
Qh  C p Ct ( z   0 ),
  zt
2
Ct   ln 
  z0t
Qq  L Cq (q z  q0 )
2
1
1
   zu 


  t  ln    m  ,

   z0 

1
  zq 
  z 

2
u


Cq   ln
 q  ln    m 


z
  0 q 
   z0 

Cd
1

,
Cdn 1  Cdn  ln zu 10  m zu L 
Cd Cdn
Ct

,
1
/
2
Ctn 1  Ctn Cdn ln  zt 10   t 
 

Cd Cdn
Ct

1/ 2
Ctn 1  Cqn Cdn
ln z q 10  q


 

Thus, we need to know either
roughness length, or neutral
transfer coefficients to
determine the fluxes!
1. Typical approach: parameterization from measurements
 To measure the flux (eddy correlation or inertial dissipation) under
the neutral conditions and the mean variables simultaneously;
 To derive experimental dependence of the neutral transfer
coefficient on the wind speed;
 To apply stability correction functions and to derive coefficients for
different stability conditions.
Cd (unstable)
Cdn
~10-3
Cd (stable)
V
Parameterizations derived from field measurements:
Garratt (1977) for the momentum flux + Garratt and Hyson (1975) for sensible
and latent fluxes. About 790 eddy correlation measurements in different
conditions from different platforms.
Cd  (0.75 0.067U10 ) 103 ,   0.0144, Ct  1.2 103 ,
Ce  1.6 103
Kruegermeyer (1976) – 124 hours of profile measurements in the tropics.
(  SST)
Cd  1.34(1  0.331Ri), Ri  3.55 10 2
, Ct  1.42(1  0.455Ri), Ce  1.20(1  0.394Ri)
u10
Hasse et al. (1978) – 1400 hours of profile measurements in the Tropical
Atlantic (coefficients for neutral conditions)
Cd  Cdn  1.25, Ct  Ctn  1.34, Ce  Cen  1.15
4. Smith and Banke (1975), Smith (1980), Smith (1988) – eddy correlation
measurements with a thrust anemometer at a platform offshore US West coast.
Stability correction: Bussinger et al. (1973), Dyer (1974), Paulson (1970).
Cdn  (0.61 0.063u10 ), Ctn  1.00, Cen  1.20,   0.012
Smith 88
Large and Pond (1981, 1982) – same platform as Smith
(1980, 1988), eddy correlation + inertial dissipation
measurements. Additionally ship measurements in the
Atlantic and Pacific were used.
1.14
u10  10m / s

Cdn  
0.49  0.065u10 u10  10m / s
1/ 2
0.0327Cdn
,
unstable
1/ 2
Ctn  
,
C

0
.
0346
C
en
dn
1/ 2
0
.
018
C
,
stable
dn

unstable
1.13,
Ctn  
,
Cen  1.15
stable
 0.75,
Scatter was slightly better for the neutral coefficients for heat
and moisture dependent on Cdn, than for the constant
coefficients.
2. Modelling of surface atmospheric layer to determine
exchange coefficients
Liu, Katsaros and Bussinger (1979) (LKB) – surface renewal theory.
Surface renewal theory was first introduced in chemical engineering
and has been applied to air-sea interface by Liu and Bussinger (1975)
and Liu et al. (1979).
Main assumption: Whereas the atmospheric (and oceanic) surface
boundary layer transports heat, mass and momentum to the interface
by turbulent motions, at the surface itself there exists an interfacial
layer of order 1 mm thick, in which molecular diffusion plays a
significant role in the transport.
Across this interfacial layer, small eddies of air transfer heat
randomly and intermittently between the “bulk” turbulent fluid, of
temperature Tb, and the surface itself which therefore warms or cools
by conduction from the eddies.
The temperature gradient and the surface heat flux are determined by the heat
conduction equation:
T
 2T
 kt 2
t
z
Thermal diffusivity
The solution for initial condition T(t=0) = Tb = constant, and surface
temperature T(z=0) = Ts = constant:
kt C p (Ts  Tb )
 T 
H (0, t )  kt C p   
(kt t )1/ 2
 z  z 0
- heat flux
Liu and Businger (1975) introduced a function to describe the areal fraction of
eddies which have been in contact with the surface for time t, and assume a
characteristic time, tc, for which an eddy remains in contact with the surface
before breaking away. For constant Ts and a random distribution of contact
duration the time-averaged temperature profile in the interfacial layer:
 z  - LKB flux-profile relationship
(T  Ts )

 1  exp 
1/ 2 
(Tb  Ts )
 ( kt t c ) 
and an average heat flux:
H
kt C p (Ts  Tb )
1/ 2
( kt t c )
Values of the exchange
coefficients for LKB, as
functions of wind
speed and stability
Variations of coefficients from different schemes
 Differences in behaviour of the coeeficients with wind are in general larger
than with stability, at least for moderate and strong winds
 The largest uncertainty in stability is observed under small winds
Typical
variations:
Cd, Ct, Ce ~
0.5x103
Recommendations:






Do not hesitate to use simple paramterizations;
Try to rely more on parameterizations derived from field observations
Under the calm or low winds use LKB, if ……[LATER]!!!!!
Never say “The best parameterization is done by XXXX” – they are all very uncertaint
Smith (1988) is considered to be most reliable
More or less “officially recommended” are Smith (1988), Large and Pond (1981, 1982), LKB
(among these very simple parameterizaions)
“field-only” schemes
universal schemes:
modelling, surface
renewal theory
Clayson et al. (1996)
Zeng et al. (1998)
ASTEX - White et al. (1995)
Beljaars (1995)
CATCH - Eymard et al. (1998)
Bourassa et al. (1996)
FASTEX – Hare et al. (1995)
LabSea: Bumke et al. (2002)
COARE-3.0 algorithm (Fairall et al. 2003)
COARE-3.0 algorithm (Fairall et al. 2003)
 Based on the TOGA-COARE results and 2777 covariance flux
measurements at the ETL;
 Tested using 4439 new values from field experiments between
1997 and 1999 including the wind speed regime beyond 10 m;
 The average (mean and median) model results agreed with the
measurements to within about 5% for moisture from 0 to 20 m.
Variations in
turbulent fluxes
due to
different
parameterizations
(A)
North
Atlantic
(B)
/helios/u2/gulev/handout:
lapo3.for - Large and Pond (1981, 1982) –with German comments
liu3.for – LKB (Liu, Katsaros and Bussinger 1979)
potsmin1.for - Smith (1988)
(all codes are for water vapor pressure, i.e. ez and not q)
Compute the fluxes of sensible heat, latent heat and momentum
for the following conditions:
SST=10C, Ta=8C, ez=9mb, V=7m/s, Pa=1010mb
SST=10C, Ta=12C, ez=11mb, V=7m/s, Pa=1010mb
SST=10C, Ta=8C, ez=9mb, V=3m/s, Pa=1010mb
SST=10C, Ta=8C, ez=9mb, V=12m/s, Pa=1010mb
/helios/u2/gulev/handout/
(for the same parameter values)
flux_test.f –
program to compute instantaneous values of urbulent fluxes,
using Liu et al. (1979), Large and pond (1981, 1982) and Simth
(1988) schemes.
Compilation:
f77 –o flux_test flux_test.f lapo3.for liu3.for potsmin1.for
Results:
flux.res
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