ISMAR
Influence of different vertical mixing schemes
and wave breaking parameterization on
forecasting surface velocities
S. Carniel1, J.C. Warner2, R.P. Signell2, J. Chiggiato3,
P.-M. Poulain4
1 CNR-ISMAR,
Venice, Italy
2 USGS, Woods Hole, USA
3 SMR-ARPA-EMR, Bologna, Italy
4 OGS, Trieste, Italy
ROMS-Oct’04
Motivations
 Most
3D circulation models compute subgrid
scale momentum and tracer mixing by means of a
two equation turbulence closure scheme, TCMs
(e.g Mellor-Yamada 2.5 or k-ε).
 These
closure schemes fail, however, in wave
affected surface layers, and eddy viscosity “errors”
produce unrealistic velocities.
Motivations
 These models are tuned to treat the sea-surface
as a solid boundary and therefore, during events of
strong wind, reproduce a log velocity profile in the
proximity of the surface.
 This
is in contradiction with recent studies and
measurements: during breaking wave conditions,
the near-surface mixing is higher and the velocity
shear lower than those modeled by usual TCMs.
Current picture
Air-sea interface is not rigid, therefore OML cannot be
patterned after a solid boundary (e.g. law of the wall)
A) Near surface region “breaking layer”, O(Z0S), all mixed;
B) region adjacent to air-sea interface, O(10 Z0S), turb. diss.
rate decays with a power law -4 (l.o.w.: -1).
(Kantha&Clayson, 2004; Drennan, 1996; Terray 1996…)
C) l.o.w. valid again at a certain distance from the surface
…most of wave generated TKE dissipated in the O(SWH)
Highly desirable to inlcude wave-breaking to explore nearsurface distributions of T, S, velocities (S&R, oil-spill
predictions, etc.)
Two-Equations
nd
2
mom. TCMs
Following Reynolds’ approach, 2nd moment quantities are
computed as u’w’ = KM (U/ Z).
Thus two extra prognostic eqs. are required:
1st for the transport of the TKE, k (or q2);
2nd for the transport of turbulence length scale, .
...integrating them, the Eddy Viscosity (Diffusivity) coeff.
for mometum (scalar) at (t,z) is KM (KH)  k
Ref: Kantha, 2004. The length scale equation in turbulence models. Nonlinear processes
3/2 7,
-11-12
in Geophysics,
Kolmogoroff relation (  k  ) allows the choices of
several … giving the name
to then=-1
2nd mom-2 eqs
k –TCM:

p=3, m=1.5,
 = c p k m n
– k n
n=1 generally kkm
k-, k-k, k- (turb. Freq.p=0,
k1/2m=1,
 -1) …i.e.
(Generic
Length
Scale
Ref: Umlauf
and Burchard,
2003.approach)
A generic length-scale equation for gephysical
turbulence. J. Marine Research, 61(2), 235-265
Tools – Numerical Models
How: integrating Umlauf & Burchard (UB 2003) GLS
method, allowing to choose among different
parameterisations of vertical mixing processes, into
Regional Ocean Model System (ROMS), a 3-D finitedifference hydrodynamical model (Warner et al., 2005)
Where:
a) idealized 20 m deep basin
b) Adriatic Sea
When: Febraury 2003 (bora event)
Sensitivity Tests 1-D ROMS
Idealized basin
20 m deep
1000x1000 m
100 stretched
levels
Wind stress udirection: 1 N/m2
(approx. 20 m/s)
Periodic BCs
NESW
…vertical resolution…
Turbulence and Wave-breaking
TKE Surface B.C.:
(Craig and Banner, 1994)
 t k
 u*3
 k z
u* 


100-150
l  k ( z  z0S )
…at z=0, =f(Z0s). k=0.4, but…
u 
a
2
Z0s =f(sea state)
z
S
0
Charnock formula (1955)
fully developed sea:
const
*
g
a: 1400
(CB 1994;
GOTM 1999,
etc.)
Sensitivity Tests 1-D ROMS -Test 1
C&B
All GLS with
K-w, NO C&B
GEN, NO C&B
(UB 2003)
GEN, CB
l  Lsft ( z  z0S )
Lsft=0.2, a=1400
A
…C&B increases surface TKE
Sensitivity Tests 1-D ROMS
C&B
All GLS with
K-w, NO C&B
GEN, NO C&B
GEN, CB
Lsft=0.2, a=1400
A
…C&B shows minor surface velocities
Sensitivity Tests 1-D ROMS
All GLS with C&B
K-w
K-eps
GEN
Lsft=0.2, a=1400
B …all including C&B... showing differences among TCMs…
Sensitivity Tests 1-D ROMS
All GLS with C&B
K-w
K-eps
GEN
Lsft=0.2, a=1400
B
…all including C&B.. see difference among TCMs…
Sensitivity Tests 1-D ROMS
All GLS with C&B
B
K-w
K-eps
GEN
Lsft=0.2, a=1400
B
…differences due to…
Sensitivity Tests 1-D ROMS
All GLS-GEN with
C&B
Lsft=0.2, a=1400
Lsft=0.2, a=14000
Lsft=0.4, a=1400
Lsft=0.4, a=14000
C
Sensitivity Tests 1-D ROMS
All GLS-GEN with
C&B
Lsft=0.2, a=1400
Lsft=0.2, a=14000
Lsft=0.4, a=1400
Lsft=0.4, a=14000
C
Sensitivity Tests 1-D ROMS
NO C&B
All GLS-GEN with
C&B
Lsft=0.2, a=1400
Lsft=0.2, a=14000
Lsft=0.4, a=1400
Lsft=0.4, a=14000
C
…value of alpha to be used?
Turbulence and Wave-breaking
TKE Surface B.C.:
(Craig and Banner, 1994)
 t k
 u*3
 k z
u* 


100-150
l  k ( z  z0S )
…at z=0, =f(Z0s)
a1400?
u 
2
Z0s =f(sea state)
z0S  a
Charnock formula (1955)
fully developed sea:
const
*
g
…in order to to
have
Z0s=O(SWH),
use O(105)
(KC 2004,
Stacey 1999)
Sensitivity Tests 1-D ROMS
C
NO C&
All GLS-GEN with
C&B
Lsft=0.2, a=1400
Lsft=0.4, a=100000
Lsft=0.2, a=100000
……
Surface Wind from LAMI model
LAMI:
3-D finitedifference,
non hydrostatic,
7 km resolution,
Forecast output
every 3 hours
Surface Currents from ROMS model
ROMS:
3-D primitive eqs,
hydrostatic,
sigma level,
finite difference
These are
surface currents
(0.5 m) from the
GLS GEN (UB
2003) case
3-D ROMS in the Adriatic
Bora
Velocity
at
5-m depth
(m/s)
Floaters release from ROMS model
GEN, No C&B
GEN, C&B
Z0S= f(Charnok),
L_sft=0.2, a=1400
Drifters data
Floaters kept at 0.5 m…
(modification to floats.in
file to the trajectory type
file in order to keep them
at a fixed depth…)
GLS as k- vs GEN
KEPS C&B
Z0S= f(Charnok),
L_sft=0.2, a=14000
GEN C&B
Z0S= f(Charnok),
L_sft=0.2, a=14000
Drifters data
GLS as k- vs GEN
GEN wave-breaking
Z0S= f(Charnok)
L_sft=0.4, a=100000
KEPS wave-breaking
Z0S= f(Charnok)
L_sft=0.4, a=100000
Drifters data
Message
 Recently it
has become possible to modify two equation
turbulence models in order to account for wave-breaking
effects.
 When wave-effects are included, near-surface shears are
significantly reduced, better matching observations, surface
currents are diminished (and are virtually less sensitive to
the near-surface grid resolution!)
 First
simulations incorporating wave-enhanced mixing
point out how model results (e.g. velocities) are sensitive to
how we parameterize the roughness scale.
Message
 How to handle the length scale near the surface (i.e what
is it at z=0) is still an open issue
 In
real-life situations the choice of correct parameters
appear to be more important than the TCM selected (at
least for this data-set and within the GLS set)
EOP
3-D ROMS in the Adriatic
Scirocco
Velocity
at
5-m depth
(m/s)
“S3” Seasonal Evolution
S
 ' '
2S
1
  w S  2  * Sobs  S 
t
z
z  ( z )
Forcings:
Wind: 1 hour
S: restoration
Run P1: k-
Run P2: one-eq
(length scale
prescribed
algebraically)
Run P3: GLS
Run P4: k-
SURFACE
BOTTOM
Where does turbulence come from?
a  F /m
u
1
1
 u  u  2  u   p    τ  g
t


R.A.N.S.= (still) the most convenient
way toReynolds’
describe complex
flow situations,
adopting
approach:
u  u  u'
where all turbulent motions are
parameterised
u
1  p by2a sub-scale
u ' u' v' u'  w' u'
 u  uturbulence
 f v   modelin
u


a statistical
sense.
t



u ' u '  u ' v'  u ' w'
x
y
z



v' u '  v' v'  v' w'
x
y
z



w' u '  w' v'  w' w'
x
y
z
 x
x
y
z
... are new unknowns for which transport
equations can be written but contain
third moment covariances… ad infinitum
Equations not closed at any level!
Turbulence is an unresolved problem in
physics!