influence of different vertical mixing schemes and wave breaking parameterization on forecasting...

Influence of different vertical mixing schemes Influence of different vertical mixing schemes and wave breaking parameterization on and wave breaking parameterization on

forecasting surface velocitiesforecasting surface velocities

S. CarnielS. Carniel11, J.C. Warner, J.C. Warner22, R.P. Signell, R.P. Signell22, J. Chiggiato, J. Chiggiato33, , P.-M. PoulainP.-M. Poulain44

1 1 CNR-ISMAR, Venice, ItalyCNR-ISMAR, Venice, Italy

22 USGS, Woods Hole, USAUSGS, Woods Hole, USA3 3 SMR-ARPA-EMR, Bologna, ItalySMR-ARPA-EMR, Bologna, Italy

4 4 OGS, Trieste, ItalyOGS, Trieste, Italy

ROMS-Oct’04

ISMARISMAR

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.

MotivationsMotivations

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.

MotivationsMotivations

Air-sea interface is not rigid, therefore OML cannot be Air-sea interface is not rigid, therefore OML cannot be patterned after a solid boundary (e.g. law of the wall)patterned after a solid boundary (e.g. law of the wall)

A) Near surface region “breaking layer”, O(ZA) Near surface region “breaking layer”, O(Z0S0S), all mixed;), all mixed;

B) region adjacent to air-sea interface, O(10 ZB) region adjacent to air-sea interface, O(10 Z0S0S), turb. diss. ), turb. diss.

rate decays with a power law -4 (l.o.w.: -1). rate decays with a power law -4 (l.o.w.: -1). (Kantha&Clayson, 2004; Drennan, 1996; Terray 1996…)(Kantha&Clayson, 2004; Drennan, 1996; Terray 1996…)

C) l.o.w. valid again at a certain distance from the surfaceC) l.o.w. valid again at a certain distance from the surface

……most of wave generated TKE dissipated in the O(SWH)most of wave generated TKE dissipated in the O(SWH)

Highly desirable to inlcude wave-breaking to explore near-Highly desirable to inlcude wave-breaking to explore near-surface distributions of T, S, velocities (S&R, oil-spill surface distributions of T, S, velocities (S&R, oil-spill

predictions, etc.)predictions, etc.)

Current pictureCurrent picture

Kolmogoroff relation ( k3/2 -1) allows the choices of several … giving the name to the 2nd mom-2 eqs TCM:

k-, k-k, k- (turb. Freq. k1/2 -1) …i.e. generally km n

(Generic Length Scale approach)

Two-Equations 2Two-Equations 2ndnd mom. TCMs mom. TCMs

Thus Thus twotwo extra prognostic eqs. are required: extra prognostic eqs. are required:11stst for the transport of the TKE, k (or q2); 22ndnd for the transport of turbulence length scale, ....integrating them, the Eddy Viscosity (Diffusivity) coeff.

for mometum (scalar) at (t,z) is KM (KH) kRef: Kantha, 2004. The length scale equation in turbulence models. Nonlinear processes

in Geophysics, 7, 1-12

Ref: Umlauf and Burchard, 2003. A generic length-scale equation for gephysical turbulence. J. Marine Research, 61(2), 235-265

= c= c pp k k m m nn

p=3, m=1.5, n=-1p=3, m=1.5, n=-1 k k – –

p=0, m=1, n=1p=0, m=1, n=1 k k – – kk

Following Reynolds’ approach, 2nd moment quantities are computed as u’w’ = KM (U/ Z).

How: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 finite-difference hydrodynamical model (Warner et al., 2005)

Tools – Numerical ModelsTools – Numerical Models

Where:Where: a) idealized 20 m deep basin

b) Adriatic Sea

When:When: Febraury 2003 (bora event)

Sensitivity Tests 1-D ROMSSensitivity Tests 1-D ROMS

Idealized basinIdealized basin

20 m deep 20 m deep

1000x1000 m1000x1000 m

100 stretched 100 stretched levelslevels

Wind stress u-Wind stress u-direction: 1 N/mdirection: 1 N/m2 2

(approx. 20 m/s)(approx. 20 m/s)

Periodic BCs Periodic BCs NESWNESW

…vertical resolution…

…Navier-Stokes eqs. describe all hydrodynamic processes, but the real world has large range of spatial/temporal scales…

• D.N.S.= accurate modeling of flows where all turbulent scales are resolved. No closure assumptions required. Applied numerically to idealised, small-scale problems. Demanding very large computer

resources.

• L.E.S.= predict large scale turbulent structures as large energy-containing eddies, while small scales into which the KE is transferred

are parameterised.

Turbulence and Wave-breakingTurbulence and Wave-breaking

TKE Surface B.C.:TKE Surface B.C.:

(Craig and Banner, 1994)(Craig and Banner, 1994)

3*u

z

k

k

t

100-150100-150

*u

14001400

(CB 1994; (CB 1994; GOTM 1999, GOTM 1999, etc.)etc.)

)( 0Szzkl ……at z=0, at z=0, =f(Z=f(Z0s0s). ). =0.4, but…=0.4, but…

ZZ0s 0s =f(sea state) =f(sea state)

Charnock formula (1955)Charnock formula (1955)

fully developed sea:fully developed sea:

g

uz S

2

*0

constconst

Sensitivity Tests 1-D ROMS -Test 1Sensitivity Tests 1-D ROMS -Test 1

…C&B increases surface TKEAA

C&BC&B

All GLS withAll GLS with

K-w, NO C&BK-w, NO C&B

GEN, NO C&BGEN, NO C&B

(UB 2003)(UB 2003)

GEN, CBGEN, CB

LLsftsft=0.2, =0.2, =1400=1400

)( 0S

sft zzLl


…C&B shows minor surface velocitiesAA

C&BC&B

All GLS withAll GLS with

K-w, NO C&BK-w, NO C&B

GEN, NO C&BGEN, NO C&B

GEN, CBGEN, CB

LLsftsft=0.2, =0.2, =1400=1400


…all including C&B... showing differences among TCMs…BB

All GLS with C&BAll GLS with C&B

K-wK-w

K-epsK-eps

GENGEN

LLsftsft=0.2, =0.2, =1400=1400


…all including C&B.. see difference among TCMs…BB

All GLS with C&BAll GLS with C&B

K-wK-w

K-epsK-eps

GENGEN

LLsftsft=0.2, =0.2, =1400=1400


…differences due to…

BBAll GLS with C&BAll GLS with C&B

K-wK-w

K-epsK-eps

GENGEN

LLsftsft=0.2, =0.2, =1400=1400

BB


CC

All GLS-GEN with All GLS-GEN with C&BC&B

LLsftsft=0.2, =0.2, =1400=1400

LLsftsft=0.2, =0.2, =14000=14000

LLsftsft=0.4, =0.4, =1400=1400

LLsftsft=0.4, =0.4, =14000=14000


All GLS-GEN with All GLS-GEN with C&BC&B

LLsftsft=0.2, =0.2, =1400=1400

LLsftsft=0.2, =0.2, =14000=14000

LLsftsft=0.4, =0.4, =1400=1400

LLsftsft=0.4, =0.4, =14000=14000

NO C&BNO C&B

CC …value of alpha to be used?



resources.


are parameterised.

Turbulence and Wave-breakingTurbulence and Wave-breaking

TKE Surface B.C.:TKE Surface B.C.:

(Craig and Banner, 1994)(Craig and Banner, 1994)

3*u

z

k

k

t

100-150100-150

*u

1400?1400?

……in order to to in order to to have have ZZ0s0s=O(SWH), =O(SWH),

use O(10use O(1055))

(KC 2004, (KC 2004, Stacey 1999)Stacey 1999)

)( 0Szzkl ……at z=0, at z=0, =f(Z=f(Z0s0s))

ZZ0s 0s =f(sea state) =f(sea state)

Charnock formula (1955)Charnock formula (1955)

fully developed sea:fully developed sea:

g

uz S

2

*0

constconst


… …

NO C&BNO C&BCCAll GLS-GEN with All GLS-GEN with

C&BC&B

LLsftsft=0.2, =0.2, =1400=1400

LLsftsft=0.4, =0.4, =100000=100000

LLsftsft=0.2, =0.2, =100000=100000

Surface Wind from LAMI modelSurface Wind from LAMI model

LAMI: LAMI:

3-D finite-3-D finite-difference, difference,

non hydrostatic,non hydrostatic,

7 km resolution,7 km resolution,

Forecast output Forecast output every 3 hoursevery 3 hours

ROMS:ROMS:

3-D primitive eqs,3-D primitive eqs,

hydrostatic,hydrostatic,

sigma level,sigma level,

finite differencefinite difference

These are surface These are surface currents (0.5 m) currents (0.5 m) from the from the GLS GLS GEN (UB 2003)GEN (UB 2003) casecase

Surface Currents from ROMS modelSurface Currents from ROMS model

3-D ROMS in the Adriatic

Bora

Velocity at

5-m depth(m/s)

Floaters release from ROMS modelFloaters release from ROMS model

GEN, No C&BGEN, No C&B

GEN, C&BGEN, C&B

Z0S= f(Charnok), Z0S= f(Charnok), L_sft=0.2, L_sft=0.2, =1400=1400

Floaters kept at 0.5 m…Floaters kept at 0.5 m…

(modification to (modification to floats.infloats.in file to the trajectory type file to the trajectory type file in order to keep them file in order to keep them at a fixed depth…)at a fixed depth…)

Drifters dataDrifters data

KEPS C&BKEPS C&B


GLS as k-GLS as k-vs GENvs GEN


GEN C&BGEN C&B


GLS as k-GLS as k-vs GENvs GEN

GEN wave-breakingGEN wave-breaking

Z0S= f(Charnok) Z0S= f(Charnok) L_sft=0.4, L_sft=0.4, =100000=100000

KEPS wave-breaking KEPS wave-breaking Z0S= f(Charnok) Z0S= f(Charnok) L_sft=0.4, L_sft=0.4, =100000=100000


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.

MessageMessage

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)

MessageMessage

EOPEOP

3-D ROMS in the Adriatic

Scirocco

Velocity at

5-m depth(m/s)

““S3” Seasonal Evolution S3” Seasonal Evolution

Forcings:Forcings:Wind: 1 hourWind: 1 hourS: restorationS: restoration

Run P1: k-Run P1: k- Run P2: one-eq Run P2: one-eq

(length scale (length scale prescribed prescribed algebraically)algebraically)

Run P3: GLS Run P3: GLS Run P4: k-Run P4: k-

SURFACE

BOTTOM

SSzz

SSw

zt

Sobs

)(

1*2

2''



resources.


are parameterised.

Where does turbulence come from?Where does turbulence come from?

adopting Reynolds’ approach:

mFa /

gτuu

11

2u

put

z

uw

y

uv

x

uuu

x

pvfuu

t

u

''''''1 2

'uuu

''''''

''''''

''''''

wwz

vwy

uwx

wvz

vvy

uvx

wuz

vuy

uux

... 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!

R.A.N.S.= (still) the most convenient way to describe

complex flow situations, where all turbulent motions are

parameterised by a sub-scale turbulence model in a statistical

sense.

influence of different vertical mixing schemes and wave breaking parameterization on forecasting...

Documents

surface region

nearsurface mixing

surface layers

forecasting surface

length scale equation

turbulence models

surface distributions

generic lengthscale