Mixed Layer

Summer School onDynamics of North Indian Ocean

June-July 2010

P. N. VinayachandranCentre for Atmospheric and Oceanic Sciences (CAOS)

Indian Institute of Science (IISc)Bangalore 560 012

Outline

Mixed Layer

Air-sea fluxes

Models of Mixed Layer

Bulk ModelsKraus – Turner

Price, Weller & Pinkle (PWP)

Profile Models

K-Profile Parameterizaion

Meller Yamada

Mixed LayerMixed Layer

Importance: Weather and climate (eg. cyclones)

Air – sea exchange is controlled my mixed layer processes

Life in the ocean: Most of the primary productivity occurs in the mixed layer

i) Most of the electromagnteic radiation is absorbed within the mixed layer

Ii) Mixing at the base of the mixed layer is crucial for sustaining biological productivity

Near – surface layer of the ocean. Quasi homogeneous

Properties (T, S, ) are nearly uniform in this layer

The layer where properties change rapidly with depth is thermocline

How do we determine the depth of themxed layer

Vinayachandran et al., 2002, JGR

Difference Criterion

Properties are assumed to be uniform within the mixed layer

Isothermal, Isohaline and Isopycnal

Temperature: 0.1 to 1.0C ( 0.2 C )

Density: 0.01 to 0.25 kg m-3 (0.03 km m-3)

Gradient Criterion

Properties are assumed to change `sharply' just below the mixed layer

Figure courtesy: S. R. Shetye

Barrier Layer

Air – sea fluxes

RadiationShortwave Downwelling radiation Day of the year Zenith angle Latitude Atmospheric transmittance (aerosol and water vapour) Cloud cover

Upwelling shortwave radiation Reflection from the sea surface

Albedo, Clear sky radiation, fractional cloud cover, noon solar elevation

Net Shortwave Radiation

SOC Flux data set. Josey, 1999

Penetration of short wave radiation

I(z) = I(0) [I1 ez/L1 - I

2 ez/L2]

L1 = 0.6 L

2 = 20m

I1 = 0.62 I

2 = 1 - I

1

i) shortwave (UV < 350nm) e-folding scale of UV ~ 5m

ii) visible (PAR 350 – 700nm) part that penetrates

Iii) IR and nIR (> 700nm) absorbed in the top 10cm

Solar radiation in the uppper ocean is given by

I(z) = I(0 )∑ n ez/Ln

I(0) = insolation at the surface

N = no. of spectral bands

Ln = length scale

Paulson and Simpson, 1977, JPO

Longwave Radiation

Incoming: Radiation from the atmosphereOutgoing: Radiation from the sea surface

Longwave Downwelling longwave radiation

Air temperature and humidity

Upwelling longwave radiation Reflection of longwave radiation Emission from the sea surface

Emittance of the sea surfaceVapor pressureCloud cover coefficient (0.5 to 0.73)

a

Net Longwave Radiation

Sensible heat flux

QH = r

a C

p w'T'

QH = r

a C

p C

h u (T

s - T

a)

Latent heat flux

QE = r

a L w 'q'

QE = r

a L C

e u (q

s - q

a)

Net heat flux

QN = Q

SW + Q

LW + Q

E + Q

H

Annual Cycle: North Indian Ocean

Surface Buoyancy Flux

B = ro [ a (ro Cp) -1 Q

net – b S

o (E – P) ]

ro = surface density

So = surface salinity

a, b = Expansion coefficients for heat and salt

Cp= heat capacity

Positive buoyancy flux is stabilizing

Source: Oberhuber

(siign reversed)

Mixed layer processes

Heating by solar radiation: Penetrative

Cooling by evaporation, mechanical mixing

Heating/Cooling : Sensible heat flux/Longwave radiation

There is no echange of salt

Freshwater exchange by Evaporation and Precipitation

Changes buoyancy flux

Figure courtesy: S. R. Shetye

Figure courtesy: S. R. Shetye

Kraus – Turner Bulk Mixed Layer Model

Kraus & Turner, Tellus, 1967a: ExperimentalKraus & Turner, Tellus, 1967b: Theory

Schemtic of the mixed layer

Denman, 1973, JPO

Assumptions

Incompressible ocean.

Stably stratified fluid (Boussinesq approximation)

Wave-like dynamical effects ignored (Gravitational, inertial and Rossby waves)

Horizontal homogenity, neglect horizontal advection

Turbulent heat flux at the base of the mixed layer

Entrainment

Integrate from z= -h to z=-h+△h

0 at z=-h

In the limit as △h 0

≤ 0 ; no entrainment; H=0

≥ 0 ; entrainment mixing ; H=1

Calculation of Entrainment Velocity

Production of TKE

1. If P > 0 ; entrainment deepening of mixed layer

2. If P < 0 ; relative importance of winds v/s convection

m is an adjustable parameter; B is the buoyancy flux

Monin-Obukhov Length

McCreary et al., 2001

Wind dominated regime

Wind speed = 12.5 m/s; No heat flux, No radiation

h after 24 hours = 37.1; after 48 hours = 47.8

Denman, JPO, 1973

Wind dominated regime

Run 1. Wind speed = 12.5 m/sRun 2. Wind speed = 17 m/s

Heat dominated regime; H= 0;

Diurnal Heating

Wind speed = 4 m/s; Profiles are plotted evey 2hrs

The PWP (Price Weller Pinkel) Model

Price et al., 1986, JGR

The (PWP) ice Weller Pinkel Model

F(0)=Q, air-sea heat flux

E(0)=S(E-P), fresh water flux times surface salinity

G(0)= , wind stress

Instability due to vertical shear in a stratifed fluid

Kelvin-Helmholtz Instability

Wikepedia

Mixing

Static stability

Mixed layer stability

Shear flow stability

h mixed layer depth difference between mixed layer and the level just beneath.

Rb bulk richardson number

Rg gradient richardson number

Vertical grid resolution, ∆z =0.5 m ; Time step, ∆t = 900 s

Begin from an initial T, S profile (eqns. 1 & 2)

Update the T, S profile for the first grid box, all the surface heat flux goes in here

Update T profile for the boxes 2 to N using penetrative part of radiaion

Calculate density using an equation of state, calculate mixed layer depth for a density criterion of 0.0001

Check for static stabiity, mix and remove all instability

Calculate veloctiy profile using winds (eqn. 3)

Check for mixed layer stability, Rb > 0.65, mix and remove instability

Check for shear flow instability, Rg > 0.25, mix and remove instability

Implementation

Rg assumed to be ≥ 0.25

If the smallest Rg < 0.25 , then , T, S and V at the two grid levels that produce Rg , j and j+1 are partially mixed according to,

is the value after mixing ; Rg' = 0.3

Rg is then recalculated from (j-1) to (j+2) and the

mixing process continues until Rg ≥ 0.25.

KPP Mixed Layer

The turbulent mixing in the oceanic boundary layer is distinctly different from the layer below

Vertical extent of oceanic boundary layer depends on surface forcing, stratificcation and shearDepth upto which an eddy in the boundary layer can penetrate before becoming stable.

Shallowest depth where Rb > 0.3

Monin-Obukhov Length:

Large and Gent, 1999, JPO

Below the boundary layer (interior) vertical mixing consists of:1. Local Ri due to instability due to resolved vertical shear2. internal wave breaking3. double diffusion

Pacanowsky&Philander type of mixing:

KPP Vertcal Mixing

Mellor Yamada Model

Mellor, 2001, JPOEzer, 2000, JGR