Mixed Layer Summer School on Dynamics of North Indian Ocean June-July 2010 P. N. Vinayachandran Centre for Atmospheric and Oceanic Sciences (CAOS) Indian Institute of Science (IISc) Bangalore

Outline Mixed Layer Air-sea fluxes Models of Mixed Layer Bulk Models Kraus – Turner Price, Weller & Pinkle (PWP) Profile Models K-Profile Parameterizaion Meller Yamada

Mixed 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 the mxed 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 Radiation Shortwave 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) [I 1 e z/L1 - I 2 e z/L2 ] L 1 = 0.6 L 2 = 20m I 1 = 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 e z/Ln I(0) = insolation at the surface N = no. of spectral bands L n = length scale Paulson and Simpson, 1977, JPO

Longwave Radiation Incoming: Radiation from the atmosphere Outgoing: 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 surface Vapor pressure Cloud cover coefficient (0.5 to 0.73) a

Net Longwave Radiation

Sensible heat flux Q H = r a C p w'T' Q H = r a C p C h u (T s - T a )

Latent heat flux Q E = r a L w 'q' Q E = r a L C e u (q s - q a )

Net heat flux Q N = Q SW + Q LW + Q E + Q H

Annual Cycle: North Indian Ocean

Surface Buoyancy Flux B = r o [ a (r o C p ) -1 Q net – b S o (E – P) ] r o = surface density S o = surface salinity a, b = Expansion coefficients for heat and salt C p = 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

Kraus – Turner Bulk Mixed Layer Model Kraus & Turner, Tellus, 1967a: Experimental Kraus & 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/s Run 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 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

R g assumed to be ≥ 0.25 If the smallest R g < 0.25, then, T, S and V at the two grid levels that produce R g, j and j+1 are partially mixed according to, is the value after mixing ; R g ' = 0.3 R g is then recalculated from (j-1) to (j+2) and the mixing process continues until R g ≥ 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 shear Depth 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 shear 2. internal wave breaking 3. double diffusion

Pacanowsky&Philander type of mixing:

KPP Vertcal Mixing

Mellor Yamada Model Mellor, 2001, JPO Ezer, 2000, JGR