A TEOS-10 compliant version of ROMS for polar applications
Ben Galton-Fenzi$^{1,2,3}$, Trevor McDougall$^4$, Glenn Hyland$^{1,2}$ and Paul Barker$^4$
1. Australian Antarctic Division
2. Antarctic Climate & Ecosystems CRC
3. Antarctic Gateway Partnership, University of Tasmania
4. University of New South Wales
2016 ROMS Asia-Pacific Workshop
17-21 October 2016
Greenland and Antarctica
Fig 13.14 IPCC. 2013.
- How much SLR are we able to adapt to over the next 100 years?
Ice age cycles
Grant et al. 2014.
The Antarctic Ice Sheet
source: NASA JPL
Ice melting into seawater
- Dynamics and thermodynamics
source: www.youtube.com/watch?v=olFzcye4iSs
TEOS-10: EOS for dynamics
Conservative temperature, $\Theta$
$\Theta = \frac{h^0}{c_p^0}$
where $c_p^0 =$ 3991.867 957 119 63 J kg$^{-1}$ K$^{-1}$
Absolute salinity, $S_A$
For seawater with a standard composition:
$S_A = S_R = \left( \frac{35.165 04 g kg^{-1}}{35} \right) S_P$, g kg$^{-1}$
Otherwise:
$S_A = S_R + \delta S_A$
where the Absolute Salinity anomaly, $\delta S_A$, requires spatial interpolation of global dataset.
$\delta S_A$
EOS seamount testcase
- Stratified ocean and zero forcing experiment. The ocean should remain at rest.
- Important test with every new domain.
GSW EOS $f(\Theta, S_A)$: Zero forcing
Modified EOS for boussinesq models following Roquet et al. 2015. Ocean Modelling
- The stiffened TEOS_10 EOS performs marginally better than the EOS-80 version.
Ice/ocean thermodynamics
Double diffusion
Huppert & Turner, Nature. 1978.
The molecular flux of heat:
$Q^T = -\rho c_p k^T \nabla T + \frac{B \mu_{S_A}}{\rho k_S T} Q^S$
Assuming the cross-diffusion coefficient $B$ can be taken to be zero, the molecular diffusion of heat is proportional to the gradient of in situ temperature, or Fourier's Law
The molecular flux of salt
$Q_w^S = -\rho k^S \left( \nabla S_A + \frac{\mu_{,P}}{\mu_{,{S_A}}} \nabla P \right) - \left[\frac{\rho k^S T}{\mu_{,{S_A}}} \left( \frac{\mu}{T} \right)_{,T} + \frac{B}{T^2} \right] \nabla T$
which shows, in the absence of a temperature gradient $\nabla T = 0$, the salt flux is proportional to both the salinity gradient and $\rho \kappa_S \frac{\mu_{,P}}{\mu_{,{S_A}}} \nabla P$, known as ``barodiffusion'' as it causes a flux of salt down the gradient of pressure.
The molecular flux of salt
Assuming the film is thin enough that the processes are occurring at constant pressure, $\frac{\mu_{,P}}{\mu_{,{S_A}}} \nabla P = 0$, and the cross-diffusion terms $B = 0$, then the conventional form of the salt flux equation, Fick's Law, is:
$Q_w^S = -\rho k^S \nabla S_A $
The Soret effect
However, for a temperature gradient not equal to zero, then the expression for the salt flux is:
$Q_w^S = -\rho k^S \nabla S_A - \left[ \frac{\rho k^S T}{\mu_{,{S_A}}} \left( \frac{\mu}{T} \right)_{,T} \right] \nabla T$
The second term on the R.H.S. is a flux of salt due to the gradient of in situ temperature and is called the Soret effect.
Composition specific $S_T$
For polar oceans under ice, diffusion driven by the Soret effect is about $S_T$ times the diffusion driven by the gradient in salinity alone, also known as Fick’s Law.
The Soret effect becomes more important with decreasing salinity gradients.
Modeling the basal melting
Gwyther et al. 2016.
Heat flux budget
$Q_{latent} = Q_M - Q_I$
$Q_M \gg Q_I$
$\rho_i L m = \rho c_w \gamma_T (T_M-T_B)$
The Three Equations
$\rho_i L m = \rho c_w \gamma_T (T_M-T_B)$
$\rho_i S_B m = \rho \gamma_S (S_M-S_B)$
$T_B = T_{linear freezing}(S_B,P)$
Exchange velocities
$\gamma_t = \frac{\kappa_t Nu}{h} = f(u^{\star}, Pr)$
$\gamma_S = \frac{\kappa_S Sh}{h} = f(u^{\star}, Sc)$
Functions are parameterized from boundary layer observations under sea-ice, e.g. McPhee, 2008.
Not consistent with ROMS turbulence closure model.
Turbulence at the interface
Large Eddy Simulation. Gayen et al. 2015
Is there need for different values of $\gamma$ for S and T?
The nature of the interface
source: ROV, MBARI, Weddell Sea
A little bit of turbulence?
A consistent approach
Assuming the total transfer, is the sum of the molecular, $\kappa$, and turbulence, $K$, diffusivities
$Nu = (\kappa_t + K)/\kappa_t$
$Sh = (\kappa_S + K)/\kappa_S$
then
$\gamma_t = \frac{\kappa_t + K}{h}$
$\gamma_S = \frac{\kappa_S + K}{h}$
where, $K$ is the component of the exchange velocity due to turbulence alone, and can be provided by a turbulence closure model.
When turbulent:
$K \gg \kappa_t$ and $K \gg \kappa_S$ and thus
$\gamma_t \approx \gamma_S$.
A useful value of $h$ is the model uppermost layer thickness, $\Delta z$, where the values of $T$, $S$ and $K$ are found.
Evolving ice base experiment
Evolving ice base experiment
ROMSIceShelf: idealised evolving ice
Galton-Fenzi, unpublished
ROMSIceShelf: idealised evolving ice
Galton-Fenzi, unpublished
For TEOS-10 compliance
Where we are going with ROMS
- ROMSIceShelf
- github https://github.com/bkgf/romsIceShelf
- Development: nonlinear freezing temperature and frazil
$\hbar^B \equiv (1 - w^{Ih})\hbar + w^{Ih} \hbar^{Ih}$
$S_A^B \equiv (1 - w^{Ih}) S_A$ - Unexploited features: Adjoint framework, 2-way nesting, sediment code, sea ice ...
Acknowledgments
- Australian Antarctic Division
- Antarctic Climate & Ecosystems CRC
- Antarctic Gateway Partnership
- National Computing Infrastructure and the Tasmanian Partnership for Advanced Computing
- David Gwyther, Eva Cougnon, Kaitlin Alexander, Mike Dinniman, John Hunter, Trevor McDougall, Paul Barker, Glenn Hyland, Rupert Gladstone, David Holland
- Software: Rutgers ROMS, github and reveal.js