Stochastic parametrization of EOS (STO)

Authors: P.-A. Bouttier

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The stochastic parametrization module aims to explicitly simulate uncertainties in the model. More particularly, Brankart [2013] has shown that, because of the nonlinearity of the seawater equation of state, unresolved scales represent a major source of uncertainties in the computation of the large scale horizontal density gradient (from T/S large scale fields), and that the impact of these uncertainties can be simulated by random processes representing unresolved T/S fluctuations.

The stochastic formulation of the equation of state can be written as:

$\displaystyle \rho = \frac{1}{2} \sum_{i=1}^m\{ \rho[T+\Delta T_i,S+\Delta S_i,p_o(z)] + \rho[T-\Delta T_i,S-\Delta S_i,p_o(z)] \}$ (14.1)

where $ p_o(z)$ is the reference pressure depending on the depth and $ \Delta T_i$ and $ \Delta S_i$ are a set of T/S perturbations defined as the scalar product of the respective local T/S gradients with random walks $ \mathbf{\xi}$:

$\displaystyle \Delta T_i = \mathbf{\xi}_i \cdot \nabla T \qquad \hbox{and} \qquad \Delta S_i = \mathbf{\xi}_i \cdot \nabla S$ (14.2)

$ \mathbf{\xi}_i$ are produced by a first-order autoregressive processes (AR-1) with a parametrized decorrelation time scale, and horizontal and vertical standard deviations $ \sigma_s$. $ \mathbf{\xi}$ are uncorrelated over the horizontal and fully correlated along the vertical.


Gurvan Madec and the NEMO Team
NEMO European Consortium2017-02-17