gausscost / std

Description

The Bayesian cost function is the basic quadratic form derived from the Gaussian assumption in the application of the Bayesian theorem for data assimilation as described here. The defining equation is:

\[J(\mathbf{x}) = \frac{1}{2} (\mathbf{x} - \mathbf{x}^\textrm{b})^\textrm{T} (\mathbf{P}^\textrm{b})^{-1} (\mathbf{x} - \mathbf{x}^\textrm{b}) + \frac{1}{2} (\mathcal{H}(\mathbf{x}) - \mathbf{y}^\textrm{o})^\textrm{T}\mathbf{R}^{-1}(\mathcal{H}(\mathbf{x}) - \mathbf{y}^\textrm{o})\]

The Plugin returns both the cost function and its gradient. The gradient is computed using the formula:

\[\nabla J_\mathbf{x} = (\mathbf{P}^\textrm{b})^{-1} (\mathbf{x} - \mathbf{x}^\textrm{b}) + \mathcal{H}^*\left[\mathbf{R}^{-1}(\mathcal{H}(\mathbf{x}) - \mathbf{y}^\textrm{o})\right]\]

All computations of the cost function and its gradient are saved in the folder $workdir/simulator to make debugging easier, as well as monitoring conveniently variational inversions during their computation.

Yaml arguments

The following arguments are used to configure the plugin. pyCIF will return an exception at the initialization if mandatory arguments are not specified, or if any argument does not fit accepted values or type:

Optional arguments

reload_from_previous: (optional): False

Use results from previous computations, i.e., reload simulated concentrations, or adjoint sensitivities from previous observation operator computations

accepted type: bool

do_svd: (optional): False

Computes the cost function based on the SVD decomposition

accepted type: bool

replace_NaNs: (optional): False

Replace NaNs in departures by 0. This option must be used with caution and only when knowing where NaNs come from.

accepted type: bool

Requirements

The current plugin requires the present plugins to run properly:

Requirement name	Requirement type	Explicit definition	Any valid	Default name	Default version
controlvect	ControlVect	True	True	standard	std
obsvect	ObsVect	False	True	standard	std
obsoperator	ObsOperator	True	True	standard	std

Yaml template

Please find below a template for a Yaml configuration:

simulator:
  plugin:
    name: gausscost
    version: std
    type: simulator

  # Optional arguments
  reload_from_previous: XXXXX  # bool
  do_svd: XXXXX  # bool
  replace_NaNs: XXXXX  # bool