1 # Modular arbitrary-order ocean-atmosphere model: Definition files formats #
3 This page describes the format of the definition files needed by the stochastic model.
5 ## MTV parameterization ##
7 The following definition files are needed by the MTV parameterization.
8 Examples of those files are joined to the code.
10 - 'mean.def' : Mean \f$\langle \boldsymbol y \rangle\f$ of the unresolved variables.
11 * **Format**: one line per \f$\langle y_i \rangle\f$ value
12 - 'correxpo.def': Coefficients \f$a_k\f$ of the fit of the elements of the correlations matrix \f$\langle \boldsymbol y \otimes \boldsymbol y^s \rangle\f$ with the function \f[ a_4+a_0 \, \exp\left(-\frac{s}{a_1}\right) \, \cos(a_2 \, s + a_3) \f] where \f$t\f$ is the lag-time and \f$\tau\f$ is the decorrelation time.
13 * **Format**: First line is two numbers: the number of unresolved variables and the value of stoch_params::maxint to be used (range of validity of the fit). \n
14 Then each line specify the fit of an element \f$i,j\f$ of the matrix \f$\langle \boldsymbol y \otimes \boldsymbol y^s \rangle\f$ as follow: \f[ i,j,a_0,a_1,a_2,a_3\f]
15 * Used if stoch_params::load_mode is set to 'expo'.
16 - 'corrspline.def': Coefficients \f$b_k\f$ of the spline used to model the elements of the correlation matrix \f$\langle \boldsymbol y \otimes \boldsymbol y^s \rangle\f$.
17 * **Format**: First line is two numbers: the number of unresolved variables and the number of points used. \n
18 Second line is the times \f$\tau_k\f$ of the points in timeunits. \n
19 Then \f$i\times j\f$ sequences of 3 lines occurs as follow:
21 2. Values of \f$\langle \boldsymbol y \otimes \boldsymbol y^s \rangle_{i,j}\f$ at \f$\tau_k\f$
22 3. Coefficients \f$b_k\f$ of the spline giving the second derivative of the interpolating function at \f$\tau\f$
23 * Used if stoch_params::load_mode is set to 'spli'.
24 - 'corrint.def': File holding the matrix \f$\boldsymbol\Sigma = \int_0^\infty \, ds \langle \, \boldsymbol y \otimes \boldsymbol y^s \rangle \f$.
25 * **Format**: Matrix in a Fortran-contiguous format
26 * Used if stoch_params::int_corr_mode is set to 'file'.
27 - 'corr2int.def': File holding the matrix \f$\boldsymbol\Sigma_2 = \int_0^\infty ds \, \left(\langle \boldsymbol y \otimes \boldsymbol y^s \rangle \otimes \langle \boldsymbol y \otimes \boldsymbol y^s \rangle\right) \f$.
28 * **Format**: Matrix in a sparse format, params::ndim sequences with
29 1. a first line with the first index \f$i\f$ of the matrix and then the number of entries the sub-matrix \f$\Sigma_{2,i,.,.,.}\f$ has
30 2. a list of the entries of the matrix in the format: \f[ i,j,k,l,v\f] where \f$v\f$ is the value of the entry
32 ------------------------------------------------------------------------
34 ## WL parameterization ##
36 The following definition files are needed by the parameterization, depending on the value of the parameters described above.
37 Examples of those files are joined to the code. The files include:
38 - 'mean.def' : Mean \f$\langle \boldsymbol y \rangle\f$ of the unresolved variables.
39 * **Format**: one line per \f$\langle y_i \rangle\f$ value
40 - 'correxpo.def': Coefficients \f$a_k\f$ of the fit of the elements of the correlations matrix \f$\langle \boldsymbol y \otimes \boldsymbol y^s \rangle\f$ with the function \f[ a_4+a_0 \, \exp\left(-\frac{s}{a_1}\right) \, \cos(a_2 \, s + a_3) \f] where \f$t\f$ is the lag-time and \f$\tau\f$ is the decorrelation time.
41 * **Format**: First line is two numbers: the number of unresolved variables and the value of stoch_params::maxint to be used (range of validity of the fit). \n
42 Then each line specify the fit of an element \f$i,j\f$ of the matrix \f$\langle \boldsymbol y \otimes \boldsymbol y^s \rangle\f$ as follow: \f[ i,j,a_0,a_1,a_2,a_3\f]
43 * Used if stoch_params::load_mode is set to 'expo'.
44 - 'corrspline.def': Coefficients \f$b_k\f$ of the spline used to model the elements of the correlation matrix \f$\langle \boldsymbol y \otimes \boldsymbol y^s \rangle\f$.
45 * **Format**: First line is two numbers: the number of unresolved variables and the number of points used. \n
46 Second line is the times \f$\tau_k\f$ of the points in timeunits. \n
47 Then \f$i\times j\f$ sequences of 3 lines occurs as follow:
49 2. Values of \f$\langle \boldsymbol y \otimes \boldsymbol y^s \rangle_{i,j}\f$ at \f$\tau_k\f$
50 3. Coefficients \f$b_k\f$ of the spline giving the second derivative of the interpolating function at \f$\tau\f$
51 * Used if stoch_params::load_mode is set to 'spli'.
52 - 'MAR_R_params.def': File specifying the \f$\boldsymbol R = \boldsymbol Q^2\f$ matrix for the MAR.
53 * **Format**: Matrix in a Fortran-contiguous format
54 - 'MAR_W_params.def': File specifying the \f$\boldsymbol W_i\f$ matrices for the MAR.
55 * **Format**: Matrix in a Fortran-contiguous format