Changeset 11340


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Timestamp:
2019-07-24T18:35:12+02:00 (10 months ago)
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clevy
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#2216: updates to STO reference manual

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  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_STO.tex

    r11123 r11340  
    88\label{chap:STO} 
    99 
    10 Authors: P.-A. Bouttier 
     10\minitoc 
    1111 
    12 \minitoc 
     12% \vfill 
     13% \begin{figure}[b] 
     14% \subsubsection*{Changes record} 
     15% \begin{tabular}{l||l|m{0.65\linewidth}} 
     16%    Release   & Author        & Modifications \\ 
     17%    {\em 4.0.1} & {\em C. Levy} & {\em 4.0.1 update}  \\ 
     18%    {\em 3.6} & {\em P.-A. Bouttier} & {\em initial version}  \\ 
     19% \end{tabular} 
     20% \end{figure} 
     21 
     22Authors: \\ 
     23C. Levy release 4.0.1 update \\ 
     24P.-A. Bouttier release 3.6 inital version 
    1325 
    1426\newpage 
    1527 
    16 The stochastic parametrization module aims to explicitly simulate uncertainties in the model. 
    17 More particularly, \cite{brankart_OM13} has shown that, 
    18 because of the nonlinearity of the seawater equation of state, unresolved scales represent a major source of 
    19 uncertainties in the computation of the large scale horizontal density gradient (from T/S large scale fields), 
    20 and that the impact of these uncertainties can be simulated by 
    21 random processes representing unresolved T/S fluctuations. 
     28As a result 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 the large-scale temperature and salinity fields. Following  \cite{brankart_OM13}, the impact of these uncertainties can be simulated by random processes representing unresolved T/S fluctuations. The Stochastic Parametrization of EOS (STO) module implements this parametrization. 
    2229 
    23 The stochastic formulation of the equation of state can be written as: 
     30As detailed in \cite{brankart_OM13}, the stochastic formulation of the equation of state can be written as: 
    2431\begin{equation} 
    2532  \label{eq:eos_sto} 
     
    2734\end{equation} 
    2835where $p_o(z)$ is the reference pressure depending on the depth and, 
    29 $\Delta T_i$ and $\Delta S_i$ are a set of T/S perturbations defined as 
     36$\Delta T_i$ and $\Delta S_i$ (i=1,m) is a set of T/S perturbations defined as 
    3037the scalar product of the respective local T/S gradients with random walks $\mathbf{\xi}$: 
    3138\begin{equation} 
     
    3340  \Delta T_i = \mathbf{\xi}_i \cdot \nabla T \qquad \hbox{and} \qquad \Delta S_i = \mathbf{\xi}_i \cdot \nabla S 
    3441\end{equation} 
    35 $\mathbf{\xi}_i$ are produced by a first-order autoregressive processes (AR-1) with 
     42$\mathbf{\xi}_i$ are produced by a first-order autoregressive process (AR-1) with 
    3643a parametrized decorrelation time scale, and horizontal and vertical standard deviations $\sigma_s$. 
    3744$\mathbf{\xi}$ are uncorrelated over the horizontal and fully correlated along the vertical. 
     
    4148\label{sec:STO_the_details} 
    4249 
    43 The starting point of our implementation of stochastic parameterizations in NEMO is to observe that 
    44 many existing parameterizations are based on autoregressive processes, 
     50There are many existing parameterizations based on autoregressive processes, 
    4551which are used as a basic source of randomness to transform a deterministic model into a probabilistic model. 
    46 A generic approach is thus to add one single new module in NEMO, 
    47 generating processes with appropriate statistics to simulate each kind of uncertainty in the model 
     52The generic approach here is to a new STO module, 
     53generating processes features with appropriate statistics to simulate these uncertainties in the model 
    4854(see \cite{brankart.candille.ea_GMD15} for more details). 
    4955 
    50 In practice, at every model grid point, 
     56In practice, at each model grid point, 
    5157independent Gaussian autoregressive processes~$\xi^{(i)},\,i=1,\ldots,m$ are first generated using 
    5258the same basic equation: 
     
    101107\noindent 
    102108In this way, higher order processes can be easily generated recursively using the same piece of code implementing 
    103 (\autoref{eq:autoreg}), and using succesively processes from order $0$ to~$n-1$ as~$w^{(i)}$. 
    104 The parameters in (\autoref{eq:ord2}) are computed so that this recursive application of 
    105 (\autoref{eq:autoreg}) leads to processes with the required standard deviation and correlation timescale, 
     109\autoref{eq:autoreg}, and using successive processes from order $0$ to~$n-1$ as~$w^{(i)}$. 
     110The parameters in \autoref{eq:ord2} are computed so that this recursive application of 
     111\autoref{eq:autoreg} leads to processes with the required standard deviation and correlation timescale, 
    106112with the additional condition that the $n-1$ first derivatives of the autocorrelation function are equal to 
    107 zero at~$t=0$, so that the resulting processes become smoother and smoother as $n$ is increased. 
     113zero at~$t=0$, so that the resulting processes become smoother and smoother as $n$ increases. 
    108114 
    109115Overall, this method provides quite a simple and generic way of generating a wide class of stochastic processes. 
    110116However, this also means that new model parameters are needed to specify each of these stochastic processes. 
    111 As in any parameterization of lacking physics, a very important issues then to tune these new parameters using 
     117As in any parameterization, the main issue is to tune the parameters using 
    112118either first principles, model simulations, or real-world observations. 
     119The parameters are set by default as described in \cite{brankart_OM13}, which has been shown in the paper 
     120to give good results for a global low resolution (2°) NEMO configuration. where this parametrization produces a major effect on the average large-scale circulation, especilally in regions of intense mesoscale activity. 
     121The set of parameters will need further investigation to find appropriate values 
     122for any other configuration or resolution of the model. 
    113123 
    114124\section{Implementation details} 
    115125\label{sec:STO_thech_details} 
    116126 
    117 %---------------------------------------namsbc-------------------------------------------------- 
    118127 
    119 \nlst{namsto} 
    120 %-------------------------------------------------------------------------------------------------------------- 
     128The code implementing stochastic parametrisation is located in the src/OCE/STO directory. 
     129It contains three modules :  
     130% \begin{description} 
    121131 
    122 The computer code implementing stochastic parametrisations can be found in the STO directory. 
    123 It involves three modules :  
    124 \begin{description} 
    125 \item[\mdl{stopar}:] 
    126   define the Stochastic parameters and their time evolution. 
    127 \item[\mdl{storng}:] 
    128   a random number generator based on (and includes) the 64-bit KISS (Keep It Simple Stupid) random number generator 
    129   distributed by George Marsaglia 
    130   (see \href{https://groups.google.com/forum/#!searchin/comp.lang.fortran/64-bit$20KISS$20RNGs}{here}) 
    131 \item[\mdl{stopts}:] 
    132   stochastic parametrisation associated with the non-linearity of the equation of seawater, 
    133   implementing \autoref{eq:sto_pert} and specific piece of code in 
    134   the equation of state implementing \autoref{eq:eos_sto}. 
    135 \end{description} 
     132\mdl{stopar} : define the Stochastic parameters and their time evolution 
    136133 
    137 The \mdl{stopar} module has 3 public routines to be called by the model (in our case, NEMO): 
     134\mdl{storng} : random number generator based on and including the 64-bit KISS (Keep It Simple Stupid) random number generator distributed by George Marsaglia 
    138135 
    139 The first routine (\rou{sto\_par}) is a direct implementation of (\autoref{eq:autoreg}), 
     136\mdl{stopts} : stochastic parametrisation associated with the non-linearity of the equation of 
     137 seawater, implementing \autoref{eq:sto_pert} so as specifics in the equation of state 
     138 implementing \autoref{eq:eos_sto}. 
     139% \end{description} 
     140 
     141The \mdl{stopar} module includes three public routines called in the model: 
     142 
     143(\rou{sto\_par}) is a direct implementation of \autoref{eq:autoreg}, 
    140144applied at each model grid point (in 2D or 3D), and called at each model time step ($k$) to 
    141145update every autoregressive process ($i=1,\ldots,m$). 
     
    143147to introduce a spatial correlation between the stochastic processes. 
    144148 
    145 The second routine (\rou{sto\_par\_init}) is an initialization routine mainly dedicated to 
    146 the computation of parameters $a^{(i)}, b^{(i)}, c^{(i)}$ for each autoregressive process, 
     149(\rou{sto\_par\_init}) is the initialization routine computing 
     150the values $a^{(i)}, b^{(i)}, c^{(i)}$ for each autoregressive process, 
    147151as a function of the statistical properties required by the model user 
    148152(mean, standard deviation, time correlation, order of the process,\ldots).  
     153This routine also includes the initialization (seeding) of the random number generator. 
    149154 
    150 Parameters for the processes can be specified through the following \ngn{namsto} namelist parameters: 
     155(\rou{sto\_rst\_write}) writes a restart file 
     156(which suffix name is given by \np{cn\_storst\_out} namelist parameter) containing the current value of 
     157all autoregressive processes to allow creating the file needed for a restart. 
     158This restart file also contains the current state of the random number generator. 
     159When \np{ln\_rststo} is set to \forcode{.true.}), 
     160the restart file (which suffix name is given by \np{cn\_storst\_in} namelist parameter) is read by 
     161the initialization routine (\rou{sto\_par\_init}). 
     162The simulation will continue exactly as if it was not interrupted only 
     163when \np{ln\_rstseed} is set to \forcode{.true.}, 
     164\ie when the state of the random number generator is read in the restart file.\\ 
     165 
     166 
     167Options and parameters \\ 
     168 
     169The \np{ln\_sto\_eos} namelist variable activates stochastic parametrisation. By default it set to \forcode{.false.}) and not active. 
     170The set of parameters is available in \ngn{namsto} namelist: 
     171%---------------------------------------namsto-------------------------------------------------- 
     172 
     173\nlst{namsto} 
     174%-------------------------------------------------------------------------------------------------------------- 
     175 
     176The variables of stochastic paramtetrisation itself (based on the global 2° experiments as in \cite{brankart_OM13} are: 
    151177\begin{description} 
    152178\item[\np{nn\_sto\_eos}:]   number of independent random walks 
    153 \item[\np{rn\_eos\_stdxy}:] random walk horz. standard deviation (in grid points) 
    154 \item[\np{rn\_eos\_stdz}:]  random walk vert. standard deviation (in grid points) 
     179\item[\np{rn\_eos\_stdxy}:] random walk horizontal standard deviation (in grid points) 
     180\item[\np{rn\_eos\_stdz}:]  random walk vertical standard deviation (in grid points) 
    155181\item[\np{rn\_eos\_tcor}:]  random walk time correlation (in timesteps) 
    156182\item[\np{nn\_eos\_ord}:]   order of autoregressive processes 
     
    158184\item[\np{rn\_eos\_lim}:]   limitation factor (default = 3.0) 
    159185\end{description} 
    160 This routine also includes the initialization (seeding) of the random number generator. 
    161186 
    162 The third routine (\rou{sto\_rst\_write}) writes a restart file 
    163 (which suffix name is given by \np{cn\_storst\_out} namelist parameter) containing the current value of 
    164 all autoregressive processes to allow restarting a simulation from where it has been interrupted. 
    165 This file also contains the current state of the random number generator. 
    166 When \np{ln\_rststo} is set to \forcode{.true.}), 
    167 the restart file (which suffix name is given by \np{cn\_storst\_in} namelist parameter) is read by 
    168 the initialization routine (\rou{sto\_par\_init}). 
    169 The simulation will continue exactly as if it was not interrupted only 
    170 when \np{ln\_rstseed} is set to \forcode{.true.}, 
    171 \ie when the state of the random number generator is read in the restart file. 
    172  
     187The first four parameters define the stochastic part of equation of state. 
    173188\biblio 
    174189 
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