diff --git a/fortran/doc/gen_doc.md b/fortran/doc/gen_doc.md index ea66ad7..cab0c29 100644 --- a/fortran/doc/gen_doc.md +++ b/fortran/doc/gen_doc.md @@ -1,8 +1,11 @@ -# Modular arbitrary-order ocean-atmosphere model: MAOOAM -- Fortran implementation # +# Modular arbitrary-order ocean-atmosphere model: MAOOAM -- Fortran implementation +## Lyapunov exponents computation version + +------------------------------------------------------------------------ ## About ## -(c) 2013-2016 Lesley De Cruz and Jonathan Demaeyer +(c) 2013-2016 Lesley De Cruz, Jonathan Demaeyer and Sebastian Schubert See [LICENSE.txt](../LICENSE.txt) for license information. @@ -27,6 +30,27 @@ A pdf version of this manual is available [here](../latex/Reference_manual.pdf). ------------------------------------------------------------------------ +## Note on the Lyapunov exponents computation + +This version of the code allows for the computation of the backward Lyapunov +exponents. The method used is described in + +* Benettin, G., Galgani, L., Giorgilli, A., and Strelcyn, J. M. : Lyapunov +characteristic exponents for smooth dynamical systems; a method for computing +all of them. Part 2: Numerical application. Meccanica, 15, 21-30, +[doi:10.1007/BF02128237](http://dx.doi.org/10.1007/BF02128237), 1980. + +This version has been used to compute the Lyapunov exponents of MAOOAM in the +following manuscript: + +* De Cruz, L., Schubert, S., Demaeyer, J., Lucarini, V., and Vannitsem, S.: +Exploring the Lyapunov instability properties of high-dimensional atmospheric +and climate models, Nonlin. Processes Geophys. Discuss., +[doi:10.5194/npg-2017-76](https://doi.org/10.5194/npg-2017-76), in +review, 2018. + +------------------------------------------------------------------------ + ## Installation ## The program can be installed with Makefile. We provide configuration files for @@ -77,7 +101,10 @@ includes all the coefficients. This tensor is computed once at the program initialization. * maooam.f90 : Main program. +* maooam_lyap.f90 : Version of the main program with the computation of the Lyapunov exponents. +* maooam_lyap_div.f90 : Version of the main program with the computation of the first Lyapunov exponents with the divergence method. * aotensor_def.f90 : Tensor aotensor computation module. +* lyap_vectors.f90 : Module for the computation of Lyapunov exponents and vectors * IC_def.f90 : A module which loads the user specified initial condition. * inprod_analytic.f90 : Inner products computation module. * rk2_integrator.f90 : A module which contains the Heun integrator for the model equations. @@ -105,6 +132,8 @@ initialization. The user first has to fill the params.nml and int_params.nml namelist files according to their needs. Indeed, model and integration parameters can be specified respectively in the params.nml and int_params.nml namelist files. Some examples related to already published article are available in the params folder. +The parameters related to the Lyapunov exponents computation are located in the int_params.nml namelist file. + The modeselection.nml namelist can then be filled : * NBOC and NBATM specify the number of blocks that will be used in respectively the ocean and the atmosphere. Each block corresponds to a given x and y wavenumber. @@ -125,7 +154,7 @@ By default a RK2 scheme is selected. Finally, the IC.nml file specifying the initial condition should be defined. To obtain an example of this configuration file corresponding to the model you have previously defined, simply delete the current IC.nml file (if it exists) -and run the program : +and run the main program : ./maooam @@ -142,6 +171,25 @@ The tangent linear and adjoint models of MAOOAM are provided in the tl_ad_tensor, rk2_tl_ad_integrator and rk4_tl_ad_integrator modules. It is documented [here](./md_doc_tl_ad_doc.html). +The computation of the Lyapunov exponents can be done by running the program : + + ./maooam_lyap + +It will generate four files: + * evol_field.dat : the recorded time evolution of the variables. + * mean_field.dat : the mean field (the climatology) + * lyapunov_exponents.dat : the recorded time evolution of the Lyapunov exponents + * mean_lyapunov.dat : the mean Lyapunov exponents as well as their variance. + +Alternatively, the first Lyapunov exponent can be computed by the divergence method, +by running : + + ./maooam_lyap_div + +It will generate three files : + * evol_field.dat : the recorded time evolution of the variables. + * mean_field.dat : the mean field (the climatology) + * lyapunov_exponents_div.dat : the recorded time evolution of the first Lyapunov exponent ------------------------------------------------------------------------ diff --git a/fortran/doc/html/LICENSE_8txt.html b/fortran/doc/html/LICENSE_8txt.html index 7a42488..f60d335 100644 --- a/fortran/doc/html/LICENSE_8txt.html +++ b/fortran/doc/html/LICENSE_8txt.html @@ -479,7 +479,7 @@

Variable Documentation

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doc/gen_doc.md
-Go to the documentation of this file.
1 # Modular arbitrary-order ocean-atmosphere model: MAOOAM -- Fortran implementation #
2 
3 ## About ##
4 
5 (c) 2013-2016 Lesley De Cruz and Jonathan Demaeyer
6 
7 See [LICENSE.txt](../LICENSE.txt) for license information.
8 
9 This software is provided as supplementary material with:
10 
11 * De Cruz, L., Demaeyer, J. and Vannitsem, S.: The Modular Arbitrary-Order
12 Ocean-Atmosphere Model: MAOOAM v1.0, Geosci. Model Dev., 9, 2793-2808,
13 [doi:10.5194/gmd-9-2793-2016](http://dx.doi.org/10.5194/gmd-9-2793-2016), 2016.
14 
15 **Please cite this article if you use (a part of) this software for a
16 publication.**
17 
18 The authors would appreciate it if you could also send a reprint of
19 your paper to <lesley.decruz@meteo.be>, <jonathan.demaeyer@meteo.be> and
20 <svn@meteo.be>.
21 
22 Consult the MAOOAM [code repository](http://www.github.com/Climdyn/MAOOAM)
23 for updates, and [our website](http://climdyn.meteo.be) for additional
24 resources.
25 
26 A pdf version of this manual is available [here](../latex/Reference_manual.pdf).
27 
28 ------------------------------------------------------------------------
29 
30 ## Installation ##
31 
32 The program can be installed with Makefile. We provide configuration files for
33 two compilers : gfortran and ifort.
34 
35 By default, gfortran is selected. To select one or the other, simply modify the
36 Makefile accordingly or pass the COMPILER flag to `make`. If gfortran is
37 selected, the code should be compiled with gfortran 4.7+ (allows for
38 allocatable arrays in namelists). If ifort is selected, the code has been
39 tested with the version 14.0.2 and we do not guarantee compatibility with older
40 compiler version.
41 
42 To install, unpack the archive in a folder or clone with git:
43 
44 ```bash
45 git clone https://github.com/Climdyn/MAOOAM.git
46 cd MAOOAM
47 ```
48 
49 and run:
50 
51 ```bash
52 make
53 ```
54 By default, the inner products of the basis functions, used to compute the
55 coefficients of the ODEs, are not stored in memory. If you want to enable the
56 storage in memory of these inner products, run make with the following flag:
57 
58 ```bash
59 make RES=store
60 ```
61 
62 Depending on the chosen resolution, storing the inner products may result in a
63 huge memory usage and is not recommended unless you need them for a specific
64 purpose.
65 
66  Remark: The command "make clean" removes the compiled files.
67 
68 For Windows users, a minimalistic GNU development environment
69  (including gfortran and make) is available at [www.mingw.org](http://www.mingw.org) .
70 
71 ------------------------------------------------------------------------
72 
73 ## Description of the files ##
74 
75 The model tendencies are represented through a tensor called aotensor which
76 includes all the coefficients. This tensor is computed once at the program
77 initialization.
78 
79 * maooam.f90 : Main program.
80 * aotensor_def.f90 : Tensor aotensor computation module.
81 * IC_def.f90 : A module which loads the user specified initial condition.
82 * inprod_analytic.f90 : Inner products computation module.
83 * rk2_integrator.f90 : A module which contains the Heun integrator for the model equations.
84 * rk4_integrator.f90 : A module which contains the RK4 integrator for the model equations.
85 * Makefile : The Makefile.
86 * params.f90 : The model parameters module.
87 * tl_ad_tensor.f90 : Tangent Linear (TL) and Adjoint (AD) model tensors definition module
88 * rk2_tl_ad_integrator.f90 : Heun Tangent Linear (TL) and Adjoint (AD) model integrators module
89 * rk4_tl_ad_integrator.f90 : RK4 Tangent Linear (TL) and Adjoint (AD) model integrators module
90 * test_tl_ad.f90 : Tests for the Tangent Linear (TL) and Adjoint (AD) model versions
91 * README.md : A read me file.
92 * LICENSE.txt : The license text of the program.
93 * util.f90 : A module with various useful functions.
94 * tensor.f90 : Tensor utility module.
95 * stat.f90 : A module for statistic accumulation.
96 * params.nml : A namelist to specify the model parameters.
97 * int_params.nml : A namelist to specify the integration parameters.
98 * modeselection.nml : A namelist to specify which spectral decomposition will be used.
99 
100 
101 ------------------------------------------------------------------------
102 
103 ## Usage ##
104 
105 The user first has to fill the params.nml and int_params.nml namelist files according to their needs.
106 Indeed, model and integration parameters can be specified respectively in the params.nml and int_params.nml namelist files. Some examples related to already published article are available in the params folder.
107 
108 The modeselection.nml namelist can then be filled :
109 * NBOC and NBATM specify the number of blocks that will be used in respectively the ocean and
110  the atmosphere. Each block corresponds to a given x and y wavenumber.
111 * The OMS and AMS arrays are integer arrays which specify which wavenumbers of
112  the spectral decomposition will be used in respectively the ocean and the
113  atmosphere. Their shapes are OMS(NBOC,2) and AMS(NBATM,2).
114 * The first dimension specifies the number attributed by the user to the block and the second
115  dimension specifies the x and the y wavenumbers.
116 * The VDDG model, described in Vannitsem et al. (2015) is given as an example
117  in the archive.
118 * Note that the variables of the model are numbered according to the chosen
119  order of the blocks.
120 
121 The Makefile allows to change the integrator being used for the time evolution.
122 The user should modify it according to its need.
123 By default a RK2 scheme is selected.
124 
125 Finally, the IC.nml file specifying the initial condition should be defined. To
126 obtain an example of this configuration file corresponding to the model you
127 have previously defined, simply delete the current IC.nml file (if it exists)
128 and run the program :
129 
130  ./maooam
131 
132 It will generate a new one and start with the 0 initial condition. If you want another
133 initial condition, stop the program, fill the newly generated file and restart :
134 
135  ./maooam
136 
137 It will generate two files :
138  * evol_field.dat : the recorded time evolution of the variables.
139  * mean_field.dat : the mean field (the climatology)
140 
141 The tangent linear and adjoint models of MAOOAM are provided in the
142 tl_ad_tensor, rk2_tl_ad_integrator and rk4_tl_ad_integrator modules. It is
143 documented [here](./md_doc_tl_ad_doc.html).
144 
145 
146 ------------------------------------------------------------------------
147 
148 ## Implementation notes ##
149 
150 As the system of differential equations is at most bilinear in \f$y_j\f$ (\f$j=1..n\f$),
151 \f$\boldsymbol{y}\f$ being the array of variables, it can be expressed as a tensor
152  contraction :
153 
154 \f[ \frac{d y_i}{dt} = \sum_{j,k=0}^{ndim} \, \mathcal{T}_{i,j,k} \, y_k \; y_j \f]
155 
156 with \f$y_0 = 1\f$.
157 
158 
159 The tensor aotensor_def::aotensor is the tensor \f$\mathcal{T}\f$ that encodes the differential equations is composed so that:
160 
161 * \f$\mathcal{T}_{i,j,k}\f$ contains the contribution of \f$dy_i/dt\f$ proportional to \f$ y_j \, y_k\f$.
162 * Furthermore, \f$y_0\f$ is always equal to 1, so that \f$\mathcal{T}_{i,0,0}\f$ is the constant
163 contribution to \f$dy_i/dt\f$
164 * \f$\mathcal{T}_{i,j,0} + \mathcal{T}_{i,0,j}\f$ is the contribution to \f$dy_i/dt\f$ which is linear in
165 \f$y_j\f$.
166 
167 Ideally, the tensor aotensor_def::aotensor is composed as an upper triangular matrix
168 (in the last two coordinates).
169 
170 The tensor for this model is composed in the aotensor_def module and uses the
171 inner products defined in the inprod_analytic module.
172 
173 
174 ------------------------------------------------------------------------
175 
176 ## Final Remarks ##
177 
178 The authors would like to thank Kris for help with the lua2fortran project. It
179 has greatly reduced the amount of (error-prone) work.
180 
181  No animals were harmed during the coding process.
+Go to the documentation of this file.
1 # Modular arbitrary-order ocean-atmosphere model: MAOOAM -- Fortran implementation
2 ## Lyapunov exponents computation version
3 
4 ------------------------------------------------------------------------
5 
6 ## About ##
7 
8 (c) 2013-2016 Lesley De Cruz, Jonathan Demaeyer and Sebastian Schubert
9 
10 See [LICENSE.txt](../LICENSE.txt) for license information.
11 
12 This software is provided as supplementary material with:
13 
14 * De Cruz, L., Demaeyer, J. and Vannitsem, S.: The Modular Arbitrary-Order
15 Ocean-Atmosphere Model: MAOOAM v1.0, Geosci. Model Dev., 9, 2793-2808,
16 [doi:10.5194/gmd-9-2793-2016](http://dx.doi.org/10.5194/gmd-9-2793-2016), 2016.
17 
18 **Please cite this article if you use (a part of) this software for a
19 publication.**
20 
21 The authors would appreciate it if you could also send a reprint of
22 your paper to <lesley.decruz@meteo.be>, <jonathan.demaeyer@meteo.be> and
23 <svn@meteo.be>.
24 
25 Consult the MAOOAM [code repository](http://www.github.com/Climdyn/MAOOAM)
26 for updates, and [our website](http://climdyn.meteo.be) for additional
27 resources.
28 
29 A pdf version of this manual is available [here](../latex/Reference_manual.pdf).
30 
31 ------------------------------------------------------------------------
32 
33 ## Note on the Lyapunov exponents computation
34 
35 This version of the code allows for the computation of the backward Lyapunov
36 exponents. The method used is described in
37 
38 * Benettin, G., Galgani, L., Giorgilli, A., and Strelcyn, J. M. : Lyapunov
39 characteristic exponents for smooth dynamical systems; a method for computing
40 all of them. Part 2: Numerical application. Meccanica, 15, 21-30,
41 [doi:10.1007/BF02128237](http://dx.doi.org/10.1007/BF02128237), 1980.
42 
43 This version has been used to compute the Lyapunov exponents of MAOOAM in the
44 following manuscript:
45 
46 * De Cruz, L., Schubert, S., Demaeyer, J., Lucarini, V., and Vannitsem, S.:
47 Exploring the Lyapunov instability properties of high-dimensional atmospheric
48 and climate models, Nonlin. Processes Geophys. Discuss.,
49 [doi:10.5194/npg-2017-76](https://doi.org/10.5194/npg-2017-76), in
50 review, 2018.
51 
52 ------------------------------------------------------------------------
53 
54 ## Installation ##
55 
56 The program can be installed with Makefile. We provide configuration files for
57 two compilers : gfortran and ifort.
58 
59 By default, gfortran is selected. To select one or the other, simply modify the
60 Makefile accordingly or pass the COMPILER flag to `make`. If gfortran is
61 selected, the code should be compiled with gfortran 4.7+ (allows for
62 allocatable arrays in namelists). If ifort is selected, the code has been
63 tested with the version 14.0.2 and we do not guarantee compatibility with older
64 compiler version.
65 
66 To install, unpack the archive in a folder or clone with git:
67 
68 ```bash
69 git clone https://github.com/Climdyn/MAOOAM.git
70 cd MAOOAM
71 ```
72 
73 and run:
74 
75 ```bash
76 make
77 ```
78 By default, the inner products of the basis functions, used to compute the
79 coefficients of the ODEs, are not stored in memory. If you want to enable the
80 storage in memory of these inner products, run make with the following flag:
81 
82 ```bash
83 make RES=store
84 ```
85 
86 Depending on the chosen resolution, storing the inner products may result in a
87 huge memory usage and is not recommended unless you need them for a specific
88 purpose.
89 
90  Remark: The command "make clean" removes the compiled files.
91 
92 For Windows users, a minimalistic GNU development environment
93  (including gfortran and make) is available at [www.mingw.org](http://www.mingw.org) .
94 
95 ------------------------------------------------------------------------
96 
97 ## Description of the files ##
98 
99 The model tendencies are represented through a tensor called aotensor which
100 includes all the coefficients. This tensor is computed once at the program
101 initialization.
102 
103 * maooam.f90 : Main program.
104 * maooam_lyap.f90 : Version of the main program with the computation of the Lyapunov exponents.
105 * maooam_lyap_div.f90 : Version of the main program with the computation of the first Lyapunov exponents with the divergence method.
106 * aotensor_def.f90 : Tensor aotensor computation module.
107 * lyap_vectors.f90 : Module for the computation of Lyapunov exponents and vectors
108 * IC_def.f90 : A module which loads the user specified initial condition.
109 * inprod_analytic.f90 : Inner products computation module.
110 * rk2_integrator.f90 : A module which contains the Heun integrator for the model equations.
111 * rk4_integrator.f90 : A module which contains the RK4 integrator for the model equations.
112 * Makefile : The Makefile.
113 * params.f90 : The model parameters module.
114 * tl_ad_tensor.f90 : Tangent Linear (TL) and Adjoint (AD) model tensors definition module
115 * rk2_tl_ad_integrator.f90 : Heun Tangent Linear (TL) and Adjoint (AD) model integrators module
116 * rk4_tl_ad_integrator.f90 : RK4 Tangent Linear (TL) and Adjoint (AD) model integrators module
117 * test_tl_ad.f90 : Tests for the Tangent Linear (TL) and Adjoint (AD) model versions
118 * README.md : A read me file.
119 * LICENSE.txt : The license text of the program.
120 * util.f90 : A module with various useful functions.
121 * tensor.f90 : Tensor utility module.
122 * stat.f90 : A module for statistic accumulation.
123 * params.nml : A namelist to specify the model parameters.
124 * int_params.nml : A namelist to specify the integration parameters.
125 * modeselection.nml : A namelist to specify which spectral decomposition will be used.
126 
127 
128 ------------------------------------------------------------------------
129 
130 ## Usage ##
131 
132 The user first has to fill the params.nml and int_params.nml namelist files according to their needs.
133 Indeed, model and integration parameters can be specified respectively in the params.nml and int_params.nml namelist files. Some examples related to already published article are available in the params folder.
134 
135 The parameters related to the Lyapunov exponents computation are located in the int_params.nml namelist file.
136 
137 The modeselection.nml namelist can then be filled :
138 * NBOC and NBATM specify the number of blocks that will be used in respectively the ocean and
139  the atmosphere. Each block corresponds to a given x and y wavenumber.
140 * The OMS and AMS arrays are integer arrays which specify which wavenumbers of
141  the spectral decomposition will be used in respectively the ocean and the
142  atmosphere. Their shapes are OMS(NBOC,2) and AMS(NBATM,2).
143 * The first dimension specifies the number attributed by the user to the block and the second
144  dimension specifies the x and the y wavenumbers.
145 * The VDDG model, described in Vannitsem et al. (2015) is given as an example
146  in the archive.
147 * Note that the variables of the model are numbered according to the chosen
148  order of the blocks.
149 
150 The Makefile allows to change the integrator being used for the time evolution.
151 The user should modify it according to its need.
152 By default a RK2 scheme is selected.
153 
154 Finally, the IC.nml file specifying the initial condition should be defined. To
155 obtain an example of this configuration file corresponding to the model you
156 have previously defined, simply delete the current IC.nml file (if it exists)
157 and run the main program :
158 
159  ./maooam
160 
161 It will generate a new one and start with the 0 initial condition. If you want another
162 initial condition, stop the program, fill the newly generated file and restart :
163 
164  ./maooam
165 
166 It will generate two files :
167  * evol_field.dat : the recorded time evolution of the variables.
168  * mean_field.dat : the mean field (the climatology)
169 
170 The tangent linear and adjoint models of MAOOAM are provided in the
171 tl_ad_tensor, rk2_tl_ad_integrator and rk4_tl_ad_integrator modules. It is
172 documented [here](./md_doc_tl_ad_doc.html).
173 
174 The computation of the Lyapunov exponents can be done by running the program :
175 
176  ./maooam_lyap
177 
178 It will generate four files:
179  * evol_field.dat : the recorded time evolution of the variables.
180  * mean_field.dat : the mean field (the climatology)
181  * lyapunov_exponents.dat : the recorded time evolution of the Lyapunov exponents
182  * mean_lyapunov.dat : the mean Lyapunov exponents as well as their variance.
183 
184 Alternatively, the first Lyapunov exponent can be computed by the divergence method,
185 by running :
186 
187  ./maooam_lyap_div
188 
189 It will generate three files :
190  * evol_field.dat : the recorded time evolution of the variables.
191  * mean_field.dat : the mean field (the climatology)
192  * lyapunov_exponents_div.dat : the recorded time evolution of the first Lyapunov exponent
193 
194 ------------------------------------------------------------------------
195 
196 ## Implementation notes ##
197 
198 As the system of differential equations is at most bilinear in \f$y_j\f$ (\f$j=1..n\f$),
199 \f$\boldsymbol{y}\f$ being the array of variables, it can be expressed as a tensor
200  contraction :
201 
202 \f[ \frac{d y_i}{dt} = \sum_{j,k=0}^{ndim} \, \mathcal{T}_{i,j,k} \, y_k \; y_j \f]
203 
204 with \f$y_0 = 1\f$.
205 
206 
207 The tensor aotensor_def::aotensor is the tensor \f$\mathcal{T}\f$ that encodes the differential equations is composed so that:
208 
209 * \f$\mathcal{T}_{i,j,k}\f$ contains the contribution of \f$dy_i/dt\f$ proportional to \f$ y_j \, y_k\f$.
210 * Furthermore, \f$y_0\f$ is always equal to 1, so that \f$\mathcal{T}_{i,0,0}\f$ is the constant
211 contribution to \f$dy_i/dt\f$
212 * \f$\mathcal{T}_{i,j,0} + \mathcal{T}_{i,0,j}\f$ is the contribution to \f$dy_i/dt\f$ which is linear in
213 \f$y_j\f$.
214 
215 Ideally, the tensor aotensor_def::aotensor is composed as an upper triangular matrix
216 (in the last two coordinates).
217 
218 The tensor for this model is composed in the aotensor_def module and uses the
219 inner products defined in the inprod_analytic module.
220 
221 
222 ------------------------------------------------------------------------
223 
224 ## Final Remarks ##
225 
226 The authors would like to thank Kris for help with the lua2fortran project. It
227 has greatly reduced the amount of (error-prone) work.
228 
229  No animals were harmed during the coding process.
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