=========================== ============================ IMCCE - Observatoire de Paris /pub/ephem/sun/la93 1996, January 17 =========================== ============================ La93.v0.83 : ========== VI/63 Earth Orbit, Precession and Insolation -20Myr to +10Myr (Laskar+ 1993) ================================================================================ Orbital, precessional, and insolation quantities for the Earth from -20 Myr to +10Myr LASKAR J., JOUTEL F., BOUDIN F. =1993A&A...270..522L (SIMBAD/NED Reference) ================================================================================ Keywords: celestial mechanics: insolation, precession - Earth - solar system: numerical methods, resonances ******************************************************************************** * * * NOTICE: * * * * This software can be freely copied and distributed provided that: * * * All the included files are kept together. * * * This notice is included in the distribution * * * no changes or alterations are made on the distributed files * * * * Any changes can be performed on the FORTRAN files, for specific use, * * but these changes cannot be included in the distribution files, and * * reference to the original programs should be included. * * * * WARNING: * * This software is not designed to be used in any possible conditions, * * and is not presently in a definite version. * * * * In particular, the user must take care that the starting and ending * * times for which he computes data are contained in the necessary files. * * The stepsize should also be the same. * * * * THE OBJECT OF THIS WORK IS TO PROVIDE A USEFUL TOOL FOR THE PALEOCLIMATE * * COMMUNITY. ANY COMMENTS OR WISH FOR IMPROVEMENTS ARE WELCOME. * * * * Authors: J. Laskar, F. Joutel and some other contributions * * (c) Astronomie et Systemes Dynamiques, Bureau des Longitudes, Paris (1993) * * * * Jacques Laskar * * Astronomie et Systemes Dynamiques, * * Bureau des Longitudes * * 77 av. Denfert-Rochereau * * 75014 Paris * * email: laskar@imcce.fr * * * ******************************************************************************** CONTAINS: ========= File Summary: (the second part lists files which can be generated in the nominal solution) -------------------------------------------------------------------------------- FileName Lrecl Records Explanations -------------------------------------------------------------------------------- Intro 80 . This file Makefile 80 98 to compile and generate derived files ORBELN.ASC 107 20101 Normal orbital solution La93(0,1), before present years (-20Myr to 0) ORBELP.ASC 107 10101 Normal orbital solution La93(0,1) after present years (0 to +10Myr) climavar.f 75 86 FORTRAN program for computation of usual climatic variables climavar.par 28 11 parameter file for climavar insola.f 79 253 FORTRAN program for computations of various insolation quantities insola.par 24 8 parameter file for insola insolsub.f 79 433 subroutines for insola.f integ.f 75 300 FORTRAN program for integration step integ.par 26 13 parameter file for integ integsub.f 82 882 FORTRAN subroutine for integ.f prepa.f 80 709 FORTRAN program for preparation step prepa.par 26 9 parameter file for prepa prepinsol.f 75 168 FORTRAN program for preparation step for insol prepinsol.par 26 10 parameter file for prepinsol CLIVAR0N.ASC 71 20001 Usual climatic variables in Nominal solution La93(0,1) before present years (-20Myr to 0) CLIVAR0P.ASC 71 10001 Usual climatic variables in Nominal solution La93(0,1) after present years (0 to +10Myr) PREC0N.ASC 59 20051 Nominal solution La93(0,1) before present years (-20Myr to 0) PREC0P.ASC 59 10051 Nominal solution La93(0,1) after present years (0 to +10Myr) -------------------------------------------------------------------------------- Byte-per-byte Description of file: ORBELN.ASC Byte-per-byte Description of file: ORBELP.ASC -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 4- 11 F8.0 1000yr t Time from J2000 in 1000 years 13- 35 D23.16 --- k = e * cos (longitude of perihelion) (e: eccentricity) 37- 59 D23.16 --- h = e * sin (longitude of perihelion) 61- 83 D23.16 --- q = q = sin(i/2) cos (longitude of node) (i: inclination from J2000 ecliptic) 85-107 D23.16 --- p = sin(i/2) sin (longitude of node) -------------------------------------------------------------------------------- Byte-per-byte Description of file: PREC0N.ASC Byte-per-byte Description of file: PREC0P.ASC -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 4- 11 F8.0 1000yr t Time from J2000 in 1000 years 13- 35 D23.16 rad eps obliquity (radians) 37- 59 D23.16 rad phi general precession in longitude (radians) -------------------------------------------------------------------------------- Byte-per-byte Description of file: CLIVAR0N.ASC Byte-per-byte Description of file: CLIVAR0P.ASC -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 4- 11 F8.0 1000yr t Time from J2000 in 1000 years 13- 31 D19.12 --- e Eccentricity 33- 51 D19.12 rad eps obliquity (radians) 53- 71 D19.12 --- CP e * sin(longitude of perihelion from moving equinox) -------------------------------------------------------------------------------- Description: La93 is a program for computing the precession and obliquity of the Earth for various values of 1) the tidal effect of the Moon (CMAR) 2) the dynamical ellipticity of the Earth (FGAM) The nominal solution La90 corresponds to (CMAR = 0., FGAM = 1). The general solution will be called La93(CMAR,FGAM), thus La90 = La93(0.,1.) and La93(1.,1.) is obtained with the same tidal effect as in Quinn, Tremaine, Duncan (1991), although these solutions are not completely identical (see Laskar, Joutel, Boudin, 1993) The files and software of this package can be used in three different manners: 1) Contruction and Use of the nominal solution La93(0,1) The ASCII files ORBEL*.ASC contain the nominal orbital solution. The ASCII files PREC0*.ASC contain the nominal precession solution. The ASCII files CLIVAR0*.ASC contain the nominal climatic solution. The files PREC*.ASC and CLIVAR*.ASC can also be generated from the enclosed files (see section 2) For the computation of insolation quantities, the user will execute the 'prepinsol' step, and then 'insola'. 2) Construction of a parametrized La93(CMAR, FGAM) new solution The user reconstructs a complete La93(CMAR, FGAM) solution. The compilation of all required programs is obtained by running the command 'make' on a Unix machine. The preparation step 'prepa' needs to be done once, in order to prepare the necessary binary files. Then 'integ' will construct the new solutions for the given parameters (CMAR, FGAM). Alternatively, change in the Makefile the values of CMAR and FGAM before running the 'make clean' command (removes the files computed using the preceding values of CMAR and FGAM), and 'make La93'. 3) Changes in the model of precession, for example to take into account some feedback resulting from redistribution of the ice on the Earth resulting from climate changes. In this case, and in this case only, the user needs to edit the FORTRAN file integ.f More precisely, the subroutines which can be eventually modified are SUBROUTINE INIPRE(IPT) SUBROUTINE PRECES(t,AK,AH,AQ,AP,DK,DH,DQ,DP,AKI,DKI) The users may also want to adapt the driver INTEG to his specific needs BIBLIOGRAPHY: ============ La90: Laskar, J.: 1990, The chaotic motion of the solar system. A numerical estimate of the chaotic zones Icarus, 88, 266 La93: Laskar, J., Joutel, F., Boudin, F.: 1993, Orbital, precessional and insolation quantities for the Earth from -20 Myr to + 10Myr Astron. Astrophys. 270, 522 ================================================================================ Detailed Description of the Program ----------------------------------- The program consists of several steps prepa : preparation step. This step generates the necessary binary files from the ASCII files containing the elliptical elements of the Earth every 1000 yr, from -20Myr to +10 Myr from the solution La90. THE USER should edit the file of command prepa.par run prepa two new files : nomfich and nomficder will be created containing the necessary data for the remaining steps for the time span from datedebut to datefin. (a user can choose to work only from -10Myr to 0) integ : integration step. This step is the integration of the equations of precession for various values of the tidal effect, and of the dynamical ellipticity of the Earth. THE USER should edit the file of command integ.par run integ THE USER will be prompted for the values of CMAR and FGAM during the execution of the program climavar : computation of the usual climatic variables prepinsol : preparation of the insolation computations insola : interactive insolation computations ******************************************************************** * NOTE: in prepa.par, integ.par, and prepinsol.par, * * the starting date 'datedebut' and final date 'datefin' * * need to be compatible, otherwise unexpected behaviour will occur.* * In the distributed files, these are set * to -20 Myr and 10 Myr, * * in order to obtain the examples ASCII files of the * * nominal solution. But the user can reduce this to a much shorter * * interval in order to gain computing time and disk space. * ******************************************************************** -------------------------------------------------------------------------------- PREPA This step uses the parameter file prepa.par with the following meaning: nomascpos: ASCII file for positive time (IN) nomascneg: ASCII file for negative time (IN) nomfich : Binary file for elliptical elements (OUT) nomficder: Binary file for derivatives (OUT) datedebut: starting time (Myr) datefin : ending time (Myr) ( -20 <= datedebut < datefin <= +10 ) statut : 'new' or 'unknown' status of the created files Example of prepa.par: -------------------------- &NAMSTD nomfich = 'ELL.BIN', nomfichder = 'DER.BIN', nomascpos = 'ORBELP.ASC', nomascneg = 'ORBELN.ASC', datedebut=-20.D0, datefin=10.D0, statut='unknown' &END -------------------------- The user may restrict himself to e.g. -2Myr to 0 by putting instead datedebut=-2.D0 datefin=0.D0 The output of the 'prepa' command gives the following ouput: ------------------------------------------------------------------------- Solution La90-La93 for the Earth La93.prepa version 0.8 preparation step (c) ASD/BdL (1993) ASCII file for positive time : ORBELP.ASC ASCII file for negative time : ORBELN.ASC Binary file for elliptical elements : ELL.BIN Binary file for derivatives of ell. el : DER.BIN starting time (Myr) : -20.00000000000000 ending time (Myr) : 0.0000000000000000E+00 The file ELL.BIN is created. The file DER.BIN is created. The preparation step is completed normally ------------------------------------------------------------------------- (Duration: about 15 minutes are necessary on a Sparc2 station) -------------------------------------------------------------------------------- INTEG This step uses the parameter file integ.par with the following meaning: nomfich : binary file for the elements t,k,h,q,p this file is computed in the preparation phase prepa. (IN) nomfichder : binary file for the derivatives of the elliptical elements. This file is computed in the preparation phase prepa. (IN) pas : integration step (in years). The default, and advised value is 200 nechant : sampling step. The results are written in the files every nechant*pas years. default nechant = 5 the files gives positions every 5*200 = 1000 years datefin : ending time (Myr) (>=0) datedebut : starting time (Myr) (<=0) ecritpos : 'oui' for output in an ASCII file for positive times 'non' screen output ecritneg : 'oui' for output in an ASCII file for negative times 'non' screen output statut : status of the created files ( 'new' or 'unknown' ) fichrespos : name of ASCII file for positif times t,eps,phi (OUT) t : time (unit = 1000yr) eps : obliquity (radians) phi : general precession in longitude (radians) fichresneg : name of ASCII file for negative times t,eps,phi (OUT) t : time (unit = 1000yr) eps : obliquity (radians) phi : general precession in longitude (radians) Example of integ.par -------------------------- &NAMSTD nomfich = 'ELL.BIN', nomfichder = 'DER.BIN', pas = 200, nechant=5, datefin= 10.D0, datedebut= -20.D0, statut= 'unknown', ecritpos = 'oui', ecritneg = 'oui', fichrespos = 'PRECP.ASC', fichresneg = 'PRECN.ASC' &END -------------------------- The dialog of the 'integ' command gives the following ouput: ------------------------------------------------------------------------- La93.integ version 0.8 integration step (c) ASD/BdL (1993) stepsize (yrs) default : 200 : 200.0000000000000 print every 5 step starting time (Myr) : -5.000000000000000 ending time (Myr) : 0.0000000000000000E+00 save results for positive time :oui save results for negative time :oui ASCII file for positive time : PRECP.ASC ASCII file for negative time : PRECN.ASC status of created files :unknown Relative change of dynamical ellipticity ENTER gamma/gamma_0 (default 1) 1 <<<<<<----------------------------------- the user need to answer FGAM = 1.000000000000000 Relative tidal effect 0 : no tidal effect 1 : -4.6 D-18 seconds**-1 ENTER cmar (default 0) 0 <<<<<<----------------------------------- the user need to answer CMAR = 0.0000000000000000E+00 Informations for internal check VITESSE ANGULAIRE DE LA TERRE 474659981.5971373 PRECESSION EN ASCENSION DROITE 5038.783333037391 ELD 3.2800511416867092E-03 RFL0 34.42998531044029 RFL1 -2.6896187697037889E-03 RFL3 3.3459472599329403E-04 RFS 15.97940304351487 RFL0+RFL1+RFL3+RFS 50.40703332991146 CP1,CP2,CP3,CP4 EN SECONDES PAR AN 37.52660322621580 -1.5651731683509029E-03 8.2602928316139284E-05 34.81861759592061 AK1 0.0000000000000000E+00 AK2 0.0000000000000000E+00 ------------------------------------------------------------------------- (Duration: about 15 minutes are necessary on a Sparc2 station) ************************************************************ * REMARK: when one ask for negative and positive time, * * the user is prompted twice for the preceding questions * ************************************************************ -------------------------------------------------------------------------------- CLIMAVAR After this integration step, if the user prefers the usual climatic variables, he can run the small program climavar which is provided as a FORTRAN source code; the parameters of climavar are taken in climavar.par with similar definitions as in the preceding steps. Alternatively, one can execute make climate -------------------------------------------------------------------------------- INSOLA The two routines prepinsol and insola are designed to compute all necessary insolation quantities derived from the orbital and precessional quantities computed above. They are given on the form of FORTRAN code, so the user can check if they correspond to his needs. He can also design his own insolation routines. A preparation step prepinsol is necessary prior to execution of 'insola'. This preparation step will construct a binary file with the useful quantities. a) set the parameters of prepinsol.par Example: --------------------------- &NAMSTD nomascpos = 'ORBELP.ASC', nomascneg = 'ORBELN.ASC', nomprecpos = 'PRECP.ASC', nomprecneg = 'PRECN.ASC', nomfich = 'SOLCLI.BIN', datedebut= -20.D0, datefin= 10.D0, statut='unknown' &END --------------------------- b) run prepinsol (these steps are automatically done with the 'make climate' command) For the actual computations of the insolation parameters, the user has to: a) set the parameters of insola.par; in this file, the 'so' parameter refers to the Solar constant expressed in W/m2. Example: ------------------------ &NAMSTD nomfich = 'SOLCLI.BIN', pas = 1.D3, datedebut = -1.D0, datefin =0.D0, statut='unknown', so = 1350.D0, &END ------------------------ b) run insola insola is a self documented program; For more details, the user can refer to La93 (reference above) ================================================================================ (End) Jacques Laskar [Bureau des Longitudes] 05-Nov-1994 ================================================================================ User feed-back is encouraged. Unless otherwise specified, send comments and bug reports to: E-mail : comments@imcce.fr Fax : (33) 1 46 33 28 34 Postal mail: IMCCE - Observatoire de Paris 77 avenue Denfert Rochereau F-75014 PARIS ================================================================================