!===============================================================================
! SVN $Id: shr_orb_mod.F90 6752 2007-10-04 21:02:15Z jwolfe $
! SVN $URL: https://svn-ccsm-models.cgd.ucar.edu/csm_share/branch_tags/cesm1_0_rel_tags/cesm1_0_rel01_share3_100616/shr/shr_orb_mod.F90 $
!===============================================================================
MODULE shr_orb_mod 14,5
use shr_kind_mod
use shr_sys_mod
use shr_const_mod
use shr_log_mod, only: s_loglev => shr_log_Level
use shr_log_mod, only: s_logunit => shr_log_Unit
IMPLICIT none
!----------------------------------------------------------------------------
! PUBLIC: Interfaces and global data
!----------------------------------------------------------------------------
public :: shr_orb_cosz
public :: shr_orb_params
public :: shr_orb_decl
public :: shr_orb_print
real (SHR_KIND_R8),public,parameter :: SHR_ORB_UNDEF_REAL = 1.e36_SHR_KIND_R8 ! undefined real
integer(SHR_KIND_IN),public,parameter :: SHR_ORB_UNDEF_INT = 2000000000 ! undefined int
!----------------------------------------------------------------------------
! PRIVATE: by default everything else is private to this module
!----------------------------------------------------------------------------
private
real (SHR_KIND_R8),parameter :: pi = SHR_CONST_PI
real (SHR_KIND_R8),parameter :: SHR_ORB_ECCEN_MIN = 0.0_SHR_KIND_R8 ! min value for eccen
real (SHR_KIND_R8),parameter :: SHR_ORB_ECCEN_MAX = 0.1_SHR_KIND_R8 ! max value for eccen
real (SHR_KIND_R8),parameter :: SHR_ORB_OBLIQ_MIN = -90.0_SHR_KIND_R8 ! min value for obliq
real (SHR_KIND_R8),parameter :: SHR_ORB_OBLIQ_MAX = +90.0_SHR_KIND_R8 ! max value for obliq
real (SHR_KIND_R8),parameter :: SHR_ORB_MVELP_MIN = 0.0_SHR_KIND_R8 ! min value for mvelp
real (SHR_KIND_R8),parameter :: SHR_ORB_MVELP_MAX = 360.0_SHR_KIND_R8 ! max value for mvelp
!===============================================================================
CONTAINS
!===============================================================================
real(SHR_KIND_R8) FUNCTION shr_orb_cosz(jday,lat,lon,declin) 4
!----------------------------------------------------------------------------
!
! FUNCTION to return the cosine of the solar zenith angle.
! Assumes 365.0 days/year.
!
!--------------- Code History -----------------------------------------------
!
! Original Author: Brian Kauffman
! Date: Jan/98
! History: adapted from statement FUNCTION in share/orb_cosz.h
!
!----------------------------------------------------------------------------
real (SHR_KIND_R8),intent(in) :: jday ! Julian cal day (1.xx to 365.xx)
real (SHR_KIND_R8),intent(in) :: lat ! Centered latitude (radians)
real (SHR_KIND_R8),intent(in) :: lon ! Centered longitude (radians)
real (SHR_KIND_R8),intent(in) :: declin ! Solar declination (radians)
!----------------------------------------------------------------------------
shr_orb_cosz = sin(lat)*sin(declin) - &
& cos(lat)*cos(declin)*cos(jday*2.0_SHR_KIND_R8*pi + lon)
END FUNCTION shr_orb_cosz
!===============================================================================
SUBROUTINE shr_orb_params( iyear_AD , eccen , obliq , mvelp , & 2,5
& obliqr , lambm0 , mvelpp, log_print )
!-------------------------------------------------------------------------------
!
! Calculate earths orbital parameters using Dave Threshers formula which
! came from Berger, Andre. 1978 "A Simple Algorithm to Compute Long-Term
! Variations of Daily Insolation". Contribution 18, Institute of Astronomy
! and Geophysics, Universite Catholique de Louvain, Louvain-la-Neuve, Belgium
!
!------------------------------Code history-------------------------------------
!
! Original Author: Erik Kluzek
! Date: Oct/97
!
!-------------------------------------------------------------------------------
!----------------------------- Arguments ------------------------------------
real (SHR_KIND_R8),intent(inout) :: eccen ! orbital eccentricity
real (SHR_KIND_R8),intent(inout) :: obliq ! obliquity in degrees
real (SHR_KIND_R8),intent(inout) :: mvelp ! moving vernal equinox long
integer(SHR_KIND_IN),intent(in) :: iyear_AD ! Year to calculate orbit for
logical ,intent(in) :: log_print ! Flags print of status/error
real (SHR_KIND_R8),intent(out) :: obliqr ! Earths obliquity in rad
real (SHR_KIND_R8),intent(out) :: lambm0 ! Mean long of perihelion at
! vernal equinox (radians)
real (SHR_KIND_R8),intent(out) :: mvelpp ! moving vernal equinox long
! of perihelion plus pi (rad)
!------------------------------ Parameters ----------------------------------
integer(SHR_KIND_IN),parameter :: poblen =47 ! # of elements in series wrt obliquity
integer(SHR_KIND_IN),parameter :: pecclen=19 ! # of elements in series wrt eccentricity
integer(SHR_KIND_IN),parameter :: pmvelen=78 ! # of elements in series wrt vernal equinox
real (SHR_KIND_R8),parameter :: psecdeg = 1.0_SHR_KIND_R8/3600.0_SHR_KIND_R8 ! arc sec to deg conversion
real (SHR_KIND_R8) :: degrad = pi/180._SHR_KIND_R8 ! degree to radian conversion factor
real (SHR_KIND_R8) :: yb4_1950AD ! number of years before 1950 AD
! Cosine series data for computation of obliquity: amplitude (arc seconds),
! rate (arc seconds/year), phase (degrees).
real (SHR_KIND_R8), parameter :: obamp(poblen) = & ! amplitudes for obliquity cos series
& (/ -2462.2214466_SHR_KIND_R8, -857.3232075_SHR_KIND_R8, -629.3231835_SHR_KIND_R8, &
& -414.2804924_SHR_KIND_R8, -311.7632587_SHR_KIND_R8, 308.9408604_SHR_KIND_R8, &
& -162.5533601_SHR_KIND_R8, -116.1077911_SHR_KIND_R8, 101.1189923_SHR_KIND_R8, &
& -67.6856209_SHR_KIND_R8, 24.9079067_SHR_KIND_R8, 22.5811241_SHR_KIND_R8, &
& -21.1648355_SHR_KIND_R8, -15.6549876_SHR_KIND_R8, 15.3936813_SHR_KIND_R8, &
& 14.6660938_SHR_KIND_R8, -11.7273029_SHR_KIND_R8, 10.2742696_SHR_KIND_R8, &
& 6.4914588_SHR_KIND_R8, 5.8539148_SHR_KIND_R8, -5.4872205_SHR_KIND_R8, &
& -5.4290191_SHR_KIND_R8, 5.1609570_SHR_KIND_R8, 5.0786314_SHR_KIND_R8, &
& -4.0735782_SHR_KIND_R8, 3.7227167_SHR_KIND_R8, 3.3971932_SHR_KIND_R8, &
& -2.8347004_SHR_KIND_R8, -2.6550721_SHR_KIND_R8, -2.5717867_SHR_KIND_R8, &
& -2.4712188_SHR_KIND_R8, 2.4625410_SHR_KIND_R8, 2.2464112_SHR_KIND_R8, &
& -2.0755511_SHR_KIND_R8, -1.9713669_SHR_KIND_R8, -1.8813061_SHR_KIND_R8, &
& -1.8468785_SHR_KIND_R8, 1.8186742_SHR_KIND_R8, 1.7601888_SHR_KIND_R8, &
& -1.5428851_SHR_KIND_R8, 1.4738838_SHR_KIND_R8, -1.4593669_SHR_KIND_R8, &
& 1.4192259_SHR_KIND_R8, -1.1818980_SHR_KIND_R8, 1.1756474_SHR_KIND_R8, &
& -1.1316126_SHR_KIND_R8, 1.0896928_SHR_KIND_R8/)
real (SHR_KIND_R8), parameter :: obrate(poblen) = & ! rates for obliquity cosine series
& (/ 31.609974_SHR_KIND_R8, 32.620504_SHR_KIND_R8, 24.172203_SHR_KIND_R8, &
& 31.983787_SHR_KIND_R8, 44.828336_SHR_KIND_R8, 30.973257_SHR_KIND_R8, &
& 43.668246_SHR_KIND_R8, 32.246691_SHR_KIND_R8, 30.599444_SHR_KIND_R8, &
& 42.681324_SHR_KIND_R8, 43.836462_SHR_KIND_R8, 47.439436_SHR_KIND_R8, &
& 63.219948_SHR_KIND_R8, 64.230478_SHR_KIND_R8, 1.010530_SHR_KIND_R8, &
& 7.437771_SHR_KIND_R8, 55.782177_SHR_KIND_R8, 0.373813_SHR_KIND_R8, &
& 13.218362_SHR_KIND_R8, 62.583231_SHR_KIND_R8, 63.593761_SHR_KIND_R8, &
& 76.438310_SHR_KIND_R8, 45.815258_SHR_KIND_R8, 8.448301_SHR_KIND_R8, &
& 56.792707_SHR_KIND_R8, 49.747842_SHR_KIND_R8, 12.058272_SHR_KIND_R8, &
& 75.278220_SHR_KIND_R8, 65.241008_SHR_KIND_R8, 64.604291_SHR_KIND_R8, &
& 1.647247_SHR_KIND_R8, 7.811584_SHR_KIND_R8, 12.207832_SHR_KIND_R8, &
& 63.856665_SHR_KIND_R8, 56.155990_SHR_KIND_R8, 77.448840_SHR_KIND_R8, &
& 6.801054_SHR_KIND_R8, 62.209418_SHR_KIND_R8, 20.656133_SHR_KIND_R8, &
& 48.344406_SHR_KIND_R8, 55.145460_SHR_KIND_R8, 69.000539_SHR_KIND_R8, &
& 11.071350_SHR_KIND_R8, 74.291298_SHR_KIND_R8, 11.047742_SHR_KIND_R8, &
& 0.636717_SHR_KIND_R8, 12.844549_SHR_KIND_R8/)
real (SHR_KIND_R8), parameter :: obphas(poblen) = & ! phases for obliquity cosine series
& (/ 251.9025_SHR_KIND_R8, 280.8325_SHR_KIND_R8, 128.3057_SHR_KIND_R8, &
& 292.7252_SHR_KIND_R8, 15.3747_SHR_KIND_R8, 263.7951_SHR_KIND_R8, &
& 308.4258_SHR_KIND_R8, 240.0099_SHR_KIND_R8, 222.9725_SHR_KIND_R8, &
& 268.7809_SHR_KIND_R8, 316.7998_SHR_KIND_R8, 319.6024_SHR_KIND_R8, &
& 143.8050_SHR_KIND_R8, 172.7351_SHR_KIND_R8, 28.9300_SHR_KIND_R8, &
& 123.5968_SHR_KIND_R8, 20.2082_SHR_KIND_R8, 40.8226_SHR_KIND_R8, &
& 123.4722_SHR_KIND_R8, 155.6977_SHR_KIND_R8, 184.6277_SHR_KIND_R8, &
& 267.2772_SHR_KIND_R8, 55.0196_SHR_KIND_R8, 152.5268_SHR_KIND_R8, &
& 49.1382_SHR_KIND_R8, 204.6609_SHR_KIND_R8, 56.5233_SHR_KIND_R8, &
& 200.3284_SHR_KIND_R8, 201.6651_SHR_KIND_R8, 213.5577_SHR_KIND_R8, &
& 17.0374_SHR_KIND_R8, 164.4194_SHR_KIND_R8, 94.5422_SHR_KIND_R8, &
& 131.9124_SHR_KIND_R8, 61.0309_SHR_KIND_R8, 296.2073_SHR_KIND_R8, &
& 135.4894_SHR_KIND_R8, 114.8750_SHR_KIND_R8, 247.0691_SHR_KIND_R8, &
& 256.6114_SHR_KIND_R8, 32.1008_SHR_KIND_R8, 143.6804_SHR_KIND_R8, &
& 16.8784_SHR_KIND_R8, 160.6835_SHR_KIND_R8, 27.5932_SHR_KIND_R8, &
& 348.1074_SHR_KIND_R8, 82.6496_SHR_KIND_R8/)
! Cosine/sine series data for computation of eccentricity and fixed vernal
! equinox longitude of perihelion (fvelp): amplitude,
! rate (arc seconds/year), phase (degrees).
real (SHR_KIND_R8), parameter :: ecamp (pecclen) = & ! ampl for eccen/fvelp cos/sin series
& (/ 0.01860798_SHR_KIND_R8, 0.01627522_SHR_KIND_R8, -0.01300660_SHR_KIND_R8, &
& 0.00988829_SHR_KIND_R8, -0.00336700_SHR_KIND_R8, 0.00333077_SHR_KIND_R8, &
& -0.00235400_SHR_KIND_R8, 0.00140015_SHR_KIND_R8, 0.00100700_SHR_KIND_R8, &
& 0.00085700_SHR_KIND_R8, 0.00064990_SHR_KIND_R8, 0.00059900_SHR_KIND_R8, &
& 0.00037800_SHR_KIND_R8, -0.00033700_SHR_KIND_R8, 0.00027600_SHR_KIND_R8, &
& 0.00018200_SHR_KIND_R8, -0.00017400_SHR_KIND_R8, -0.00012400_SHR_KIND_R8, &
& 0.00001250_SHR_KIND_R8/)
real (SHR_KIND_R8), parameter :: ecrate(pecclen) = & ! rates for eccen/fvelp cos/sin series
& (/ 4.2072050_SHR_KIND_R8, 7.3460910_SHR_KIND_R8, 17.8572630_SHR_KIND_R8, &
& 17.2205460_SHR_KIND_R8, 16.8467330_SHR_KIND_R8, 5.1990790_SHR_KIND_R8, &
& 18.2310760_SHR_KIND_R8, 26.2167580_SHR_KIND_R8, 6.3591690_SHR_KIND_R8, &
& 16.2100160_SHR_KIND_R8, 3.0651810_SHR_KIND_R8, 16.5838290_SHR_KIND_R8, &
& 18.4939800_SHR_KIND_R8, 6.1909530_SHR_KIND_R8, 18.8677930_SHR_KIND_R8, &
& 17.4255670_SHR_KIND_R8, 6.1860010_SHR_KIND_R8, 18.4174410_SHR_KIND_R8, &
& 0.6678630_SHR_KIND_R8/)
real (SHR_KIND_R8), parameter :: ecphas(pecclen) = & ! phases for eccen/fvelp cos/sin series
& (/ 28.620089_SHR_KIND_R8, 193.788772_SHR_KIND_R8, 308.307024_SHR_KIND_R8, &
& 320.199637_SHR_KIND_R8, 279.376984_SHR_KIND_R8, 87.195000_SHR_KIND_R8, &
& 349.129677_SHR_KIND_R8, 128.443387_SHR_KIND_R8, 154.143880_SHR_KIND_R8, &
& 291.269597_SHR_KIND_R8, 114.860583_SHR_KIND_R8, 332.092251_SHR_KIND_R8, &
& 296.414411_SHR_KIND_R8, 145.769910_SHR_KIND_R8, 337.237063_SHR_KIND_R8, &
& 152.092288_SHR_KIND_R8, 126.839891_SHR_KIND_R8, 210.667199_SHR_KIND_R8, &
& 72.108838_SHR_KIND_R8/)
! Sine series data for computation of moving vernal equinox longitude of
! perihelion: amplitude (arc seconds), rate (arc sec/year), phase (degrees).
real (SHR_KIND_R8), parameter :: mvamp (pmvelen) = & ! amplitudes for mvelp sine series
& (/ 7391.0225890_SHR_KIND_R8, 2555.1526947_SHR_KIND_R8, 2022.7629188_SHR_KIND_R8, &
& -1973.6517951_SHR_KIND_R8, 1240.2321818_SHR_KIND_R8, 953.8679112_SHR_KIND_R8, &
& -931.7537108_SHR_KIND_R8, 872.3795383_SHR_KIND_R8, 606.3544732_SHR_KIND_R8, &
& -496.0274038_SHR_KIND_R8, 456.9608039_SHR_KIND_R8, 346.9462320_SHR_KIND_R8, &
& -305.8412902_SHR_KIND_R8, 249.6173246_SHR_KIND_R8, -199.1027200_SHR_KIND_R8, &
& 191.0560889_SHR_KIND_R8, -175.2936572_SHR_KIND_R8, 165.9068833_SHR_KIND_R8, &
& 161.1285917_SHR_KIND_R8, 139.7878093_SHR_KIND_R8, -133.5228399_SHR_KIND_R8, &
& 117.0673811_SHR_KIND_R8, 104.6907281_SHR_KIND_R8, 95.3227476_SHR_KIND_R8, &
& 86.7824524_SHR_KIND_R8, 86.0857729_SHR_KIND_R8, 70.5893698_SHR_KIND_R8, &
& -69.9719343_SHR_KIND_R8, -62.5817473_SHR_KIND_R8, 61.5450059_SHR_KIND_R8, &
& -57.9364011_SHR_KIND_R8, 57.1899832_SHR_KIND_R8, -57.0236109_SHR_KIND_R8, &
& -54.2119253_SHR_KIND_R8, 53.2834147_SHR_KIND_R8, 52.1223575_SHR_KIND_R8, &
& -49.0059908_SHR_KIND_R8, -48.3118757_SHR_KIND_R8, -45.4191685_SHR_KIND_R8, &
& -42.2357920_SHR_KIND_R8, -34.7971099_SHR_KIND_R8, 34.4623613_SHR_KIND_R8, &
& -33.8356643_SHR_KIND_R8, 33.6689362_SHR_KIND_R8, -31.2521586_SHR_KIND_R8, &
& -30.8798701_SHR_KIND_R8, 28.4640769_SHR_KIND_R8, -27.1960802_SHR_KIND_R8, &
& 27.0860736_SHR_KIND_R8, -26.3437456_SHR_KIND_R8, 24.7253740_SHR_KIND_R8, &
& 24.6732126_SHR_KIND_R8, 24.4272733_SHR_KIND_R8, 24.0127327_SHR_KIND_R8, &
& 21.7150294_SHR_KIND_R8, -21.5375347_SHR_KIND_R8, 18.1148363_SHR_KIND_R8, &
& -16.9603104_SHR_KIND_R8, -16.1765215_SHR_KIND_R8, 15.5567653_SHR_KIND_R8, &
& 15.4846529_SHR_KIND_R8, 15.2150632_SHR_KIND_R8, 14.5047426_SHR_KIND_R8, &
& -14.3873316_SHR_KIND_R8, 13.1351419_SHR_KIND_R8, 12.8776311_SHR_KIND_R8, &
& 11.9867234_SHR_KIND_R8, 11.9385578_SHR_KIND_R8, 11.7030822_SHR_KIND_R8, &
& 11.6018181_SHR_KIND_R8, -11.2617293_SHR_KIND_R8, -10.4664199_SHR_KIND_R8, &
& 10.4333970_SHR_KIND_R8, -10.2377466_SHR_KIND_R8, 10.1934446_SHR_KIND_R8, &
& -10.1280191_SHR_KIND_R8, 10.0289441_SHR_KIND_R8, -10.0034259_SHR_KIND_R8/)
real (SHR_KIND_R8), parameter :: mvrate(pmvelen) = & ! rates for mvelp sine series
& (/ 31.609974_SHR_KIND_R8, 32.620504_SHR_KIND_R8, 24.172203_SHR_KIND_R8, &
& 0.636717_SHR_KIND_R8, 31.983787_SHR_KIND_R8, 3.138886_SHR_KIND_R8, &
& 30.973257_SHR_KIND_R8, 44.828336_SHR_KIND_R8, 0.991874_SHR_KIND_R8, &
& 0.373813_SHR_KIND_R8, 43.668246_SHR_KIND_R8, 32.246691_SHR_KIND_R8, &
& 30.599444_SHR_KIND_R8, 2.147012_SHR_KIND_R8, 10.511172_SHR_KIND_R8, &
& 42.681324_SHR_KIND_R8, 13.650058_SHR_KIND_R8, 0.986922_SHR_KIND_R8, &
& 9.874455_SHR_KIND_R8, 13.013341_SHR_KIND_R8, 0.262904_SHR_KIND_R8, &
& 0.004952_SHR_KIND_R8, 1.142024_SHR_KIND_R8, 63.219948_SHR_KIND_R8, &
& 0.205021_SHR_KIND_R8, 2.151964_SHR_KIND_R8, 64.230478_SHR_KIND_R8, &
& 43.836462_SHR_KIND_R8, 47.439436_SHR_KIND_R8, 1.384343_SHR_KIND_R8, &
& 7.437771_SHR_KIND_R8, 18.829299_SHR_KIND_R8, 9.500642_SHR_KIND_R8, &
& 0.431696_SHR_KIND_R8, 1.160090_SHR_KIND_R8, 55.782177_SHR_KIND_R8, &
& 12.639528_SHR_KIND_R8, 1.155138_SHR_KIND_R8, 0.168216_SHR_KIND_R8, &
& 1.647247_SHR_KIND_R8, 10.884985_SHR_KIND_R8, 5.610937_SHR_KIND_R8, &
& 12.658184_SHR_KIND_R8, 1.010530_SHR_KIND_R8, 1.983748_SHR_KIND_R8, &
& 14.023871_SHR_KIND_R8, 0.560178_SHR_KIND_R8, 1.273434_SHR_KIND_R8, &
& 12.021467_SHR_KIND_R8, 62.583231_SHR_KIND_R8, 63.593761_SHR_KIND_R8, &
& 76.438310_SHR_KIND_R8, 4.280910_SHR_KIND_R8, 13.218362_SHR_KIND_R8, &
& 17.818769_SHR_KIND_R8, 8.359495_SHR_KIND_R8, 56.792707_SHR_KIND_R8, &
& 8.448301_SHR_KIND_R8, 1.978796_SHR_KIND_R8, 8.863925_SHR_KIND_R8, &
& 0.186365_SHR_KIND_R8, 8.996212_SHR_KIND_R8, 6.771027_SHR_KIND_R8, &
& 45.815258_SHR_KIND_R8, 12.002811_SHR_KIND_R8, 75.278220_SHR_KIND_R8, &
& 65.241008_SHR_KIND_R8, 18.870667_SHR_KIND_R8, 22.009553_SHR_KIND_R8, &
& 64.604291_SHR_KIND_R8, 11.498094_SHR_KIND_R8, 0.578834_SHR_KIND_R8, &
& 9.237738_SHR_KIND_R8, 49.747842_SHR_KIND_R8, 2.147012_SHR_KIND_R8, &
& 1.196895_SHR_KIND_R8, 2.133898_SHR_KIND_R8, 0.173168_SHR_KIND_R8/)
real (SHR_KIND_R8), parameter :: mvphas(pmvelen) = & ! phases for mvelp sine series
& (/ 251.9025_SHR_KIND_R8, 280.8325_SHR_KIND_R8, 128.3057_SHR_KIND_R8, &
& 348.1074_SHR_KIND_R8, 292.7252_SHR_KIND_R8, 165.1686_SHR_KIND_R8, &
& 263.7951_SHR_KIND_R8, 15.3747_SHR_KIND_R8, 58.5749_SHR_KIND_R8, &
& 40.8226_SHR_KIND_R8, 308.4258_SHR_KIND_R8, 240.0099_SHR_KIND_R8, &
& 222.9725_SHR_KIND_R8, 106.5937_SHR_KIND_R8, 114.5182_SHR_KIND_R8, &
& 268.7809_SHR_KIND_R8, 279.6869_SHR_KIND_R8, 39.6448_SHR_KIND_R8, &
& 126.4108_SHR_KIND_R8, 291.5795_SHR_KIND_R8, 307.2848_SHR_KIND_R8, &
& 18.9300_SHR_KIND_R8, 273.7596_SHR_KIND_R8, 143.8050_SHR_KIND_R8, &
& 191.8927_SHR_KIND_R8, 125.5237_SHR_KIND_R8, 172.7351_SHR_KIND_R8, &
& 316.7998_SHR_KIND_R8, 319.6024_SHR_KIND_R8, 69.7526_SHR_KIND_R8, &
& 123.5968_SHR_KIND_R8, 217.6432_SHR_KIND_R8, 85.5882_SHR_KIND_R8, &
& 156.2147_SHR_KIND_R8, 66.9489_SHR_KIND_R8, 20.2082_SHR_KIND_R8, &
& 250.7568_SHR_KIND_R8, 48.0188_SHR_KIND_R8, 8.3739_SHR_KIND_R8, &
& 17.0374_SHR_KIND_R8, 155.3409_SHR_KIND_R8, 94.1709_SHR_KIND_R8, &
& 221.1120_SHR_KIND_R8, 28.9300_SHR_KIND_R8, 117.1498_SHR_KIND_R8, &
& 320.5095_SHR_KIND_R8, 262.3602_SHR_KIND_R8, 336.2148_SHR_KIND_R8, &
& 233.0046_SHR_KIND_R8, 155.6977_SHR_KIND_R8, 184.6277_SHR_KIND_R8, &
& 267.2772_SHR_KIND_R8, 78.9281_SHR_KIND_R8, 123.4722_SHR_KIND_R8, &
& 188.7132_SHR_KIND_R8, 180.1364_SHR_KIND_R8, 49.1382_SHR_KIND_R8, &
& 152.5268_SHR_KIND_R8, 98.2198_SHR_KIND_R8, 97.4808_SHR_KIND_R8, &
& 221.5376_SHR_KIND_R8, 168.2438_SHR_KIND_R8, 161.1199_SHR_KIND_R8, &
& 55.0196_SHR_KIND_R8, 262.6495_SHR_KIND_R8, 200.3284_SHR_KIND_R8, &
& 201.6651_SHR_KIND_R8, 294.6547_SHR_KIND_R8, 99.8233_SHR_KIND_R8, &
& 213.5577_SHR_KIND_R8, 154.1631_SHR_KIND_R8, 232.7153_SHR_KIND_R8, &
& 138.3034_SHR_KIND_R8, 204.6609_SHR_KIND_R8, 106.5938_SHR_KIND_R8, &
& 250.4676_SHR_KIND_R8, 332.3345_SHR_KIND_R8, 27.3039_SHR_KIND_R8/)
!---------------------------Local variables----------------------------------
integer(SHR_KIND_IN) :: i ! Index for series summations
real (SHR_KIND_R8) :: obsum ! Obliquity series summation
real (SHR_KIND_R8) :: cossum ! Cos series summation for eccentricity/fvelp
real (SHR_KIND_R8) :: sinsum ! Sin series summation for eccentricity/fvelp
real (SHR_KIND_R8) :: fvelp ! Fixed vernal equinox long of perihelion
real (SHR_KIND_R8) :: mvsum ! mvelp series summation
real (SHR_KIND_R8) :: beta ! Intermediate argument for lambm0
real (SHR_KIND_R8) :: years ! Years to time of interest ( pos <=> future)
real (SHR_KIND_R8) :: eccen2 ! eccentricity squared
real (SHR_KIND_R8) :: eccen3 ! eccentricity cubed
!-------------------------- Formats -----------------------------------------
character(*),parameter :: svnID = "SVN " // &
"$Id: shr_orb_mod.F90 6752 2007-10-04 21:02:15Z jwolfe $"
character(*),parameter :: svnURL = "SVN <unknown URL>"
! character(*),parameter :: svnURL = "SVN " // &
! "$URL: https://svn-ccsm-models.cgd.ucar.edu/csm_share/branch_tags/cesm1_0_rel_tags/cesm1_0_rel01_share3_100616/shr/shr_orb_mod.F90 $"
character(len=*),parameter :: F00 = "('(shr_orb_params) ',4a)"
character(len=*),parameter :: F01 = "('(shr_orb_params) ',a,i9)"
character(len=*),parameter :: F02 = "('(shr_orb_params) ',a,f6.3)"
character(len=*),parameter :: F03 = "('(shr_orb_params) ',a,es14.6)"
!----------------------------------------------------------------------------
! radinp and algorithms below will need a degree to radian conversion factor
if ( log_print .and. s_loglev > 0 ) then
write(s_logunit,F00) 'Calculate characteristics of the orbit:'
write(s_logunit,F00) svnID
write(s_logunit,F00) svnURL
end if
! Check for flag to use input orbit parameters
IF ( iyear_AD == SHR_ORB_UNDEF_INT ) THEN
! Check input obliq, eccen, and mvelp to ensure reasonable
if( obliq == SHR_ORB_UNDEF_REAL )then
write(s_logunit,F00) 'Have to specify orbital parameters:'
write(s_logunit,F00) 'Either set: iyear_AD, OR [obliq, eccen, and mvelp]:'
write(s_logunit,F00) 'iyear_AD is the year to simulate orbit for (ie. 1950): '
write(s_logunit,F00) 'obliq, eccen, mvelp specify the orbit directly:'
write(s_logunit,F00) 'The AMIP II settings (for a 1995 orbit) are: '
write(s_logunit,F00) ' obliq = 23.4441'
write(s_logunit,F00) ' eccen = 0.016715'
write(s_logunit,F00) ' mvelp = 102.7'
call shr_sys_abort()
else if ( log_print ) then
write(s_logunit,F00) 'Use input orbital parameters: '
end if
if( (obliq < SHR_ORB_OBLIQ_MIN).or.(obliq > SHR_ORB_OBLIQ_MAX) ) then
write(s_logunit,F03) 'Input obliquity unreasonable: ', obliq
call shr_sys_abort()
end if
if( (eccen < SHR_ORB_ECCEN_MIN).or.(eccen > SHR_ORB_ECCEN_MAX) ) then
write(s_logunit,F03) 'Input eccentricity unreasonable: ', eccen
call shr_sys_abort()
end if
if( (mvelp < SHR_ORB_MVELP_MIN).or.(mvelp > SHR_ORB_MVELP_MAX) ) then
write(s_logunit,F03) 'Input mvelp unreasonable: ' , mvelp
call shr_sys_abort()
end if
eccen2 = eccen*eccen
eccen3 = eccen2*eccen
ELSE ! Otherwise calculate based on years before present
if ( log_print .and. s_loglev > 0) then
write(s_logunit,F01) 'Calculate orbit for year: ' , iyear_AD
end if
yb4_1950AD = 1950.0_SHR_KIND_R8 - real(iyear_AD,SHR_KIND_R8)
if ( abs(yb4_1950AD) .gt. 1000000.0_SHR_KIND_R8 )then
write(s_logunit,F00) 'orbit only valid for years+-1000000'
write(s_logunit,F00) 'Relative to 1950 AD'
write(s_logunit,F03) '# of years before 1950: ',yb4_1950AD
write(s_logunit,F01) 'Year to simulate was : ',iyear_AD
call shr_sys_abort()
end if
! The following calculates the earths obliquity, orbital eccentricity
! (and various powers of it) and vernal equinox mean longitude of
! perihelion for years in the past (future = negative of years past),
! using constants (see parameter section) given in the program of:
!
! Berger, Andre. 1978 A Simple Algorithm to Compute Long-Term Variations
! of Daily Insolation. Contribution 18, Institute of Astronomy and
! Geophysics, Universite Catholique de Louvain, Louvain-la-Neuve, Belgium.
!
! and formulas given in the paper (where less precise constants are also
! given):
!
! Berger, Andre. 1978. Long-Term Variations of Daily Insolation and
! Quaternary Climatic Changes. J. of the Atmo. Sci. 35:2362-2367
!
! The algorithm is valid only to 1,000,000 years past or hence.
! For a solution valid to 5-10 million years past see the above author.
! Algorithm below is better for years closer to present than is the
! 5-10 million year solution.
!
! Years to time of interest must be negative of years before present
! (1950) in formulas that follow.
years = - yb4_1950AD
! In the summations below, cosine or sine arguments, which end up in
! degrees, must be converted to radians via multiplication by degrad.
!
! Summation of cosine series for obliquity (epsilon in Berger 1978) in
! degrees. Convert the amplitudes and rates, which are in arc secs, into
! degrees via multiplication by psecdeg (arc seconds to degrees conversion
! factor). For obliq, first term is Berger 1978 epsilon star; second
! term is series summation in degrees.
obsum = 0.0_SHR_KIND_R8
do i = 1, poblen
obsum = obsum + obamp(i)*psecdeg*cos((obrate(i)*psecdeg*years + &
& obphas(i))*degrad)
end do
obliq = 23.320556_SHR_KIND_R8 + obsum
! Summation of cosine and sine series for computation of eccentricity
! (eccen; e in Berger 1978) and fixed vernal equinox longitude of
! perihelion (fvelp; pi in Berger 1978), which is used for computation
! of moving vernal equinox longitude of perihelion. Convert the rates,
! which are in arc seconds, into degrees via multiplication by psecdeg.
cossum = 0.0_SHR_KIND_R8
do i = 1, pecclen
cossum = cossum+ecamp(i)*cos((ecrate(i)*psecdeg*years+ecphas(i))*degrad)
end do
sinsum = 0.0_SHR_KIND_R8
do i = 1, pecclen
sinsum = sinsum+ecamp(i)*sin((ecrate(i)*psecdeg*years+ecphas(i))*degrad)
end do
! Use summations to calculate eccentricity
eccen2 = cossum*cossum + sinsum*sinsum
eccen = sqrt(eccen2)
eccen3 = eccen2*eccen
! A series of cases for fvelp, which is in radians.
if (abs(cossum) .le. 1.0E-8_SHR_KIND_R8) then
if (sinsum .eq. 0.0_SHR_KIND_R8) then
fvelp = 0.0_SHR_KIND_R8
else if (sinsum .lt. 0.0_SHR_KIND_R8) then
fvelp = 1.5_SHR_KIND_R8*pi
else if (sinsum .gt. 0.0_SHR_KIND_R8) then
fvelp = .5_SHR_KIND_R8*pi
endif
else if (cossum .lt. 0.0_SHR_KIND_R8) then
fvelp = atan(sinsum/cossum) + pi
else if (cossum .gt. 0.0_SHR_KIND_R8) then
if (sinsum .lt. 0.0_SHR_KIND_R8) then
fvelp = atan(sinsum/cossum) + 2.0_SHR_KIND_R8*pi
else
fvelp = atan(sinsum/cossum)
endif
endif
! Summation of sin series for computation of moving vernal equinox long
! of perihelion (mvelp; omega bar in Berger 1978) in degrees. For mvelp,
! first term is fvelp in degrees; second term is Berger 1978 psi bar
! times years and in degrees; third term is Berger 1978 zeta; fourth
! term is series summation in degrees. Convert the amplitudes and rates,
! which are in arc seconds, into degrees via multiplication by psecdeg.
! Series summation plus second and third terms constitute Berger 1978
! psi, which is the general precession.
mvsum = 0.0_SHR_KIND_R8
do i = 1, pmvelen
mvsum = mvsum + mvamp(i)*psecdeg*sin((mvrate(i)*psecdeg*years + &
& mvphas(i))*degrad)
end do
mvelp = fvelp/degrad + 50.439273_SHR_KIND_R8*psecdeg*years + 3.392506_SHR_KIND_R8 + mvsum
! Cases to make sure mvelp is between 0 and 360.
do while (mvelp .lt. 0.0_SHR_KIND_R8)
mvelp = mvelp + 360.0_SHR_KIND_R8
end do
do while (mvelp .ge. 360.0_SHR_KIND_R8)
mvelp = mvelp - 360.0_SHR_KIND_R8
end do
END IF ! end of test on whether to calculate or use input orbital params
! Orbit needs the obliquity in radians
obliqr = obliq*degrad
! 180 degrees must be added to mvelp since observations are made from the
! earth and the sun is considered (wrongly for the algorithm) to go around
! the earth. For a more graphic explanation see Appendix B in:
!
! A. Berger, M. Loutre and C. Tricot. 1993. Insolation and Earth Orbital
! Periods. J. of Geophysical Research 98:10,341-10,362.
!
! Additionally, orbit will need this value in radians. So mvelp becomes
! mvelpp (mvelp plus pi)
mvelpp = (mvelp + 180._SHR_KIND_R8)*degrad
! Set up an argument used several times in lambm0 calculation ahead.
beta = sqrt(1._SHR_KIND_R8 - eccen2)
! The mean longitude at the vernal equinox (lambda m nought in Berger
! 1978; in radians) is calculated from the following formula given in
! Berger 1978. At the vernal equinox the true longitude (lambda in Berger
! 1978) is 0.
lambm0 = 2._SHR_KIND_R8*((.5_SHR_KIND_R8*eccen + .125_SHR_KIND_R8*eccen3)*(1._SHR_KIND_R8 + beta)*sin(mvelpp) &
& - .250_SHR_KIND_R8*eccen2*(.5_SHR_KIND_R8 + beta)*sin(2._SHR_KIND_R8*mvelpp) &
& + .125_SHR_KIND_R8*eccen3*(1._SHR_KIND_R8/3._SHR_KIND_R8 + beta)*sin(3._SHR_KIND_R8*mvelpp))
if ( log_print ) then
write(s_logunit,F03) '------ Computed Orbital Parameters ------'
write(s_logunit,F03) 'Eccentricity = ',eccen
write(s_logunit,F03) 'Obliquity (deg) = ',obliq
write(s_logunit,F03) 'Obliquity (rad) = ',obliqr
write(s_logunit,F03) 'Long of perh(deg) = ',mvelp
write(s_logunit,F03) 'Long of perh(rad) = ',mvelpp
write(s_logunit,F03) 'Long at v.e.(rad) = ',lambm0
write(s_logunit,F03) '-----------------------------------------'
end if
END SUBROUTINE shr_orb_params
!===============================================================================
SUBROUTINE shr_orb_decl(calday ,eccen ,mvelpp ,lambm0 ,obliqr ,delta ,eccf) 11
!-------------------------------------------------------------------------------
!
! Compute earth/orbit parameters using formula suggested by
! Duane Thresher.
!
!---------------------------Code history----------------------------------------
!
! Original version: Erik Kluzek
! Date: Oct/1997
!
!-------------------------------------------------------------------------------
!------------------------------Arguments--------------------------------
real (SHR_KIND_R8),intent(in) :: calday ! Calendar day, including fraction
real (SHR_KIND_R8),intent(in) :: eccen ! Eccentricity
real (SHR_KIND_R8),intent(in) :: obliqr ! Earths obliquity in radians
real (SHR_KIND_R8),intent(in) :: lambm0 ! Mean long of perihelion at the
! vernal equinox (radians)
real (SHR_KIND_R8),intent(in) :: mvelpp ! moving vernal equinox longitude
! of perihelion plus pi (radians)
real (SHR_KIND_R8),intent(out) :: delta ! Solar declination angle in rad
real (SHR_KIND_R8),intent(out) :: eccf ! Earth-sun distance factor (ie. (1/r)**2)
!---------------------------Local variables-----------------------------
real (SHR_KIND_R8),parameter :: dayspy = 365.0_SHR_KIND_R8 ! days per year
real (SHR_KIND_R8),parameter :: ve = 80.5_SHR_KIND_R8 ! Calday of vernal equinox
! assumes Jan 1 = calday 1
real (SHR_KIND_R8) :: lambm ! Lambda m, mean long of perihelion (rad)
real (SHR_KIND_R8) :: lmm ! Intermediate argument involving lambm
real (SHR_KIND_R8) :: lamb ! Lambda, the earths long of perihelion
real (SHR_KIND_R8) :: invrho ! Inverse normalized sun/earth distance
real (SHR_KIND_R8) :: sinl ! Sine of lmm
! Compute eccentricity factor and solar declination using
! day value where a round day (such as 213.0) refers to 0z at
! Greenwich longitude.
!
! Use formulas from Berger, Andre 1978: Long-Term Variations of Daily
! Insolation and Quaternary Climatic Changes. J. of the Atmo. Sci.
! 35:2362-2367.
!
! To get the earths true longitude (position in orbit; lambda in Berger
! 1978) which is necessary to find the eccentricity factor and declination,
! must first calculate the mean longitude (lambda m in Berger 1978) at
! the present day. This is done by adding to lambm0 (the mean longitude
! at the vernal equinox, set as March 21 at noon, when lambda=0; in radians)
! an increment (delta lambda m in Berger 1978) that is the number of
! days past or before (a negative increment) the vernal equinox divided by
! the days in a model year times the 2*pi radians in a complete orbit.
lambm = lambm0 + (calday - ve)*2._SHR_KIND_R8*pi/dayspy
lmm = lambm - mvelpp
! The earths true longitude, in radians, is then found from
! the formula in Berger 1978:
sinl = sin(lmm)
lamb = lambm + eccen*(2._SHR_KIND_R8*sinl + eccen*(1.25_SHR_KIND_R8*sin(2._SHR_KIND_R8*lmm) &
& + eccen*((13.0_SHR_KIND_R8/12.0_SHR_KIND_R8)*sin(3._SHR_KIND_R8*lmm) - 0.25_SHR_KIND_R8*sinl)))
! Using the obliquity, eccentricity, moving vernal equinox longitude of
! perihelion (plus), and earths true longitude, the declination (delta)
! and the normalized earth/sun distance (rho in Berger 1978; actually inverse
! rho will be used), and thus the eccentricity factor (eccf), can be
! calculated from formulas given in Berger 1978.
invrho = (1._SHR_KIND_R8 + eccen*cos(lamb - mvelpp)) / (1._SHR_KIND_R8 - eccen*eccen)
! Set solar declination and eccentricity factor
delta = asin(sin(obliqr)*sin(lamb))
eccf = invrho*invrho
return
END SUBROUTINE shr_orb_decl
!===============================================================================
SUBROUTINE shr_orb_print( iyear_AD, eccen, obliq, mvelp )
!-------------------------------------------------------------------------------
!
! Print out the information on the Earths input orbital characteristics
!
!---------------------------Code history----------------------------------------
!
! Original version: Erik Kluzek
! Date: Oct/1997
!
!-------------------------------------------------------------------------------
!---------------------------Arguments----------------------------------------
integer(SHR_KIND_IN),intent(in) :: iyear_AD ! requested Year (AD)
real (SHR_KIND_R8),intent(in) :: eccen ! eccentricity (unitless)
! (typically 0 to 0.1)
real (SHR_KIND_R8),intent(in) :: obliq ! obliquity (-90 to +90 degrees)
! typically 22-26
real (SHR_KIND_R8),intent(in) :: mvelp ! moving vernal equinox at perhel
! (0 to 360 degrees)
!-------------------------- Formats -----------------------------------------
character(len=*),parameter :: F00 = "('(shr_orb_print) ',4a)"
character(len=*),parameter :: F01 = "('(shr_orb_print) ',a,i9.4)"
character(len=*),parameter :: F02 = "('(shr_orb_print) ',a,f6.3)"
character(len=*),parameter :: F03 = "('(shr_orb_print) ',a,es14.6)"
!----------------------------------------------------------------------------
if (s_loglev > 0) then
if ( iyear_AD .ne. SHR_ORB_UNDEF_INT ) then
if ( iyear_AD > 0 ) then
write(s_logunit,F01) 'Orbital parameters calculated for year: AD ',iyear_AD
else
write(s_logunit,F01) 'Orbital parameters calculated for year: BC ',iyear_AD
end if
else if ( obliq /= SHR_ORB_UNDEF_REAL ) then
write(s_logunit,F03) 'Orbital parameters: '
write(s_logunit,F03) 'Obliquity (degree): ', obliq
write(s_logunit,F03) 'Eccentricity (unitless): ', eccen
write(s_logunit,F03) 'Long. of moving Perhelion (deg): ', mvelp
else
write(s_logunit,F03) 'Orbit parameters not set!'
end if
endif
END SUBROUTINE shr_orb_print
!===============================================================================
END MODULE shr_orb_mod