Last updated on .
Version: v1.1
Date: July 1, 1999
Contact: Isaac Held
Computes the diurnally varying zenith angle, and
a non-dimensional incident solar flux at the top
of the atmosphere, taking into account the varying
Earth-Sun distance in the orbital ellipse.
Also provides averages suitable for use in
diurnally-averaged and sesaonally-averaged models.
Useful for simple energy balance climate models as well as GCMs.
The orbital geometry (eccentricity, obliquity, longitude of the
perihelion) defaults to the current conditions for Earth, but
can be changed.
Time can be managed using the calendar options and the time_types
defined by time_manager_mod, in which case the solar day is
constrained to be 86400 seconds and the length of the year is
determined by the kind of calendar chosen (i.e., no_leap
(365 solar days) or Julian (365.25 solar days))
Or these can be bypassed.
Diurnal averages are computed analytically, assuming that the
Earth-Sun distance does not change significantly over one day.
The diurnally varying incident solar flux can also be averaged
over a specified time interval (the model time-step), so that
there is no time truncation error in the time-averaged irradiance.
The module initializes itself when first called,
and computes a table of finely-spaced orbital positions
as a function of time, using 4th-order Runge-Kutta,
which is then interpolated upon.
The solar fluxes are normalized so that multiplication by
the "solar constant" produces the correct flux
at the top of the atmosphere
In particular, the average over the sphere is equal
to 1/4 for an eccentricity of 0.0 .
When the eccentricity, ecc, is non-zero, the average over
the sphere is (1/4)* [(1.0 - ecc**2)**(-0.5)], as
appropriate for a fixed solar constant
The geometry of the Earth-Sum system, and the equations underlying
these computations, are described in
astronomy.ps
Utilities_mod
Time_manager_mod
This module has been tested using v1.0 of both of these modules
use astronomy_mod [,only: get_orbital_parameters, &
set_orbital_parameters, &
get_ref_date_of_ae , &
set_ref_date_of_ae , &
diurnal_solar , &
daily_mean_solar , &
annual_mean_solar ]
set_orbital_parameters : resets values of orbital parameters
(if not called, parameters default to
present day earth conditions)
get_orbital_parameters : returns values of orbital parameters
set_ref_date_of_ae : relates calendar to orbit by setting
date of autumnal equinox in northern hem.
(if not called, parameters default to
present day earth conditions)
get_ref_date_of_ae : returns date of autumnal equinox
diurnal_solar : returns instantaneous cos(zenith angle), cosz,
and "normalized solar flux"
= cosz*(((a/r)**2),
where r is the earth-sun distance and
a is the semi-major axis of the
orbital ellipse
these instantaneous values can also be
averaged over any time interval < 12 hours
daily_mean_solar : returns daily averaged normalized irradiance
and an effective zenith angle that would
produce the correct total irradiance if
the sun where fixed at that position in the
sky for the daylight hours only.
annual_mean_solar : returns annually averaged flux and
effective zenith angle by averaging output
from daily_mean_solar over the year.
the effective zenith angle is obtained by
weighting the daily effective zenith angle
by the daily averaged flux
notes:
1) there is no namelist
2) no data files or restart files are required
3) a line is appended to the file logfile.out containing the version
number of the module
there is no public data
==========================================================================
call set_orbital_parameters(ecc, obliq, per)
input:
ecc, real
eccentricity of orbital ellipse, nondimensional
obliq, real
obliquity (angle between rotation axis and plane of
orbit), in degrees (not radians)
per, real
orbital angle between perihelion and autumnal equinox
in the northern hemisphere, in degrees (not radians)
( 0.0 => perihelion at nh autumnal equinox
90.0 => perihelion at nh winter solstice
180.0 => perihelion at nh vernal equinox
270.0 => perihelion at nh summer solstice
if this routine is not called the values will default to
ecc = 0.01671
obliq = 23.439
per = 102.932
==========================================================================
call get_orbital_parameters(ecc, obliq, per)
output:
ecc , real
obliq , real
per , real
(see set_orbital_parameters above)
==========================================================================
call set_ref_date_of_ae(day, month, year, [second, minute, hour])
input:
day, integer
day of month
month, integer
number of month (1 -12)
year, integer
optional input:
second, integer
(0-59)
minute, integer
(0-59)
hour, integer
hour of day (0-23)
(second, minute, hour) default to (0,0,0)
if all three are not in argument list
if this routine is not called the values will default to
day = 23
month = 9
year = 1998
hour = 5
minute = 37
second = 0
note: if a calendar with no leap years is chosen, autumnal equinox
will occur at the same date each year
if the julian calendar is chosen, autumnal equinox
will drift by 1/4 day for three years, and then shift
back on the fourth year; it is for this reason that a
year must be chosen while setting the autumnal equinox
==========================================================================
call get_ref_date_of_ae(day, month, year, second, minute, hour)
output:
day , integer
month , integer
year , integer
second , integer
minute , integer
hour , integer
(see set_ref_date_of_ae above)
==========================================================================
a) call diurnal_solar(cosz, solar, lat, lon, time, [dt_time])
or
b) call diurnal_solar(cosz, solar, lat, lon, ut, ot, [dt])
(this interface has two permissible forms)
option a: for those using time_manager_mod for time-keeping
input:
lat -- real, dimension(:,:)
latitudes of 2-d array of points at which output is desired,
in radians
lon -- real, dimension(:,:)
longitudes of 2-d array of points at which output is desired,
in radians
(these arrays are 2d to allow for general grids;
if the grid is lon-lat then
lon(i,:) = lon(i) and lat(:,j) = lat(j) )
time -- type(time_type)
the universal time for which output is desired
(universal time = time at 0 longitude)
(time_type is provided by time_manager_mod)
optional input:
dt_time -- type(time_type)
if present, output is averaged analytically
over interval between time and time + dt_time
(this option should always be turned on in a diurnal
gcm to avoid time truncation error in the
total incident flux)
output:
cosz -- real, dimension(:,:)
cosine of the zenith angle, the angle that the sun makes
with the local vertical.
nondimensional
solar -- real, dimension(:,:)
normalized solar irradiance, solar = cosz*((a/r)**2),
where r is the earth-sun distance and a is the semi-major
axis of the orbital ellipse.
nondimensional
cosz(:,:) and solar(:,:) must conform exactly to
lat(:,:) and lon(:,:)
cosz is set to 0.0 in polar night
alternative dimensions:
one can also call this routine with 1-dimensional or 0-dimensional
input and output, as long as the input and output conform exactly
real, dimension(:) :: cosz, solar, lat, lon
or
real :: cosz, solar, lat, lon
option b: for those not using time_manager_mod for time-keeping
input:
lat -- as in a
lon -- as in a
ut -- real
universal time of day (time at 0 longitude)
in radians
length of day = 2*pi
ot -- real
orbital time, time of year
(time = 0 at autumnal equinox in northern hem!)
in radians
length of year = 2*pi
optional input:
dt -- real
if present, output is averaged analytically
over interval between ut and ut+dt
in radians, where 2*pi = length of day
(must be less than pi)
output: as in a
alternative dimensions: as in a
==========================================================================
a) call daily_mean_solar(cosz, solar, lat, time)
or
b) call daily_mean_solar(cosz, solar, lat, ot)
option a: for those using time_manager_mod for time-keeping
input:
lat -- real, dimension(:,:)
latitudes of 2-d array of points at which output is desired,
in radians
(this array is 2d to allow for general grids;
if the grid is lon-lat then lat(:,j) = lat(j) )
time -- type(time_type)
the universal time for which output is desired
(universal time = time at 0 longitude)
(time_type is provided by time_manager_mod)
output:
cosz -- real, dimension(:,:)
cosine of an effective zenith angle that would produce
the correct daily mean flux if the sun where fixed
at that position for the daylight hours.
dimensionless
solar -- real, dimension(:,:)
diurnally averaged normalized solar flux,
solar = cosz*((a/r)**2)*h/pi
where h is the "half-day-length" in radians
(so h/pi is the fraction of the day in which
the sun is shining )
and where r is the earth-sun distance and a is the semi-major
axis of the orbital ellipse
dimensionless
cosz(:,:) and solar(:,:) must conform exactly to lat(:,:)
cosz is set to 0.0 in polar night
alternative dimensions:
one can also call this routine with 1-dimensional or 0-dimensional
input and output, as long as the input and output conform exactly
real, dimension(:) :: cosz, solar, lat
or
real :: cosz, solar, lat
option b: for those not using time_manager_mod for time-keeping
input:
lat -- as in a
ot -- real
orbital time, time of year
(time = 0 at autumnal equinox in northern hem!)
in radians
length of year = 2*pi
output: as in a
alternative dimensions: as in a
==========================================================================
call annual_mean_solar(cosz, solar, lat)
input:
lat -- real, dimension(:,:)
latitudes at which result is desired
in radians
(this array is 2d to allow for general grids;
if the grid is lon-lat then lat(:,j) = lat(j) )
output:
solar -- real, dimension(:,:)
annual mean normalized solar flux, computed by averaging
the output of daily_mean_solar around the year
nondimensional
cosz -- real, dimension(:,:)
cosine of effective zenith angle,
= sum(cosz *solar)/sum(solar), where cosz and solar
are the output from daily mean solar, and sum represents
an integration over the year.
nondimensional
input and output dimensions must conform exactly
alternative dimensions:
input and output can also be 1d
real, dimension(:) :: cosz, solar, lat
-- as usual, all dimensions must conform exactly
There is no namelist
There is no diagnostic output
No data sets are used
v1.1 is a documented and cleaned-up version of v1.0
It should reproduce v1.0 exactly
A list of error messages by routine and what it means.
See astronomy.ps
On the T90, compiler must be 3.1.0.0 or later
None needed
None needed
None known
The orbital integration becomes inaccurate if the
eccentricity approaches unity (of no concern for
the Earth)
Because the diurnal averages are computed analytically by
assuming that the earth-sun distance is constant within
the day, daily_mean_solar and annual_mean_solar
are only accurate if length of solar day << length of year
(also not of concern for the Earth)
One must be careful when constructing a diurnal GCM
with a modified rotation rate. Changing the rotation
rate in constants_mod, which is where the dynamical
core looks for the rotation rate, will not change the
length of the solar day. In the current version
of the time manager, the length of the solar day is fixed
to 86400 seconds, so one would have to use the
option B form of the call to diurnal_solar. As of July, 1999
the atmospheric model is not set up to handle this.
The issue does not arise in non-diurnal models.
(Ideally, one should always have
(2*pi)/solar_day = (2*pi)/siderial_day - (2*pi)/year
where (2*pi)/siderial_day is the angular velocity
of the rotation)
If time_manager_mod were generalized, there would be
no need for the two forms of the calls to
diurnal_solar and daily_solar, and the GCM could be
coded for arbitrary rotation rate in a more transparent way