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Last data update: 2014.03.03

R: Time-integrated insolation

Insol_l1l2

R Documentation

Time-integrated insolation

Description

Computes time-integrated incoming solar radiation (Insol) either between given true solar longitudes (Insol_l1l2) or days of year (Insol_d1d2) for a given orbit and latitude

Usage

Insol_l1l2 (orbit,l1=0,l2=2*pi,lat=65*pi/180,avg=FALSE,ell=TRUE,...)
Insol_d1d2 (orbit,d1,d2,lat=65*pi/180,avg=FALSE,...)

Arguments

`orbit`	Output from a solution, such as `ber78`, `ber90` or `la04`
`lat`	latitude
`l1`	lower true solar longitude bound of the time-integral
`l2`	upper true solar longitude bound of the time-integral
`d1`	lower calendar day (360-day-year) of the time-integral
`d2`	upper calendar day (360-day-year) of the time-integral
`avg`	performs a time-average.
`ell`	uses elliptic integrals for the calculation (much faster)
`...`	other arguments to be passed to `Insol`

Details

All angles input measured in radiants.

Note that in contrast to Berger (2010) we consider the tropic year as the reference, rather than the sideral year, which partly explains some of the small differences with the original publication

Value

Time-integrated insolation in kJ/m2 if avg=TRUE, else time-average in W/m2

Author(s)

Michel Crucifix, U. catholique de Louvain, Belgium.

References

Berger, A., Loutre, M.F. and Yin Q. (2010), Total irradiation during any time interval of the year using elliptic integrals, Quaternary Science Reviews, 29, 1968 - 1982, doi:10.1016/j.quascirev.2010.05.007

Examples

## reproduces Table 1a of Berger et al. 2010:
lat <- seq(85, -85, -10) * pi/180. ## angles in radiants. 
orbit=c(eps=  23.446 * pi/180., ecc= 0.016724, varpi= (102.04 - 180)* pi/180. )
T <-  sapply(lat, function(x) c(lat = x * 180/pi, 
        m1 =  Insol_l1l2(orbit, 0, 70 * pi/180, lat=x, ell= TRUE, S0=1368) / 1e3,
        m2 =  Insol_l1l2(orbit, 0, 70 * pi/180, lat=x, ell=FALSE, S0=1368) / 1e3) ) 
data.frame(t(T))
 ## reproduces Table 1b of Berger et al. 2010:
lat <- c(85, 55, 0, -55, -85) * pi/180. ## angles in radiants. 
T <-  sapply(lat, function(x) c(lat = x * 180/pi, 
         m1 =  Insol_l1l2(orbit, 30 * pi/180. , 75 * pi/180, 
               lat=x, ell= TRUE, S0=1368) / 1e3,
         m2 =  Insol_l1l2(orbit, 30 * pi/180. , 75 * pi/180, 
               lat=x, ell=FALSE, S0=1368) / 1e3) ) 
 ## reproduces Table 2a of Berger et al. 2010:
lat <- seq(85, -85, -10) * pi/180. ## angles in radiants. 

## 21 march in a 360-d year. By definition : day 80 = 21 march at 12u
d1 = 79.5 
d2 = 79.5 + (10 + 30 + 30 ) * 360/365.2425 ## 30th May in a 360-d year

T <-  sapply(lat, function(x) c(lat = x * 180/pi, 
        m1 =  Insol_d1d2(orbit, d1,d2, lat=x, ell= TRUE, S0=1368) / 1e3,
        m2 =  Insol_d1d2(orbit, d1,d2, lat=x, ell= FALSE, S0=1368) / 1e3))
                          
## I did not quite get the same results as on the table 
## on this one; probably a matter of calendar
## note : the authors in fact used S0=1368 (pers. comm.) 
## 1366 in the paper is a misprint

data.frame(t(T))