Modeling incoming solar radiation

Ehrhard Raschke (Hamburg)

Stefan Kinne (Hamburg)

Yoko Tsuschima (Yokohama)

Stephan Bakan (Hamburg)

With data contributions from GISS and LaRC

Is it so easy?

In principle the incoming solar irradiance reaching the Top of the atmosphere (ToA) can be computed easily using the principles of spherical geometry and the astro-mechanical parameters (distance Sun-Earth, obliquity of the orbit, perhelion and inclination of the rotational axis), which are determining the Earth‘s orbit around the Sun.

Summary of possible error sources in computations of the insolation at ToA:

Total solar irradiance (TSI = ~ 1361 Wm-2), solar cycles

Orbital parameters : eccentricity, obliquity, perihelion

Inclusion of a leapday (strictly the tropical year?)

Spatial resolution, time resolution

Definition of sunset and sunrise

Definition of TOA

and

Occasional bugs in the code !

J F M A M J J A S O N D

Monthly zonal anomalies in IPPC models related to ISCCP

1985 - 1988

6 weeks with patiently repeated questions to modelers for information

Deriving Eccentricity and Perihelion from ISCCP s0/S0

Input: ISCCP Daily TOA Full-incoming Solar FLux s0 from our table:

FS0

data\full_isolation.asc

rows FS0( ) 365.0000 cols FS0( ) 2.0000

day# 1->365 Full_insolation at TOA

Daily TOA full-incoming solar s0 at Aphelion, Perihelion and its annual mean S0

i 1 365 s0i FS0i 2

max s0( ) 1413.8225 min s0( ) 1322.4624 S0 mean s0( ) S0 1367.1586

Since s0/S0 = r^2/R^2, where s0 = Daily TOA Full-incoming Solar, S0 = its annual mean, r = daily Sun-Earth distance (in AU) and R = its annual mean = 1 AU as taken now

Earth-Sun distance r AT Aphelion and Perihelion We have:

ris0i

S0

max r( ) 1.0169 min r( ) 0.9835

AB=2a; CD=2b; F1F2=2c, rmax=a+c & rmin=a-c In the ellipse: a

max r( ) min r( )

2 c

max r( ) min r( )

2 b a

2c2

Eccentricity: eec

a ee 0.0167 Eaxctly equal to the correct Earth-Sun orbit's e = 0.0167 now

And our Perihelion and Aphelion (in AU) = 0.9835 and 1.0169, respectively:

Plot the Earth's orbit to Sun j 1 43 tj j 1( ) 0.15 x j a cos tj y j b sin tj

1 0.5 0 0.5 1

1

0.5

0

0.5

1

Earth-Sun Orbit

Sun at one focus

y j

b 1

x j a c 1

Masterpiece by Y.-C. Zhang

Modelers (e.g. for the IPCC AR4) and also climatologists (ISCCP and SRB) obtain often different results ! Should we tolerate ?

Tild of axis ±0.5 degrees

CONTROL RUN For Enhanced Insolation For Reduced Insolation

Total cloud cover

ISCCP minus SRB: Monthly global averages of the insolation at TOA Why do the seasonal differences increase with time ?

Data from ISCCP and SRB projects

-0,25

-0,2

-0,15

-0,1

-0,05

0

0,05

0,1

0,15

0,2

1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Global monthly insolation at TOA: ISCCP minus SRB: June 2007

IPCC 2007

How are the other radiation climatologies computing the

insolation at TOA?

-.-.-.-

Please don’t forget: There is only one Sun – Earth - System !

Therefore modelers and climatologists should compute the same solar input into the climate

system.

From G. Schmidt, GISS, 2006

0.5 hours

2.5 hours

S

S

S

-1

-0,8

-0,6

-0,4

-0,2

0

0,2

0 6 12 18 24 30 36

SRB-ISCCP CER-ISCCP

Monthly global averages of the insolation at TOA : Jan 01 to Dec 03

0,08

0,1

0,12

0,14

0,16

0,18

0 6 12 18 24 30 36

ISCCP SRB CERES

Global monthly averages (up-down ratio) of surface albedo (%)

Jan 2001 to Dec 2003