This post is an update. It reports 3 more months
of irradiance data than the last edition. These
newer data did not change any major conclusions
in this analysis.

-.-. --.- Roger
=-=-=-=-=-=-=
New Data Show Solar Irradiance Continuing to Slowly Fall
By Roger Coppock 02/08

ABSTRACT:
An analysis of newly available satellite Solar irradiance
measurements from 1976 to 2008 shows a small but statistically
significant decrease of -0.0066 +- 0.0005 Watts per square
meter per year over the 32-year period.

PROCEDURE AND RESULTS:
The location of the data's end points within the Solar cycle
biases a simple linear regression and produces an incorrect
result. (Roughly twice the correct magnitude, or
-0.0118 +- 0.0006 W/m^2 per year.) Therefore, the analysis
required a non-linear curve fit to a 'line plus sine'
expression:

B1 + B2*Year + B3*SIN(B4+(Year*2Pi)/B5)

where the determined coefficients B1, B2, B3, B4, and B5
are known as the intercept, slope, amplitude, phase, and
period respectively.

After correcting for the appropriate cycle of the SIN()
function, (B30.0 and 2*PiB4=0.0), the results of the
10725-point curve fit are as follows:

Irad ~ beta1 + beta2 * Year +
beta3 * sin(beta4 + (Year * 2*Pi)/beta5)

Parameters:
Estimate Std. Error t value Pr(|t|)
beta1 1.379e+03 9.511e-01 1450.132 2e-16
beta2 -6.647e-03 4.772e-04 -13.930 2e-16
beta3 4.974e-01 5.908e-03 84.195 2e-16
beta4 1.148e-01 2.746e+00 0.042 0.967
beta5 1.015e+01 2.258e-02 449.405 2e-16

Residual standard error: 0.4324 on 10720 degrees of freedom

Please note the large standard error on beta4, the phase
of the SIN function. Only three cycles of high variance
data produce this. As an exercise, try to locate the
peeks and valleys of these data in this graph. Please see:

http://members.cox.net/rcoppock/Solrad.jpg

The data are black. The linear component, both intercept
and slope, is green. The total 'line plus sine' function
is red.

The curve fit was performed by the "R" statistical package
for Power PC OSX, Version 2.2.1.

The dual cavity radiometer Solar irradiance data come from
PMODWRC. They cover the period from 1/12/1976 to 01/03/2008.

http://www.pmodwrc.ch/pmod.php?topic.../SolarConstant

ftp://ftp.pmodwrc.ch/pub/data/irradi...41_61_0801.dat

A preprocessing program converted month and day information
into fractional years and removed data marked by PMODWRC as
invalid.


DISCUSSION:
Global warming 'skeptics' often claim that increases in Solar
radiation reaching the top of Earth's atmosphere, not rising CO2
concentrations in the atmosphere, are responsible for the observed
climb of the global mean near surface temperatures in the last
thirty years. This argument was not supported by the facts.
Now it is even less so. When the solar cycle was statistically
removed, prior data showed no significant long term change in
Solar irradiance large enough to explain the warming, (about
3 W/m^2 over the last two centuries are needed.) Present data
actually show a very small but statistically significant decrease
in solar output over the last three solar cycles. It is very
hard to support any claim of a solar cause for global warming
when measurements clearly show decreasing solar output.

For more information, please see:

http://www.terradaily.com/reports/Ch...rming_999.html

http://environment.newscientist.com/...l-warming.html