## How variable is Nature?

Real World ProblemsPosted by Peter Thejll May 05, 2013 02:31PMOur efforts to measure albedo precisely and accurately are limited by the natural variability. Albedo is inherently a quite variable property of the Earth - viewed day-to-day [see presentation linked to below for details on the GERB data variability!]. Just how much does global-mean albedo vary - in the short run and over many years?

We have CERES albedo data for the period 2000 to 2012. It is given as monthly mean data for a 360x180 degree grid. We take this and calculate global-mean monthly values. Some results are here:

*Data downloaded from: http://ceres.larc.nasa.gov/cmip5_data.php*

these are the monthly-mean data prepared by NASA for the CMIP5 effort.

I calculate the global weighted means for the given monthly-mean values

of upward and incoming shortwave light at TOA.

The linfit slope is:

Slope: 5.4920926e-08 +/- 5.7758642e-07 in albedo units/day.

This is an INsignificant slope - per decade it would amount to 0.09 %

of the mean albedo. Using, instead of the slope, the +/- errors on the slope we get:

+/- 0.97 % per decade.

The mean we get is:

Mean albedo: 0.218214

this is small. Publications using these data say: 0.29 ... there is some

problem with accounting for regions' weights. I omit all areas where the

incoming flux at TOA is less than 12 W/m² - this helps avoid Inf's and

NaN's. I weight each area with the cosine of the latitude of cell middle.

Month Albedo S.D. S.D. as % of mean

1 0.228720 +/- 0.000820013 or, +/- 0.358522 %.

2 0.222061 +/- 0.000866032 or, +/- 0.389997 %.

3 0.206976 +/- 0.000856246 or, +/- 0.413694 %.

4 0.215791 +/- 0.000886397 or, +/- 0.410766 %.

5 0.219209 +/- 0.00129653 or, +/- 0.591460 %.

6 0.219878 +/- 0.00122390 or, +/- 0.556628 %.

7 0.215800 +/- 0.000900811 or, +/- 0.417429 %.

8 0.212036 +/- 0.000893605 or, +/- 0.421440 %.

9 0.203454 +/- 0.000899703 or, +/- 0.442214 %.

10 0.215973 +/- 0.00123064 or, +/- 0.569814 %.

11 0.227462 +/- 0.000582274 or, +/- 0.255988 %.

12 0.231050 +/- 0.00111927 or, +/- 0.484429 %.

these are the monthly-mean data prepared by NASA for the CMIP5 effort.

I calculate the global weighted means for the given monthly-mean values

of upward and incoming shortwave light at TOA.

The linfit slope is:

Slope: 5.4920926e-08 +/- 5.7758642e-07 in albedo units/day.

This is an INsignificant slope - per decade it would amount to 0.09 %

of the mean albedo. Using, instead of the slope, the +/- errors on the slope we get:

+/- 0.97 % per decade.

The mean we get is:

Mean albedo: 0.218214

this is small. Publications using these data say: 0.29 ... there is some

problem with accounting for regions' weights. I omit all areas where the

incoming flux at TOA is less than 12 W/m² - this helps avoid Inf's and

NaN's. I weight each area with the cosine of the latitude of cell middle.

Month Albedo S.D. S.D. as % of mean

1 0.228720 +/- 0.000820013 or, +/- 0.358522 %.

2 0.222061 +/- 0.000866032 or, +/- 0.389997 %.

3 0.206976 +/- 0.000856246 or, +/- 0.413694 %.

4 0.215791 +/- 0.000886397 or, +/- 0.410766 %.

5 0.219209 +/- 0.00129653 or, +/- 0.591460 %.

6 0.219878 +/- 0.00122390 or, +/- 0.556628 %.

7 0.215800 +/- 0.000900811 or, +/- 0.417429 %.

8 0.212036 +/- 0.000893605 or, +/- 0.421440 %.

9 0.203454 +/- 0.000899703 or, +/- 0.442214 %.

10 0.215973 +/- 0.00123064 or, +/- 0.569814 %.

11 0.227462 +/- 0.000582274 or, +/- 0.255988 %.

12 0.231050 +/- 0.00111927 or, +/- 0.484429 %.

What do we learn?

We learn that albedo is remarkably constant when observed by satellite. There is no discernible slope to the data but if we use the 1 sigma uncertainties on the slope as upper limits we find that per decade the albedo has changed less than 1%.

The monthly means follow an understandable annual cycle (maxima in NH and SH winters with minima in March and September). The spread around monthly means amount to 0.25 to 0.6% of the monthly mean value.

Climatologically it is an open question whether albedo ought to change with climate drift. During the observing period global mean surface temperatures have changed by about +0.1 degree C [see http://www.ncdc.noaa.gov/sotc/service/global/global-land-ocean-mntp-anom/201101-201112.png ]. This is during the 'hesitation period' that is much discussed presently. During other decades mean T has risen much more - but we have no albedo data from these periods.

Using the above 1 sigma upper limits on slope of 1% per decade we see that if the slope is due to changes in T then the relationship is 1% per 0.1 degree or 10% per degree. This is based on an upper limit and the true value is closer to 0% per degree.

Note that the previous argument is unrelated to the EBM based relationship that works for equilibrium climate only - there, and only there, the expected relationship is -1% per degree.

So, what does that give us? If we were to observe a larger slope we could use the data in the "satellites are getting it wrong" mode - as Pallé et al did for a while. If we measure no slope we can hope to set more stringent limits to the slope than the above satellite values do - can we determine the slope of global mean albedo to better than the 1% per decade above? In this presentation I found upper limits of 0.2% per decade based on a null hypothesis of 'no albedo change' and realistic observing limitations. The numbers used were based on Frida Benders CERES data, but they do not differ enormously from the present, longer, ones.

So can we reach 0.2% error per decade, observationally?

This requires a discussion of the single-frame errors we get as well as the period-mean data we can expect. More alter!