# Earthshine blog

## "Earthshine blog"

A blog about a telescopic system at the Mauna Loa Observatory on Hawaii to determine terrestrial albedo by earthshine observations. Feasible thanks to sheer determination.

## Albedo variations in CERES data

Error budget Posted on Mar 09, 2012 10:25

What is the variability in global-mean daily-average values of albedo?

We need this number in order to argue for the levels of precision we are striving for: A main counter-argument to very high instrumetal and method precision could be ‘the natural variability is much higher, so you need not work so hard’. A much worse counter-argument would be ‘you must have much higher precision to catch the very small variations expected’. The worst is probably ‘natural variability is much higher than all climate change variations of interest so you will never be able to say anything interesting using your – or satellite – albedo data’.

We estimate what the daily global-mean albedo variability is. We necessarily have to do this from satellite data, and use the CERES data product (click on the link).

Downloading 1×1 degree daily-average CERES albedo for ‘all sky’ conditions and averaging all data points not flagged as ‘bad data’ we get a daily series for several years with seasonal variations – like the Figure 1 in Bender et al. Extracting and removing the seasonal cycle, and removing all obvious glitches in the data we get the daily albedo anomaly series. We calculate the standard deviation of this series and express it as a percentage of mean albedo.

We find that the CERES-based global-mean albedo varies by 1% from day to day (1SD is 1.07% of the mean).

We did not weight the data with a cosine law towards the poles, but the effect of this is minor. The 1SD on albedo is therefore near 0.003.

We simulated daily observations of albedo data drawn from a population with the Bender et al seasonal cycle and daily noise added with the 1% SD from above. This is an experiment in sampling a constant albedo. We simulated 10, 20 and 30 years of data. We fitted straight lines to the data using 365 points a year (unrealistic) or 100 points a year (realistic) and expressed the change in albedo, according to the straight-line fit, at the end of the 10, 20 or 30 years period as a perecentage of the mean albedo.

The plot shows histograms from 1000 realisations of the above process. To the left are results for 365 samples a year. To the right for 100 samples a year, and each row is for 10, 20 and 30 years of data, respectively. The histograms show what the chances are of observing an albedo slope of a certain value when the noise is realistic and the actual underlying albedo is constant. For 10 years of data and 100 observations per year the chances of observing an albedo slope between -0.35% and +0.35%, when the slope is really 0, are thus about 68 in 100 (expressed that way to avoid using “%” twice in the same sentence … ). For 20 years of data the same odds apply to the +/- 0.24% range. 30 is – 0.2%.

These results differ from those in the previous post on this subject (below) by the value used for the standard deviation of the variability. In that post we had used the values for scatter in Bender, and they are valid for monthly means and are about 3 times smaller than what we used here. As sqrt(30) is about 5.5 we learn that daily albedo values are not independent – there are about 3 days between independent data points for global-mean albedo!

What have we learned? If our instrument and methods can really give us 1 datapoint each night with 0.1% precision then we are slightly on the luxury side – natural variability will falsely show us slopes of +/- 3 times that number in 10 years of data, and even for 30 years of data we are still a factor of 2 better than we ‘need to be’.

However, if the instrument and methods are not quite up to the 0.1% level we have aimed for (a realistic situation, actually … ) then we are not being over-perfectionists.

Likewise, reported and discussed changes in albedo slope are quite large. Bender et al show in their Figure 1 a change in observed albedo, between the CERES data and the ERBE data of 4% over about 15 years. Nobody believes this change is real – it is due to instrument calibration issues – but the numbers serve to show what we are up against: We should ask, can we rule out 4% change in albedo over 15 years with our earthshine data? The answer would seem to be – yes, we will be able to verify changes in global-mean albedo to the +/- 0.35% level with 10 years of data.

So we are doing all right with our idea!

We should repeat the above with an analysis of what can be done with 1, 2 etc instruments; or a global network of instruments with the occassional dropout due to realistic bad weather, and so on.

## JD2455996

Observing log Posted on Mar 09, 2012 10:05

Hazy – ring around the Moon.

## measuring linearly changing albedo

Error budget Posted on Mar 09, 2012 05:41

Simulation of 100 albedo measurements per year of a linearly rising
albedo of 1 percent per decade. The simulation is based on the mean monthly global albedo estimates over several decades from a suite of models as in Bender et al . 2006 (Tellus, 58A, 320) figure 3.

grey crosses : individual measurements

green line — monthly averages

red circles — annual averages

the black lines are the fits to the monthly averages — they both come out with the correct slope – so it does work!

the two panels show the effect of 1 percent (lower) and 0.1 percent scatter (upper) on
the individual albedo measurements due to natural variability.

the 0.1% case allows the underlying model to be seen clearly.

1% scatter in the daily albedo makes things look a deal noisier — but the right slope comes out and one can get a pretty good seasonal pattern
from the monthly means and better stull by folding the data into a year.

we are looking further into what daily variations naturally arise — the Bender paper is not clear on this.