Yes you do. The only way you can bridge the gap between emissions and co2 rise in 2006 is if the estimates for emissions are overvalued and the estimates of co2 rise are undervalued. You require both to be true. I have said that you can do this for individual years using very liberal error rates for both co2 emissions and co2 level measurements, but when you extend this analysis over X years you don't get to multiply the error rate by X too. The error rate is not linear with the number of years, so what emerges is that over such periods of time is not possible for human co2 emissions to be less than the atmospheric co2 rise.

My point is that it is not, you require a specific case where the co2 emissions and rise are both off by a signficant amount in a certain direction. You talk about possibility, but not probability. I can see that the 2006 figures being off by so much and off in the direction you need has low probability - there is a far better chance that 2006 did see emissions more than co2 rise.

But furthermore for a period of 10 years or more the probability of human emissions being less than the co2 rise falls even further.

Why would it be poor maths? I am simply taking the 20ppm rise seen in the last 10 years (hell lets make it 22ppm), and taking a total of co2 emissions in that time (in fact the total I use is actually lower than the estimated figures as it assumes 22gTC every year even though recent year figures are around 28 and even 1997 was about 25)

Then we use the formula Natural contribution = co2 rise - human contribution

Even if we
18 * 7.8 = 171 gTC rise in atmospheric co2
10 * 22 = 220 gTC rise in human emissions

So over that 10 year period NC = 171 - 220
NC = -59

And that's using the error ranges for co2 emissions and co2 concentration that you used for a single year. This is what I mean about the uncertainty in a single year making it possible (although unlikely) that co2 rise > anthropogenic emissions, but as you take a range of more years, the uncertainty does not rise linearly with the number of extra years, and what you get is that you require higher and higher error ranges in order to make co2 concentration rise meet anthropogenic emissions.

I don't need to do that because even the last 10 year period makes it clear humans have emitted more. Like I said an individual year could be subject to more inaccuracy, but over a long time period the actual situation emerges.

Actually the figures are over 260Gt co2 emissions over the last 10 years before you start applying errors, so I was using a 15% lower figure and still co2 emissions were 50GtC higher than the co2 rise in that 10 year period.

Are you implying that isn't justified? Seeing as we agreed that co2 measurements are accurate to 1ppm, 2006 measurements are about 380ppm +-1ppm and 1996 measured about 360ppm +-1ppm. Which makes a total of 20ppm rise with only 2ppm error - ie 20ppm +-2ppm. I could even point out that the further you deviate from the 20ppm mean, the less confidence you have. A 22ppm rise and a 18ppm rise is less likely than a 20ppm rise for example. 22 and 18 are possible, but not likely.

Because we don't calculate the emissions over 10 years as emissions in 2006 minus emissions in 1997

As I pointed out, you get more than that figure just by using the actual figures. Over 260GtC in 10 years.

Natural background noise is not eliminated. You only have to look at the measurements taken over a single year to see it.

But as the table says, a minimum of 3.1GtC of that 6GtC must be put in "Storage in the atmosphere" within 90% confidence interval. Setting it at 0GtC is going to fall well outside that 90% confidence interval.

No Im not. The second part of the table is titled "Partitioning among reservoirs", ie you have to partition the amount of human emissions amount the reservoirs. You don't get to partition a higher number than human emissions among the reservoirs.

So you are claiming that mathematically, statistically, logically and intuitively you can spend $15.5 of $9 given to you....

The important thing is that the table is including them as anthropogenic emissions. The 2nd part of the table would have lower values if they had left land use changes out.

Given that it's a 90% condifence interval you don't have much room to go outside them. You certainly have no scope for going 16 times outside the confidence interval by saying the atmosphere took zero (which falls way outside the 3.1-3.5 90% confidence range). It's not the case that any value outside that range has 10% chance. A value less than 3.1 has 5% chance (the other 5% is for above 3.5). And the further you go down from 3.1 the lower the probability goes.

$0 for "Lost it" falls outside of the 90% range of $1-$3, so there is less than 5% chance that they lost none (5% for anything lower than $1). Probably less than that depending on where the 99% condifidence interval lies, you are twice the 90% confidence range out so it's going to be lower than 5%

You are saying that 0 of the carbon is partitioned into the atmosphere, wheras the 90% confidence interval given is 3.1-3.5. That means:

--------5%--------|-90%-|---------5%-------

there is less than 5% chance of no < 3.1 GtC going into the atmosphere. But it's going to be much less than 5% given that you are so far from the 90% range. It will look like this:

------2.5------|A-2.5%-|----90%----|-2.5%-B|-------2.5--------

Where A and B represent the 95% confidence interval, and it can be subdivided further into 99% and beyond. zero co2 is going to fall outside of a very large confidence interval given that it is 16 times outside the 90% interval.

What will be the case is that the further a figure gets from the mean of 3.3, the less confidence there is. There is less than 10% confidence of it being more than 0.2 from 3.3GtC. Yet a zero figure is 3.3 off, not just 0.2. That is going to be outside even the 99.9% confidence interval.