Or as your favorite site http://www.realclimate.org/index.php?p=87 says:
Over the last 150 years, carbon dioxide (CO2) concentrations have risen from 280 to nearly 380 parts per million (ppm). The fact that this is due virtually entirely to human activities is so well established that one rarely sees it questioned. Yet it is quite reasonable to ask how we know this.
They throw around their usual 1/2 science blather and prove nothing except that some part of the increased CO2 is anthro. Now you use the word predominantly, what does that mean exactly? The change in 13C/12C is 0.15% and the increase in CO2 is 21%, so the only way to force a conclusion like "virtually entirely" or your less emphatic "predominantly" is to assume a ridiculously long cycle time for CO2. Your source says 60 years, a "virtually entirely" conclusion requires at least 150 years, but the actual cycle time is 5-6 years. The human part of the increase comes out to about 1/5th or 1/6th.
The Wigley 1993 reference might be useful here. Ask and Google shall giveth:
First note: makes a deal about the so-called "missing carbon sink". My recollection is that this has been better quantified since 1993, and though there's still a gap, it's only abou 15-20%, not like 50% in the 1980s. I think they nailed more boreal forest CO2 uptake than expected for part of the reduction.
Second note: I think that the question can be related to to a (dastardly simple) kitchen sink model of atmospheric CO2 concentrations. Imagine a nearly-full sink where the water is pouring in from the faucet and the drain is open. The flow from the faucet has been adjusted such that the level of the water in the sink is not changing at all.
On the kitchen counter, you have a five gallon bucket of water colored red with food coloring. You start to add water from the bucket into the sink. Questions: what will happen to the level of the water in the sink, and what will happen to the color of the water in the sink?
Answer to question 1: the level of water in the sink will rise. What is responsible for the rise? Answer: the water being added from the bucket is entirely, 100%, totally responsible for the rising level of water in the sink.
Answer to question 2: the water in the sink will slowly get redder. But because the red water being added is mixing with the much larger volume of water in the sink, it will take considerable time for the water to get appreciably red. So even though the water being added from the bucket is 100% responsible for the increase in the level in the sink, it's only a small part of the total amount of water in the sink. So a small measured dilution effect can indicate a much more significant change. Right?
If we imagine that the sink is the atmosphere, the water from the faucet is the CO2 flux from the ocean (and other places). [Noting that current measurements indicate that the ocean is a net CO2 sink, a point that I'm not sure drrocket has addressed.*] drrocket appears to be indicating that even though we're obviously adding water from the bucket (anthropogenic CO2 emissions), the reason that the water in the sink (atmospheric CO2 concentrations) is rising is that the flow rate from the faucet (natural oceanic flux) is increasing.
Right?
* I tried to get some of the Pieter Tans et al. references to support this (there are several), but they are all in Science or Nature.