How can we accurately quantify the degree of scientific certainty that global heating is caused by humans?

Question

How can we accurately quantify the degree of scientific certainty that global heating is caused by humans?

It seem virtually certain that the huge 100 ppm spike in $\small\mathsf{CO_2}$ since 1950 can only be caused by humans. Can we be as sure that this huge spike in $\small\mathsf{CO_2}$ caused the 1 $\small\mathsf{^o}$C increase in global temperatures as we are that tobacco causes cancer?

Do validated alternative explanations exist?

What kinds of objective measures are typically used to determine the specific degree of scientific certainty?

There is a trend showing an increasing slope in the following graph data
1910 to 1960---0.41---50 years / 0.41 = 122 years per degree
1960 to 2018---1.03---58 years / 0.87 = 67 years per degree

https://data.giss.nasa.gov/gistemp/graphs/graph_data/Global_Mean_Estimates_based_on_Land_and_Ocean_Data/graph.txt

I am trying to point out exactly how implausible global heating NOT CAUSED BY BY HUMANS really is to skeptical minds that are not very good with science.

Answer 1

There are a few ways

Basically the best way is to see how many experts in the field are convinced, as great as it would be to assess the evidence individually, one person can't be an expert in everything and unless you and your audience are a climate scientists most papers are going to be beyond a lay assessment. So the best thing you can do for the lay public is look to the experts, people who have spent decades researching the subject and have the best ability to assess the data, and see what their assessment is.

NASA has a wonderful site dedicated to collecting assessments. They fall into three rough categories.

Meta analysis

A meta analysis of published works shows the number of scientific papers rejecting anthropomorphic climate change is vanishingly small (0.7%) and shrinking. those uncertain was even smaller (0.3%)

Professional survey

the same analysis also surveyed 29,000 published climatologists and showed a 97% support for anthropomorphic climate change and the rest being largely no-position. this is even skewed by expertise, when accounting for the number of published papers (a rough way of measuring expertise) it shows even stronger support among more published authors with most of the opposition being from authors that only publish a small number of papers.

Public statements by relevant scientific societies.

The American Meteorological Society and Geological Society of America as well as many others have made public statements in favor of anthropomorphic climate change. And of course you have the statements by the Intergovernmental Panel on Climate Change.

Answer 2

No, it is not possible to establish a human cause with the degree of certainty you are asking for. There have been similar episodes in the distant past when either there were no humans at all, or the total emissions of all the worlds cooking fires were comparable with the emissions of one solitary and unremarkable volcano If global heating with humans as the sole cause were as certain as the existence of gravity, there would be no controversy or debate about it.

What can be established with certainty is that since the industrial revolution got well under way there has been a fairly substantial ppm rise in atmospheric CO2, and this has coincided with a small but measurable rise in global temperature. Whether this is entirely coincidence or whether it is cause and effect is hotly debated, and there is not unanimous agreement even among professional meteorologists and climatologists. There was already some global warming (called an interglacial) long before the industrial revolution added some extra CO2 to the atmosphere, but most scientists think this additional CO2 has accelerated global warming.

There are natural mechanisms which extract CO2 from the atmosphere, and these natural mechanisms are very slightly more effective when CO2 content increases. However, if the increase is too rapid it can be more than these natural mechanisms can deal with. Climate change is a natural phenomenon which has been under way for the past 4.5 billion years and is likely to continue for as long as the world exists.