However, about that 800 year lag. What's the relevance to today's conditions when CO2 is increasing, not because of warming (as presumably those charts show), but supposedly due to human activity?
Total greenhouse gasses (CO2 + methane + water vapor) have increased from roughly 94.3 to 95.0 (CO2 is a very, very small percent of the total greenhouse gas effect.) That has NOT changed temperature.
Cloud cover decreased from 1920 - 1935 -> temps rose measurably, and were equal to (or slightly higher than) today's temps. CO2 was low, about 1/3 less than today's level.
Cloud cover decreased in the 40 - early 70’s -> temps decreased for some 36 years. CO2 was steadily increasing the whole time.
Cloud cover decreased between 70 and 1998 -> temp’s increased again. CO2 was steadily increasing. THIS IS THE ONLY PERIOD WHEN THE AGW THEORIES WORK - They fail at every other time in the past 120 years.
Cloud cover remained constant from 1998 - 2007 -> temps remained constant. CO2 was steadily increasing.
Today’s increasing CO2 levels are fertilizing crops and increasing the feed and food we need by factors of 12% to 26%. They do not affect temperature now, nor have they affected temperature in the past.
You cannot establish how much of today's increase in CO2 is due to man's releases - compared to how much is getting emitted from the oceans as they warm up from the (800 year previous) Little Ice Age. Look at the mass of CO2 required to go from 280 ppm to 380 ppm, then compare it to 35 years of carbon burning (minus the CO2 removed by plant matter.