If I want to measure how much business a shopping mall gets, I can stand by an entrance way and count the number of people who go into the mall. If I stop every tenth person on the way out and frisk them for their receipts, I can estimate the per-person amount of money spent, and multiply that by ten to get an idea of how much business is represented by the particular entrance way I am sampling. This would work. I wouldn't know how much money was spent in the mall because I have no information about other entrance ways, but I could track changes over time in business, and I'd probably be able to pick up weekly patterns and seasonal holiday shopping patterns.

But say one of the anchor stores has a big sale one weekend, and everybody tries to park near that store because they are going to go there. That would bias the relationship between my estimate and the the overall trend. I might see a drop in spending because my entrance way is on the other side of the mall from the anchor store, or if my sampling point is at that store, I might see an increase, and in either case, my estimate may be biased. Or, there may be roadwork on the route to the part of the huge parking lot of the shopping mall nearest my entrance way, causing a reduction of how many customers go into that store. Or a store that sells really expensive stuff and is really successful opens up in part of the mall and, again, depending on my sampling location, I would end up with a biased estimate because I either over-count cash flow from my 1 in ten sampling of recipes, or undercount it, again, depending on my sampling perspective.

This is like trying to estimate changes in the overall temperature of the earth under global warming. The part of the sun's energy that lands on the Earth heats the surface (and a bit of the atmosphere) and then, that surface heat radiates back into space. Adding persistent greenhouse gasses like Carbon Dioxide slows the escape of this heat from our atmosphere, so there is more heat to warm the atmosphere, the surface of the land, and the surface of the oceans. Some of this heat, especially that which finds its way to the ocean surface, is then subducted into deeper strata. The vast majority of the heat that is found in the deepest parts of the ocean gets there from surface waters, ultimately.

In order to track global warming caused by adding persistent greenhouse gasses you can just measure the temperature of the air at any given point, all day and night and all year, for many years. But since the atmosphere is complex, this estimate would be very inaccurate and increases and decreases over time may be the result of the atmosphere being complex rather than changes in the effects of the greenhouse gasses. So you can measure a thousand points around the globe and average those readings out. But some of the heat might contribute to melting sea ice and glaciers, so you'd have to factor that in too. But some of the heat is held in the sea surface, so it is also necessary to measure the sea surface temperature at many locations. But some of that heat ends up in the deeper ocean, and over time, the rate of transfer of heat to the deeper ocean changes, so you'd better measure that too. And so on and so forth.

Eventually you'll have enough measurements that you can track the movement of heat between all its reservoirs and get a good total. This would be analogous to placing research assistants at every entranceway to the shopping mall and sampling the receipts of the consumers more densely.

For the last several years the amount of heat that is building up in the atmosphere and the sea surface has been less than the previous several year. This heat has increased over this time, on average, but not as much as previously. However, this estimate misses the heat used to melt sea ice and glaciers, and it also misses the heat that is subducted into the deep ocean. When that is added in, it turns out that over both long and short terms, the amount of additional heat retained on the surface of the earth (including air and water and everything else) because of the additional of persistent greenhouse gasses to the atmosphere has been increasing.

But, there is still a problem with the measurements that have been used to make these estimates. One of the biggest problems is the temperature in the Arctic region. There has simply been less data from this region than elsewhere. Also, a few other areas of the earth, like big chunks of the African Continent, have not been sampled. A new study uses new approaches to fill in these missing blanks. The bottom line is this: The change in temperature of the atmosphere and sea surface, which combined is the most commonly referred to measurement used to track global warming, has been under-estimating the amount of warming over the last several years.

Here's the info on the paper:

Title: Coverage bias in the HadCRUT4 temperature series and its impact on recent temperature trends Abstract: Incomplete global coverage is a potential source of bias in global temperature reconstructions if the unsampled regions are not uniformly distributed over the planet's surface. The widely used HadCRUT4 dataset covers on average about 84% of the globe over recent decades, with the unsampled regions being concentrated at the poles and over Africa. Three existing reconstructions with near-global coverage are examined, each suggesting that HadCRUT4 is subject to bias due to its treatment of unobserved regions. Two alternative approaches for reconstructing global temperatures are explored, one based on an optimal interpolation algorithm and the other a hybrid method incorporating additional information from the satellite temperature record. The methods are validated on the basis of their skill at reconstructing omitted sets of observations. Both methods provide superior results than excluding the unsampled regions, with the hybrid method showing particular skill around the regions where no observations are available. Temperature trends are compared for the hybrid global temperature reconstruction and the raw HadCRUT4 data. The widely quoted trend since 1997 in the hybrid global reconstruction is two and a half times greater than the corresponding trend in the coverage-biased HadCRUT4 data. Coverage bias causes a cool bias in recent temperatures relative to the late 1990s which increases from around 1998 to the present. Trends starting in 1997 or 1998 are particularly biased with respect to the global trend. The issue is exacerbated by the strong El Niño event of 1997-1998, which also tends to suppress trends starting during those years.

The authors of the paper produced this video explaining what they did, and what they found:

Dana Nuccitelli has written up an excellent blog post explaining this research here: Global warming since 1997 more than twice as fast as previously estimated, new study shows: A new study fills in the gaps missed by the Met Office, and finds the warming 'pause' is barely a speed bump.

Stefan Rahmstorf has another excellent writeup, currently in German but you can hit "Translate" on your browser if you don't read German (I'll add the english version of it when I get it): Erwärmung unterschätzt

UPDATE: Two more posts on the topic:

At Real Climate: Global Warming Since 1997 Underestimated by Half

At Planet 3.0: The Disappearing Hiatus