<h2>Active WebGL plot of decadal regional temperature trends using ERSST V5 and GHCN V4</h2>

I have maintained a page of local trends over periods that users could choose. It was based on GHCN V3, and mesh display, and can still be seen here. But I need to upgrade to GHCN V4, and I have decided to update to LOESS graphics as well. But there is one further upgrade - instead of a choice of a fixed number of intervals ending in present, you can now choose any period of decades back to 1900. The maths of this is quite interesting, and I'll say more below. The new page is here, with the link in the page list top right.

The plot itself is the usual WebGL trackball. You can drag the globe around, or more quickly relocate by clicking on the small map above. Clicking on the plot shows the trend for the chosen period at that location. You can choose periods with the buttons on the right. The endpoints are colored, so the start state of 1980 and 2020 means the period will be Jan 1980 to Dec 2019, with missing months suitably handled. If you click outside the range, the range will extend; if you click inside, the red color will move to your choice. If you wanted to move the pink end, click the pink button to make it red. When you have chosen, click the Show button at the top to get the new plot. The average global trend for the period will show at the bottom as well.

Methods

As usual, the sphere is a trackball that you drag into position, or you can quickly set by clicking on the small map at the top. Beside that map are checkboxes which let you switch the objects displayed. The icosahedral mesh and nodes are initially not shown.

The map is created by first getting monthly averages on the 5762 icosahedral nodes, as described here and here. The trends are then calculated on those nodes. The LOESS method takes a weighted local linear regression on the closest station/SST data, even if it is not close at all. In Antarctica, for example, before 1960 that generally means ocean data. So trends for Antarctica for early times should be ignored. Elsewhere, there is loss of resolution according to station data, but it is still reasonably based. GHCN V4, of course, has much better coverage than V3.

Note that the color scheme is centered for zero trend, but the range varies with the length of period.

Discussion

I think there is a lot to learn from the graphic, and I'll write a more detailed post. For example, recent periods show the extent to which warming dominates the Arctic, but if you look at the most recent decade, it's more mixed, with pronounced cooling over Greenland and the Canadian islands, but warming around Bering Strait. In earlier periods The warming extends to N Siberia as well.

It's interesting to look at the period 1910-1940, often used by skeptics to say that AGW is refute. It's often accompanied by a whinge about how that warming is being suppressed, often showing a plot of Hansen in 1981 or NCAR in 1974 to claim that their warming has been watered down since.

But this plot shows what was happening. Again Arctic warming dominates, and to a lesser extent, N America and N Atlantic. But the S Hemisphere and most oceans show very little warming. Those earlier plots were land only, with data heavily weighted to the N Hemisphere. The reduced warming in later calculations have the advantage of this knowledge.

I originally started out here to do a corresponding plot of the differences between GHCN V3 and V4, and that will be an upcoming post. It is working - just a little more checking.

Trend methods

I'll just say a little about the data handling here. I try to keep the volume of data down; not so much for my web storage, but because of download time. So I used moments. The zero'th moment of numbers yₖ with location is just the sum. The first central moment is the sum Σ(k-kₒ)yₖ, where kₒ is trhe mean. And the trend is just the first central moment, normalised by division by the moment of a unit trend.

There is a trick with moments familiar from calculating angular momentum, say. To get the moment of some bodies, you can just add the moments of their masses (zeroth moments) at their centres of mass, and add in the central first moments of each body. So here, I can just calculate and transmit the zero'th and first moments of the decades, and then I can work out the trend for any sequence of decades.