re: Earth - schematic of historical temperature data

quote:

---

Serious question:
How are sea levels accurately measured across large areas to a point of precision that operates in millimeters?

---

With a LOT of data. And even then, the actual average sea level cannot be known to mm precision. There are far too many variables that change by the second. However, while you cannot know the precise level at a point in time, you can determine a trend (or rate of change) with a lot of averaging and other methods.

Imagine trying to determine the water level in a hot tub while it's running. Impossible to know to the mm, right? Probably the best you can do is put a few stilling wells in there to calm most of the turbulence, and then eyeball the level best you can at a few points and average. Then do it again and again, every hour or whatever, and keep records. After a while you can plot your data on a chart and determine not only whether the water level is rising, falling, or staying the same, but you can also pretty accurately determine the rate of change.

And even if your spot measurements are only accurate to the cm, you will be able to determine the rate of change quite accurately, because all of the noise and error is averaged out over a length of time. For example, let's say you measure a level of 10cm +/- 1cm. Could be 9, could be 11, or anything in between. You measure every day, but each time your precision is +/- 1cm. After a few months you start measuring 11cm every now and then. Mostly still 10, but sometimes 11. A few months later you measure mostly 11, and only rarely 10. A few months later you start getting 12cm sometimes. Maybe after a year you are measuring 12cm most days. It still fluctuates, and still only precise to +/- 1cm, but you are still getting mostly 12cm. But now you have a year of data, so you can filter out most of the noise and calculate a rate of change. Maybe you average all the daily measurements from the first and last months, and you get 9.8cm and 12.2cm, which is 24mm/year, or 2mm/month, or 240mm/decade, etc.

So you can take an average of many measurements to increase the accuracy, and then slice it up over a span of time to effectively divide the unit of measurement to be more precise. It doesn't matter that I can't take a single measurement to within 1 cm, I can still be reasonably certain that the daily rate of change is 0.066mm given enough measurements.



There is obviously a lot more to it, and a lot of math and statistics involved that I have almost zero clue about, but I hope this example can help explain why even though we can't measure the global average sea level all that accurately, we can still be pretty certain that it is actually rising by about 3mm per year. It sounds absurd, because it's hard enough to measure that amount of change in a 5 gallon bucket, much less all the oceans of the world. But it is absolutely possible because we aren't actually measuring sea level that precisely. We are measuring rates of change.