Anybody who claims wiggles on graphs of measurements made of natural phenomena are not random, will have to prove it mathematically. Tamino has a blog where he regularly shows data to be significant or not with relation to a 'visual first guess'. (You'll have to search his posts for 'significance' or such terms to see his work on this sort of thing.)
Climate scientists have a rule of thumb that trends that are less then about 30 years may not be statistically significant. Trends (or changed trends) spanning less than a decade are seldom significant. See for example, Tamino's numerous posts on the 'global warming pause' following 1998 el nino (e.g. here).
Rich, there are other aspects of your faith in NASA data that are misplaced, there being very many known and unknown (think of Cheney's various categories, all relevant) influences on accuracy and precision of measurements, what is being measured, and how those measurements are interpreted.
There is difference between saying that there is some randomness in the underlying natural phenomena (which I agree with) and saying that the resulting data is random.
The random element in nature plays a part in determining the true result of GMSL. There is only one true GMSL at a given point in time. The data that NASA provides is a function of the true GMSL and the accuracy of the measurement. Period.
Is the NASA data perfect? No. They provide a margin of error on their measurement of 0.80mm. Is there a better source? Not to my knowledge.
In the absence of any specific reason to doubt the NASA data and in the presence of lots of other data points which cogently fit the picture of accelerating SLR, I'm going to accept that the data paints a materially accurate picture of SLR. I'm going to use it to help me understand what is going in the world and try to help highlight a potential evolving risk for others.
If we wait until until we have 100% proof that the SLR is fundamentally accelerating in order to take action, we lose time to prepare. If we prepare for something that doesn't ultimately materialize, we waste resources. There is a risk / reward profile associated with waiting as well as with making projections. In the absence of a crystal ball, what do we do?
My choice is to try and add value and get people to think critically about the data that is out there. I'm highlighting something different than other people are highlighting for a reason and I'm encouraging people to kick the tires.
SLR during most of the 20th century averaged 1.5mm / yr. From the satellite era until 2010, the average was 3 mm / yr. Since 2010, things certainly seem to have picked up. The intervals such as 2011-2015 are not yet statistically proven to be indicative of what will happen going forward. That proof of what will happen in the future can only come with more time. But at the same time, we can ask ourselves if we have any experience with intervals like these. The answer is no.
The only parallels we can look at is the paleo-record and we have lost ice a lost faster than 8 mm / year in relatively recent geologic times.
Are we in the early stages of hockey stick type progression of SLR? I can't say for sure. If we were in the early stages of a hockey stick type progression, what would the curve look like? I think it might look a lot like the data that NASA is presenting.
My personal process of trial and error is to try and eliminate the possibility that 8mm / year represents a new baseline in the absence of specific negative SLR events such as El Nino. The data doesn't let me do it.
The 8mm / year was reported by NASA from 2011 to 2015, paused for the 2016 El Nino and resumed for all of 2017 and half of 2018 so far. I'm actually quite interested in someone explaining a system that produces that result and then reverts back to a lower baseline. No one has been able to do that so far.
In the absence of anyone being able to provide a cogent alternative argument for the emerging slope of the SLR curve, I think people should take the possibility of an emerging hockey stick seriously.