Brief Comment by Kip Hansen
Have you ever noticed that whenever NASA or NOAA presents a graph of satellite-era Global Mean Sea Level rise, there are no error bars? There are no Confidence Intervals? There is no Uncertainty Range? In a previous essay on SLR, I annotated the graph at the left to show that while tide gauge-based SLR data had (way-too-small) error bars, satellite-based global mean sea level was [sarcastically] “errorless” — meaning only that it shows no indication of uncertainty.
Here’s what I mean, this is the most current version of satellite Global Mean SLR from NOAA:
This version of the graph does not have the seasonal signals removed [meaning it is less processed], shows the satellite mission that produced the data, and rather interestingly shows that, as of yesterday, satellite-derived Global Mean SLR has slowed to 2.8 ± 0.4 mm/year. NOAA NESDIS STAR has been reporting this as 2.9 ± 0.4 mm/yr since 1994, but earlier this year, in January, they were reporting it as 3.0 ± 0.4 mm/yr.
But the point is, in the graph shown above, captured yesterday; nothing is shown to indicate any measure of uncertainty — none at all.
Readers who have followed my series here on Sea Level Rise, or who have followed Dr. Judith Curry’s series at Climate Etc. (or Rud Istvan’s essays there) are already aware that satellite-derived sea level data is seriously confounded by factors orders of magnitude greater that of the actual rise of sea surface height and, while the magnitudes of those confounders can be estimated, their specific values can only be guessed at. Never-the-less, these estimated values are then used to “correct” the satellite results. This fact means that there must be a great deal of uncertainty in the final values graphed as Global Mean Sea Level.
Why do we never, ever see this uncertainty shown on the resultant graphical presentations of satellite-derived GMSL? Part of the answer is that, in Science today, there is the odd, and wholly incorrect, idea that “if we average enough numbers, average enough measurements, then all uncertainty disappears” [or something like that — I have written about this issue, and battled ‘statisticians’ in comments endlessly, in my series on The Laws of Averages].
Despite this odd belief, there still holds the idea of the “standard deviation of the mean” and its related (but not identical) “standard error of the mean”. While these can be tricky concepts, it is enough here to say that “The standard deviation, or SD, measures the amount of variability or dispersion for a subject set of data from the mean, while the standard error of the mean, or SEM, measures how far the sample mean of the data is likely to be from the true population mean.” [source].
We find the source of the numerical data that makes up the satellite-derived GMSL graph in a text file of the data made available on a regular basis by NASA/JPL’s Physical Oceanography Distributed Active Archive Center (PO.DAAC). In that text file? There we find, in column 9 “GMSL (Global Isostatic Adjustment (GIA) applied) variation (mm) ) with respect to 20-year mean” and in column 10, “standard deviation of GMSL (GIA applied) variation estimate (mm)”.
Here’s is what we find out in regards to the previously-imagined “errorless satellite-derived GMSL:
This is Column 9. “GMSL (Global Isostatic Adjustment (GIA) applied) variation (mm) ) with respect to 20-year mean” [source file]
If we adjust the scale and add the one-standard-deviation as error whiskers (light grey shading):
Add a couple annotations:
The standard deviation of the individual Global Means is very consistent and averages around 92 mm. The change in global mean sea level, over the entire 25-year satellite era, is about 100 mm. All of the SD whisker bars overlap all the other SDs by about 50% (or more).
Exactly what this might mean is a matter of opinion:
1) “If two SEM error bars do overlap, and the sample sizes are equal or nearly equal, then you know that the P value is (much) greater than 0.05, so the difference is not statistically significant.” [source]
2) “When standard deviation errors bars overlap quite a bit, it’s a clue that the difference is not statistically significant. You must actually perform a statistical test to draw a conclusion. “ [source]
In this case, we are not quite sure if we are dealing with simple standard deviations in the data used to derive the individual means, or if the numerical data from PODACC represents “standard deviation of the [global] mean [sea level]”. [ PODACC uses this language to describe the SD data: “standard deviation of GMSL (GIA applied) variation estimate (mm)”. ]
Given the data presented above, repeated here in an animation:
What can we conclude about:
1) Accuracy and precision of the GMSL derived from satellite data?
2) The likelihood that the delta (change) in the 25 years of satellite data is actually significant?
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Author’s Comment Policy: This essay is not about Global Warming, Global Cooling, Carbon oxides, or Climate (changing or not). It is about the “measurement” of the height of the sea surface via satellite altimetry and the derivation of the [probably ‘imaginary”] metric that NOAA/NASA calls Global Mean Sea Level (and its rise or fall).
Remember: Sea Level and its rise or fall is an ongoing Scientific Controversy, especially in regards to its magnitude, acceleration (increasing or decreasing speed of change), significance for human civilization and causes. The consensus position of the field may just be a representation of the prevailing bias. Almost everything you read about it, including this essay, is tainted by opinion and world view.
I look forward to reading your opinions on the questions posed at the end of the essay.
If your comment is direction at me, please begin it with “Kip…” so that I don’t miss the opportunity to respond.
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R Shearer April 3, 2018 at 12:35 pm
“The grass would grow by more than that in a short while.”
Possibly so, and instantaneous sea level in any one spot changes constantly
I could be mistaken but that the averaging of measurements, under the same conditions, of one single thing, can get closer to the “real” value, seems straightforward and understandable in term of human actions and human senses. That errors across measurement of different items, events, etc. can not be averaged out also seems reasonable to me but might involve some more subtle factors of which I am unaware.
In the case of measuring a single thing under identical conditions, the precision is increased through averaging multiple measurements No?
In other cases, for example determining the average height of adult females in the US population, could be more accurately estimated from a large, random sample – but the precision of that calculation would still be the precision with which a single individual’s height can be measured. Correct?
Willie Soon gave this lecture on satellite altimeter measurements of sea level.
He claims that the maximum resolution of the microwave frequency used in 5 centimeters; I’m thinking that means +/- 2.5 cm. He lists a number of other unavoidable errors, that largest of which he says is 10 cm.
Somewhere recently I read that the official user’s manual for the satellite data says the error is, I believe, +/- 3.4 cm. Perhaps that was in one of Kip’s recent articles.
Assuming that these figures are correct, and even without any of the other objections raised by Soon, Kip, or others, can any champion of the satellite sea level data justify, and explain that justification is real terms, that any claim from the satellite data that there is any change in sea level, either up or down, does not need to be based on the change in calculated average being more than 3.4 cm different from the first good measurements?
About the satellite measurements, we need to know how much of the uncertainty is systematic and how much is random.
If you use the same instrument in the same situation for all measurements in the data set this systematic component can be more or less discounted. All you are after is the trendline, not the absolute values.
KZB ==> All the factors that answer that question are highly uncertain.
The earth is an oblate spheroid that bulges at the equator due to rotational velocity. What happens when the earth’s rotational velocity slows … say from 23:57:00 in 2000 to 23:57:01 per rotation in 2100 (which is approximately the current rate of slowing)? Does the bulge become smaller and if so how much? And what happens to the sea level at the equator and at the poles?
Ken ==> And does it matter for anything? or is it just interesting?
Is it something new? or has it happened before?
Lots of interesting questions — some of them have interesting answers.
The bulge will decrease, but I doubt we have any instruments that are capable of measuring the change.
Wouldn’t a thousand pictures be worth a million words? I mean, where are all the pictures for evidence of sea level rise around the globe over the past 100 years. There should be millions of them actually.
DR ==> Sure! and you’d think that if they had pictures, they’d just post them for all to see.
Trouble is, it is easy to find places where we are pretty sure that the sea was prehistorically a hundred feet higher than today, and see places that are now underwater that used to be on the seashore.
8-12 inches ago (say a hundred to 150 years) — not so much.
It is only since the GPS satellite system went up that we can tell if the land is sinking or the sea rising (or vice versa).
Give us another 20 years and we’ll have it figured out.
Kip,
There is one extremely clear indication that the trend is robust and that using 1 standard deviation as any sort of measure is spread is highly suspect — the clear annual oscillation. If the uncertainly was indeed ~ 100 mm as your diagram implies, then the annual signal would be lost. The fact that the annual signal shows up load and clear suggests that the measurements can indeed pick up variations on the order of a few mm.
Tim ==> Such oscillations can easily be artifacts of processing, orbital features, seasonal features of the atmosphere (air pressure) or the seas that have nothing to do with sea surface height.
It is an interesting thought.
Whether the annual oscillations are the result of a true signal in the sea level or simply an artifact of something else, the oscillations are clearly visible by averaging the ‘noise’. With 400,000 data points, even this large standard deviation produces a very small standard error of the mean. These oscillations — and the overall slope — are both clear features of this data set. (Without further knowledge, I can’t judge if it is real or artifact, but it it there! Your huge error bars are way to wide!)
TJ ==> They are NOT error bars — they simply represent the +/- one Standard Deviation, with the SD provided by JPL/NASA.
Tony Heller on the sc@m of global MSL rise exposed by Tuvalu, the Maldives and other rent-seeking, trough-feeding fr@udsters:
There’s clearly a lot of statistical expertise available from certain contributors on here.
What a pity these persons are not asked to review articles before they get posted !
TJ ==> Read William Briggs Uncertainty. Just because they are able to derive some sort slope out of out of very vague, very very numerically uncertain data doesn’t mean that the “detected” slope 1) is Physically Real, 2) is Accurate or Precise, 3) Isn’t just an artifact of the processing method, 4) Isn’t an artifact of the equipment used to ‘measure”. All of those certainly apply to the unmeasurably small delta in SSH.
Statistics do not create reality — they are simply a way to investigate some number set. Statistics do not necessarily reflect the physical world, despite following its careful rules regarding numbers.
Statistics cannot and do not eliminate ignored physical measurement errors orders of magnitude greater than the magnitude of the thing being measured.
Without a very in depth look at the processing method, it is impossible to say if the very-near-zero delta in sea surface height is REAL — it requires external verification.
I’m sure they have their math right — I’m do know that the “corrections” and “adjustments” made to the to satellite signals measured deal with factors, confounders, that are multiple orders of magnitude greater then the sea surface height change signal they are looking for, and that those corrections and adjustments are rough guesses of unknown and unknowable elements.
Well said, especially about ignoring physical measurement uncertainties!
Kip -that might be fair enough if you hadn’t based your article on statistical arguments in the first place. Your points about corrections and adjustments may have real value, but it wasn’t what took my attention.
When you say statistics cannot eliminate ignored physical measurement errors, well that depends on the nature of the “ignored” errors. If they are random errors then yes a signal can still be extracted from the data.
KZB ==> I just used the data supplied by JPL/NASA, which, in place of physically-based error bars concerning measurement uncertainty they supplied simply the Standard Deviation of the 300,000 or so individual calculated guesses at sea surface height used to calculate a Global average sea surface height, from which they calculate an anomaly…….
KZB ==> Take the time to investigate the number of steps and the processing path between the original satellite measurement, which is of a return time of a KU band signal, which hits the earth over a km wide area and bounces back, and a scatter factor, which is used to estimate the sea surface conditions. From those two numerical values, they have to try and determine the average sea surface height of the area off of which the signal bounced. The sea surface may be smooth to within centimeters — but NEVER smoother than that, usually the roughness of the surface is measured in meters and sometimes tens of meters. Meters are a thousands times larger than the millimetric precision they claim.
If they were actually on the sea in average conditions, say Force 3 or 4 seas, they could not measure actual sea surface height to even inches or centimeters — no less millimeters.
The Tide Gauge long-term rate of SLR is 1.7-1.8 mm/yr — the thickness of a US quarter. satellite since 1993 gives about 2.9 mm/yr, less than the thickness of two US quarters stacked on top of one another. They claim to be able to detect this change of a surface no part of which is ever that smooth.
Hey, statistics are wonderful — for some things — but measurement, not so much.
RB ==> Look at the photos. I haven’t got the document yet, but the synopsis doesn’t seen to tell how sea level is found from varying wave heights especially to a precision of mm. The altimeter may read to mm, yet can the sea level be determined to that precision? If so, please tell us how.
Rob ==> I am familiar with Shum et al.(1995) — and although far out f date, it does outline the process and sources of error. In 1995, they wewre happy to be able to claim +/- 2 inches (5 cm) and that was not real either.
Population mean is meaningless if the measurements are known to contain large numbers of errors of unknown quantitative magnitude — Shum makes some of the guesses that they still use today.
Measuring a million different tress at a million different times and places doesn’t tell you how tall the pine tree you about to cut is. Lots of vague guesses averaged and then averaged again doesn’t result in a precise answer that can be expected to agree with a physical actuality.