By Kip Hansen – Re-Blogged From http://www.WattsUpWithThat.com

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?

**# # # # #**

** 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.