From Watts Up With That?

By Dr. Alan Welch FBIS FRAS

This report presents and analyses the sea level data for 2025.  It was a roller coaster year for sea level data that turned into a “Hunt the Data” exercise.  As a consequence, the analyses main purpose is to link the new data to the old and produce a new methodology so that changes to sea levels in 2026 can be more easily judged.

The NOAA site:    https://www.star.nesdis.noaa.gov/socd/lsa/SeaLevelRise/LSA_SLR_timeseries.php

gave data for the end of January then no more for the rest of the year.  Does anyone know why and/or if the data is available any other way?

The NASA site: https://science.nasa.gov/earth/explore/earth-indicators/sea-level

produced data for January, April, July, August, September, November and December but in July 2025 NASA changed dramatically the amount of data being provided.  Up to April 2025 the data consisted of 13 columns giving number of readings, standard deviations and results with and without a 60-day Gaussian type filter applied, with and without GIA not applied and with and without annual and semi-annual signal removed.  The data analysed was from COLUMN 12 which was for smoothed (60-day Gaussian type filter) GMSL (GIA not applied) variation (mm); annual and semi-annual signal removed.

Whereas in July only 3 columns of data appear:-

HDR 1 year+fraction of year

HDR 2 GMSL (cm)

HDR 3 GMSL with 60-day smoothing applied (cm)

with the 3^rd column being used in the analysis.

Also, up to April 2025 data appeared on a roughly 10-day cycle but in July this changed to a 7- day cycle.  To add more misery the U.S. Government shut down stopped any data at all being provided for a couple of months.

To show he differences in the data used for the analyses Figures 1 and 2 give the diagrams provided by NASA for April and July 2025.

How to proceed?

Up to April 2025, after 7 years of studying the NASA data, several standard Excel spreadsheets had been created producing plots of the Full Data with best fit Linear, Quadratic and Sinusoidal curves with the associated equations and plots of residuals, measured from the linear line, with best fit Quadratic and Sinusoidal curves.  Also, statistical results have been produced and historical plots of how the so called “accelerations” had changed with time.

One approach would be to use the data as it is with the old spreadsheets, but this would lead to very “bumpy” plots.  The annual and semi-annual signal vary from -4.33 to 5.46mm which is quite large when compared with an annual average increase of about 3.3mm.

A second method would be to do a moving annual average which would eliminate the bumps but would also lose a lot of the El Niño/La Niña effects which are useful to show.

The annual and semi-annual signal is a regular variation that repeats year in year out with the same shape, so the amount involved only depends on the date in the year.  Using this fact the signal’s value at any time in the year can be ascertained from the readings with and without it included.  This was done using the difference between columns 11 and 12 of the April 2025 data, creating a list of dates and differences then subtracting the year value from the date.  This leaves 2 columns for the partial year date and the annual and semi-annual signal which is shown in figure 3.

An 8-order polynomial curve was fitted to the graph in figure 3 using the LINEST Function in Excel, resulting in

y = -6643.928484 x⁸ + 25497.575242 x⁷ – 37890.084128 x⁶ + 27118.787657 x⁵ – 9446.372672 x⁴ +

1420.212996 x³ – 37.494970 x² – 18.784928 x + 0.200699                                               Equation 1

The order and accuracy may look excessive, but a 6-order was found to be too inaccurate at the extreme ends of the graph and although 2 less significant figures only changed the graph slightly it was decided to stay with this equation.  Figure 4 shows a plot of the actual and fitted curves indicating only a small inaccuracy at the extreme ends of about 0.1mm.

The new data with annual and semi-annual signals can now be processed by taking the sea level and calculate the part year by using a calculation in Excel

Part year = year – INT(year)

and then calculating the annual and semi-annual signal using Equation 1.  This can then be taken off the listed sea level and the normal processing carried out.

I wish life was that easy.

This process was applied to the NASA Aug 2025 data which only had data with the signal included.  The result was not satisfactory with the Aug data having a seemingly larger variation than what was shown in previous data releases.

Another source of readings is from our friends at the University of Colardo. Their site https://sealevel.colorado.edu/data is a useful source of information even if you don’t like the conclusions they reach like extrapolated sea levels in 2100.  The site has 2 sets of processed data shown in figures 5 and 6.  The “acceleration” indicated is 0.071mm/year² which is line with other estimations.  Strangely this site has removed several figures for analyses carried out between 2020 and 2025.

Repeating the process shown in Figure 3 resulted in

The equation for an eight-order polynomial is given by Equation 2.

y = -7765.207058 x⁸ + 32631.342618 x⁷ – 54125.59435 x⁶ + 44768.098468 x⁵ – 19273.077711 x⁴ +

4111.056244 x³ – 321.22496 x² – 25.210076 x + 1.282815                                               Equation 2

The comparison of this eight-order polynomial with the actual values is shown in Figure 8.

This shows a similar form with some small differences in shape and is generally about 30% more than in Figure 3.  The best option therefore is to use the data as supplied by NASA and accept that any graphs will be affected by the annual signals.

The sets of data analysed are therefore January and April 2025 with the full data and July, August, September , November,  and December 2025 with the reduced data.  The data for April 2025 and December 2025 will both be processed for comparison. 

Figures 9 and 10 show the linear and quadratic best fits of the full data.

The differences in the equation’s coefficients seem larger than would be expected but it is more revealing the change year on year with consistent sets of data so 2026 data will be more revealing.

The residuals are plotted in Figures 11 and 12 together with the quadratic best fit curves and the standard deviations of the errors added.  To check this process is carried out correctly the quadratic terms are compared with that for the full data and the linear fits checked as being given by y = 0 x + 0.

Next in Figures 13 and 14, the residuals are plotted together with a sinusoidal curve having an amplitude of 4.2 mm and a period of 29 years.  The value of 29 years has been used for a couple of years having been originally eyed in and is probably not quite the best fit curve but not far off.

The standard deviations of errors with the sinusoidal curve are lower than the quadratic for both the April and December analyses.  The inclusion of the annual and semi-annual signal greatly increases the standard deviation for both curves.

Figures 15 to 18 show histogram plots of errors for the two analyses.

Figures 15 and 17 show more normal distributions whereas in Figures 16 and 18 the shape of the annual and semi-annual signal makes them slightly skew.

Figures 19 and 20 shows the result of the spectral analysis for the full data. 

Both show that there is a very long-term variation and in figure 20 the annual and semi-annual signal appears as a spike at a period of 1 year.  On this plot it appears very small  compared with other peaks due to Solar and Lunar cycles but is better judged on the residual spectral analysis shown in figure 22 below.

Figures 21 and 22 shows the result of the spectral analysis for the residuals in the NASA analysis. 

Figures 23 and 24 plot the “acceleration” values against the date they were determined based on the data from the start of 1993 up to that date.  The effect of El Niños and the annual and semi-annual signal can be seen. If the residuals had followed a sinusoidal variation based on the 29-year sinusoidal curve an equivalent set of “accelerations” could have been determined.  Remember the curve labelled “sinusoidal” is NOT a sinusoidal curve but a curve of “accelerations” based on the residuals having a sinusoidal variation.

Figures 25 and 26 show the  “accelerations” as at the end of Jan 2025 with the long term predicted  “accelerations” up to the 2060’s calculated using quadratic curve fitting to a set of data obtained from a 29-year curve.  The validity or not of the curve will be seen earlier by about 2034 when, if correct, “accelerations” will be approaching values seen in the long-term Tidal Gauges i.e. values of about 0.01 mm/year².

No conclusions about sea levels during 2025 have been deduced.  The comparisons between April 2025 and December 2025 show no major differences and so the ongoing work must turn to the changes during 2026.  Figure 26 is considered the most revealing graph, now somewhat complicated by the annual and semi-annual signal, which masks the El Niño variations, but assuming no more complications with data presentation by NASA there should be a steady drop in “accelerations” throughout 2026.

If any readers have stayed the course, I wish them all the best for 2026 and hopefully I’ll be reporting on 2026 in twelve months’ time .

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