Willis writes: I wanted to see if there was acceleration in the TOPEX sea level record. I have looked all over the web to find either the data used to create the following image of the sea level rise as measured by the TOPEX satellite, available here, or some estimate of any acceleration that might be present in the trend. I could find neither. Here’s the record cited above:
Fig. 1 Original graph of the change in sea level rise. Note that the trend is estimated to the nearest hundredth of a mm per year.
Being unable to find the data, I resorted to my usual technique “¢’¬? digitize it myself. This was difficult, because they used large colored circles for the data points, so it was hard to decipher the graph. As this procedure may be of interest to readers, here’s what I did.
I found the exact dates of the starting and ending of each TOPEX cycle. I used my CAD software (Vectorworks, but you can do it in other programs as well) to convert a text file of these dates to vertical lines, spaced by date. I overlaid this grid on the image to give me the exact horizontal coordinates. I then was able to figure out where all the data points were located. Here’s a closeup of the procedure in process:
Figure 2. Closeup of the digitization process. Blue circles are added by hand, and adjusted to the exact location of each data point.
Note that I left out the Poseidon satellite data, as I wanted to have a clean set of TOPEX data. This seems to be the modern preference when analyzing the data as well. Also, note that the addition of the lines for the dates allowed me to determine exactly which blob represented which data point.
To verify my digitizations, I always make up a graph in Excel, and then overlay it on the data. I found they matched exactly. Here is my reconstruction:
Figure 3. Digitized reconstruction of Figure 1.
Now, this all looks very reasonable. There is a clear annual signal, plus an overall trend. So I decided to remove the annual signal, so I could see what the underlying trends actually look like. The result was quite surprising.
Figure 4. TOPEX data with monthly anomalies removed. Note the apparent misalignment of the records, which is not visible in Fig. 1. The lines at the bottom are the Gaussian residuals, i.e., the remainder after the 7 month Gaussian average is subtracted from the data. Note the decrease in error in 1997. Red dot marks the start of the degradation of the Altimeter “A” signal.
As you can see, we are back to the old “spliced records” problem. Of course, this is known to the scientists who did the splice. A good description of the splicing procedure is shown here. They say that the changeover between altimeters A and B was because of gradually increasing inaccuracy in altimeter A from cycle 130 onwards. They also show the ~1 cm difference between the two altimeters at the time of the changeover. However, they have not removed the bad signal from the graph.
Under the reasonable assumption of a quasi-lineal change during the gradual increase in inaccuracy, it is possible to linearly remove the increasing error following cycle 130. This gives us the following graph:
Figure 5. TOPEX data showing the adjustment after Cycle 130
And now that we have a coherent record, although it is still spliced, we can look for changes in the trend. Here is the full record, with the monthly anomalies removed:
Figure 6. TOPEX sea level record with monthly anomaly removed, and trends in the TOPEX sea level record. One year and two year trailing trends of the sea level record are shown at the bottom of the record.
Note the one year and two year trailing trends. There is no significant change in these over the period of the record. The trend increased in the middle of the record, and then decreased again.
Overall, then, to date there is no sign of any acceleration in the TOPEX record of the sea level rise.