Looking for formulations used in sea level calculations

[CFDoc]

TL;DR Summary

Uncertainty propagation, stochastic data, gradients of noise, overall uncertainty in mean values.

Hello all,

I've been on the hunt throughout the scientific literature for a little while now for some information, but I'm coming up empty. I'm hoping there's some expertise here in the area of altimetry as it relates to sea level calculations. More specifically, I'm trying to find the actual formulations, raw data filtering, and uncertainty propagation methods implemented in the global sea level average calculation.

My searching thus far has included reviewing the IPCC reports, Colorado State & Tolouse France journal articles, and JPL/NASA websites describing the TOPEX/Poseidon/Jason/etc. missions. However, the more scientific detail related information I am looking for has been difficult to come by. That is to say, I can't seem to find the more detailed information regarding how researchers took the instantaneous measurements over a given sampling period and calculated the low order moments reported in the literature.

For example, the JPL document for the TOPEX/Poseidon mission contains information regarding instrumentation used, orbital paths, and expected precision/accuracy of the instrumentation used. For sea level measurements, the instantaneous measurement shows an accuracy of +- 14cm.

See: JPL Poseidon Link

I am therefore taking this to mean that, in the raw data that would be a given sample in time, one would expect that measurement to be a distance measurement accurate to within +- 14cm. There are several other sources of error in the measurements such as orbit shifts/decays, atmospheric noise, etc.

However, when I read the documents discussing the average sea level height calculation during the TOPEX/Poseidon mission, I see accuracies listed as +- 0.1mm.

See: IPCC report

The information I can't seem to find is the detailed formulas used for (a) the ensemble mean calculations, (b) the propagation of all uncertainties throughout the dynamic period of sampling, (c) the justification for how instrumentation with accuracies on the order of tens of centimeters can yield low order moments on the order of tenths of a millimeter, and (d) how gradients of stochastic samples are somehow reducing, not increasing, the overall uncertainty in the calculated statistics.

For (d) I am referencing the rate of changes and accelerations being reported to the hundredths and thousandths of a millimeter, respectively.

If anybody knows where I can find this information and read these papers, I would appreciate it.

Thanks in advance.

 

[Genava]

Tolouse France journal

You mean Toulouse?

For sea level measurements, the instantaneous measurement shows an accuracy of +- 14cm.

If it is a single reading, it is plausible. Normally you get a better estimation with multiples readings over a longer period of time.

My searching thus far has included reviewing the IPCC reports, Colorado State & Tolouse France journal articles, and JPL/NASA websites describing the TOPEX/Poseidon/Jason/etc. missions. However, the more scientific detail related information I am looking for has been difficult to come by. That is to say, I can't seem to find the more detailed information regarding how researchers took the instantaneous measurements over a given sampling period and calculated the low order moments reported in the literature.

There is a bit more details here, in this article about comparing dataset and methodologies:

<< Computation of the altimetry-based GMSL time series
Satellite altimetry measures the travel time of a microwave radar pulse reflecting from the ocean surface and, thus, provides the distance between satellite and sea surface. By subtracting the radial position of the satellite with respect to a fixed reference, it becomes possible to compute the instantaneous sea surface height. A number of geophysical corrections are applied to the data. These corrections include the ionospheric correction, wet and dry tropospheric corrections, sea state bias, and dynamic response of the ocean to the atmospheric loading, as well as solid earth, ocean and pole tides (Chelton et al. 2001). The computation of the GMSL time series is based on the geographical averaging of instantaneous SSH over the oceanic domain during successive orbital cycles. To do this, different approaches are used by the processing groups. The method followed by CU consists of computing the GMSL by simply averaging along-track SSH measurements, each SSH value being multiplied by the cosine of latitude of the point measurement (Nerem 1995; http://www.sealevel.colorado.edu/). As done by CU, a criterion on bathymetry (>120 m) is used in order to select measurements over the “open ocean” only. This criterion is supposed to avoid inaccurate coastal ocean tide corrections. The method developed by AVISO requires two steps (http://www.aviso.oceanobs.com/fr/accueil/index.html): (1) along-track SSH measurements are first averaged into 2∘×2∘ grids for each orbital cycle (all along-track measurements within a 2∘×2∘ grid cell are averaged together, giving a mean value for the considered grid cell). In principle, this method allows equally distribution of all measurements on the ocean surface, and hence reduces, through spatial smoothing, anomalous data and measurement noise. Then, the GMSL is estimated at each time step by geographically averaging all grid cells after area weighting (i.e., each gridded value is multiplied by the cosine of latitude of the centre of the cell; Traon et al. 1998). >>
https://link.springer.com/article/10.1007/s00190-013-0687-3

If you need much more details, then maybe you should start with textbooks.
https://www.taylorfrancis.com/books...stammer-anny-cazenave/e/10.1201/9781315151779
https://www.sciencedirect.com/bookseries/international-geophysics/vol/69/suppl/C

 

[CFDoc]

You mean Toulouse?

Yes.

If it is a single reading, it is plausible. Normally you get a better estimation with multiples readings over a longer period of time.

Yes, which is why I'm trying to find the methods used to drive this result. I have a background in generating/analyzing noisy, stochastic data from physical processes surrounding turbulent combustion. Hence my interest in generating low order statistics and gradients 3-4 orders of magnitude below the accuracy of the instrument itself.

There is a bit more details here, in this article about comparing dataset and methodologies:

https://link.springer.com/article/10.1007/s00190-013-0687-3

If you need much more details, then maybe you should start with textbooks.
https://www.taylorfrancis.com/books...stammer-anny-cazenave/e/10.1201/9781315151779
https://www.sciencedirect.com/bookseries/international-geophysics/vol/69/suppl/C

Thanks I have downloaded the book. Also, that M. Albain author from Toulouse is one of my main sources in digging for information.