Aslak Grinsted‎ > ‎Misc. Debris‎ > ‎

Non-Optimal interpolation of global sea level.

posted Nov 17, 2009, 3:21 AM by Aslak Grinsted   [ updated Apr 14, 2011, 12:40 AM ]
The best data set for reconstructing global mean sea level over the last century is the Tide gauge records archived at the Permanent Service for Mean Sea Level. There are several ways to combine all these records into a global sea level series. The most commonly used method is a variation on the "Optimal Interpolation" (OI) method. This method extrapolates the spatial patterns of variability observed in near-global satellite altimetry record (obtained using EOF analysis) back in time. However, there are severe problems with this approach:
  1. The altimetry record is short and thus can not capture the spatial patterns that occur on longer than decadal scales.
  2. The method require a high density of tide gauges to be able to distinguish the spatial patterns.
We noted these problems here (see also attachment on this page). Indeed, Kaplan (a pioneer of the OI technique), warns against using such short records for establishing the EOF patterns here.

How good is OI on surrogate data?
Bo Christiansen et al. investigated how well the "Optimal Interpolation" technique works on surrogate sea level records obtained from modelled thermosteric sea level rise. They found that a simple average performs better than OI (Christiansen 2010 (accepted manuscript)). I think this paper will be a good starting point for understanding the strengths and weaknesses of the different reconstruction strategies. Llovel et al. 2009 also finds that the performance of OI relies crucially on the temporal length of data used for getting the EOFs. The satellite record is just too short to be able to get good trends.

Variations to traditional OI
One of the variations to the standard OI scheme is the inclusion of an artificial zeroth EOF. This artificial EOF has constant loading coefficients. Another variation is related to the problem that the tide gauge measurements does not have a common reference level. These ad-hoc devices are clearly necessary to force the OI tool onto the sea level problem. OI is just not designed for that purpose. However, with these modifications I question by what metric this modified method can be called "optimal".

Alternative sea level reconstructions
  1. Jevrejeva et al 2008. Our virtual station weighted average.
  2. Llovel et al. 2009. OI-based but with EOFs estimated from model runs rather than altimetry.
I also like reconstructions based on averaging selected tide gauges (see e.g. Douglas 1997). There are many more.

Aslak Grinsted,
Nov 17, 2009, 6:08 AM