Inferring the global mean sea level from a global tide gauge network

An attempt is made to infer the global mean sea level (GMSL) from a global tide gauge network and frame the problem in terms of the limitations of the network. The network, owing to its limited number of gauges and poor geographical distribution complicated further by unknown vertical land movements, is ill suited for measuring the GMSL. Yet it remains the only available source for deciphering the sea level rise over the last 100 a. The poor sampling characteristics of the tide gauge network have necessitated the usage of statistical inference. A linear optimal estimator based on the Gauss-Markov theorem seems well suited for the job. This still leaves a great deal of freedom in choosing the estimator. GMSL is poorly correlated with tide gauge measurements because the small uniform rise and fall of sea level are masked by the far larger regional signals. On the other hand, a regional mean sea level (RMSL) is much better correlated with the corresponding regional tide gauge measurements. Since the GMSL is simply the sum of RMSLs, the problem is transformed to one of estimating the RMSLs from regional tide gauge measurements. Specifically for the annual heating and cooling cycle, we separate the global ocean into 10°-latitude bands and compute for each 10°-latitude band the estimator that predicts its RMSL from tide gauges within. In the future, the statistical correlations are to be computed using satellite altimetry. However, as a first attempt, we have used numerical model outputs instead to isolate the problem so as not to get distracted by altimetry or tide gauge errors. That is, model outputs for sea level at tide gauge locations of the GLOSS network are taken as tide gauge measurements, and the RMSLs are computed from the model outputs. The results show an estimation error of approximately 2 mm versus an error of 2.7 cm if we simply average the tide gauge measurements to estimate the GMSL, caused by the much larger regional seasonal cycle and mesoscale variation plaguing the individual tide gauges. The numerical model, Los Alamos POP model Run 11 lasting 3 1/4 a, is one of the best eddy-resolving models and does a good job simulating the annual heating and cooling cycle, but it has no global or regional trend. Thus it has basically succeeded in estimating the seasonal cycle of the GMSL. This is still going to be the case even if we use the altimetry data because the RMSLs are dominated by the seasonal cycle in relatively short periods. For estimating the GMSL trend, longer records and low-pass filtering to isolate the statistical relations that are of interest. Here we have managed to avoid the much larger regional seasonal cycle plaguing individual tide gauges to get a fairly accurate estimate of the much smaller seasonal cycle in the GMSL so as to enhance the prospect of an accurate estimate of GMSL trend in short periods. One should reasonably expect to be able to do the same for longer periods during which tide gauges are plagued by much larger regional interannual (e. g., ENSO events) and decadal sea level variations. In the future, with the availability of the satellite altimeter data, we could use the same approach adopted here to estimate the seasonal variations of GMSL and RMSL accurately and remove these seasonal variations accordingly so as to get a more accurate statistical inference between the tide gauge data and the RMSLs (therefore the GMSL) at periods longer than 1 a, i. e., the long-term trend.