email: mitchum@soest.hawaii.edu
Recently, Nerem (1995a,b) has reported an estimate of global mean sea level change that was computed from the altimetric sea surface heights measured by the TOPEX/POSEIDON (T/P) satellite. The use of altimeters for measuring the globally averaged sea level rise rate is an exciting application, because the nearly global coverage provided by satellites avoids some of the ambiguity due to uneven spatial sampling of the ocean's surface by tide gauges. In principle, by computing the true global average of the sea surface at nearly synoptic time scales, the altimeter avoids complications due to redistribution of mass in the ocean, as opposed to true volume change.
Nerem found that the sea level trend over approximately the first 2 years of the T/P mission was 3.8 (0.8) mm/yr. The number in parentheses is a one standard deviation error bar; this convention for reporting rates will be used through the remainder of this paper. Nerem points out that the mean sea level change over this period is significantly larger than the accepted background rate of sea level change of 1.8 (0.1) mm/yr (Douglas, 1991), but cautions that this cannot be assumed to indicate an acceleration of the sea level rise rate. He points out the possibility that this rate represents an interannual fluctuation, and he also shows that the mean sea level change is correlated with globally averaged sea surface temperature (SST).
More importantly for the purposes of this note, however, is the fact that the rate Nerem quotes is obtained after applying a correction for the drift rate of the TOPEX altimeter. Since most of the heights obtained by T/P are from the TOPEX altimeter, the trend estimate should more properly be considered as due to the TOPEX instrument, which is known to be drifting (Hayne et al., 1994). The drift rate determined by Hayne et al. is from an internal calibration onboard the satellite, and the value adopted by Nerem was 2.8 mm/yr. Discussion of the drift rate for the TOPEX heights is the main point of this paper.
Of course, the internal calibration is not the only estimate being done for the TOPEX drift rate. Estimates are being done at the Harvest calibration platform (Christensen et al., 1995), over the Great Lakes (Morris and Gill, 1995), and by intercomparison with the POSEIDON altimeter (LeTraon, pers. comm.). In addition, an estimate is also being made from the in situ tide gauge network (Mitchum, 1995), and it is this latter estimate that I will focus on now. But it should first be noted that all of these estimation strategies share one key advantage over the internal calibration. Specifically, all of them measure the drift in the final TOPEX height measurements, rather than simply for the instrument itself. For example, if one of the environmental corrections applied to the TOPEX heights were to be systematically drifting, these latter estimates should show it; the internal calibration would not.
The idea of using tide gauges to monitor low frequency drifts of altimeters was discussed a number of years ago by Wyrtki and Mitchum (1990). Their analysis, using GEOSAT data, was motivated by potential drift due to orbit errors, which is not as significant an issue for T/P. The basic idea still applies, however, and an example application to T/P, which was the forerunner of the present work, was given by Mitchum (1995). The idea is simply that the tide gauges provide an independent measurement of the sea surface height variations, and differences between ideal tide gauges and ideal altimetric heights should not have a significant trend over long time and space scales. It is interesting to note that there is a very compelling analog with the use of tide poles to monitor drift in tide gauges. The tide pole measurements, although typically noisy, can be used over sufficiently long time periods to check the stability of the tide gauge measurements. The tide pole measurements are valuable for this purpose because they are independent, and also because they are from a much simpler measurement system that is less likely to drift than the mechanical tide gauge system. By analogy, tide gauges are independent of the altimetric measurements and are relatively simple, at least as compared to altimetric instruments, as well. Hence, the idea arises that tide gauges can be pressed into service as "tide poles" for TOPEX.
The tide gauge data used in this study were selected from the stations available via the WOCE "Fast Delivery" Sea Level Center (Mitchum, 1990). Time series from 101 stations were examined, and data from the nearest 4 passes of the TOPEX altimeter were used to construct independent time series of the altimeter minus tide gauge differences. The time series were subjected to a number of screening tests; e.g., requiring at least 50 TOPEX passes with valid data limited the set to 200 series from 76 stations. The details of the selection criteria will be described in a manuscript that is presently in preparation, so only a brief summary is given here. First, very noisy series that resulted in poorly determined drift estimates were rejected. Also, tide gauges with unrealistic seasonal variability, most likely due to freshwater run-off, and obvious land motion problems were rejected. The net result is that 144 series from 54 stations (Figure 1) were used in the analyses.
The data from these 144 series were first used to reproduce the simple index proposed by Mitchum (1995). The result is shown in (Figure 2), and the TOPEX drift estimate, which includes the drift that is measured by the internal calibration, is 4.7 (1.2) mm/yr. The problem with this method, however, is that all time series and stations are given equal weight. Ideally, one would like to give more weight to stations where the drift is better determined. On the other hand, one should also downweight stations that are close enough together that they cannot be considered statistically independent.
The following approach allowed the application of these considerations. First, each time series was assigned a weight factor, which is to be determined. Next, the variance of the drift estimate was computed as a function of the (unknown) weights, and this variance was then minimized by an appropriate choice of the weights. This minimization problem can be posed as a standard quadratic programming problem and solved with readily available routines. The required input is the spatial correlation function, which was estimated by fitting to the data themselves. Again, the details of this procedure will be described in the paper referred to earlier. The result of this calculation is a drift rate estimate of 5.4 (1.0) mm/yr. This rate is somewhat larger than the value from the original technique, but the difference is not statistically significant. In either case, however, the estimated drift rate is significantly larger than the internal calibration result of 2.8 mm/yr adopted by Nerem.
Taking the drift rate as determined by the tide gauges to be 5.4 (1.0) mm/yr and subtracting the internal calibration rate of 2.8 mm/yr leaves 2.6 (1.0) mm/yr of drift that is unaccounted for, and may be due to other causes, such as the environmental corrections. If we assume for the moment that the tide gauge drift estimate is the correct one for the total TOPEX system, then the mean sea level trend computed by Nerem becomes 1.3 (1.3) mm/yr, which is not significantly different from the background rate of 1.8 mm/yr cited earlier. It is also interesting to speculate that the additional 2.6 mm/yr of drift may be the source of the correlation with globally averaged SST reported by Nerem, rather than any true trend in ocean volume. One scenario that would fit this would be that one of the environmental corrections is slightly off, and also correlated with SST. An obvious culprit would be the wet tropospheric, or water vapor, correction. Of course, there is no way to determine if this is the case with the present data. This speculation is intended, rather, as simply an alternate hypothesis for the correlation with SST.
The source of the additional drift estimated from tide gauges relative to that from the internal calibration, is unknown at this time. It is certainly possible that there is a systematic bias in the tide gauge analysis that would account for the larger drift estimate. It seems likely, however, that these issues can be sorted out in the next year or two, and the mean sea level trend will be determined to better than 1 mm/yr with only a few years of data from high quality altimetric data. The consequences of this for monitoring ocean volume changes are both obvious and exciting.
References
Christensen, E.J. and 14 others, Calibration of TOPEX/POSEIDON at Platform Harvest, J. Geophys. Res., 99, 24465-24486, 1995.
Douglas, B.C., Global Sea Level Rise, J. Geophys. Res., 96, 6981-6992, 1991.
Hayne, G.S., S.W. Hancock III, and C.L. Purdy, TOPEX altimeter range stability estimates from calibration mode data, TOPEX/POSEIDON Research News, 3, 18-20, JPL410-42, 1994.
Mitchum, G., U.S. WOCE supports global sea level data collection, WOCE Notes, 2(6), 10- 12, Texas A&M Univ., College Station, Texas, 1990.
Mitchum, G., Comparison of TOPEX sea surface heights and tide gauge sea levels, J. Geophys. Res., 99, 24541-24553, 1995.
Morris, C.S., and S.K. Gill, Evaluation of the TOPEX/POSEIDON altimeter system over the Great Lakes, J. Geophys. Res., 99, 24527-24540, 1995.
Nerem, R.S., Global mean sea level variations from TOPEX/POSEIDON altimeter data, Science, 268, 708-710, 1995a.
Nerem, R.S., Measuring global mean sea level variations using TOPEX/POSEIDON altimeter data, J. Geophys. Res., in press, 1995b.
Wyrtki, K. and G.T. Mitchum, Interannual differences of Geosat altimeter heights and sea level: The importance of a datum. J. Geophys. Res., 95, 2969-2975, 1990.
Figure Captions
Figure 1 : Tide gauge locations used in this study.
Figure 2 : Estimate of the TOPEX drift using the method proposed by Mitchum (1995). For each 10-day repeat cycle, the differences between TOPEX and tide gauge heights for all available passes (maximum of 4) were averaged at each of the 54 stations. The median of the se 54 values was then computed to estimate the cycle-averaged difference. The resulting time series (solid circles) was then fit to a linear trend (solid line) and the standard deviation of the trend was computed assuming that the residuals were uncorrelated. This assumption was supported by a runs test, which found no significant serial correlation in the residual time series.
