Calibrating the Mean Sea Level Measurements

We now want to correct the T/P mean sea level time series (Fig. 6.8) using the tide gauge instrument calibration time series (Fig. 6.5) to get our final estimate of the rate of sea level change. Note that we prefer to identify altimeter measurement error detected by the tide gauges, and directly correct the altimeter data, as done in the past for the oscillator correction (Nerem, 1997) and the wet troposphere correction (Keihm et al, 1998). For this discussion, we also remove annual and semiannual variations from the time series because there is some evidence that the tide gauge calibration might have small errors at this frequency (the tide gauges are more sensitive to localized seasonal variations in heating, freshwater flux, and coastal trapped waves (Mitchum, 1998). Figure 6.9 shows the final time series of global mean sea level change from T/P. A simple least-squares linear fit to these data give a rate of +2.5 mm/yr with a formal error ±0.25 mm/yr (based on the scatter of the fit). We use formal error here because we cannot assemble a realistic error budget for global mean sea level otherwise, since we need to know the globally integrated errors due to mismodeling of the orbit, ionosphere, troposphere, tides, and so on. The formal error assumes the point-to-point measurement errors (one 10-day estimate of mean sea level to the next) are uncorrelated. If we account for the autocorrelation of the fit residuals (e.g., Maul and Martin, 1993), this increases the formal error to 0.4 mm/yr. However, we also corrected the T/P data using the tide gauge calibration values (to account for measurement errors that are otherwise inaccessible to us), and the estimated error in these values needs to be added to the formal error. Our estimate of the error in the tide gauge determination of the instrument drift is ±0.6 mm/yr, which is dominated by the land motion errors. The root-sum-square of the formal error and the instrument drift error gives a total error of 1.3 mm/yr. Our final rate estimate of +2.5 ±0.7 mm/yr (Nerem et al, 1999) is valid only over the 6 years covering 1993-1998; we really cannot say if it is representative of the rate of long-term sea level change (as we will show later, the effects of ENSO variability significantly affect the rate estimate). Note that in any case, this estimate of sea level rise over 1993 to 1998 is statistically indistinguishable from the long-term rate determined from the tide gauge data (Douglas, 1991).

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Figure 6.9 Same as Fig. 6.8, but after correction for instrument effects using the tide gauge calibration time series (Fig. 6.5) and removal of annual and semiannual variations.

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Figure 6.9 Same as Fig. 6.8, but after correction for instrument effects using the tide gauge calibration time series (Fig. 6.5) and removal of annual and semiannual variations.

6.4.4 Comparison to Sea Surface Temperature Changes

When studying measurements of sea level change, we often examine measurements of ocean temperature to determine if the observed changes in sea level are due to thermal expansion. However, measurements of temperature over the water column can only be made with in situ instrumentation (hydrographic measurements from ships, buoys, sondes, etc.), which have limited spatial extent. Sea surface temperature (SST) can be observed from space, using either infrared or microwave techniques, thus making SST a natural variable for comparison to the global measurements of sea level collected by T/P. Unfortunately, SST measurements reveal nothing about the temperature of the entire water column, and thus some assumptions (mixed layer thickness and temperature, thermal expansion coefficient, etc.) must be invoked to directly compare these measurements to sea level. For this discussion, we will qualitatively compare the observed spatial and temporal variations of sea level and SST, but need to remember that they need not be in agreement if the SST is not representative of the temperature of the mixed layer or if phenomena other than thermal expansion of the mixed layer are driving the sea level change.

We use a global 1° X 1° SST data set covering 1982-present compiled at weekly intervals by Reynolds and Smith (1994), which is based on thermal infrared images collected by the advanced very high resolution radiometer (AVHRR) on board the NOAA satellites and is calibrated with in situ data. Using equiarea weighting, we can compute variations in global mean SST since 1982. This is dominated by a large annual change in global mean SST as described by Chen et al. (1998), which is initially surprising since the annual change in global mean sea level is only 2-3 mm. Chen et al. (1998) and Minster et al. (1999) reconciled this difference by observing that annual changes in continental water storage effectively cancel out the annual sea level change caused by changes in SST.

For the present discussion, we will simply remove the annual and semiannual SST variations from the original data set, and compute the global mean SST variations as shown in Fig. 6.10. In addition, we apply 60-day smoothing to be consistent with the smoothing of the sea level time series. A large increase in global mean SST is observed for each major ENSO event since 1982, with the largest change (0.35°C) occurring during the 1997-1998 event. Also shown in Fig. 6.10 is the variation in global mean sea level from T/P, after correcting for instrument effects using the tide gauge calibration (Fig.

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Figure 6.10 Comparison of global mean variations of sea level (Fig. 6.9) and sea surface temperature (Reynolds and Smith, 1994), after removal of annual and semiannual variations.

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Figure 6.10 Comparison of global mean variations of sea level (Fig. 6.9) and sea surface temperature (Reynolds and Smith, 1994), after removal of annual and semiannual variations.

6.5), removing seasonal variations, and applying 60-day smoothing. Qualitatively, the comparison is quite compelling. Note that the increases in sea level and in SST at the beginning of 1997 occur nearly simultaneously, while the decrease of SST in 1998 lags that of sea level by several months, suggesting that temperatures in the subsurface returned to normal before the surface temperatures. These results suggest that the rise and fall in sea level during 1997-1998 were directly related to the ENSO event, and we will further demonstrate this by examining the spatial variation of these changes in the next section.

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