We can gain further insight into the cause of the observed mean sea level variations by examining the spatial variations in sea level change that contribute to the global mean. While variations in global mean sea level have great scientific and public interest as a barometer of environmental change, the true scientific and social implications will be determined by the spatial patterns of sea level change. As an example, anthropogenic-induced climate change, while likely to cause a rise in globally averaged sea level, will actually cause sea level to decline at some locations and rise in others (Russell et al., 1995). This type of information will be critical for planning mitigation efforts related to sea level change. In addition, the spatial pattern of sea level change, if it could be mapped, provides another powerful constraint on climate change models by mapping the geographic "fingerprint" of the change. If the spatial variation of sea level change could be mapped using satellite altimetry and a similar pattern were identified in the output of the global climate models, this would be a powerful corroboration of the validity of the models.
Clearly, the true power of satellite altimetry lies in its ability to map the geographic variation of sea level change. As an example, T/P was the first altimeter mission to accurately map the seasonal variations in sea level, as shown in Fig. 6.11 (see color plate). There are many different spatio-temporal analysis techniques that may be employed to extract the spatial variability of sea level change from the T/P data records. A relatively simple technique for mapping the geographic variation of long-term sea level change is to compute the linear trend of sea level at each geographic location, as shown in Fig. 6.12 (see color plate) for the T/P mission. These trends were determined via a least-squares fit of secular, annual, and semiannual terms at each location along the T/P groundtrack. The problem with this technique is that sea level change at a single location often has considerable deviations from a linear trend, and these deviations tend to corrupt the trend estimate unless a long time series is available. Currently, the trends during the T/P mission are dominated by variability from recent ENSO events, which are clearly manifested in the satellite-observed sea surface temperature results (Reynolds and Smith, 1994) of the same time period (Fig. 6.12), as well as in numerical ocean models (Stammer et al., 1996). However, as the sea level record from satellite altimetry lengthens, the ENSO variations will gradually average out, allowing the detection of climate signals. However, decadal variability may limit this approach until many decades of data are available.
More quantitative results can be obtained using statistically based analysis methods. The method of empirical orthogonal functions analysis (EOFs, also called principal component analysis) identifies linear transformations of the data set that concentrate as much of the variance as possible into a small number of variables (Preisendorfer, 1988). This method has been used in a variety of oceanographic and meteorological analyses to identify the principal modes of variability. If the spatial and temporal characteristics of a mode can be used to identify a physical cause, then the method can be a very powerful data analysis tool. Several investigators have used EOF techniques to help isolate the cause of the sea level change signals observed by T/P (Hendricks et al., 1996; Nerem et al., 1997b). Unfortunately, EOFs have so far been unable to separate ENSO-related variations from long-term sea level change, possibly because these processes may be interrelated (Cane et al., 1996; Trenberth and Hoar, 1996). We will nevertheless review the EOF results here because they provide considerable insight into the cause of the mean sea level variations observed by T/P.
We start by converting the raw T/P sea level measurements into 1° X 1° maps of sea level at 10-day intervals as described by Tapley et al. (1994a). If sea level at a given latitude (<p) and longitude (A) map location is represented by h((p, A, t), where t ranges over each T/P cycle, then the EOF representation of sea level can be written as h(<}>, A, i) = j^SM, A)fl,(i), ¿=1
where .S', (0, A) is the ith spatial EOF and a,(/) is its temporal history. These are determined from the eigenmodes of the spatial-temporal covariance matrix of the T/P sea level grids; thus each mode attempts to describe as much of the sea level variance as possible. Figure 6.13 (see color plate) shows the four leading (highest variance) EOF modes for sea level and SST (Reynolds and Smith, 1994) over the time frame of the T/P mission, where the temporal history of these modes has been scaled to represent their contribution to global mean sea level. Note that the first two "ENSO modes" describe most of the 1997-1998. ENSO event in global mean sea level. Mode 1 began rising at the beginning of 1997, peaked in early 1998 at 8 mm, and then fell back to zero by the end of 1998. Mode 2 began rising at the beginning of 1998, peaking at 11 mm near the end of 1998. Both of these modes show large signals in the tropics, as expected, but also large extratropical signals, especially in the Southern Ocean. Peterson and White (1998) have seen similar ENSO-related extratropical signals in sea surface temperature, which they attribute to atmospheric coupling between the two regions. Also note the large signal in the southwestern Indian Ocean between 5 and 10°S, which has been described by Chambers et al. (1998) and is correlated with ENSO in the Pacific. The EOF analysis establishes that most of the observed variations in global mean sea level are related to the ENSO phenomena.
Leuliette and Wahr (1999) have taken this idea one step further by conducting a coupled pattern analysis (Bretherton et al., 1992; Wallace et al., 1992) of the variations in mean sea level and SST (basically an EOF analysis of the cross covariance matrix of sea level and SST). This technique allows a more rigorous method of identifying the common EOF mode causing the changes in mean sea level, although the conclusions are basically the same as computing EOFs of the individual fields. Thus, they have also concluded that most of the long-term sea level change signal observed by T/P is being caused by changes in sea surface temperature related to the ENSO phenomena.
Clearly it would be desirable to remove the ENSO signals from the T/P sea level record so that we could begin to search for smaller signals, such as those related to climate change. It would be tempting to use the leading EOF modes (the ENSO modes) of sea level and SST in such a computation. However, these results must be interpreted carefully, as there is evidence that ENSO and climate change are not unrelated processes (Trenberth and Hoar, 1996), and thus removing the leading EOFs might also remove a climate signal. In addition, the EOF technique by no means guarantees that each mode will correspond to only a single process. In fact, processes that have spatial similarities will tend to coalesce into a single mode. There are many other statistical techniques that can be explored, so this should be considered an area of active research as of this writing.
6.5 THE FUTURE
As mentioned in the first section, we are primarily interested in determining whether the rate of mean sea level is accelerating in response to global climate change, as suggested by the Intergovernmental Panel on Climate Change (IPCC) in their recent report (Houghton et al., 1996). For the 20th century overall, no statistically significant acceleration of sea level has been found in tide gauge data (Douglas, 1992; Chapter 3; Woodworth, 1990), but tide gauge data do not possess the ability to detect a global acceleration in less than many decades. One strategy is to use the tide gauge estimate of the historical rate of 1.8 (±0.1) mm/yr (Douglas, 1991) as the background rate, determine independently a rate from recent altimetric data, and then ask whether the altimetric rate is significantly different from the background rate. Although we will describe the present altimetric estimate of the recent sea level changes, we are mainly concerned with a careful error analysis of this approach in order to know what is required to make this calculation as sensitive as possible, and in particular how long of a time series will be required from satellite altimetry to detect climate signals. In the near future, however, we believe that it may be possible to quantitatively test the IPCC projections using this method. It will be much better when the acceleration of the rate can be measured directly using satellite altimetry, but this will require several decades of measurements.
We have shown that the 20-mm rise and fall of global mean sea level during 1997-1998 is almost certainly related to the ENSO phenomena. The presence of ENSO-scale variability in global mean sea level means that a longer time series will be needed to reduce this variability through averaging to reveal the smaller climate signals, unless reliable techniques can be developed to remove the ENSO signal from the data. To assess the impact of such variability, Nerem et al. (1999) developed two simulated long time series of global mean sea level variations, both containing ENSO variability. The first was an ~100-year-long (1882-1998) time series of the Southern Oscillation Index (SOI), which was linearly regressed against T/P mean sea level over 1993-1998 to determine the proper regression coefficients. The regression coefficients were then used to scale the SOI and simulate an ~100-year-long time series of global mean sea level. A similar technique was applied to a set of reconstructed global mean SST anomalies (Smith et al., 1996) covering 1950-1998. In addition, the rate and acceleration of each of these time series were set to zero. Note that these estimates do not include errors in the tide gauge calibrations, but as mentioned previously, these errors should be significantly smaller than those caused by ENSO variability if geodetic monitoring is performed at each gauge.
Each of these time series was then used to perform two simulations. In the first simulation, a 2 mm/yr secular sea level change was added to the time series, and a series of Monte Carlo solutions was performed to determine the error in the estimated sea level rate by a least-squares solution using varying data spans with a random midpoint time. The result of these simulations is a plot of the accuracy of the sea level rise estimate versus the length of the data span of altimeter data employed (see Nerem et al., 1999). Both simulations (using SOI or SST simulated sea level) suggest that 10 years of T/P class altimetry will be required to determine the rate of mean sea level change to an accuracy of 0.5 mm/yr. These simulations were repeated by adding an acceleration of mean sea level of 0.06 mm/yr2 and estimating both the rate and the acceleration of sea level change. The SST results are invalid after about 20 years because the time series is of insufficient length to test longer data spans. However, the SOI results suggest that ~30 years of T/P class altimetry will be needed to detect an acceleration of mean sea level to an accuracy of 0.02 mm/yr2. It should be noted that these results assume that the ENSO variability cannot be removed by other techniques; the situation could be improved considerably if this were so.
In summary, we should be able to detect a difference from the Douglas (1991) tide gauge-determined rate with a decade of T/P-class altimeter data, which will provide a limited test of the IPCC predictions. A more meaningful test, where the acceleration of mean sea level change is measured, will require at least 2-3 decades of similar data, unless decadal variability in global mean sea level is a significant contaminant to the computation. There is currently no way to assess the level of decadal variability in time series of global mean sea level computed using satellite altimetry. While two decades is a long time, it is much shorter than would be required using only the tide gauges.
If a sea level time series of several decades in length will be needed to test different sea level change predictions from climate change models, such a time series cannot be provided by a single satellite mission such as T/P; thus measurements from multiple missions will be needed to assemble a time series of sufficient length. A single 10-day averaged global mean sea level measurement from T/P has a precision of roughly 3-5 mm; thus we would like to link measurements from future missions to T/P with roughly the same accuracy.
Historically, this has proven to be a difficult task, as each mission has a unique set of time-varying measurement errors. Guman (1997) presented an analysis combining measurement from Geosat, ERS-1, and T/P. Because the ERS-1 and T/P missions significantly overlapped in time, establishing the relative bias between the two sets of measurements can be obtained through a straightforward differencing of their measurements at crossover points. However, the multiyear gap between the end of the Geosat mission and the beginning of the ERS-1 and T/P missions is more difficult to overcome. Tide gauge measurements spanning these missions provide the best basis for linking the sea level time series provided by these missions. However, the errors in this approach will be significant because of the unknown vertical movement of the tide gauges, and because of their poor geographic sampling of the altimeter measurement errors. This is particularly true for Geosat, which had much larger measurement and orbit errors than T/P. Guman (1997) implements a novel method for correcting the Geosat measurements using tide gauge comparisons; however, the combined Geosat/ERS-l/T/P sea level time series only loosely constrained the sea level change over the intervening decade.
The first missions likely to be used to extend the T/P measurement record are Jason-1 and Envisat, scheduled for launch in late 2000 and mid-2001, respectively. However, Envisat is in a sun-synchronous orbit, and thus tidal aliasing (Parke et al., 1987) may be a significant error source since errors in the model of the solar tides will alias to zero frequency, potentially contaminating measurements of global mean sea level. If T/P is still operating when these spacecraft are launched, then computing the relative biases between these missions at a given time epoch will be relatively straightforward, and changes in these biases can be monitored using the tide gauges as discussed earlier. Indeed, it is currently planned to fly T/P and Jason-1 in tandem (in the same orbit separated in time by only a few minutes) for a short time to conduct a detailed study of the measurement differences. However, if the instruments on board T/P fail before the launch of these missions (there is enough propel-lant to maintain the orbit, but some of the satellite instruments have already exceeded their design lifetime by a factor of two!), it may be necessary to use tide gauges to bridge the measurement gap (Geosat Follow-On and ERS-2 may also be useful for bridging the gap, despite their larger errors relative to T/P). Envisat and Jason-1 will provide measurements of comparable accuracy to T/P, so the task of linking these measurements together will be much easier than encountered by Guman (1997) with Geosat. In this case, the largest error source is likely to be the vertical movement of the tide gauges. For a 1-year measurement gap, each tide gauge could be expected to move between 1 and 10 mm (due to postglacial rebound) if gauges in areas of known tectonic activity or subsidence are disregarded. For this reason, efforts to monitor the vertical motion of several tide gauges in the Pacific using the Global Positioning System have recently been initiated (Merrifield and Bevis, personal communication). A GPS-derived height time series of several years in length can determine the rate of vertical land motion to better than 1 mm/yr. Thus, while the problem will require careful study, it is likely that the T/P sea level time series can be extended in a seamless fashion using Envisat and/or Jason-1 measurements (the latter being preferable because they will fly in identical orbits). One caveat on this conclusion is the maintenance of the reference frame within which these measurements are made. As mentioned earlier, great care will have to be taken to ensure that the reference frame definition is maintained over several decades since the space geodetic technologies that are used to define the frame (and that also track the altimeter satellites) are undergoing rapid change as technology improves.
The first 6 years of T/P data have demonstrated that very precise measurements of global mean sea level can be made using satellite altimeters. In addition, the T/P results have shown that global mean sea level contains significant ENSO variability, which can be regarded as an error source for determining the long-term rate of sea level change, but is also of significant scientific interest in itself. We have shown that a series of T/P-Jason class satellite altimeter missions should be able to measure the long-term rate of sea level rise with about a decade of measurements, provided the instruments are precisely monitored using GPS-positioned tide gauges. Measuring the acceleration of sea level rise—a more important quantity for corroborating the climate models—will require 2-3 decades of measurements. We believe these objectives can be achieved given the current performance of T/P and the tide gauge calibration technique. Uncertainties in this assessment include (1) the unknown effects of decadal variability in global mean sea level,
(2) the possibility of gaps in the time series due to satellite failure, and
(3) the successful implementation of GPS monitoring at each of the tide gauges. Despite these uncertainties, satellite altimetry is already defining a new paradigm in studies of sea level change.
We thank Eric Leuliette for producing some of the plots used in this paper, and Don Chambers for participating in many fruitful discussions regarding these results. The altimeter data base used in this study was developed by researchers at the Center for Space Research under the direction of Byron Tapley. This work was supported by a NASA Jason-1 Project Science Investigation.
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