TOPEX/POSEIDON: The 2-cm Solution

Bob Cheney, Laury Miller, Russ Agreen, Nancy Doyle, and John Lillibridge

National Ocean Service, NOAA, Silver Spring MD 20910

J. Geophys. Res., 99 (C12), 24555-24564, 1994.

ABSTRACT

The unprecedented accuracy of TOPEX/POSEIDON (T/P) altimeter data warrant a new evaluation of the methods typically used to form time series of sea level change. Whereas explicit removal of orbit error has always been required as a first step in altimeter data processing, the T/P analysis presented here is based simply on unadjusted, monthly averages. This approach has the advantage of retaining the large-scale ocean signal, which would be distorted by orbit adjustment. Using 16 months of data, we have evaluated the T/P monthly means on spatial scales ranging from mesoscale to global. In the tropical Pacific, comparisons with 17 island tide gauge records and dynamic height derived from 36 thermistor moorings show that the altimeter data have an accuracy of approximately 2 cm when averaged over spatial scales of a few hundred km. On basin scales in the northern hemisphere, similar agreement is found between the T/P data and the dynamic height climatology of Levitus (1982). These new altimeter observations are thus providing the first reliable view of global sea level changes on seasonal-to-interannual time scales.

1. INTRODUCTION

Observations from satellite altimeters during the past two decades have provided dramatic descriptions of sea level variability, but the spatial scales which could be reliably studied were limited by orbit uncertainty. Seasat data, with radial orbit errors of approximately 1 m, were suitable only for studies of mesoscale eddies and western boundary currents (Cheney et al., 1983; Fu, 1983). With Geosat and ERS-1, new gravity models and orbit determination techniques ultimately reduced the orbit error to a few decimeters, expanding the capability of altimetry to include larger-scale variations, such as those in the tropical Pacific (Cheney et al., 1991; Lillibridge et al., 1993). However in all cases, processing the altimeter data involved adjustments to eliminate the residual orbit error, a procedure which invariably removed some portion of the ocean signal (Wagner and Tai, 1994). Various methods have been used in an attempt to restore the missing altimetric sea level signal, such as blending the altimetry with island tide gauge data (Miller et al., 1993) or dynamic height measurements (Carton and Katz, 1990). But such methods are limited to regions where sufficient contemporaneous in situ data can be found.

The objective of the TOPEX/POSEIDON (T/P) mission is to measure sea level with an accuracy of a few centimeters for temporal scales of one month or longer and distances of hundreds to thousands of kilometers. It is these larger scales which are the most difficult to observe and yet which bear most significantly on global change. With more than one year of data collected, the T/P goal appears to have been achieved; altimeter errors, including environmental corrections, are estimated to be only 5 cm for single-pass sea level measurements (Fu et al., 1994). This does not include ocean tide model corrections which have uncertainties of comparable magnitude, but the T/P data are enabling these errors to be addressed explicitly, e.g. Wagner et al., (1994a). In this paper, we investigate the extent to which simple averaging in time and space can further reduce the T/P measurement error. By avoiding the usual orbit adjustment process, this approach has the potential of recovering the complete sea level signal on all relevant spatial scales. Based on comparisons with tide gauge data and in situ observations of dynamic height, we show that monthly mean sea level, averaged over spatial scales of a few hundred km, can be determined from T/P data with an accuracy of 2 cm.

2. DATA PREPARATION

Environmental and Geophysical Corrections.

Analyses presented here are based on altimeter data from both the TOPEX (U.S.) and POSEIDON (French) altimeters during the first 16 months of the mission; this required removal of a 21.5-cm relative bias between the two instruments (see summary below). The POSEIDON altimeter was operated only about 7 percent of the time during these first 51 10-day cycles. Data were edited based on quality flags and parameter ranges as recommended in the user handbook (Callahan, 1993). The following corrections were applied to both TOPEX and POSEIDON data: water vapor from the onboard radiometer, dry troposphere and inverted barometer, electromagnetic bias, center of gravity, solid earth tide, pole tide, and a net instrument correction. The ocean tide model of Cartwright and Ray (1991) was used, with corrections to the M2, S2, K1, and O1 constituents based on the TOPEX analysis of Wagner et al. (1994a); the effect of these additional tidal corrections will be shown in the next section. For the ionosphere correction, the dual-frequency altimeter measurement was used for Topex, whereas a value derived from DORIS tracking system measurements was used for POSEIDON (Picot and Escudier, 1994). The standard NASA Goddard precise orbit based on the joint gravity model (JGM- 2) was used throughout.

TOPEX-POSEIDON Bias.

Although the TOPEX and POSEIDON altimeters share a common antenna, they are different instruments, and laser-overflight calibrations indicate a bias between the two of approximately 20 cm (Fu et al., 1994). To obtain a more accurate value, we analyzed collinear differences between successive 10-day cycles of TOPEX and POSEIDON altimeter data. Only ocean data between 60oS and 60oN were used to avoid possible contamination from sea ice. The results, summarized in Table 1, show a consistent bias of 21.5 cm (TOPEX giving a higher value of sea level than POSEIDON). The analysis was based on cycles 20 and 41 when the POSEIDON altimeter was operating continuously. Whereas successive TOPEX cycles show that global mean sea level changes by only a few tenths of a centimeter in 10 days, switching from one altimeter to another between successive cycles results in a distinct 21.5-cm (average) step. The POSEIDON altimeter was also operating during cycle 31, but because a substantial amount of global data was lost, we have excluded this cycle from the bias calculation.

3. COLLINEAR DIFFERENCES

Altimeter passes were sorted into ascending and descending collinear nests, and sea heights were interpolated at common 1-s intervals (6.2 km spacing) along the satellite track. Cycle 18 was chosen as the reference for computing collinear differences because (a) it was one of the first complete Topex cycles, and (b) it is located near the middle of the 2-km envelope formed by the collection of collinear passes. This second consideration reduces height errors arising from non- collinearity and cross-track geoid gradients to about 1 cm rms (Rapp and Yi, 1994). Height differences with respect to the reference cycle were then averaged along 1o-latitude segments, and the resulting time series were adjusted to have zero mean over 1993. Finally, regular grids of monthly mean heights were generated by collecting the data in boxes with dimensions of 4 degrees longitude by 1o latitude. Each 4x1 cell is sampled between 2 and 4 times every 10 days, providing 6 to 12 altimeter profiles per month. Selection of 4x1 cells is a compromise which provides a certain amount of spatial averaging while retaining adequate resolution for the large-scale patterns of ocean variability. Cells of this dimension are especially appropriate for resolving the zonally- banded structure of the equatorial oceans. Figure 1 shows a typical time series for a 4x1 cell in the tropical Pacific. The 1o-average heights from individual altimeter passes are shown as plus symbols; the solid line is the monthly mean computed from these data which will be used in the next section to compare with in situ observations. The scatter of the pass-by-pass observations is due to a combination of net error and sea level variations within the cell.

Figure 1. Typical T/P sea level time series for the 4-deg longitude x 1-deg latitude cell centered at 8S, sampled 4 times every 10 days. Each plus symbol represents one altimeter pass, where the sea height has been averaged along a 1-deg segment of the satellite track. The solid line is the monthly average. 4x1 monthly means form the basis for all in situ comparisons in this paper.

Statistics generated by the global T/P collinear differences provide an indication of the overall altimeter system precision. In Figure 2a, we show the rms difference (based on the 1-s samples) of each pass from 60N to 60S relative to its collinear partner in cycle 18. The altimeter data are fully corrected as summarized above, but no orbit adjustment has been made. The rms difference for all 12,400 passes together is 14.2 cm, a remarkably small value considering that it includes errors of the altimeter and tide model plus the complete (non-tidal) sea level variability signal of the global oceans over a 16-month period. A number of outliers exist, but virtually all of these are short passes in areas of high natural variability, such as the Agulhas Current, i.e. they represent ocean signal rather than noise.

Figure 2. (a) The rms collinear difference of each pass of T/P data, from 60N to 60S, for cycles 1-51 with respect to cycle 18. (b) Solid line: the same statistics as above, collected in 10-day cycles; selected cycles are labeled. The minimum of 8 cm is the crossover difference value of cycle 18 with respect to itself. Dashed line: same statistics when the additional tide corrections of Wagner et al. (1994a) are not included. The distinct 60-day periodicity is aliasing of the M2 and S2 terms of the Cartwright and Ray (1991) tide model.

It is also apparent from this scatter plot that the variability grows as a function of increasing time between the collinear passes. This is illustrated more clearly by the solid curve in Figure 2b, in which the variability has been computed for each 10-day cycle (still relative to cycle 18). Because collinear differences of cycle 18 cannot be formed with itself, we have substituted the cycle 18 global rms crossover difference value, 8 cm. From this minimum, the variability increases symmetrically, reaching 12-13 cm when the time difference is one month. Thereafter, the increase is more gradual, levelling off at 16 cm for passes 6 months apart. Beyond 6 months, the variability decreases, an indication of the seasonal cycle of sea level change in the ocean (see sections 5 and 6).

The dashed curve in Figure 2b demonstrates the sensitivity of T/P data to the ocean tide model used. Recall that in our basic analysis (the solid curve), the Cartwright and Ray (1991) ocean tide model was used together with corrections to the first four major tidal constituents derived from TOPEX data by Wagner et al. (1994a). The dashed curve shows the result when the Wagner corrections are not included. The distinct 60-day periodicity is an indication of M2 and S2 error in the Cartwright and Ray model (Wagner et al., 1994b). (The 9.916-day repeat period of the satellite track aliases the M2 and S2 tides into 62.1-day and 58.7-day periods, respectively. Errors of the K1 and O1 constituents, with aliases at 173.2 days and 45.7 days, are not apparent due to the relatively long period of the former and the small amplitude of the latter.) Wagner's corrections reduce the overall T/P global variability from 15.4 to 14.2 cm, indicating that the net tidal error removed had an rms amplitude of 6 cm. Such tide model improvement is critical for achievement of the T/P goals.

4. TROPICAL PACIFIC SEA LEVEL VARIATIONS

The tropical Pacific Ocean is an ideal region for evaluating the T/P time series because it is monitored by a large number of island tide gauges and mid-ocean thermistor moorings. Moreover, point measurements in the tropics can be considered to be representative of significantly larger areas; White et al. (1985) found that equatorial Pacific decorrelation scales are 15o in longitude and 3o in latitude. In terms of sampling, tropical tide gauge and mooring data averaged over monthly periods can therefore be considered equivalent to the 4x1 altimeter cells described above. With regard to accuracy, tide gauge monthly means have estimated errors of only 1-2 cm (Wyrtki and Nakahara, 1984) while the tropical atmosphere ocean (TAO) moorings have slightly larger expected errors: 2-3 cm in the eastern Pacific and 3-4 cm in the west (Busalacchi et al., 1994). TAO dynamic heights are less accurate because (a) mean temperature/salinity relationships must be used, (b) sampling is at only 10 discrete levels in the vertical, and (c) they represent only the upper 500 m. In addition, dynamic heights do not include the barotropic signals, thought to be about 1 cm in the tropics (Luther, 1980).

Maps in Figure 3 summarize comparisons between the T/P data and 16-month records from 50 tide gauges and 36 moorings, all located between 30o N and 30o S.

Figure 3. Based on 16 months of data, comparison of T/P monthly means with sea level from 50 tide gauges (dots) and dynamic height from 36 thermistor moorings (circles). Symbols indicate locations of the 4x1 altimeter cells used, making the few coastal gauges used to appear offshore. Best agreement is within 10 degrees of the equator where rms differences less than 3 cm and correlations greater than 0.8 are common.

The rms difference and correlation distributions tend to be symmetric about the equator with best agreement found in a band from 10S to 10N and gradual degradation toward higher latitudes. We do not interpret this to mean that the altimeter errors grow as a function of latitude, but rather that the decreasing scales of variability away from the equator cause the in situ point measurements to be less representative of the 4x1 altimeter averages. Slowly-propagating ocean signals at certain mid-latitude locations can also introduce temporal lags between the altimeter and tide gauge time series; for example, Mitchum (1994) shows that at Wake Island, better correlations can be obtained if Rossby wave propagation speeds are assumed. It seems clear that for quantitative comparisons at the level of a few centimeters, the altimeter 4x1 averages have no in situ counterpart outside of the tropics .

Figure 4 shows the results only for locations within 10 degrees of the equator where the in situ data can be most confidently used to evaluate the altimeter accuracy. Separate scatter plots indicate that the T/P data agree better with the island tide gauge records than with TAO dynamic heights: the 17 gauges yield an rms difference of 2.2 cm and correlation of 0.88, while the corresponding values for the 36 moorings are 3.1 cm and 0.80 correlation. This result is consistent with the larger errors expected of the TAO dynamic heights.

Figure 4. Scatter plots of all T/P comparisons within the equatorial region, 10N to 10S. (a) 17 island tide gauges yield a tight envelope with rms difference of only 2.2 cm and correlation of 0.88. (b) 36 thermistor moorings show more scatter with rms difference of 3.1 cm and correlation of 0.80.

Figure 5 presents time series at 10 of the island locations where the rms differences range from only 1.1 to 2.0 cm. The existence of this many high-quality comparisons presents a strong case that the T/P 4x1 monthly means are accurate at the level of 2 cm.

Figure 5. Time series from 10 island gauges (thin line) within 10 degrees of the equator at which particularly good agreement was found with T/P data (heavy line). The existence of so many examples such as this argues that T/P is achieving accuracies at the 2 cm level for monthly mean heights in 4x1 cells, without orbit adjustment.

5. THE SEASONAL CYCLE

Many of the tropical Pacific time series shown in Figure 5 are dominated by fluctuations with an annual period. Examination of the global distribution of the phase and amplitude of this signal, which is known in general but not in detail, allows qualitative evaluation of the T/P data. Much of the existing information about the seasonal sea level cycle is derived from decades of shipboard observations compiled by Levitus (1982). This monthly dynamic height climatology shows that at mid-latitudes, the seasonal cycle of warming and cooling produces peak-to-peak amplitudes of about 10 cm with northern and southern hemisphere maxima occurring in their respective fall seasons. The T/P result in Figure 6 is consistent with this; the North Pacific and North Atlantic have nearly uniform phase with maximum sea level in October, while the Southern Ocean sea level peaks in April. The largest mid-latitude seasonal signals are associated with the western boundary currents, where amplitudes of 15 cm (30 cm peak-to-peak) are common. In the tropical oceans, the largest signals are found near 10oN, corresponding to the intertropical convergence zone where seasonal migration of the trade winds predominate.

Figure 6. Annual phase and amplitude derived from a harmonic analysis of T/P time series. Phases are in terms of the month of maximum sea level, with the second half of the calendar year shaded. Amplitudes are in cm, greater than 6 cm shaded. Click here to see this figure in color.

Figure 7 compares the patterns of large-scale sea level change seen by T/P with the Levitus (1982) climatology for (a) 20-deg latitude bins, and (b) northern and southern hemispheres. In computing averages, both altimeter and dynamic heights (relative to 1500 dbar) were normalized by the cosine of latitude to account for the fact that neither data set is based on an equal-area grid. In the northern hemisphere, the similarity between the altimetry and climatology is quite remarkable, especially considering that it is a comparison between a 1-year snapshot and an average over many decades. The phases are virtually the same, and the amplitude of the altimeter signal is only about 2 cm larger than the climatology. In the southern hemisphere, however, the agreement is considerably worse. In this case, the dynamic height is larger than the altimeter height by about 1 cm, but the main discrepancy is the phase, which differs by as much as 3 months. Of course, in common with most in situ oceanographic observations in the southern hemisphere, the Levitus data set is quite sparse here; it is therefore likely that T/P is giving the more reliable view. As evidence of this, note that the dynamic height signal is symmetric about the equator, whereas the altimeter signal is significantly larger in the northern hemisphere than in the south, in agreement with the seasonal cycle of sea surface temperature (Shea et al., 1992.)

Figure 7. Variation in sea level from T/P (heavy line) and the Levitus (1982) climatology of dynamic height relative to 1500 dbar (dashed line). Results are shown for (a) global 20-deg latitude bands and (b) the northern and southern hemispheres. Profiles are offset by 10 cm.

6. GLOBAL SEA LEVEL

Of the various applications of altimeter data, the most challenging is determination of the rate of change of global sea level, estimated from tide gauge observations to be approximately 2 mm per year over the past century (Douglas, 1991). Wagner and Cheney (1992) used Geosat and Seasat altimetry in a feasibility study and found that the principle errors to overcome were those associated with the ionospheric correction and absolute calibration of the altimeter, including the orbit. Both of these have been explicitly addressed with T/P, the ionosphere being measured by the dual- frequency altimeter and the calibration being monitored over the lifetime of the mission in a variety of ways.

Figure 8 shows the globally-averaged (60N to 60S) variation of sea level from T/P data; within these latitude limits, the northern hemisphere ocean makes up 40 percent of the global ocean by area. Excluding the first two months, the curve has a 3-cm peak-to-peak amplitude and phase similar to the northern hemisphere. The smaller undulations (maximum in April, minimum in November) are contributed by the southern hemisphere. Given that satellite altimeters are unique in their ability to collect sea level observations over the entire global ocean, there are no independent data capable of estimating the accuracy of this record. If the 2-cm error for 4x1 monthly means were completely random, the global average would have sub-millimeter accuracy, but a more sophisticated approach to the global error analysis is obviously required. Nevertheless, the T/P data hold great promise for a more reliable determination of the rate of global sea level change.

Figure 8. Variation in global sea level from T/P. Measurements during the first 2 months may not be reliable due to satellite pointing errors which were corrected in December 1992 (Fu et al., 1994). Thereafter a regular seasonal cycle is evident with phase similar to the northern hemisphere (see Figure 7).

7. CONCLUSIONS

In a strict sense, our 2-cm accuracy estimate for T/P 4x1 monthly means applies only to the tropical Pacific, where the temporal and spatial averaging scheme employed is compatible with the time and space scales of sea level variability. However, the major altimeter error sources are only weakly dependent on geographic location. The orbit is determined from a globally-distributed network of laser and DORIS stations, water vapor and ionosphere corrections are continually measured by onboard instruments, and the ocean tides are well-determined by the T/P data themselves. It is true that increased altimeter noise and added uncertainty in the electromagnetic bias correction would be expected in areas such as the Southern Ocean, where high sea state and wind speed are common. But spatial and temporal averaging would tend to reduce the impact of such errors. It is therefore reasonable to expect that the tropical ocean results apply to all T/P observations.

It is more difficult to estimate the accuracy of the larger-scale T/P observations because existing in situ data are inadequate, particularly in the southern hemisphere. In the northern hemisphere, the seasonal cycle described by T/P agrees quite well with the best independent data set, the dynamic height climatology of Levitus (1982); for global averages in 20-deg latitude bands, phases are virtually identical and amplitudes differ by 2 cm or less. When expressed as maps of annual harmonics, the T/P data also present a picture that is consistent with seasonal variability of the tropical trade winds together with large-scale heating and cooling at higher latitudes. Altimeter observations of the quality of T/P should ultimately be capable of addressing the issue of global sea level change, although years of data will be required.

In the field of satellite altimetry, it is typical for journal articles to be dominated by discussions of techniques at the expense of science. T/P may change this. The accuracy of these data on both small and large scales is unprecedented. Furthermore, only minimal processing is required. Except for simple differencing, binning, and averaging, our results are based on sea heights taken directly from the geophysical data records (with the exception of the ocean tide model). No special knowledge in areas of geodesy, tropospheric modelling, or orbit mechanics was needed. Availability of such a simple, yet reliable, data set for the global oceans will encourage their use by a broad range of scientists.

ACKNOWLEDGMENTS

TAO mooring data were provided by Mike McPhaden of NOAA/PMEL and were converted to dynamic height by Ben Giese of Texas A&M University. Tide gauge data were obtained via Gary Mitchum at the University of Hawaii. Carl Wagner assisted in the analysis of the dynamic height climatology and implementation of the tide corrections. This work is partially supported by the NOAA Climate and Global Change Program.

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