a comparison of ocean topography derived from the …ieee transactions on geoscience and remote...

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 38, NO. 3, MAY 2000 1425

A Comparison of Ocean Topography Derived from theShuttle Laser Altimeter-01 and TOPEX/POSEIDON

Mark D. Behn and Maria T. Zuber

Abstract—To assess the utility of laser altimetry for studies indynamical oceanography, we present a comparison of the ShuttleLaser Altimeter (SLA)-01 and the TOPEX/POSEIDON (T/P)radar altimeter on global and regional scales. We compare all

1.1 million SLA-01 range measurements over the oceans to theCSRMSS95 gridded mean sea surface model and find the overallroot mean square (RMS) difference to be 2.33 m. The misfit wasimproved significantly by removing the mean and trend fromindividual SLA-01 profiles, often resulting in RMS differencesless than 1 m. We also show that in regions where sea surfaceheight varies dramatically over relatively short horizontal scalessuch as across major subduction zones, SLA-01 was capable ofresolving rapid changes in sea surface height. Finally, we examinea number of coastal zones and illustrate SLA-01’s ability to trackcontinuously across the land–sea interface, even in regions ofdramatic coastal topography.

The dominant sources of radial error in the SLA-01 data aretime-interval unit (TIU) error ( 0.75 m) and radial orbit error (1m RMS). Therefore, limitations of the SLA-01 data set are causedprimarily by system constraints as opposed to instrumentationerror. Our results indicate that future laser altimeters will providevaluable information regarding ocean topography. In particular,laser altimetry data can be used to supplement orbiting microwaveranging systems in coastal areas where such sensors are incapableof maintaining lock across the continent–ocean transition.

Index Terms—Distance measurement, geodesy, remote sensing,sea, semiconductor lasers.

I. INTRODUCTION

OCEAN topography represents a critical component to ourunderstanding of the oceans and provides important in-

formation regarding the coupling between the oceans, atmos-phere, and solid Earth. To first order, sea surface height (SSH)is controlled by the Earth’s gravitational field [1]. The marinegeoid represents the gravitational equipotential surface at whichthe sea surface would be located if the Earth were at rest. How-ever, effects such as the Earth’s rotation, lunar and solar tides,wind patterns, and ocean currents cause actual sea surface tovary slightly from the geoid. These variations correspond to dy-namic topography and have maximum amplitudes of 1–2 m [2].

Manuscript received July 6, 1999; revised November 19, 1999. This workwas supported by a Department of Defense Graduate Research Fellowship.

M. D. Behn is with the Department of Earth, Atmospheric, and Planetary Sci-ences, Massachusetts Institute of Technology, Cambridge MA 02139 USA, andalso with the Marine Geology and Geophysics Program, Woods Hole Oceano-graphic Institution, Woods Hole, MA 02543 USA (e-mail: [email protected]).

M. T. Zuber is with the Department of Earth, Atmospheric, and PlanetarySciences, Massachusetts Institute of Technology, Cambridge, MA 02139 USA,and also the Laboratory for Terrestrial Physics, NASA/Goddard Space FlightCenter, Greenbelt, MA 20771 USA.

Publisher Item Identifier S 0196-2892(00)04132-2.

Knowledge of ocean topography is essential in the study ofvarious oceanographic and geophysical problems, includingglobal ocean circulation patterns, the Earth’s gravitational field,marine crustal structure, and global sea level change. To date,most remote measurements of ocean topography have employedmicrowave techniques such as radar altimeters, scatterometers,and synthetic aperture systems. Early calculations of meansea surface using data from GEOS-3 and SEASAT achievedmeter-scale vertical accuracy with a minimum horizontal reso-lution of 25 km [3]. More recently, high resolution data (5–10km along-track and as little as 2 km across-track) have beenobtained from the Geosat Geodetic Mission, with additionalhigh quality but lower resolution observations derived fromthe Geosat Exact Repeat Mission and the ERS-1 mission [4].TOPEX/POSEIDON (T/P) observations are the most preciseto date [5], with an accuracy of 3–4 cm [6]. However, due tothe desire to achieve 10-day temporal repetition, T/P has lowacross-track resolution (316 km at the equator [5]).

While radar systems provide very high accuracy measure-ments of sea surface topography over the open ocean, it hasbeen shown that once land is present within the altimeter’s foot-print, SSH measurements may become contaminated [7]. Re-cent studies of TOPEX data in the Pacific found SSH measure-ments to be affected up to 15 km from the coast as the altimeterapproaches the shoreline and up to 35 km as the altimeter re-cedes from the shoreline [8]. Furthermore, ground-track sepa-ration often precludes the interpretation of radar data up to 100km from the coastline. In a recent study, Strub and James [9]showed that TOPEX and ERS-1 altimetry data alone were in-sufficient to detect eddies and boundary currents off the coastsof California, South Africa, and Chile. Rather, it was necessaryto incorporate sea surface temperature (SST) and tide gauge datawith the altimetry measurements before these features could beresolved.

Although coastal zones represent those areas least accessibleto modern radar altimetry systems, they also represent someof the Earth’s most intriguing scientific regions. Coastal zonescontain many diverse ecosystems, including some that directlyinvolve humans and are affected by human activity. In addition,coastal areas are especially sensitive to climate variability andother complex interactions within the continent-ocean transi-tion. Characterization of near-shore currents and eddies is crit-ical because these phenomena provide temporal and spatial es-timates of the energy available in the coastal system to drivesedimentological and biological processes.

In this study, we examine the utility of orbital laser altimetryfor coastal studies of ocean topography. In particular, we com-pare data collected by the Shuttle Laser Altimeter (SLA)-01

0196–2892/00$10.00 © 2000 IEEE

1426 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 38, NO. 3, MAY 2000

Fig. 1. Schematic diagram of a laser altimeter ranging to the ocean surfaceassuming a slight off-nadir incidence. The variablez represents the range fromthe satellite to the sea surface, which must be differenced with the altimeter’sorbital altitude in order to calculate ocean topography. The parameter� is thedivergence of the transmitted laser signal, which typically results in a footprintsize of 100 m for SLA-01.

with the University of Texas, Austin, Center for Space Re-search gridded mean sea surface (CSRMSS95) over the openoceans and with time-averaged T/P measurements of SSH incoastal regions in order to evaluate the quality and resolutionof the SLA-01 data set. Laser altimetry is an Earth-observingtechnology whose application to coastal studies in physicaloceanography has not been previously assessed. The shortwavelength of the laser’s optical radiation (1064 nm) and itsability to emit a narrow collimated beam, enable focused,high-resolution measurements to be made from a single laserpulse. Thus, by their nature, laser measurements are notcorrupted by the land-sea transition and allow geodeticallyreferenced measurement of the sea surface near the coast.

II. TECHNICAL BACKGROUND

A. Recovering Sea Surface from Laser Ranging

Laser altimeters determine range by measuring the roundtriptravel time of a pulse of electromagnetic radiation to and fromthe surface of interest. The transmitted pulse, generated byan instrument aboard an airborne or spaceborne platform, isbackscattered from the incident surface, and a fraction of thereflected energy is received at the system telescope (Fig. 1).Optical scattering and absorption at the surface cause thereceived pulse to be spread in time and reduced in energycompared to the transmitted pulse (Fig. 2). The range to thesurface is determined from the two-way travel time by

where is the speed of light in a vacuum. Commonly, the arrivaltime of the reflected pulse is defined by the time at which thenumber of photons accumulated on the detector exceeds a spec-ified threshold. This is known as leading edge detection and wasused in the SLA-01 system.

To determine topographic elevations from orbital laser rangedata, it is necessary to compute precise spacecraft orbits, whichare subtracted from range profiles to yield relative surface eleva-

Fig. 2. Schematic diagram of the laser ranging process, illustrating the time offlight measurement of a single outgoing laser pulse with a specified transmittedpowerP and widthw . The received pulse is characterized by a reduction inpeak powerP and an increase in pulse widthw due to interaction with thereflecting surface. The roundtrip travel time of the pulse to the surface is definedwhen the number of photons accumulated on the altimeter detector exceeds aspecified detection thresholdT . Figure adapted from Bufton [34].

tions. Elevations derived from the ranges are in a center-of-massreference frame, most commonly referenced to the ellipsoid.SLA-01 precision orbits were computed using NASA GoddardSpace Flight Center’s, Greenbelt, MD, GEODYN/SOLVE orbitanalysis programs [10], which numerically integrate the space-craft state and force model partial derivatives using a high orderpredictor-corrector model.

The absolute accuracy of the derived elevations is generallydominated by radial orbit error and range walk (i.e., shifting ofthe received pulse’s leading edge due to spreading associatedwith surface scattering). Smaller magnitude errors include in-strument (clock) error, spacecraft pointing and jitter, and foot-print-scale surface roughness of the incident surface [11].

One major difference between laser and radar altimetry is theeffect of wave height on the SSH measurements. Radar altime-ters utilize a pulse-limited geometry, in which a relatively widebeam with short pulses is incident on the sea surface [12]. Thismethod requires that multiple pulses be averaged in order to ob-tain a single SSH estimate. As the roughness of the sea surfaceincreases, the radar footprint grows in order to maintain con-stant range accuracy at the expense of along-track resolution. Incontrast, laser altimeters are capable of obtaining useful infor-mation from each individual range measurement. Rougher seastates will result in broader return waveforms, which may resultin range walk in leading edge detection systems [13]. However,the information in the waveform provides both an estimate of thewave height and the ability to correct for range walk in roughersea states.

B. Shuttle Laser Altimeter (SLA-01) Mission

The SLA-01 mission was conducted during the flight of theSpace Shuttle Endeavor (STS-72) during January, 1996 [14].The instrument was positioned in the shuttle cargo bay and di-rected approximately three million laser pulses at the surfaceof Earth with the instrument in a nadir-pointing orientation andfiring at 10 Hz. Of the total pulses, 37% were backscattered fromthe ocean surface in a limited latitude band of28.5 . Each in-dividual observation includes the time-tagged roundtrip traveltime of the laser pulse to the surface and the digitized waveformof the returned pulse.

BEHN AND ZUBER: COMPARISON OF OCEAN TOPOGRAPHY 1427

Fig. 3. Coverage map showing the location of the SLA-01 ground tracks superimposed on the CSRMSS95 mean sea surface. Ground tracks shown in red indicatethe position of the profiles illustrated in Fig. 6.

The SLA-01 range measurements were obtained during five9 h and one 10 h observation arcs. The arcs generally spanned“quiet” periods aboard the shuttle (i.e., periods in which therewere no attitude changes or orbital maneuvers). During the firstfour observation arcs, measurements were obtained when theshuttle’s roll, pitch, and yaw were controlled to1 . However,during the final two arcs, the shuttle was controlled within a

0.1 attitude “dead-band.” Although the two0.1 dead-bandarcs require more attitude-hold thrusting, which increases theerror in the orbit estimation, these periods were desired in orderto keep the instrument as near to nadir-pointing as possible[15]. Pointing errors were corrected using the measured attitudequaternions from the shuttle’s star trackers [16], allowingthe shuttle’s attitude to be determined in an inertial referenceframe.

SLA-01 obtained range profiles consisting of one 100-mdiameter pulse every 740 m along-track, with a vertical res-olution of 0.75 m [14]. Across-track resolution varied, asshown by the plot of orbit tracks in Fig. 3. Recovery of validsea surface heights was limited in certain areas due to cloudcover. Thus, before analyzing the range data from the oceans,it was necessary to remove the cloud-corrupted returns. Mostreturned waveforms were saturated because the system outper-formed prelaunch signal-to-noise estimates, and no hardwareprovisions had been made to facilitate calibration [J. B. Blair,personal communication, 1997]. However, in certain regions,unsaturated ocean waveforms were obtained [16].

The goal of meter-scale ranging accuracy for SLA-01called for a significant improvement in orbit determinationover the nominal 90-m radial error budget for the shuttle.For this reason, orbit determination was accomplished via aTOPEX-tracking and data relay satellite (TDRS)-STS link[15]. Because tracking of the TDRS spacecraft is only accurateto 30–50 m, the TOPEX-TDRS-STS link was utilized in orderto take advantage of the very precise tracking of TOPEX [16].Based on orbital crossover analyses, Rowlandset al. [15]estimate the orbit error remaining after these corrections to beat the 1-m RMS level.

C. Data Analysis

Before the orbit-referenced SLA-01 range measurementscould be compared to radar altimetry estimates of SSH, anumber of additional corrections had to be made to the SLA-01data. First, the dry troposphere correction was applied in orderto account for the propagation delay due to the dry componentof the atmosphere [17]. Second, the inverted barometer correc-tion was used to correct the SLA-01 range measurements foratmospheric loading [18]. To be consistent with the correctionsapplied to the T/P data, the surface pressure data used inboth the dry troposphere and inverted barometer correctionswere acquired from the European Centre for Medium-RangeWeather Forecasting, Reading, U.K., 6-h database. Finally, tocompare SLA-01 with the radar altimetry data, the SLA-01


TABLE IGLOBAL COMPARISON OFSLA-01 WITH THE EGM96 GEOID AND THE

CSRMSS95 MEAN SEA SURFACE. RMS DIFFERENCES ARESHOWN FOREACH

OF THESIX OBSERVATION ARCS AND FOR THEENTIRE SLA-01 DATASET

range measurements were corrected for ocean and load tidesusing the SR95.1 tide model (an updated version of thatdescribed by Schrama and Ray [19]) and the pole tide via themethod of Munk and MacDonald [20].

III. RESULTS

A. Global Comparison of SLA-01 with the EGM96 Geoid

In order to make a first-order assessment of the quality of theSLA-01 data, the SLA-01 SSH measurements were comparedto the marine geoid. The best current geoid estimate comes fromthe Earth Gravity Model ’96 (EGM96), a joint global gravi-tational field model solution produced by the Goddard SpaceFlight Center, the National Imagery and Mapping Agency, St.Louis, MO, and the Ohio State University, Columbus, [21]. Ateach SLA-01 data point located a distance greater than 100 kmfrom the coastline, the SLA-01 range measurement was com-pared to the interpolated EGM96 geoid height. To remove out-liers and SLA-01 ranges corrupted by cloud cover, SLA-01 datapoints that deviated from the geoid by more than 10 m wereeliminated from the comparison. The overall RMS differencebetween the SLA-01 data set and the EGM96 geoid is 2.49 m.The RMS difference during each of the six observation arcsranged from 2.20–3.17 m, with the smallest differences occur-ring during the two 0.1 dead-band arcs (see Table I). This re-sult illustrates the improvement in ranging accuracy that resultsfrom reducing the pointing error associated with the attitude ofthe shuttle from 1 to 0.1 .

Although comparing the SLA-01 data to the marine geoidneglects any effects due to dynamic topography, this analysisdoes provide a rough estimate of the quality of the SLA-01 dataset. In addition, by examining local regions where the geoidvaries significantly over a short horizontal distance, it is possibleto assess the ability of SLA-01 to resolve rapid changes in seasurface height. One area of particular interest is along the BoninArc, southeast of Japan. In this region, the geoid is depresseddirectly over the subduction zone but has a local high situatedover the arc. Thus, along a profile running perpendicular to theBonin arc, geoid height can vary up to 25 m over a horizontaldistance of only 125 km. This high-low couple is a characteristicfeature of many subduction zones and results from the combinedeffects of the topographic depression of the trench and the massanomaly associated with the subducting slab [22].

Fig. 4 shows nine SLA-01 profiles extending across theBonin Arc. Although several of the profiles contain only asparse number of range measurements due to cloud cover in theregion, the successful ranges to the sea surface illustrate thatSLA-01 is clearly capable of resolving these high amplitude,short wavelength geoid variations. The profiles shown in Fig. 4also illustrate a number of the important characteristics of theSLA-01 data set. The spread in the SLA-01 data along eachprofile is the result of the clock error inherent in the system.The time-interval unit (TIU) of SLA-01 allows the roundtriptravel time of each laser pulse to be measured with a resolutionof 5 nsec or 0.75 m [16]. Because clock error represents arandom process, smoothing is a valid method for removingmuch of the noise associated with the TIU uncertainty. Todetermine the appropriate interval for smoothing, we examinedthe power spectra of SLA-01 profiles extending across thePacific and Atlantic Ocean basins. The power in the SLA-01data typically drops to white-noise around a frequency of 1 Hz,implying that along-track SLA-01 can resolve features on aspatial scale of 7.5 km. Thus, any smoothing of the SLA-01data set should reflect this result. Throughout this study, weperform no smoothing in order to characterize the quality ofthe raw SLA-01 data. However, we note that smoothing of theSLA-01 data will result in a reduced RMS difference with theradar-derived SSH estimates.

A second important characteristic of the SLA-01 data set isthe presence of periods during which the SLA-01 range mea-surements fall into a banded pattern. During these periods, therange measurements are organized in linear patterns as opposedto appearing randomly distributed. An excellent example of thiscan be seen in the second and third southernmost profiles inFig. 4. The cause of these periods is a combination of the TIUerror associated with SLA-01 and the nonconstant orbital alti-tude of the shuttle. Because the timing precision of SLA-01 is1.5 m, the range measurements fall into individual bins as theshuttle drifts relative to the center of the Earth. Thus, the rawrange measurements will resemble a step function with 1.5-mstep heights, which will then appear to be tipped to one side oncethe orbital corrections are applied (see Fig. 5). The net result ofthis effect is that during periods when the shuttle is moving awayfrom the Earth, linear patterns will develop aligned up and to thewest, and at times when the shuttle is moving toward the Earth,these patterns will be aligned up and to the east.

B. Global Comparison of SLA-01 to Mean Sea Surface

To account for the effects of dynamic topography in our eval-uation of the SLA-01 data set, we next analyzed the SLA-01range measurements with respect to radar altimetry estimatesof mean sea surface height. Studies that analyze multiple setsof track-line geophysical data often examine only the crossingpoints of the tracks to eliminate the problem of interpolating oneof the data sets at each analysis point. However, because of theinherent differences between laser and radar systems, the use ofcrossover analyses is not practical when comparing the SLA-01and T/P data sets. Coherent fading requires that radar systemsuse pulse averaging to obtain individual measurements of SSH[12], with the incident beam covering a relatively broad surfacearea. In contrast, for a laser altimeter, the laser wavelength, the


Fig. 4. SLA-01 profiles across the Bonin arc south of Japan. The upper frame shows the location of the profiles superimposed on the EGM96 geoid height, whilethe lower frame illustrates the altimeter profiles (stacked north-to-south from top-to-bottom). Note the ability of SLA-01 to accurately resolve the rapid changesin SSH across the arc. The “resonance patterns” observed in several of the profiles are the result of TIU error associated with SLA-01 and the nonuniform orbitalaltitude of the shuttle.


Fig. 5. Schematic diagram illustrating the cause of the “resonance patterns” in the SLA-01 data set. The left-hand frame depicts raw range measurements madeto a flat surface as the shuttle moves away from the Earth. The right-hand frame illustrates these same range measurements after correction for the shuttle’s orbitalaltitude. Notice the apparent banding of the orbit-corrected range measurements.

diameter of the transmitted beam on the reflecting surface, andthe diameter of the receiving telescope are all different, and socoherent fading or speckle does not induce significant noise onindividual returned pulses [23]. Thus, valid measurements areobtained from single shots. In addition, the area over which en-ergy is incident on the sea surface is different for both SLA-01and T/P. SLA-01 has a footprint size of 100 m compared tothe 7-km average footprint of T/P [1]. Therefore, a single lasermeasurement may be influenced by individual waves or swells,while radar systems assume that on the scale of the footprintsize, these features will be averaged out.

For these reasons, we compare the SLA-01 data to theCSRMSS95 gridded mean sea surface [M.-C. Kim, personalcommunication, 1999]. The CSRMSS95 model combinestwo years of TOPEX data, two years of Geosat (exact repeatmission), 1.7 years of ERS 1 35-day data, and two cycles ofERS 1 168-day data onto a 0.5 0.5 grid and representsa high resolution model of all available radar altimetry data.Although we realize that this method ignores any variationsin ocean topography during the SLA-01 mission, on average,these variations will be much less than the 1.5-m precisionof SLA-01, and thus should not affect the conclusions of thisstudy. The overall RMS difference between the SLA-01 andthe CSRMSS95 mean sea surface is 2.33 m. Table I showsthe RMS difference between the SLA-01 and the CSRMSS95model for each of the six observation arcs. Similar to the resultsof the geoid analysis, the differences between the SLA-01 andthe CSRMSS95 model for the two0.1 deadband arcs aresmaller than the differences for those arcs in a1 deadband.

In addition to the global analysis, profiles across the Atlanticand Pacific Ocean basins were extracted during each arc andanalyzed individually (e.g., Fig. 6). To improve the agreementbetween the SLA-01 and CSRMSS95 model, we removed themean and trend from the residuals along each profile. This cor-rection served mainly to reduce any orbital error remaining inthe SLA-01 data, but also improved misfits associated with tem-poral and spatial sampling. The Pacific profiles were also fil-tered in order to remove frequencies /rev in the resid-uals. This correction was applied in order to remove an anoma-

lous 3/rev signal observed in many of the residuals. We believethat this signal may represent uncorrected orbit error, possiblycaused by an error in the degree 3 (or 6) term of the EGM96gravity model [D.E. Smith, personal communication, 1998]. Nofiltering was performed on the Atlantic profiles because noneof these tracks contained a sufficient number of data points toapply filters with a satisfactorily sharp band cutoff. The finalresults of the profile analysis are given in Table II. Notice thesignificant decrease in the RMS residuals once the mean andtrend have been removed and also once the profiles across thePacific have been filtered. Table III shows a comparison of theSLA-01 profiles versus the EGM96 geoid. The RMS residualsare larger than for the comparison with the CSRMSS95 model,illustrating the effect of dynamic topography being includedin the CSRMSS95 mean sea surface, but not in the EGM96geoid. However, the RMS residuals after removing the meanand trend from the SLA-01 profiles are quite similar to theCSRMSS95 comparison. This may reflect the fact that by re-moving the long-wavelength variations from the SLA-01 data,we have also removed the dynamic topography signal from ourdata. This illustrates the difficulty in separating the uncorrectedorbital error remaining in the SLA-01 data with long wavelengthdynamic topography.

One important feature that can be observed along many of theSLA-01 profiles are short wavelength, but high amplitude devi-ations from the CSRMSS95 mean sea surface (e.g., 140–145Ealong Profile A in Fig. 6). These features typically occur in areaswhere the mean sea surface varies rapidly over a relatively smallhorizontal distance and thus, are not resolved in the 0.50.5CSRMSS95 model. In an attempt to illustrate that these devi-ations are not a limitation of the SLA-01 system, and to showthe quality of the along-track laser data on a regional scale, wecompare the SLA-01 data to time-averaged along-track T/P SSHdata [24] using multiresolution optimal interpolation.

C. Multiresolution Optimal Interpolation Analysis

The multiresolution estimation framework used for analyzingthe T/P data in this study was developed by Fieguthet al. [25].


Fig. 6. Typical SLA-01 profiles across the Pacific (profiles A & B) and Atlantic (profiles C & D) Ocean basins. (a) SLA-01 data with the mean and trend of theresiduals removed are shown in red, while the CSRMSS95 mean sea surface is shown in blue for comparison. Profiles A and B were also filtered to remove anyfrequencies� 4/rev in the residuals and (b) residuals of the corrected SLA-01 data.


Fig. 6. (Continued.)Typical SLA-01 profiles across the Pacific (profiles A & B) and Atlantic (profiles C & D) Ocean basins. (c) Power spectrum of the residuals.Notice the long-wavelength signal remaining in the unfiltered Atlantic profiles. The spectral peak near 0.0006 Hz in profiles (c) and (d) corresponds to orbitalfrequency of 3/rev.


TABLE IIRMS DIFFERENCEBETWEEN THESLA-01 DATA AND THE CSRMSS95 MEAN SEA SURFACE ALONG PROFILESACROSS THEPACIFIC AND ATLANTIC OCEAN

BASINS. NOTE THESIGNIFICANT IMPROVEMENT IN THECOMPARISONONCE THEMEAN AND TREND HAVE BEEN REMOVED AND THE PACIFIC PROFILESFILTERED

TABLE IIIRMS DIFFERENCEBETWEEN THESLA-01 DATA AND THE EGM96 GEOID ALONG PROFILESACROSS THEPACIFIC AND ATLANTIC OCEAN BASINS.

NOTE THAT ONCE THE MEAN AND TREND HAVE BEEN REMOVED, THE COMPARISON VERSUS THEGEOID IS SLIGHTLY BETTER

THAN THE COMPARISONVERSUS THET/P ESTIMATE OF MEAN SEA LEVEL

Multiresolution optimal interpolation (or multiscale estimation)offers a number of advantages for interpolating irregularly-sam-pled geophysical data sets. First, the complexity of multiscaleestimation scales linearly with size and thus is very compu-tationally efficient. Second, this algorithm provides interpola-tion estimates at various spatial scales. Finally, the multiscalescheme provides error estimates, which can be used to evaluatethe significance of observed SSH anomalies [25]. See Fieguthet al. [25] and Fieguth [26] for a complete description of themultiscale model.

The inability to accurately define the multiscale model pa-rameters over large spatial scales prevents the use of this estima-tion scheme on a global scale [26]. However, Fig. 7 illustratesthe utility of the multiscale method when comparing SLA-01and T/P data on a regional basis. Along the coast of Chile, thesubducting Nazca Plate causes a downward deflection in thegeoid extending parallel to the coastline [see Fig. 7(a)]. Due tothe poor across-track resolution of T/P in this region, the down-ward deflection of the geoid cannot be resolved using minimumcurvature interpolation [27] of the T/P SSH data [Fig. 7(b)].Similarly, the multiscale estimation scheme does not resolve thegeoid variations. However, it does provide an estimate of wherethe interpolated T/P values may be in error [Fig. 7(c)]. This errorestimation is critical because it allows a comparison to be madebetween the SLA-01 and T/P data specifically in those regionswhere the interpolation error is low.

The importance of the multiscale estimation scheme becomesapparent when examining profiles of SLA-01 data across the re-gion. The SLA-01 data compares extremely well with the geoidalong the entire length of each profile, and fairly well with the

T/P data west of 285W (see Fig. 7). On the other hand, in theregions above the downward deflected geoid, the SLA-01 andinterpolated T/P data diverge dramatically. By using multiscaleinterpolation and only examining those points for which the es-timated interpolation error is less than one standard error (0.25m), the RMS difference between the SLA-01 and T/P data dropsfrom 1.51 m RMS to 0.90 m RMS for all the profiles across theregion. The results of the three separate comparisons for the en-tire region and the four profiles shown in Fig. 7 are given inTable IV.

While the multiscale estimation scheme provides a usefulmethod for comparing the SLA-01 and T/P data sets, the dif-ferences between the multiscale and minimum curvature esti-mates of the T/P data are somewhat troubling. Although thesediscrepancies may represent true SSH features that have beensmoothed out of the minimum curvature estimate, it is also pos-sible that these discrepancies represent an error in the multi-scale result. The multiscale scheme described by Fieguth [26]requires isotropy in the system being examined (a fact that isclearly not true for SSH in the Chilean region). However, whilefurther analysis would be necessary to determine the validity ofthe multiscale estimate in this region, the key point for this studyis the close agreement between the SLA-01 and T/P data sets inareas where the interpolation error associated with T/P is low.

D. Analysis of SLA-01 Data in Coastal Regions

To analyze the quality of the SLA-01 data across the land-sea transition, we examine profiles from various coastal zones.Fig. 8 shows two representative SLA-01 profiles across the


Fig. 7. Analysis of the SLA-01 data versus EGM96 geoid height and time-averaged T/P data for the region offshore of Chile: (a) EGM96 geoid height. Blacklines represent SLA-01 ground tracks, while white lines illustrate T/P coverage. Location of profiles shown in lower frame are depicted with thick red lines (b)T/P data interpolated using minimum curvature and (c) T/P data interpolated using multiscale optimal interpolation. White contour lines denote onestandard errorin the interpolation scheme. The lower frame illustrates four representative altimeter profiles across the Chilean region. The SLA-01 data is shownin black, theEGM96 geoid estimate in blue, and the T/P data in red (thin for minimum curvature estimate and thick for multiscale estimate). The multiscale estimateis onlyshown in those regions where the error estimate is less than one standard error. Notice the ability of SLA-01 to accurately resolve the geoid depression over theChile–Peru trench.


land-sea interface, one across the Chilean coast and one acrossthe Red Sea. Along each of these profiles, we compare SLA-01measurements to the EGM96 geoid over the oceans and the Na-tional Geophysical Data Center’s TerrainBase elevations overthe land. The region off the coast of Chile represents a particu-larly good area for this analysis because of the rapid geoid vari-ations across the coastal zone and the dramatic topography ofthe Andes immediately adjacent to the coastline.

These profiles illustrate SLA-01’s ability to continuouslytrack across the land-sea transition with no increase in thespread of the range measurements as SLA-01 approachesthe coastline. The profile across the Red Sea is of particularimportance because it shows that there is no significant timelag before SLA-01 regains “lock” on the sea surface as it makesthe transition from measurements over land to measurementsover the sea surface.

IV. DISCUSSION

The results of this study show that after the removal of bi-ases and long-wavelength discrepancies, the SLA-01 data set iscapable of resolving SSH at the 1-m RMS level. While this re-sult might seem disappointing in comparison to the 3–4 cm T/Paccuracy, the overall implications of this study are extremely en-couraging. Early radar altimeters such as GEOS-3 and SEASATprovided measurements of mean sea surface with only meter-scale vertical accuracy [3]. Moreover, performance tests of earlyradar systems were generally performed with respect to geoidheight. Chapman and Talwani [22] compared geoid height asmeasured by GEOS-3 with the best available 11 gravi-metric geoids in the North Atlantic, Northwest Pacific, and In-dian Oceans. They found that after the removal of long-wave-length discrepancies, the agreement between the altimetric andgravimetric geoids was between 1.7 and 2.7 m RMS.

Furthermore, the resolution of early radar systems was oftenevaluated based on their ability to resolve rapid variations ingeoid height in regions such as subduction zones [22] and islandarcs [28]. The results of this study clearly show that SLA-01 isalso capable of resolving changes in geoid height on small spa-tial scales (Figs. 4 and 7). Moreover, the slight deviations be-tween the SLA-01 and EGM96 geoid heights across the Peru-Chile trench (see profiles in Fig. 7) suggest that SLA-01 is actu-ally detecting geoid features that cannot be resolved in the 360

360 spherical harmonic EGM96 geoid model. Thus, for re-gional gravity studies, particularly in those areas where SLA-01ground-track coverage is dense, it may be beneficial to incor-porate SLA-01 or other laser altimetry with traditional sourcesof gravimetric data in order to generate more accurate geoidmodels.

The most significant implication of this study for applica-tions to coastal studies of physical oceanography is the abilityof SLA-01 to track across the land-sea interface with no lossof resolution or signal strength. This achievement represents asignificant innovation over all current microwave systems. Theability of SLA-01 to emit a narrow collimated beam allows thelaser to cross the ocean-continent transition with no signal cor-ruption. Moreover, unlike microwave systems, which may re-quire 30–40 km to regain lock on the sea surface after passing

TABLE IVCOMPARISON OF THESLA-01 DATA WITH THE EGM96 GEOID, T/P

MEAN SEA LEVEL INTERPOLATED USING MINIMUM CURVATURE AND

T/P MEAN SEA LEVEL INTERPOLATED USING MULTISCALE OPTIMAL

INTERPOLATION. ONLY SLA-01 DATA POINTS FORWHICH THE MULTISCALE

ERRORESTIMATE WAS LESS THANONE STANDARD ERRORWEREUSED IN THE

MULTISCALE COMPARISON

across large land masses, lasers immediately return valid mea-surements regardless of the roughness of the adjacent topog-raphy (see Fig. 8).

However, while laser systems clearly represent a promisingtool for high resolution studies of ocean topography, the systemconstraints associated SLA-01 ultimately limit its capability toresolve dynamic topography. At long wavelengths, the shuttle’s1-m orbital uncertainty makes it extremely difficult to distin-guish between 1000-km SSH anomalies and drift due to uncor-rected orbital error. At shorter wavelengths, the 1.5-m TIU erroreliminates the possibility of using SLA-01 to resolve eddy-scaledynamic topography, which typically have amplitudes of 50 cm[29]. In addition, the lack of unsaturated waveforms makes itdifficult to evaluate the effect of wave height on the SSH mea-surements. Gardner [13] has shown that rougher sea states willresult in broader return waveforms, which can cause range walkin the SSH estimates. Moreover, even if enough unsaturatedwaveforms were available, the amplitude of the TIU error wouldmake it hard to distinguish between timing error and range walkassociated with pulse broadening.

However, while these constraints prohibit the use of theSLA-01 data set for studies of dynamic topography, they do notrepresent fundamental limitations to laser altimetry systems.For laser altimetry to equal the accuracy of current radaraltimetry systems, it is necessary to obtain SSH measurementswith an accuracy of 3–4 cm over an along-track distance of7000 km. If typical ocean waves have an RMS height variationof 1 m over wavelengths of several hundred meters, then theinherent accuracy of the mean sea surface measured by eachlaser shot would be 1 m. Assuming future laser altimeters havefootprints smaller than the wavelength of ocean waves and arecapable of obtaining range measurements with 1 cm accuracy,then in order to achieve the desired accuracy (with a footprintspacing similar to SLA-01) it would be necessary to increasethe pulse rate from 10–1000 Hz. While these repetition rates areat the limit of current laser technology, a 500 Hz laser systemhas been designed and tested by Blairet al. [30] and 2000 Hzsystems are currently in the development process [31]. Thus, itappears that the future laser mission will provide an excellentopportunity for further studies of ocean topography.

Two upcoming laser missions are expected to providecontinuous, high-precision range measurements over the globaloceans. The first of these missions, the vegetation canopy lidar(VCL), is scheduled for launch in 2000 and has the primary


Fig. 8. Two profiles illustrating the ability of SLA-01 to track across the land-sea interface without losing lock. The red dots in the profiles represent the SLA-01range measurements, while the blue line is a combination of the EGM96 geoid over the oceans and NGDC TerrainBase elevations over land.

goal of monitoring global vegetation density and the secondarygoal of returning a global data set of topographic spot heightsand transects [32]. VCL will consist of five laser altimeters,which will make range measurements with an average footprintdiameter of 25 m in a 65 latitude band.

The geoscience laser altimeter system (GLAS) is the secondorbital laser altimeter currently in the design process and isscheduled for launch in 2001 [33]. GLAS is designed as a15-year, three-satellite mission to monitor the global ice volumeof the polar caps. GLAS will have a near polar orbit and has apreliminary error budget calling for 10-cm orbital accuracy and10-cm ranging precision. Although neither VCL nor GLASwere specifically designed to measure ocean topography, bothmissions offer excellent opportunities for high accuracy SSHstudies. The error budgets associated with both VCL and GLASrepresent an order of magnitude increase in precision over

SLA-01, and because both instruments will fly aboard fixedorbiting platforms, long term studies of ocean topography andthe marine gravity field will be possible.

V. CONCLUSIONS

While it is clear that orbital microwave remote sensingtechniques will remain the method of choice for long term,systematic mapping of ocean circulation, this study illustratesthe value of laser altimetry as a supplementary tool for re-gional studies of ocean topography. The global RMS differ-ence between SLA-01 and the CSRMSS95 mean sea surfaceis 2.33 m. This comparison is significantly improved by theremoval of a mean and trend from individual SLA-01 pro-files across the Atlantic and Pacific Ocean basins, resultingin differences at the 1-m RMS level. Most significantly, this


study illustrates the ability of SLA-01 to track directly up tothe land-sea interface with no degradation or loss of signal.This is particularly important because T/P has been shownto be unable to resolve SSH within tens of kilometers of thecoastline.

Although the TIU error 0.75 m and orbital uncertainty(1 m RMS) preclude the estimation of dynamic topographyfrom the SLA-01 data set, the overall results of this studystrongly support continued research into the utility of laseraltimeters for coastal studies of ocean topography. In particular,the upcoming VCL and GLAS missions, which will possesshighly accurate laser altimeters and well-monitored rangingplatforms, will allow centimeter-scale ranging precision andthus should provide an excellent opportunity for coastal studiesof ocean topography.

ACKNOWLEDGMENT

The authors wish to thank J. Garvin for providing the SLAdata set and answering many questions about its use, D. Row-lands and S. Lutchke for their assistance in orbit determination,and C. Wunsch for input regarding the TOPEX comparison andfor providing helpful comments on the draft manuscript. Theyalso wish to thank S. Nerem and an anonymous reviewer forcomments that significantly improved this manuscript.

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Mark D. Behn received the B.S. degree in math,physics, and geology from Bates College, Lewiston,ME, in 1996. He is currently pursuing the Ph.D.degree at the Massachusetts Institute of Tech-nology/Woods Hole Oceanographic InstitutionJoint Program in Oceanography and Applied OceanScience and Engineering, Cambridge, MA.

His research interests include marine geology andgeophysics, in particular, the use of theoretical andnumerical models to solve scientific problems thataddress socially relevant issues.

Maria T. Zuber received the B.A. degree inastrophysics from the University of Pennsylvania,Philadelphia, PA, in 1980, and the Sc.M. and Ph.D.degrees in geophysics from Brown University,Providence, RI, in 1983 and 1986, respectively.

She is currently the E.A. Griswold Professor ofGeophysics and Planetary Sciences, MassachusettsInstitute of Technology, Cambridge, MA, and a Se-nior Research Scientist, NASA Goddard Space FlightCenter, Greenbelt, MD. She held a faculty positionwith Johns Hopkins University, Baltimore, MD, and

was Staff with the Goddard Space Flight Center. Her research interests includegeophysical modeling and the use of altimetry and gravity to understand the dy-namics and evolution of the Earth and planets. She was on the geophysics teamof the Clementine Mission to the Moon and is Deputy Principal Investigator ofthe Mars Orbiter Laser Altimeter on the Mars Global Surveyor spacecraft, TeamLeader of the laser ranging investigation on the Near Earth Asteroid RendezvousMission, and lead of the geophysics investigation of the MESSENGER missionto Mercury.

Dr. Zuber is a member of the AGU, DPS, and AAAS, and currently serves onthe editorial board ofScience.

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