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Seasonal analysis of topex/poseidon altimeter DataCorrectionsJ. M. Myrick a , M. E. Parke a & G. H. Born ba Colorado Center for Astrodynamics Research , University of Colorado , Boulder, Colorado,USAb Colorado Center for Astrodynamics Research , University of Colorado , Campus Box 431,Boulder, CO, 80309–0431, USA E-mail:Published online: 10 Jan 2009.

To cite this article: J. M. Myrick , M. E. Parke & G. H. Born (1998) Seasonal analysis of topex/poseidon altimeter DataCorrections, Marine Geodesy, 21:1, 3-24, DOI: 10.1080/01490419809388119

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Seasonal Analysis of TOPEX/POSEIDON AltimeterData Corrections

J. M. MYRICKM. E. PARKEG. H. BORN

Colorado Center for Astrodynamics ResearchUniversity of ColoradoBoulder, Colorado. USA

One year of global TOPEX altimeter sea-level and correction data were analyzed toconsider the effect on the statistics of altimeter range corrections due to (1) seasonalvariability. (2) removal of shallow water, (3) area and data-density weighting, and14) separate consideration of the equatorial region. Seasonal analysis was done toprovide a better understanding of the temporal behavior of the statistics. The effectsof shallow water were removed, since shallow water has different dynamics than deepwater and could skew some resuts. Area and data-density weighting was performedto keep the disproportionate amount of data available at the turning latitude frombiasing the results. Finally, the equatorial region was considered separately, sinceequatorial conditions and dynamics are different than those at mid and high latitudes.It was determined that the statistics of each of the corrections was affected by one ormore of these factors. Knowledge of these statistics should be useful in applying thecorrections to future altimeter measurements. Overall, this effort should provide abetter basis for using advanced filter techniques to improve altimeter sea-level heights.

Keywords satellite altimetry. TOPEX/POSEIDON

Errors in altimeter range measurements have been reduced substantially with advancingtechnology. Until recently, the accuracy of altimeter sea-surface height measurementswas limited by the accuracy of the radial component of the satellite's position, theionospheric correlation, and the wet troposphere correction. Due to the advanced instru-ments on board the TOPEX/POSEIDON (T/P) satellite, the accuracy of altimeter mea-surements has reached the point that errors of even a few centimeters are no longertolerable (Kantha et al. . 1994). In fact, T/P has brought the error levels of sea-surfaceheight measurements down to the order of the uncertainty in environmental corrections.Thus, in order to further improve upon the accuracy of the sea-surface height measure-ments, this article takes a closer look at these corrections to understand their characteristicsbetter.

Received 23 July 1997; accepted 4 September 1997.Work performed at the Colorado Center for Astrodynamics Research was supported by a

NASA Graduate Student Fellowship in Global Change Research (NASA Reference Number 4138-GC93-0217) and JPL contract no. 957388. TOPEX\lata were obtained from the NASA PhysicalOceanography Distributed Active Archive Center at the Jet Propulsion Laboratory, CaliforniaInstitute of Technology.

Address correspondence to Dr. George H. Born, Colorado Center for Astrodynamics Re-search, University of Colorado. Campus Box 431, Boulder. CO 80309-0431. USA. E-mail:georgeb(<< orbit.colorado.edu

Marine Geodesy. 21:3-24. 199SCopyright © 1998 Taylor & Francis

0149-0419/98 $12.00 + .00

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This research specifically involved determining the extent of the correlations amongsome of the corrections to the TOPEX altimeter sea-surface height measurements. Thecorrelation analysis was based on the work of Victor Zlotnicki (Zlotnicki, 1994). Hisresults showed that significant correlation exists among the corrections and that theserelationships affect the accuracy of the sea-level height measurements. We began ouranalysis by first confirming his results and using them as a baseline for the remainder ofour research. To get an idea of the relative magnitude of each of the corrections, theirmeans and standard deviations were first determined for the data set. Then the correlationcoefficients of the corrections and the corrected sea-level height were calculated in orderto examine the interrelationship of the corrections.

As an extension of previous work, four areas were explored. First, the seasonalvariation of each of the corrections was examined in an effort to understand better thetemporal fluctuations of the statistics. Second, the effects of removing data over shallowwater was explored to investigate the influence of shallow water on the global data set.Third, the data set was weighted according to latitude and data density to deemphasizethe relatively large amount of data collected at high latitudes. Finally, separate treatmentof the equatorial region was considered, since equatorial conditions and dynamics aredifferent than those at high latitudes.

Data

The data for this analysis were obtained from the Jet Propulsion Laboratory (JPL) PhysicalOceanography Distributed Active Archive Center (PODAAC) merged geophysical datarecords (MGDR) (Benada, 1993), which contain data from both the TOPEX dual-frequency altimeter and the POSEIDON solid-state altimeter. For each cycle, data were"stripped" off the archives using in-house software developed explicitly for this purpose.The extracted data encompasses information related to tidal effects, satellite positioning,and atmospheric corrections. Specifically, the data set included the following parameters:

Time of measurement in seconds past 1992 (/)Latitude (<J>)Longitude (X.)Satellite altitude above the reference ellipsoid (sett—alt)Altimeter range corrected for instrumental effects (h—alt)Meteorological field-interpolated dry tropospheric correction (dry)Inverted barometer (IB) correction (inv—bar)Microwave radiometer wet tropospheric correction (wet)Dual-frequency ionospheric correction (iono)NASA Ku-band electromagnetic (EM) bias correction (em—bias)Mean sea-surface height (h—mss) (Basic & Rapp, 1992)Cartwright and Ray ocean tide (h-eot) (Cartwright & Ray, 1991)Solid earth tide (hsei)Geocentric pole tide height (h—pol)

These data were subsequently examined to verify their validity. Data were edited ifcertain requirements were not met. These conditions include ensuring that the altimeterflags (alt-bad-1 and alt-bad-2) indicated that both frequencies of the TOPEX altimeterwere healthy and operational, that the altimeter mode flag (current—mode—I) was at the"fine track" data retrieval setting, and that none of the data were set at their defaultvalues (Zlotnicki, 1994). Data over land, ice, and rain, as indicated by data flags geo—bad

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Seasonal Analysis of TOPEXIPOSEIDON Altimeter 5

_ / and geo-bad-2 from the PODAAC MGDR (Benada, 1993), were also excludedfrom the data set.

The next step involved calculating the values of the corrected sea-level height at eachpoint using the following formula:

li_sl(4>, X, /) = sat_alt(§, X, t)— h_alt(§, X. /) - em_bias(<&, X, t)

— io«o(4>. A., /) - dryify, A, ;) - ur/(4>, \ , t) i\\

— h_eot(<\>, X, t) — h_set($, k, t) - h_pol(<&, k, t)

— inv_bar(§, X, t) — h_mss(<$>, X, r)

These corrected sea-level height values were then tested for validity. Any value that hada magnitude greater than 3 m was discarded, along with the corresponding correction datafor that point (Zlotnicki, 1994).

Once the spurious data were removed, the remaining data were interpolated to aonce-per-second latitude/longitude grid (Hendricks et al., 1996), which facilitated thecalculation of collinear statistics. Thus, for each cycle, the data set consisted of a maxi-mum of 856,711 equally spaced points. To save computation time, the data set wasdecimated by a factor of 5, resulting in a maximum of 171.342 data points per cycle.Areas of sparse data were removed, thus decreasing slightly the number of availablepoints. At each point, the sea-level residuals were calculated by subtracting off the meansea level for the entire data set from the sea-level height measurements:

h_res(<$>, X, /) = h_sl($. X, /) - - Z h_sH<$>, X, /,.) . (2)tx t _ i

Global Statistics of the Corrections

The mean for each parameter of interest was computed, along with two sets of standarddeviation values. This mean is considered the "full" mean, since it is the average ofeach variable over the whole data set. The formula is simply:

(3)

where .r,, represents the data value at each grid point over each cycle. Here and insubsequent equations, N always represents the number of grid points per cycle, and K isthe number of cycles of data.

The "full" standard deviation was determined with this "full" mean value by usingthe equation for the standard deviation of a sample:

where .x0 represents the data value at each grid point over each cycle and x, is the meanof.v.

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6 J. M. Myrick et al.

The "collinear" mean is the average value at each point over several cycles of data.In simple terms, each point of a cycle is averaged with its corresponding points from theother cycles at the same latitude and longitude. Thus, we obtained a mean value for eachlatitude/longitude point. This can be defined mathematically as

A:

x, = S ^ for/ = 1 N (5)

where xr, represents the K data values at each A' latitude/longitude point.The basic structure of the "collinear" standard deviation is the same as that for the

"full" standard deviation. The difference, of course, is that here the "collinear" meanis used:

- #11 *TPwhere .v,, represents the K data values and .vr is the collinear mean at each N latitude/longitude point. •

The means and standard deviations were calculated for the global data set of TOPEXcycles 11—47, which includes data spanning from 31 December 1992 through 2 January1994. The parameters of interest were, in keeping with Zlotnicki (1994),

The ocean tide (h—eot)The sea-level residuals (h—res)The inverted barometer (IB) correction (inv—bar)The wet tropospheric correction (wet)The electromagnetic (EM) bias correction (em—bias)The ionospheric correction (iono)The dry tropospheric correction (dry)

The values of the correlation coefficients were then calculated to determine therelationship of the corrections to each other and to the corrected sea-level values. Herewe also have two sets of equations—one for the "full" value and the other for the"collinear" value. The full value was determined using

P / u . v ) ^NK i , ,

where .r,v represents the value of variable #1 at each point, xr is the mean value of x, y(/

represents the value of variable #2 at each point, v is the mean value of v, a,(.t) is thefull standard deviation of x, and a/v) is the full standard deviation of v.

Similarly, the collinear correlation coefficients were calculated:

N K _

NK ,•_„•_, cr,(.r)ov(v)

where xu represents the value of variable # 1 at each point, !r,, is the collinear mean valueof x at each latitude/longitude point, v,, represents the value of variable #2 at each point.

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Seasonal Analysis of T0PEXIP0SE1D0N Altimeter 7

y,.t is the collinear mean value of y at each latitude/longitude point, G,{X) is the collinearstandard deviation of*, and o-,.(y) is the collinear standard deviation of y.

The standard deviation values and mean results of the global data set are shown inTable 1. The first two columns list the collinear standard deviation values of each of theabove parameters, both in millimeters and as a percentage of the corrected sea-level heightvalues. In the third and fourth columns, the full standard deviation values of each param-eter are listed in the same format. Here, the collinear standard deviation values reflect theenergy due to time variability only, while the full values represent the energy due to bothgeographic and time variability (Zlotnicki, 1994). The final column of data shows themean values of each correction, while the mean of residual sea-surface height is mean-ingless, since its mean was already removed from the data.

The ocean tide correction is the only correction with more energy than the correctedsea-level residuals, which explains why even small uncertainties in the tidal models causelarge errors in sea-surface height signals (Knudsen, 1994). The inverted barometer (IB)correction is the second more energetic correction. It is significant to note that these twocorrections do not compensate for erroneous sea-level measurements due to path delays,but instead attempt to model and remove temporal variations in the ocean surface itself.In fact, the ocean, tide and IB signals are removed primarily so that the rest of thecorrections can be studied (Zlotnicki, 1994).

These results show favorable agreement with Zlotnicki (1994). The standard devia-tions, for example, are within 1-3 mm of each other, as expected. These small variationscan be easily attributed to the slightly different data sets that were used in the twoanalyses—namely, the addition of TOPEX cycles 11, 45. 46, and 47 in this study.

The results of the two sets of mean values have more prominent differences. Thesign difference is because of personal preferences in designating sign conventions forcorrections (Zlotnicki, 1996a). The sign convention used here is consistent with thePODAAC MGDR. The inconsistency in the inverted barometer (IB) correction meanrequires more explanation. The mean value of zero from Zlotnicki (1994) is the result ofremoving the 10-day global pressure average when calculating the IB correction (Zlot-

Table 1Full and collinear standard deviations and full mean values for TOPEX cycles 11-47

Ocean tideResidual SSHInverted barometerWet troposphereEM biasIonosphereDry troposphere

Collinearstandarddeviation

(mm)

3041068146272819

(%)

2871007743262718

Full standarddeviation

(mm)

30522913392353232

(%)

1331005840151414

Mean

(mm)

1—44

-148- 6 2- 4 3

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8 J. M. Myrick et al.

nicki, 1996b). The IB correction for this study was taken directly off the PODAACMGDR, and consequently did not have the pressure average removed (Benada, 1993).

The correlation coefficients were also calculated for the parameters above, with theexception of the dry tropospheric correction. Since this correction is linearly proportionalto the IB correction (by a factor of approximately 4.4), using both of these parameters inthis analysis would be redundant (Benada, 1993). Table 2 shows the results of thisanalysis. Both full and collinear correlation coefficient values are shown here, with thefull values representing the energy due to both geographic and time variability, while thecollinear values reflect the energy due to time variability only (Zlotnicki, 1994).

The largest full correlation was found to be between the electromagnetic (EM) biasand wet tropospheric corrections at —46%, while the collinear value is only - 14%. Thedifference in magnitude between the full and collinear values suggests that the correlationhas a geographic or latitudinal dependence. A closer look confirms this hypothesis. HighEM biases are associated with high ocean waves, while high wet tropospheric errors arerelated to high water vapor content in the atmosphere. Because there are typically highwaves at high southern latitudes, where the air is relatively dry, and since the sea surfaceis comparatively calm near the equator, where there is abundant water vapor, a sizablenegative correlation results.

Another large correlation was found to exist between the ionospheric and wet tro-pospheric corrections. Geographic dependence is also suggested here, since the full valueis rather significant at 40%. while the collinear value is only 7%. Since the ionosphericelectron content typically has maximum values near the equator and tapers off toward thepoles similar to water vapor content, this makes sense. In addition, because of the datasampling characteristics of T/P, there is a high correlation between local time of day andlatitude (Zlotnicki, 1994), thus leading to a high correlation between water vapor andelectron content.

Also of interest is a large correlation between the EM bias and IB corrections. In thiscase, both the full and collinear values have significant magnitudes, at - 3 8 % and - 3 1 % ,respectively, suggesting variations with both time and latitude. The IB correction isdependent on atmospheric surface pressure, while the EM bias correction is a function ofsignificant wave height. Since high waves are correlated with low-pressure systems in theatmosphere at all latitudes, a negative collinear correlation would be expected. Correlationdue to latitudinal dependence also exists, since near the poles there are high waves, highwinds, and low atmospheric pressures compared to equatorial regions.

Table 2Full and collinear correlation coefficients for TOPEX cycles 11—47

[collinear values in brackets]

Residual SSHInverted barometerWet troposphereOcean tideEM biasIonosphere

Res.SSH

-0 .03-0 .22

0.020.06

-0 .08

Inv.Bar.

[-0.07]—

0.30-0 .01-0 .38

0.14

WetTrop.

[-0.07][-0.11]

—-0.01-0 .46

0.40

OceanTide

[0.04][0.00][0.01]

—0.01

-0.01

EMBias

[0.01][-0.31][-0.14]

[0.00]—

-0.31

Iono.

[-0.031[0.00][0.07]

[-0.01][-0.131

—

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Seasonal Analysis of TOPEXIPOSEIDON Altimeter 9

Other notable results include the full correlation values between the EM bias andionospheric corrections at —31% (due to higher electron content near the equator, wherethere are lower waves), and between the IB and wet tropospheric corrections at 30% (dueto high pressure at the equator, where there are large amounts of water vapor). Also,lesser correlations for the full values were found between the corrected sea-level heightresiduals and the wet tropospheric correction at —22% and between the IB and iono-spheric corrections at 14%. The ocean tide model did not exhibit any significant corre-lation to the other corrections. This agrees well with previous results (Zlotnicki, 1994).

Seasonal Variation of the Corrections

After establishing a research baseline with the global results discussed above, the seasonalvariability of each of the corrections was investigated. First, the data from each cyclewere divided into the northern and southern hemispheres as appropriate for seasonalobservations. Then values for the means, standard deviations, and correlation coefficientswere calculated by hemisphere for each cycle and plotted to evaluate trends in the data.

Sample results of the seasonal variations of the corrections are shown in Figures 1and 2. (Notice that due to the negative sign convention used both here and in the MGDR,maxima may be mistaken for minima.) In Figure 1, one can observe that the mean valuesof the wet troposphere correction have a definite seasonal variation. In fact, the correctionactually shows opposing variation in the northern and southern hemispheres, as one wouldexpect. The maximum value for the northern hemisphere occurs during mid-July, whilethe maximum for the southern hemisphere occurs during early February. Thus, the max-ima in both hemispheres occur in local summers, when there is more evaporation due tothe warmer water and when the warmer air is better able to hold water. Conversely, there

-100

-250

Seasonal Variation of the Wet Troposphere Correction (Radiometer) Mean Values

! -200 -

i I i i i i ! I 1 1 1 1 I 1 1 1 1 1 1 t 1 f t t i 1 1 1 1 1

* North

O South

11121314151617181921222324252627282930323334353637383940424344454647Jan. Apr. JuL Oct. 1993

Seasonal Variation of the Wet Troposphere Correction (Radiometer) Standard Deviations

11121314151617181921222324252627282930323334353637383940424344454647Jan. Apr. Jul. Oct 1993

Figure I. Seasonal comparison of mean values and standard deviations of the wet tropospherecorrection over TOPEX cycles 11 -47.

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-80

Seasonal Variation of the Ionosphere Correction (Dual Freq.) Mean Values

X North

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11121314151617181921222324252627282930323334353637383940424344454647Jan. • Apr. Jul. Oct 1993

Seasonal Variation of the Ionosphere Correction (Dual Freq.) Standard Deviations

* North

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11121314151617181921222324252627282930323334353637383940424344454647Jan. Apr. Jul. Oct 1993

Figure 2. Seasonal comparison of mean values and standard deviations of the ionosphere correctionover TOPEX cycles 11-47.

is less water vapor in the atmosphere during the corresponding winter seasons for eachhemisphere.

The standard deviation values of the wet troposphere are also shown in Figure 1.Here we can see that the variability is larger in the northern hemisphere than in thesouthern hemisphere with the maxima in both regions occurring during the correspondinglocal autumn season..This behavior may be due to the higher occurrence of storms thatis typical during that time of the year.

Figure 2 shows the mean and standard deviation values for the ionospheric correction.Here, the statistics have similar variations in both hemispheres. The magnitudes and thevariabilities are greatest from about the middle of February and until the beginning ofMarch 1993, which corresponded with a period of high solar flux and X-ray backgroundvalues (NOAA/ERL, 1993). It is interesting to point out that the correlation between thewet troposphere and ionosphere corrections is rather significant, as shown in Figure 3,due to the fact that both water vapor and electron content are highest near the equator.

Shallow Water Removal

The purpose of this study was to determine how removing data over shallow water wouldaffect the seasonal statistics. Shallow water has different dynamics than deep water, andexcluding data from shallow water regions could have a significant impact on the statistics.To implement the removal of shallow water, data from regions where the water had adepth of 1,000 m or less were discarded. The means, standard deviations, and correlationcoefficients were then computed and compared with those from the nominal seasonalstatistics. Overall, the removal of shallow water resulted in the elimination of approxi-mately 12% of the data points in the northern hemisphere, while less than 5% were

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Seasonal Analysis ofTOPEXIPOSEIDON Altimeter II

removed in the southern hemisphere. Thus, shallow water removal would be expected tohave a larger effect on the statistics in the northern hemisphere.

In Figures 4 and 5, the effect of shallow water removal on the mean and standarddeviation values of the Cartwright and Ray ocean tide model is shown. For each figure,the statistics for the nominal case are shown first, followed by those for the case whendata over shallow water are removed, and the difference between these two cases is shownlast. Here we can see that excluding data over shallow water from our data set did affectthe statistics in both hemispheres, but, as expected, the effect was considerably larger inthe northern hemisphere. The largest difference from the nominal case was attributed toa decrease in data variability by approximately 40 mm during the autumn season in thenorthern hemisphere. The amplification of tides in shallow water might account for suchsignificant contribution of the variability.

Figures 6 and 7 show the effects of shallow water removal on the statistics for theIB correction. Once again, the effect on the statistics was more significant in the northernhemisphere than in the southern hemisphere. The largest changes in both the mean andstandard deviation values occurred during the local winter in the northern hemisphere.These effects can be attributed to the presence of higher pressure magnitudes and varia-bilities near coastal regions that occur during colder seasons. The large (~7 cm) biasbetween the northern and southern hemispheres in the first two panels of Figure 6 maybe due to the influence of the disproportionate number of points near the T/P turninglatitudes, which would have a larger effect on the southern hemisphere statistics becauseof increased water surface area in the southern oceans. This effect is investigated furtherin the next section.

The correlation coefficient values between the ocean tide model and the IB correctionare shown in Figure 8. Note that the removal of data in shallow regions had little effecton the correlation of these two parameters. In fact, the net effect was at or lower than1%, with the largest effect found to be slightly less than 4%. Even this largest effect wasonly evident for one T/P cycle (#44), which corresponded to the winter season in thenorthern hemisphere.

Area and Data-Density Weighting

Weighting the data according to area and data density was considered because the surfacearea of the Earth decreases with latitude while the number of altimeter data points

Seasonal Variation of Correlation Coefficients for the TOPEX Altimeter CorrectionsBetween Wet Troposphere (Rad.) & Ionosphere Corrections (Dual Freq.)

111213141516171819 2122 232425 26 27 28 29 30 3233 34 35 36 3738 39 40 42 4344 45 46 47Jan. Apr. Jul. , Oct. 1993

Figure 3. Seasonal comparison of correlation coefficient values of the wet troposphere and iono-sphere corrections over TOPEX cycles 11-47.

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-100

Seasonal Variation of TOPEX Altimeter Mean ValuesCartwright & Ray Ocean Tide Model [Nominal Case]

* North

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-100

Cartwright & Ray Ocean Tide Model [No Shallow Water!

* North

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Cartwright & Ray Ocean Tide Model [No Shallow Water - Nominal Case]

1112131415161718192122232425262728 2930323334353637383940424344454647Jan. Apr. Jul. Oct 1993

Figure 4. Effect of shallow water removal on mean values of the Cartwright and Ray ocean tidemodel over TOPEX cycles 11-47. The top panel shows the nominal case, while the middle panelillustrates the nominal case with shallow water removed, and the bottom panel depicts the differencebetween these two cases (shallow-water-removed case minus nominal case).

increases dramatically near the turning latitude. In Figure 9, one can observe this effectin regard to the latitude distribution of data for one T/P cycle. Thus, without weighting,results are biased toward high latitudes. This is especially true in the southern hemisphere,where there is a significant amount of open water near the T/P turning latitude.

The following formula was used to implement the weighting on the mean values ofthe T/P correction data (Bendat & Piersol, 1971):

2 T - , [cos 4>/TI(<|>,)](9)

where N is the total number of points, .r, represents the correction data points, 4>y is thelatitude of each point, and T)(4>y) is the number of points at each latitude.

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Seasonal Analysis ofTOPEXIPOSElDON Altimeter 13

In Figure 10, we can see the resulting weighted mean values for the IB correction.Compared to panel 2 in Figure 6, it is apparent that weighting the correction data had adramatic impact on the statistics in the southern hemisphere, while those in the northernhemisphere were relatively unaffected. The weighted mean values for this correction aresignificantly lower than the unweighted statistics, which is possibly due to extremepressure lows in the unweighted southern ocean data set. Some seasonal variation is stillpresent in the mean values, which may be a result of basing the MGDR IB correction ona constant pressure instead of subtracting off a 10-day global pressure average (Hendricksetal., 1996; Minster etal. , 1995).

Figures 11 and 12 show the effect of area and data-density weighting on the statisticsfor the EM bias correction. As expected, data weighting had a more significant impacton data in the southern hemisphere than in the northern hemisphere. In fact, both the

Seasonal Variation of TOPEX Altimeter Standard DeviationsCartwright & Ray Ocean Tide Model [Nominal Case]

11121314151617181921222324252627282930323334353637383940424344454647Jan. Apr. Jul. Oct 1993

Cartwright & Ray Ocean Tide Model [No Shallow Water]

11121314151617181921222324252627282930323334353637383940424344454647Jaa Apr. Jul. Oct 1993

Cartwright & Ray Ocean Tide Model [No Shallow Water - Nominal Casel

* North

O South

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Figure 5. Effect of shallow water removal on standard deviation values of the Cartwright and Rayocean tide model over TOPEX cycles 11-47. The top panel shows the nominal case, while themiddle panel illustrates the nominal case with shallow water removed, and the bottom panel depictsthe difference between these two cases (shallow-water-removed case minus nominal case).

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14 J. M. Myrick et til.

-50

Seasonal Variation of TOFEX Altimeter Mean ValuesInverse Barometer Correction [Nominal Case]

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Inverse Barometer Correction [No Shallow Water]

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Inverse Barometer Correction [No Shallow Water - Nominal Case]

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Figure 6. Effect of shallow water removal on mean values of the inverted barometer correctionoverTOPEX cycles 11-47. The top panel shows the nominal case, while the middle panel illustratesthe nominal case with shallow water removed, and the bottom panel depicts the difference betweenthese two cases (shallow-water-removed case minus nominal case).

magnitudes and the variabilities of the EM bias correction decreased in the southernhemisphere as a result of weighting the data. This result can be attributed to the deem-phasizing of data associated with the large waves present in the southern ocean.

The effect of weighting on the mean and standard deviation values for the wettroposphere correction is shown in Figures 13 and 14. Due to weighting, there is anincrease in both of these statistics because more emphasis is placed on data in theequatorial region, where the water vapor content is larger than in higher latitude regions.

Figure 15 shows the correlation coefficient values for the EM bias and wet tropo-sphere corrections. There is virtually no change in the statistics in the northern hemispheredue to weighting, but there is a small (<1%) seasonal difference in the southern hemi-sphere. This effect occurs during the local summer and corresponds to the deemphasis onthe Circumpolar Current.

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Seasonal Variation in the Equatorial Region

The equatorial region was considered separately, since equatorial conditions and dynamicsare different than those at high latitudes. For our studies, the equatorial region was definedto be within ±20° latitude of the equator. Figure 16 shows the mean and standarddeviation values for the wet troposphere correction. It is interesting to observe thatseasonal variations are present even when only such low latitudes are considered. Com-paring these statistics with the global values in Figure 13, the signals are very similar infrequency, though they are different in amplitude. As we would expect, the magnitudeof water vapor content is greater in the equatorial region, while the variability is less thanwith the larger data set.

The statistics for the EM bias correction in the equatorial region are shown in Fig-ure 17. Again, a seasonal signal is apparent for this region that is similar to the one that

Seasonal Variation of TOPEX Altimeter Standard DeviationsInverse Barometer Correction [Nominal Case]

11121314151617181921222324252627282930323334353637383940424344454647Jan. Apr. Jul. Oct 1993

Inverse Barometer Correction [No Shallow Waterl

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Inverse Barometer Correction [No Shallow Water - Nominal Case]3

1 C i i i i i i i i

>-9-6-Q-&-t>-e-e-o-^-^-Q-c>--C) o o o o-e-o-e-^-e-cH >

1 t 1 1 ! 1 1 1 1 1 1 t 1 1 I 1 t 1 1 1 1 1 1

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Figure 7. Effect of shallow water removal on standard deviation values of the inverted barometercorrection over TOPEX cycles 11-47. The top panel shows the nominal case, while the middlepanel illustrates the nominal case with shallow water removed, and the bottom panel depicts thedifference between these two cases (shallow-water-removed case minus nominal case).

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-0.2

Seasonal Variation of TOPEX Altimeter Correlation CoefficientsOcean Tide Model (C&R) & Inverse Barometer Correction [Nominal Casel

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Ocean Tide Model (C&R) & Inverse Barometer Correction [No Shallow Water]

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Ocean Tide Model (C&R) Sc Inverse Barometer Correction [No Shallow Water - Nominal Case]0.04

-0.0411121314151617181921222324252627282930323334353637383940424344454647Jan. Apr. Jul. OcL 1993

Figure 8. Effect of shallow water removal on correlation coefficient values of the Cartwright andRay ocean tide model and the inverted barometer correction over TOPEX cycles 11-47. The toppanel shows the nominal case, while the middle panel illustrates the nominal case with shallowwater removed, and the bottom panel depicts the difference between these two cases (shallow-water-removed case minus nominal case).

appears in the larger data set, shown in Figure 11. Both the magnitudes and the variabilityof the EM bias correction are less in the equatorial region than those in the larger dataset. This difference is due largely to the effects of the Circumpolar Current that wereincluded in the global data set, but were obviously not factors in the equatorial region.

Figure 18 shows the correlation coefficient values between the wet troposphere andEM bias corrections in the equatorial region. Compared to equivalent values for the globaldata set, which are shown in Figure 15, the correlations are significantly less in magnitudein the equatorial region, while the seasonal variations are less distinct at low latitudes.

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Seasonal Analysis ofTOPEXIPOSEIDON Altimeter

Latitude Coverage Excluding Bad Data and Data over Land (decimated 1/5)

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Latitude (deg)

Figure 9. T/P satellite coverage for one cycle decimated by a factor of 5 and edited to exclude dataover land. ice. rain, and bad data according to the alt—bad—1. alt—bad—2, and current—mode—Idata flags (Benada, 1993).

Summary

In this study, a statistical analysis was performed on the environmental corrections for a1-year global data set from the TOPEX altimeter on the T/P satellite to determine theextent that those corrections are correlated among each other. This effort began with aconfirmation of the existence of correlations among the corrections, which was originallyestablished by Zlotnicki (1994). For each correction, mean and standard deviation valueswere calculated to obtain information about their relative magnitudes. The ocean tide wasfound to be the most energetic of the corrections, while the dry troposphere correctionhad the smallest variance. The correlation coefficients for each combination of the cor-rections were also determined. The highest correlation was found to be between the EM

Seasonal Variation of TOFEX Altimeter Mean Values (Shallow Water Removed)

Area & Data-Density Weighted Inverse Barometer Correction

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Figure 10. Area and data-density weighted mean values of the inverted barometer correction overTOPEX cycles 11-47.

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Seasonal Variation of TOPEX Altimeter Mean Values (Shallow Water Removed)

NASA K-Band EM Bias Correction [Nominal Casel

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NASA K-Band EM Bias Correction [Area & Data-Density Weighted]

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NASA K-Band EM Bias Correction [Weighted - Nominal Case]

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Figure 11. Effect of area and data-density weighting on mean values of the EM bias correctionoverTOPEX cycles 11-47. The top panel shows the nominal case, while the middle panel illustratesthe nominal case weighted according to latitude and data density, and the bottom panel depicts thedifference between these two cases (weighted case minus nominal case).

bias and the wet troposphere corrections at - 4 6 % . Other notable results included largecorrelations between the ionosphere and wet troposphere corrections at +40% and be-tween the IB and EM bias corrections at —38%. These results confirm that substantialcorrelations exist among the corrections, and it has been proposed that, because of thesecorrelations, the effectiveness of the correlations to altimeter measurements might becompromised (Zlotnicki, 1994).

The seasonal analysis presented here served as an extension to the global study ofthe corrections. For the same year of TOPEX data (which was separated into northernand southern hemispheres), the mean values, standard deviations, and correlation coef-ficients were determined for each relevant environmental correction and evaluated at each

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Seasonal Analysis ofTOPEXIPOSElDON Altimeter 19

of 34 orbital repeat cycles. Collectively this provided enough information to obtain apattern of the variation of the statistics over the course of that year. The results showedthat many of these statistics had significant seasonal dependencies.

An additional step was taken to remove shallow water from the data set. It wassuspected that the original results might be skewed by the inclusion of shallow waterdata, since its dynamics tend to be different from the rest of the ocean basin. Shallowwater removal was found to significantly affect the statistics in the northern hemisphere,while the effect on the southern hemisphere was negligible.

Several factors, such as the convergence of ground tracks at high latitudes and thedistribution of continents, affect the geographic distribution of altimeter data points,potentially biasing statistics. Therefore, the data were weighted to compensate for such

Seasonal Variation of TOPEX Altimeter Standard Deviaions (Shallow Water Removed)NASA K-Band EM Bias Correction [Nominal Case!

5 30

I

V • ' / N i e ' ' ¥ tn n ' Q-4

> i , i i i i i I i i i < , i i ; ; i ; i i > > i . < ; i i <

1112131415161718192122232425262728 2930323334353637383940424344454647Jan. Apr. Jul. Oct 1993

NASA K-Band EM Bias Correction [Area & Data-Density Weighted]

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NASA K-Band EM Bias Correction [Weighted - Nominal Case]

1112131415161718192122232425262728 2930323334353637383940424344454647Jan. Apr. Jul. Oct. 1993

Figure 12. Effect of area and data-density weighting on standard deviation values of the EM biascorrection over TOPEX cycles 11-47. The top panel shows the nominal case, while the middlepanel illustrates the nominal case weighted according to latitude and data density, and the bottompanel depicts the difference between these two cases (weighted case minus nominal case).

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j j -200

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Seasonal Variation of TOPEX Altimeter Mean Values (Shallow Water Removed)Microwave Radiometer Wet Troposphere Correction (Nominal Case]

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-100Microwave Radiometer Wet Troposphere Correction [Area & Data-Density Weighted]

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Microwave Radiometer Wet Troposphere Correction [Weighted - Nominal Case]

X XX-

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Figure 13. Effect of area and data-density weighting on mean values of the wet tropospherecorrection over TOPEX cycles 11—47. The top panel shows the nominal case, while the middlepanel illustrates the nominal case weighted according to latitude and data density, and the bottompanel depicts the difference between these two cases (weighted case minus nominal case).

biases. Because a large proportion of the altimeter data in the southern hemisphere wasconcentrated at far southern latitudes near the Antarctic Circumpolar Current, weightingaffected statistics in the southern hemisphere significantly while only minimally affectingthose in the northern hemisphere.

A similar analysis was done separately on the equatorial region, since the conditionsand dynamics there are different than those of high latitudes. This exercise also providedsome insight into the latitudinal dependence of the corrections. Interestingly, the statisticsof some of the corrections were found to vary seasonally even within ± 20° of the equator.

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Seasonal Analysis ofTOPEX/POSEIDON Altimeter 21

Conclusions

Correlations among the corrections were recently shown to exist by Zlotnicki (1994), andthese correlations have been shown to be important factors in the effectiveness of thecorrections. Here we have shown how seasonal variations, shallow water data removal,area and data-density weighting, and latitudinal dependencies each affect some of thecorrections. We believe that the adjusted statistics will be useful in applying the correc-

Seasonal Variation of TOPEX Altimeter Standard Deviations (Shallow Water Removed)Microwave Radiometer Wet Troposphere Correction [Nominal Casel

111213141516171819 2122 23 24 25 26 27 28 29 30 32 33 34 35 36 37 38 39 40 4213 44 45 46 47Jan. Apr. Jul. Oct. 1993

Microwave Radiometer Wet Troposphere Correction [Area & Data-Density Weighted]

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Microwave Radiometer Wet Troposphere Correction [Weighted - Nominall

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Figure 14. Effect of area and data-density weighting on standard deviation values of the wettroposphere correction over TOPEX cycles 11-47. The top panel shows the nominal case, whilethe middle panel illustrates the nominal case weighted according to latitude and data density, andthe bottom panel depicts the difference between these two cases (weighted case minus nominalcase).

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22 J. M. Myrick el al.

tions to future altimeter measurements. We intend to continue this research by imple-menting adaptive filtering techniques to minimize correlation effects between the correc-tions and hence improve the resulting altimeter sea-surface height.

ReferencesBasic, T., and R. H. Rapp. 1992. Ocean wide prediction of gravity anomalies and sea surface

heights using Geos-3, Seasat and Geosat altimeter data, and ETOPO5U bathymetric data,OSU-DGS&S Rep. 416. Columbus, OH: Ohio State University.

Seasonal Variation of TOPEX Altimeter Correlation Coefficients (Shallow Water Removed)Wet Troposphere (Rad.) & EM Bias (K-Band) Corrections [Nominal Case]

* North

O South

11121314151617181921222324252627282930323334353637383940424344454647Jan. Apr. Jul. Oct. 1993

Wet Troposphere (Rad.) & EM Bias (K-Band) Corrections [Area & Data-Density Weighted]

* North

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0.05Wet Troposphere (Rad.) & EM Bias (K-Band) Corrections [Weighted - Nominal Case]

U

U-0.05

-0.111121314151617181921222324252627282930323334353637383940424344454647Jan. Apr. Jul. Oct. 1993

Figure 15. Effect of area and data-density weighting on correlation coefficient values of the EMbias wet troposphere corrections over TOPEX cycles 11-47. The top panel shows the nominal case,while the middle panel illustrates the nominal case weighted according to latitude and data density,andthe bottom panel depicts the difference between these two cases (weighted case minus nominalcase).

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Seasonal Analysis ofTOPEX/POSEIDON Altimeter

Seasonal Variation of the Wet Troposphere Correction in the Equatorial Region

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Seasonal Variation of the Wet Troposphere Correction in the Equatorial Region

11121314151617181921222324252627282930323334353637383940424344454647Jan. Apr. Jul. Oct 1993

Figure 16.. Seasonal comparison of mean values and standard deviation values of the wet tropo-sphere correction in the equatorial region of ± 20° latitude (shallow water removed) over TOPEXcycles 11-47." " "

Benada, R. 1993. PO.DAAC merged GDR (TOPEXIPOSEIDON) users handbook. Version 1.0,JPL D-1 1007. Pasadena, CA: Physical Oceanography Distributed Active Archive Center, JetPropulsion Laboratory.

Bendat, J. S., and A. G. Piersol. 1971. Random data: Analysis and measurement procedures. NewYork: Wiley-Interscience.

Cartwright, D. E., and R. D. Ray. 1991. Energetics of global ocean tides from Geosat altimetry.J. Geophys. Res. 96: 16897-168162.

Hendricks, J. R., R. R. Leben, and G. H. Born. 1996. Empirical orthogonal function analysis ofglobal TOPEX/POSEIDON altimeter data and implications for detection of global sea levelrise. J. Geophys. Res. 101:14131-14145.

Kantha, L., K. Whitmer, and G. Born. 1994. The inverted barometer effect in altimetry: A studyin the North Pacific. TOPEX/POSEIDON Res. News 2:18-23.

Knudsen, P. 1994. Global low harmonic degree models of the seasonal variability and residualocean tides from TOPEX/POSEIDON altimeter data. J. Geophys. Res. 99(C12):24643-24655.

Minster, J.-F., C. Brossier, and P. Rogel. 1995. Variation of the mean sea level from TOPEX/POSEIDON data. J. Geophys. Res. 100:25153-25161.

NOAA/ERL. 1993. Preliminary report and forecast of solar geophysical data, Rep. SESC PRF914. Boulder, CO: Space Environment Services Center. Space Environment Laboratory, Na-tional Oceanic and Atmospheric Administration.

Zlotnicki, V. 1994. Correlated environmental corrections in TOPEX/POSEIDON, with a note onionospheric accuracy. J. Geophys. Res. 99(C12):24907-24914.

Zlotnicki, V. 1996a. Personal communication, 26 February.Zlotnicki, V. 1996b. Personal communication, 1 April.

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Seasonal Variation of the EM Bias Correction in the Equatorial Region

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Seasonal Variation of the EM Bias Correction in the Equatorial Region

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Figure 17. Seasonal comparison of mean values and standard deviation values of the EM biascorrection in the equatorial region of ±20° latitude (shallow water removed) over TOPEX cycles11-47.

Seasonal Variation of Correlation Coefficients for the TOPEX Altimeter CorrectionsBetween Wet Troposphere (Rad.) & EM Bias Corrections (K-Band)

-0.411121314151617181921222324252627282930323334353637383940424344454647Jan. Apr. Jul. Oct 1993

Figure 18. Seasonal comparison of correlation coefficient values of the wet troposphere and EMbias corrections in the equatorial region of ±20° latitude (shallow water removed) over TOPEXcycles 11-47.

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