Product 2: The Gridded Data Set

Description

A time series of gridded monthly sea surface height variations with respect to a 1993 mean reference has been generated from all available altimeter observations provided by Seasat, Geosat, ERS-1, and T/P. The grids are created from height anomalies of cross over or collinear data relative to a mean reference set of collinear ground tracks. The data processing procedure is outlined below:

    • Obtain, analyze, and apply the latest state-of-the-art corrections and models, consistent across missions, whenever possible.

    • Compute improved GDRs.

    • Spatially and temporally interpolate to reference ground-track at 1/sec sampling.

    • Apply editing criteria to extract bad data.

    • Compute mean reference surface from mean T/P and ERS data sets.

    • Compute crossover anomalies for non-ERS or T/P data sets.

    • Adjust cross over or collinear anomalies into mean surface.

    • Compute grid from anomalies within a given month.

Algorithm
 1. Mean Reference Surface

The mean reference surface was computed from merged ERS-1 and T/P annual mean heights along ground-tracks for 1993 by adjusting the 35-day ERS-1 mean profile for 1993 into the T/P geodetic frame. The ERS-1 Phase C altimetry was first updated with Delft DGM-E04 JGM3 based orbits and a number of improved geophysical and altimeter range corrections (see Section 2). A mean profile is then computed at each geo-referenced location employing standard edit procedures, including a minimum cycle requirement to avoid seasonal aliasing. Adjustment of the ERS-1 mean profile with respect to the T/P mean profile was performed by crossover minimization within 30° zonal bands modeled by a simple tilt and bias. Crossover analysis of the adjusted ERS-1 mean profile with the T/P mean resulted in a residual rms of less than 3 cm. The " blending " of ERS-1 and T/P mean profiles generates a dense ground-track providing a statistical robust sample of crossover and collinear sea surface height residuals (see Figure 1).

    • Figure 1. Coverage of blended ERS-1 and T/P groundtracks that form reference surface for grids.

 

2. Adjustment Procedure

Significant improvements have been made to the orbit computation based on the JGM3 gravity field for Seasat, Geosat, and ERS missions. However, the orbits have not reached the accuracy of the T/P altimeter mission. Therefore, sea surface height variations computed from Seasat, Geosat, and ERS crossover or collinear residuals with respect to the 1993 reference have been adjusted to remove systematic orbit errors and geocentric offsets. These errors are modeled with a 1 cycle per revolution sinusoid and bias term from the simultaneous crossover minimization of single and dual crossovers to the T/P mean profile.

 

Reduction of systematic orbit errors employing crossover minimization techniques has a long heritage (e.g., Rapp, 1977; Tai, 1988, 1994; Hwang, 1989; Yi, 1995). It is well known that the orbit error has dominant power at one cycle per revolution (cpr) with secondary peaks at 2 cpr and 3 cpr (Rosborough and Tapley, 1987; Engelis, 1988; Chelton and Schlax, 1993). A low degree polynomial or Fourier series have been used to model the orbit error. An important aspect in using these kinds of error models is that improper use of the error model could remove ocean variability (Tai, 1989; Wagner and Tai, 1994). In order to minimize the loss of ocean dynamics, the polynomial expansion or Fourier series of the lowest possible degree and order have to be chosen. In our study the sinusoidal error model is chosen for one revolution of the altimeter data:

(1) r(t) = a + b cos wt + c sin wt

where w = 2 p /T is the one cpr for the nodal period of the altimeter mission, a, b and c and are the estimated coefficients for a single revolution. This error model has an along-track wavelength of 40,000 km, thus any effect on the ocean variability has to be at signals with wavelengths of 40,000 km or longer.

 

The residual sea surface at the single-crossover point (single altimeter mission) is:

(2) Dhij = r(ti) – r(tj) + d*(ti,tj)

 

where ti,tj are the times of the ascending and descending arcs at the crossover point; d (ti,tj) is the time varying sea surface height and error of the environmental corrections at the crossover point. Assuming the TOPEX/POSEIDON mean profile is free of orbit error, the residual sea surface height at the dual crossover point (dual altimeter missions) is:

 

(3) Dhij = r(ti) + d*(ti,tj)

 

 

Where d*(ti,tj) is the sea surface height variation at the crossover point respect to the TOPEX/POSEIDON mean profile and the error of the environmental corrections in both altimeter missions.

 

Equation (2) and (3) form two observation equations, and the parameters a, b and c for each revolution are estimated through the standard least squares adjustment.

 

The crossover adjustment procedure has been applied to the Seasat, ERS-1 phase C and Geosat missions. The following table gives the RMS values of the residual sea surface height at the crossover point before and after adjustment.

 

 

  • Table 2 RMS values of the residual sea surface height at the crossover points before and after the adjustment (meters).

    •  

    Single Satellite

    		  

    Dual Satellites

    Number

    Before Adj.

    After Adj.

    		  

    Number

    Before Adj.

    After Adj.

    Seasat (3days)

    Cycle 2

    516

    0.265

    0.137

    		  

    3797

    0.534

    0.136
     

    Cycle 5

    521

    0.257

    0.127

    		  

    3728

    0.509

    0.128
     

    Cycle 8

    461

    0.329

    0.121

    		  

    3556

    0.578

    0.139
                     

    Seasat (17 day)

    Cycle 1

    3050

    0.523

    0.121

    		  

    9547

    0.558

    0.134
     

    Cycle 3

    6562

    0.312

    0.119

    		  

    14063

    0.536

    0.135
                     

    Geosat ERM

    Cycle 21

    14231

    0.151

    0.101

    		  

    20862

    0.197

    0.120
     

    Cycle 30

    17218

    0.163

    0.088

    		  

    25066

    0.212

    0.105
     

    Cycle 45

    9736

    0.222

    0.101

    		  

    17029

    0.226

    0.110
                     

    Geosat GM

    Cycle 14

    35976

    0.153

    0.086

    		  

    37732

    0.181

    0.098
     

    Cycle 19

    22255

    0.136

    0.084

    		  

    30302

    0.181

    0.100

    Cycle 25

    19081

    0.128

    0.084

    27196

    0.171

    0.102
                     

    ERS-1 (35 day)

    Cycle10

    32507

    0.126

    0.093

    		  

    49441

    0.421

    0.088
     

    Cycle 15

    28467

    0.129

    0.097

    		  

    35839

    0.475

    0.100
     

    Cycle 17

    27109

    0.117

    0.093

    		  

    39075

    0.449

    0.099

    3. Grid Computation

      Monthly grids were derived by estimating at each point P on a 1° X 1° regular grid a weighted average of adjacent (within a 3° radius) cross over or collinear differences with respect to the mean 1993 reference surface. Figure 2 shows typical crossover density of points between Geosat GM and the reference surface in mid-latitude regions. In lieu of using an optimal estimator based on local values of the height covariance for smoothing weights, the data weights were derived using an isotropic Gaussian function depending only on the distance from the calculation point P(f ,l ) to the data point at (f i,l i).
    • Figure 2. Groundtrack coverage with respect to 1993 reference frame from
    • a)Geosat Primary Mission groundtracks and

    • b) Geosat Exact Repeat groundtracks.

    • Eq. 9 Grid Algorithm

      • Where, wi= exp(-s d2); d = spherical distance between P(f ,l ) and the data points (f i,l i); s = smoothness parameter defined by the half weight t , such that: exp(-s t 2) =1/2 à s =ln(2)t -2. For our grids, we have selected t =1° . Grids of the sea surface height variations are computed using an interpolation procedure to predict a weighted average SSH residual within a defined search radius of the desired grid node. The procedure is fully described in Nerem et al. (1994). Several tests showed that the crossover densities were sufficient to permit a half weight parameter of 1° , and a search radius of 3° (see Figures 3 & 4). The validation of these grids against tide gauge height changes (summarized in Fig. 7) showed that these parameters represent the original data on a global scale. Report #2: Validation Handbook provides complete validation details regarding these grids.

  • Figure 3 Global density of crossover measurements within each grid node from Geosat Primary Mission for a month (November 1985).

  • Figure 4 Gridded crossover sea surface height residual for Geosat GM November 1985 with respect to 1993 reference.

  • Figure 5 Validation of Gridded Altimetry Against Tide Gauge Network. The Mean RMS Difference of the Monthly Grids vs. Tide Gauge is 4.6cm.

    • REFERENCES:

    Chelton, D.B. and M.G. Schlax, "Spectral characteristics of the time-dependent orbit errors in altimeter height measurements", Journal of Geophysical Research,98, 12579-12600, 1993.

    Engelis, T., "On the simultaneous improvement of satellite orbit determination of sea surface topography using altimeter data",Man. Geod., 13, 180-190, 1988.

    Hwang, C., "High precision gravity anomaly and sea surface height estimation from Geos-3/Seasat satellite altimeter data", Rep. 399, Dept. of Geodetic Science, The Ohio State University, 1989.

    Nerem, R.S., E.J. Schrama, C.J. Koblinsky, B.D. Beckley, "A preliminary evaluation of ocean topography from the TOPEX/POSEIDON mission",Journal of Geophysical Research, 99, 24565-24583, 1994b.

    Rapp, R.H., "Mean gravity anomalies and sea surface height degradation from Geos-3 altimeter data", Rep. 268, Dept. of Geodetic Science, The Ohio State University, 1977.

    Rosborough, G.W., and B.D. Tapley, "Radial, transverse and normal satellite position perturbations due to the geopotential", Celestial Mechanics, 40, 409-421, 1987.

    Tai, C.K., "Geosat crossover analysis in the tropical Pacific. 1. Constrained sinusoidal crossover adjustment",Journal of Geophysical Research, 93,10621-10629, 1988.

    Tai, C.K., "Accuracy assessment of widely-used orbit error approximations in satellite altimetry", J. Atmos. Oceanic Tech., 6, 147-150, 1989.

    Tai, C.K., and J. Kuhn, "On reducing the large-scale time-dependent errors in satellite altimetry while preserving the ocean signal: orbit and tide error reduction for TOPEX/POSEIDON", NOAA Tech. Mem. NOS OES 9, 1994.

    Wagner, C.A., and C.K. Tai, "Degradation of ocean signals in satellite altimetry due to orbit removal processes",Journal of Geophysical Research, 99, 16255-16267, 1994.

    Yi, Y., "Determination of gridded mean sea surface from TOPEX, ERS-1 and Geosat altimeter data", Report No. 434, Dept. of Geodetic Science, The Ohio State University, 1995.