Engineering topics

Rapp, Richard H.

Publications and source records attributed to Rapp, Richard H..

At least 19 records

NASA NTRS1998

The Development of a Degree 360 Expansion of the Dynamic Ocean Topography of the POCM_4B Global Circulation Model

This paper documents the development of a degree 360 expansion of the dynamic ocean topography (DOT) of the POCM_4B ocean circulation model. The principles and software used that led to the final model are described. A key principle was the development of interpolated DOT values into land areas to avoid discontinuities at or near the land/ocean interface. The power spectrum of the POCM_4B is also presented with comparisons made between orthonormal (ON) and spherical harmonic magnitudes to degree 24. A merged file of ON and SH computed degree variances is proposed for applications where the DOT power spectrum from low to high (360) degrees is needed.

Rapp, Richard H.↗

NASA NTRS1994

Mean sea surface and geoid gradient comparisons with TOPEX altimeter data

Cycles 4 to 54 of TOPEX data have been analyzed through comparisons with the mean sea surface given on the disturbed geophysical data record (GDR). Two inverted barometer correction procedures were considered for the data reduction. One used a constant atmospheric pressure for all data while the one adopted for use, for most computations, introduced a cycle average pressure. The maximum difference between the two estimates was 3.0 cm with a clear annual signal. With the modified correction the TOPEX sea surface was compared to The Ohio State University (OSU) mean sea surface, given on the GDR, to estimate three translations ( delta x = -2.3 cm; delta y = 25.0 cm; delta z = -0.3 cm) and a bias (43.3 cm) between the two surfaces. The only significant translation is delta y which indicates the reference frame of the TOPEX system differs from that used in the OSU mean sea surface system. The bias between the TOPEX mean sea surface and the OSU mean sea surface was used to estimate an equatorial radius of 6,378,136.55 m based on an 18-cm biased estimate of the TOPEX altimeter. Examination of the average difference, by cycle, between the TOPEX sea surface and the OSU mean sea surface suggested a bias change of 3.1 +/- 2.2 mm/yr with a positive sign indicating the average ocean surface is rising or the altimeter measured distance is decreasing. Models were implemented that solved directly for a bias, bias rate annual/semiannual, and tide correction terms. The computations indicated that a simultaneous solution for this bias, bias rate, and annual/semiannual terms gave the most accurate results. Nonsimultaneous solutions led to slightly different bias rate values. The root mean square difference between the TOPEX sea surface and OSU sea surface, after translation and bias correction, was +/- 17 cm for a typical cycle. Some locations were indentified where the difference could reach 2.3 cm and were repeated over several cycles indicating errors in the mean sea surface. Most of the large differences occur in regions lacking altimeter data prior to the TOPEX/POSEIDON mission and/or areas of significant bathymetric signature. Geoid gradients are needed for the reduction of individual track data to a reference track. The accuracy of the determination of such gradients was determined through the comparison of predicted along-track gradients to the observed gradients. Among four mean sea surfaces tested the best agreement was found with the OSU mean sea surface placed on the TOPEX geophysical data record.

Rapp, Richard H.↗

NASA NTRS1994

Preliminary estimates of Gulf Stream characteristics from TOPEX data and a precise gravimetric geoid

TOPEX sea surface height data has been used, with a gravimetric geoid, to calculate sea surface topography across the Gulf Stream. This topography was initially computed for nine tracks on cycles 21 to 29. Due to inaccurate geoid undulations on one track, results for eight tracks are reported. The sea surface topography estimates were used to calculate parameters that describe Gulf Stream characteristics from two models of the Gulf Stream. One model was based on a Gaussian representation of the velocity while the other was a hyperbolic representation of velocity or the sea surface topography. The parameters of the Gaussian velocity model fit were a width parameter, a maximum velocity value, and the location of the maximum velocity. The parameters of the hyperbolic sea surface topography model were the width, the height jump, position, and sea surface topography at the center of the stream. Both models were used for the eight tracks and nine cycles studied. Comparisons were made between the width parameters, the maximum velocities, and the height jumps. Some of the parameter estimates were found to be highly (0.9) correlated when the hyperbolic sea surface topography fit was carried out, but such correlations were reduced for either the Gaussian velocity fits or the hyperbolic velocity model fit. A comparison of the parameters derived from 1-year TOPEX data showed good agreement with values derived by Kelly (1991) using 2.5 years of Geosat data near 38 deg N, 66 deg W longitude. Accuracy of the geoid undulations used in the calculations was of order of +/- 16 cm with the accuracy of a geoid undulation difference equal to +/- 15 cm over a 100-km line in areas with good terrestrial data coverage. This paper demonstrates that our knowledge or geoid undulations and undulation differences, in a portion of the Gulf Stream region, is sufficiently accurate to determine characteristics of the jet when used with TOPEX altimeter data. The method used here has not been shown to be more accurate than methods that average altimeter data to form a reference surface used in analysis to obtain the Gulf Stream characteristics. However, the results show the geoid approach may be used in areas where lack of current meandering reduces the accuracy of the average surface procedure.

Rapp, Richard H.↗

NASA NTRS1993

Geoid undulation accuracy

The determination of the geoid and equipotential surface of the Earth's gravity field, has long been of interest to geodesists and oceanographers. The geoid provides a surface to which the actual ocean surface can be compared with the differences implying information on the circulation patterns of the oceans. For use in oceanographic applications the geoid is ideally needed to a high accuracy and to a high resolution. There are applications that require geoid undulation information to an accuracy of +/- 10 cm with a resolution of 50 km. We are far from this goal today but substantial improvement in geoid determination has been made. In 1979 the cumulative geoid undulation error to spherical harmonic degree 20 was +/- 1.4 m for the GEM10 potential coefficient model. Today the corresponding value has been reduced to +/- 25 cm for GEM-T3 or +/- 11 cm for the OSU91A model. Similar improvements are noted by harmonic degree (wave-length) and in resolution. Potential coefficient models now exist to degree 360 based on a combination of data types. This paper discusses the accuracy changes that have taken place in the past 12 years in the determination of geoid undulations.

Rapp, Richard H.↗

NASA NTRS1992

Oceanwide gravity anomalies from Geos-3, Seasat and Geosat altimeter data

Three kinds of satellite altimeter data have been combined, along with 5 x 5 arcmin bathymetric data, to calculate a 0.125 deg ocean wide gridded set of 2.3 x 10 exp 6 free-air gravity anomalies. The procedure used was least squares collocation that yields the predicted anomaly and standard deviation. The value of including the bathymetric data was shown in a test around the Dowd Seamount where the root mean square (rms) difference between ship gravity measurements decreased from +/- 40 mgal to +/- 20 mgal when the bathymetry was included. Comparisons between the predicted anomalies and ship gravity data is described in three cases. In the Banda Sea the rms differences were +/- 20 mgal for two lines. In the South Atlantic rms differences over lines of 2000 km in length were +/- 7 mgal. For cruise data in the Antarctica region the discrepancies were +/- 12 mgal. Comparisons of anomalies derived from the Geosat geodetic mission data by Marks and McAdoo (1992) with ship dta gave differences of +/- 6 mgal showing the value of the much denser Geosat geodetic mission altimeter data.

Rapp, Richard H.↗

NASA NTRS1992

Improvement of the Earth's gravity field from terrestrial and satellite data

The determination of the Earth's gravitational potential can be done through the analysis of satellite perturbations, the analysis of surface gravity data, or both. The combination of the two data types yields a solution that combines the strength of each method: the longer wavelength strength in the satellite analysis with the better high frequency information from surface gravity data. Since 1972, Ohio State has carried out activities that have provided surface gravity data to a number of organizations who have developed combination potential coefficient models that describe the Earth's gravitational potential.

Rapp, Richard H.↗

NASA NTRS1992

Altimeter and gravity data analysis

The studies carried out under this grant fell into two broad areas. The first area was the analysis of surface gravity data with the ultimate goal of providing normal equations that could be used in combination with normal equations from the analysis of satellite orbit perturbations to obtain an optimal estimate of the gravitational potential coefficients of the Earth. The second main research activity was the estimation of gravity anomalies in ocean areas from satellite altimeter data. Such anomalies could enable the improved calibration of potential coefficient models derived solely from the analysis of orbital perturbation information. The studies in these two areas are discussed.

Rapp, Richard H.↗

NASA NTRS1992

The determination of a one year mean sea surface height track from Geosat altimeter data and ocean variability implications

Results are presented for determinations of mean sea surface along a reference Geosat altimeter tracking, using Geosat data from the first year of the exact repeat mission (ERM) and improved orbits. The results were used to study the time variability of the ocean surface, and a map was constructed of the major current structure. The data included 21 complete and one incomplete ERMs, with the sea surface heights being referenced to the single reference track through the application of geoid gradient corrections. This Geosat surface can be used as a reference surface to which other altimeter data could be incorporated; the data could then be used for the recovery of geoid undulations and gravity anomalies in the ocean areas.

Wang, Yan M.↗

NASA NTRS1992

High resolution gravity models combining terrestrial and satellite data

Spherical harmonic expansions to degree 360 have been developed that combine satellite potential coefficient information, terrestrial gravity data, satellite altimeter information as a direct tracking data type and topographic information. These models define improved representations of the Earth's gravitational potential beyond that available from just satellite or terrestrial data. The development of the degree 360 models, however, does not imply a uniform accuracy in the determination of the gravity field as numerous geographic areas are devoid of terrestrial data or the resolution of such data is limited to, for example, 100 km. This paper will consider theoretical and numerical questions related to the combination of the various data types. Various models of the combination process are discussed with a discussion of various correction terms for the different models. Various sources of gravity data will be described. The new OSU91 360 model will be discussed with comparisons made to previous 360 models and to other potential coefficient models that are complete to degree 50. Future directions in high degree potential coefficient models will be discussed.

Rapp, Richard H.↗

NASA NTRS1991

Mean sea surface and gravity investigations using TOPEX/Poseidon altimeter data

From a broad point of view, we will be concerned with studying global ocean circulation patterns on the basis of ocean surface determinations with geoid undulation information. In addition, we will study local variations of the gravity field implied by the altimeter data. These general goals are reflected in the title of our investigation. To meet our general goal, we have defined a number of specific objectives: (1) sea surface topography representation; (2) mean sea surface determination; (3) development of local geoid models; (4) mean sea surface comparisons; (5) sea surface topographic files; and (6) gravity anomaly determination.

Rapp, Richard H.↗

NASA NTRS1991

The Ohio State 1991 geopotential and sea surface topography harmonic coefficient models

The computation is described of a geopotential model to deg 360, a sea surface topography model to deg 10/15, and adjusted Geosat orbits for the first year of the exact repeat mission (ERM). This study started from the GEM-T2 potential coefficient model and it's error covariance matrix and Geosat orbits (for 22 ERMs) computed by Haines et al. using the GEM-T2 model. The first step followed the general procedures which use a radial orbit error theory originally developed by English. The Geosat data was processed to find corrections to the a priori geopotential model, corrections to a radial orbit error model for 76 Geosat arcs, and coefficients of a harmonic representation of the sea surface topography. The second stage of the analysis took place by doing a combination of the GEM-T2 coefficients with 30 deg gravity data derived from surface gravity data and anomalies obtained from altimeter data. The analysis has shown how a high degree spherical harmonic model can be determined combining the best aspects of two different analysis techniques. The error analysis was described that has led to the accuracy estimates for all the coefficients to deg 360. Significant work is needed to improve the modeling effort.

Rapp, Richard H.↗

NASA NTRS1991

Report of the panel on geopotential fields: Gravity field, section 8

The objective of the Geopotential Panel was to develop a program of data acquisition and model development for the Earth's gravity and magnetic fields that meet the basic science requirements of the solid Earth and ocean studies. Presented here are the requirements for gravity information and models through the end of the century, the present status of our knowledge, data acquisition techniques, and an outline of a program to meet the requirements.

Anderson, Allen Joel↗

NASA NTRS1991

Consideration of permanent tidal deformation in the orbit determination and data analysis for the Topex/Poseidon mission

The effects of the permanent tidal effects of the Sun and Moon with specific applications to satellite altimeter data reduction are reviewed in the context of a consistent definition of geoid undulations. Three situations are applicable not only for altimeter reduction and geoid definition, but also for the second degree zonal harmonic of the geopotential and the equatorial radius. A recommendation is made that sea surface heights and geoid undulations placed on the Topex/Poseidon geophysical data record should be referred to the mean Earth case (i.e., with the permanent effects of the Sun and Moon included). Numerical constants for a number of parameters, including a flattening and geoid geopotential, are included.

Rapp, Richard H.↗

NASA NTRS1990

The development and analysis of geopotential coefficient models to spherical harmonic degree 360

Two new geopotential coefficient models to spherical harmonic degree 360 are developed using recent advances made in theoretical modeling methods, satellite gravitational models, and expanded and improved terrestrial data. The new models are based on the combination of a satellite potential coefficient model (GEM-T2) to degree 50 with 30-arc mean gravity anomalies, yielding an adjusted set of coefficients and gravity anomalies, which were then harmonically analyzed to yield a set of potential coefficients to degree 360. The models were verified in several ways including satellite orbit residual analysis, demonstrating a substantial improvement over previous high-degree expansions.

Rapp, Richard H.↗

NASA NTRS1990

Geodetic and oceanographic results from the analysis of 1 year of Geosat data

The radial error model of Engelis (1987) is extended using the altimeter data obtained by the Geosat Exact Repeat Mission for simultaneous measurements of the stationary sea surface topography and geopotential coefficients. It is shown that the proper utilization of the Geosat altimeter data significantly improved the quality of field modeling at wave numbers by providing, simultaneously, the solution for improved orbits and the oceanographic information on the global scale. A new set of Geosat geophysical data records with the improved orbits was created, which also contains the values of the geoid undulation computed from a recent spherical harmonic expansion to degree 360.

Denker, Heiner↗

NASA NTRS1990

The development of the July 1989 1 deg x 1 deg and 30' x 30' terrestrial mean free-air anomaly data bases

In June 1986 a 1 x 1 deg/mean free-air anomaly data file containing 48955 anomalies was completed. In August 1986 a 30 x 30 min mean free-air anomaly file was defined containing 31787 values. For the past three years data has been collected to upgrade these mean anomaly files. The primary emphasis was the collection of data to be used for the estimation of 30 min means anomalies in land areas. The emphasis on land areas was due to the anticipated use of 30 min anomalies derived from satellite altimeter data in the ocean areas. There were 10 data sources in the August 1986 file. Twenty-eight sources were added based on the collection of both point and mean anomalies from a number of individuals and organizations. A preliminary 30 min file was constructed from the 38 data sources. This file was used to calculate 1 x 1 deg mean anomalies. This 1 x 1 deg file was merged with a 1 x 1 deg file which was a merger of the June 1986 file plus a 1 x 1 deg file made available by DMA Aerospace Center. Certain bad 30 min anomalies were identified and deleted from the preliminary 30 min file leading to the final 30 min file (the July 1989 30 min file) with 66990 anomalies and their accuracy. These anomalies were used to again compute 1 x 1 deg anomalies which were merged with the previous June 86 DMAAC data file. The final 1 x 1 deg mean anomaly file (the July 89 1 x 1 deg data base) contained 50793 anomalies and their accuracy. The anomaly data files were significantly improved over the prior data sets in the following geographic regions: Africa, Scandinavia, Canada, United States, Mexico, Central and South America. Substantial land areas remain where there is little or no available data.

Kim, Jeong-Hee↗

NASA NTRS1989

Progress in the Determination of the Earth's Gravity Field

Topics addressed include: global gravity model development; methods for approximation of the gravity field; gravity field measuring techniques; global gravity field applications and requirements in geophysics and oceanography; and future gravity missions.

Rapp, Richard H.↗

NASA NTRS1989

Progress in the development of high degree potential coefficient models

A natural extension of the recent satellite derived potential coefficient models is the development of high degree (maximum 180 or 360) expansions. Such expansions are based on the combination of the satellite derived models with terrestrial gravity data and satellite altimeter data. Such models are useful for more precise geoid undulation computations, for simulation studies involving different typed of future missions (e.g., gradiometry), and as reference fields for different types of gravimetric computations. The attention is to the effect of the terrain, ellipsoidal terms, and weighting. The basic methods used for the high degree solutions are reviewed. Various correction terms are described and recent models are discussed and compared.

Rapp, Richard H.↗