Regional gravity field refinement for (quasi-) geoid determination based on spherical radial basis functions in Colorado

Abstract This study presents a solution of the ‘1 cm Geoid Experiment’ (Colorado Experiment) using spherical radial basis functions (SRBFs). As the only group using SRBFs among the fourteen participated institutions from all over the world, we highlight the methodology of SRBFs in this paper. Detailed explanations are given regarding the settings of the four most important factors that influence the performance of SRBFs in gravity field modeling, namely (1) the choosing bandwidth, (2) the locations of the SRBFs, (3) the type of the SRBFs as well as (4) the extensions of the data zone for reducing the edge effect. Two types of basis functions covering the same spectral range are used for the terrestrial and the airborne measurements, respectively. The non-smoothing Shannon function is applied to the terrestrial data to avoid the loss of spectral information. The cubic polynomial (CuP) function which has smoothing features is applied to the airborne data as a low-pass filter for filtering the high-frequency noise. Although the idea of combining different SRBFs for different observations was proven in theory to be possible, it is applied to real data for the first time, in this study. The RMS error of our height anomaly result along the GSVS17 benchmarks w.r.t the validation data (which is the mean results of the other contributions in the ‘Colorado Experiment’) drops by 5% when combining the Shannon function for the terrestrial data and the CuP function for the airborne data, compared to those obtained by using the Shannon function for both the two data sets. This improvement indicates the validity and benefits of using different SRBFs for different observation types. Global gravity model (GGM), topographic model, the terrestrial gravity data, as well as the airborne gravity data are combined, and the contribution of each data set to the final solution is discussed. By adding the terrestrial data to the GGM and the topographic model, the RMS error of the height anomaly result w.r.t the validation data drops from 4 to 1.8 cm, and it is further reduced to 1 cm by including the airborne data. Comparisons with the mean results of all the contributions show that our height anomaly and geoid height solutions at the GSVS17 benchmarks have an RMS error of 1.0 cm and 1.3 cm, respectively; and our height anomaly results give an RMS value of 1.6 cm in the whole study area, which are all the smallest among the participants.

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The combination and contribution of different gravity measurements in regional quasi-geoid determination based on spherical radial basis functions

10.5194/egusphere-egu21-8457 ◽

2021 ◽

Author(s):

Qing Liu ◽

Michael Schmidt ◽

Laura Sánchez

Keyword(s):

Radial Basis Functions ◽

Gravity Data ◽

Basis Functions ◽

Airborne Gravity ◽

Frequency Noise ◽

Geoid Model ◽

Topographic Model ◽

Radial Basis ◽

Spherical Radial Basis Functions ◽

Terrestrial Data

In this study, we investigate the optimal combination of local gravity observations and their contributions to the regional quasi-geoid model. The study area is located in Colorado, USA, with two types of regional data sets, namely terrestrial gravity data and airborne gravity data, available within the &#8220;1 cm geoid experiment&#8221;. The approach based on series expansions in terms of spherical radial basis functions (SRBF) is applied, which has been developed at DGFI-TUM in the last two decades. We use two different types of basis functions covering the same spectral domain separately for the terrestrial and the airborne measurements. The Shannon function is applied to the terrestrial data, and the Cubic Polynomial (CuP) function which has smoothing features is applied to the airborne data for filtering their high-frequency noise.To assess the contributions of the regional terrestrial and airborne gravity data to the final quasi-geoid model, four solutions are compared, namely the combined solution, the terrestrial only, the airborne only, and finally the model only solution, i.e., only the global gravity model and the topographic model are used without any gravity data from regional measurements. By adding the terrestrial data to the GGM and the topographic model, the RMS error of the quasi-geoid model w.r.t the validation data (the mean solution of independent computations delivered by fourteen institutions from all over the world) drops from 4 to 1.8 cm, and it is further reduced to 1 cm by including the airborne data.

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The use of different spherical radial basis functions to combine terrestrial and airborne measurements for regional gravity field refinement

10.5194/egusphere-egu2020-9565 ◽

2020 ◽

Author(s):

Qing Liu ◽

Michael Schmidt ◽

Laura Sánchez

Keyword(s):

Gravity Data ◽

Basis Functions ◽

Airborne Gravity ◽

Shannon Function ◽

Airborne Measurements ◽

Different Types ◽

Low Pass ◽

Spherical Radial Basis Functions ◽

Regional Gravity ◽

Terrestrial Data

The objective of this study is the combination of different types of basis functions applied separately to different kinds of gravity observations. We use two types of regional data sets: terrestrial gravity data and airborne gravity data, covering an area of about 500 km &#215; 800 km in Colorado, USA. These data are available within the &#8220;1 cm geoid experiment&#8221; (also known as the &#8220;Colorado Experiment&#8221;). We apply an approach for regional gravity modeling based on series expansions in terms of spherical radial basis functions (SRBF). Two types of basis functions covering the same spectral domain are used, one for the terrestrial data and another one for the airborne measurements. To be more specific, the non-smoothing Shannon function is applied to the terrestrial data to avoid the loss of spectral information. The Cubic Polynomial (CuP) function is applied to the airborne data as a low-pass filter, and the smoothing features of this type of SRBF are used for filtering the high-frequency noise in the airborne data. In the parameter estimation procedure, these two modeling parts are combined to calculate the quasi-geoid.The performance of our regional quasi-geoid model is validated by comparing the results with the mean solution of independent computations delivered by fourteen institutions from all over the world. The comparison shows that the low-pass filtering of the airborne gravity data by the CuP function improves the model accuracy by 5% compared to that using the Shannon function. This result also makes evident the advantage of combining different SRBFs covering the same spectral domain for different types of observations.

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Ground-based Measurements of Atmospheric Trace Gases in Beijing during the Olympic Games

Sci ◽

10.3390/sci1010006 ◽

2018 ◽

Vol 1 (1) ◽

pp. 6

Author(s):

Jie Cheng

Keyword(s):

Olympic Games ◽

Trace Gases ◽

Fourier Transform Spectrometer ◽

Atmospheric Trace Gases ◽

Validation Data ◽

Solar Absorption ◽

The Mean ◽

The City ◽

Total Column ◽

The Olympic Games

A portable Fourier Transform Spectrometer (B3M-IR) is built and used to measure atmospheric trace gases in the city of Beijing during Olympic Games in 2008. A short description of the instrument is first provided in this paper. A detailed spectral analysis is then presented. The total columns of ozone (O3), carbon monoxide (CO), methane (CH4) and nitrous oxide (N2O) are retrieved from the ground-based solar absorption spectra recorded by the B3M-IR during the Olympic Games. Lacking validation data, only the retrieved total column of O3 is compared with that retrieved by MAX-DOAS, which is deployed at the same station. The mean difference between the two methods of measurement is 6.5%, demonstrating the performance and reliability of B3M-IR.

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Validation and update of OMI Total Column Water Vapor product

Atmospheric Chemistry and Physics ◽

10.5194/acp-16-11379-2016 ◽

2016 ◽

Vol 16 (17) ◽

pp. 11379-11393 ◽

Cited By ~ 11

Author(s):

Huiqun Wang ◽

Gonzalo Gonzalez Abad ◽

Xiong Liu ◽

Kelly Chance

Keyword(s):

Water Vapor ◽

Liquid Water ◽

Retrieval Algorithm ◽

Ozone Monitoring Instrument ◽

Validation Data ◽

Data Set ◽

Wide Range ◽

Key Factor ◽

The Mean ◽

Total Column

Abstract. The collection 3 Ozone Monitoring Instrument (OMI) Total Column Water Vapor (TCWV) data generated by the Smithsonian Astrophysical Observatory's (SAO) algorithm version 1.0 and archived at the Aura Validation Data Center (AVDC) are compared with NCAR's ground-based GPS data, AERONET's sun-photometer data, and Remote Sensing System's (RSS) SSMIS data. Results show that the OMI data track the seasonal and interannual variability of TCWV for a wide range of climate regimes. During the period from 2005 to 2009, the mean OMI−GPS over land is −0.3 mm and the mean OMI−AERONET over land is 0 mm. For July 2005, the mean OMI−SSMIS over the ocean is −4.3 mm. The better agreement over land than over the ocean is corroborated by the smaller fitting residuals over land and suggests that liquid water is a key factor for the fitting quality over the ocean in the version 1.0 retrieval algorithm. We find that the influence of liquid water is reduced using a shorter optimized retrieval window of 427.7–465 nm. As a result, the TCWV retrieved with the new algorithm increases significantly over the ocean and only slightly over land. We have also made several updates to the air mass factor (AMF) calculation. The updated version 2.1 retrieval algorithm improves the land/ocean consistency and the overall quality of the OMI TCWV data set. The version 2.1 OMI data largely eliminate the low bias of the version 1.0 OMI data over the ocean and are 1.5 mm higher than RSS's “clear” sky SSMIS data in July 2005. Over the ocean, the mean of version 2.1 OMI−GlobVapour is 1 mm for July 2005 and 0 mm for January 2005. Over land, the version 2.1 OMI data are about 1 mm higher than GlobVapour when TCWV  <  15 mm and about 1 mm lower when TCWV  >  15 mm.

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Artifacts in regional gravity representations with spherical radial basis functions

Journal of Geodetic Science ◽

10.2478/jogs-2013-0029 ◽

2013 ◽

Vol 3 (3) ◽

Cited By ~ 9

Author(s):

K. Bentel ◽

M. Schmidt ◽

C. Rolstad Denby

Keyword(s):

Radial Basis Functions ◽

Basis Functions ◽

Radial Basis ◽

Spherical Radial Basis Functions ◽

Regional Gravity

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All-frequency precomputed radiance transfer using spherical radial basis functions and clustered tensor approximation

ACM SIGGRAPH 2006 Research posters on - SIGGRAPH '06 ◽

10.1145/1179352.1141981 ◽

2006 ◽

Cited By ~ 11

Author(s):

Yu-Ting Tsai ◽

Zen-Chung Shih

Keyword(s):

Radial Basis Functions ◽

Basis Functions ◽

Radial Basis ◽

Spherical Radial Basis Functions ◽

Tensor Approximation ◽

Precomputed Radiance Transfer

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Centimeter Precision Geoid Model for Jeddah Region (Saudi Arabia)

Remote Sensing ◽

10.3390/rs12122066 ◽

2020 ◽

Vol 12 (12) ◽

pp. 2066

Author(s):

Alessandra Borghi ◽

Riccardo Barzaghi ◽

Omar Al-Bayari ◽

Suhail Al Madani

Keyword(s):

Gravity Field ◽

Ocean Circulation ◽

Gravity Data ◽

Independent Set ◽

Geoid Undulation ◽

Height Anomaly ◽

Geoid Model ◽

Satellite Gravity ◽

Earth’S Gravity Field ◽

Long Wavelength

In 2014, the Jeddah Municipality made a call for an estimate of a centimetric precision geoid model to be used for engineering and surveying applications, because the regional geoid model available at that time did not reach a sufficient precision. A project was set up to this end and dedicated sets of gravity and Global Positioning System (GPS)/levelling data were acquired in the framework of this project. In this paper, a thorough analysis of these newly acquired data and of the last available Global Gravity Field Models (GGMs) has been done in order to obtain a geoid undulation estimate with the prescribed precision. In the framework of the Remove–Compute–Restore (RCR) approach, the collocation method was used to obtain the height anomaly estimation that was then converted to geoid undulation. The remove and restore steps of the RCR approach were based on GGMs, derived from the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) and Gravity Recovery and Climate Experiment (GRACE) dedicated gravity satellite missions, which were used to improve the long wavelength components of the Earth’s gravity field. Furthermore, two different quasi-geoid collocation estimates were computed, based on gravity data only and on gravity plus GPS/levelling data (the so-called hybrid estimate). The best solutions were obtained with the hybrid geoid estimate. This was tested by comparison with an independent set of GPS/levelling geoid undulations that were not included in the computed solutions. By these tests, the precision of the hybrid geoid is estimated to be 3.7 cm. This precision proved to be better, by a factor of two, than the corresponding one estimated from the pure gravimetric geoid. This project has been also useful to verify the importance and reliability of GGMs developed from the last satellite gravity missions (GOCE and GRACE) that have significantly improved our knowledge of the long wavelength components of the Earth’s gravity field, especially in areas with poor coverage of terrestrial gravity data. In fact, the geoid models based on satellite-only GGMs proved to have a better performance, despite the lower spatial resolution with respect to high-resolution models (i.e., Earth Gravitational Model 2008 (EGM2008)).

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A Model for the Angular Distribution of Sky Radiance

Journal of Solar Energy Engineering ◽

10.1115/1.3266154 ◽

1980 ◽

Vol 102 (3) ◽

pp. 196-202 ◽

Cited By ~ 34

Author(s):

F. C. Hooper ◽

A. P. Brunger

Keyword(s):

Continuous Distribution ◽

Total Solar Radiation ◽

Diffuse Component ◽

Clear Sky ◽

Solar Radiation Incident ◽

The Mean ◽

Rms Error ◽

Sky Radiance ◽

Sky Conditions ◽

Overcast Sky

A flexible mathematical model is introduced which describes the radiance of the dome of the sky under various conditions. This three-component continuous distribution (TCCD) model is compounded by the superposition of three separate terms, isotropic, circumsolar and horizon-brightening factors, each representing the contribution of a distinguishable sky characteristic. In use, a particular sky condition is characterized by the values of the coefficients of each of these three terms, defining the distribution of the total diffuse component. The TCCD model has been demonstrated to fit both the normalized clear sky data and the normalized overcast sky data with an RMS error of about ten percent of the mean overall sky radiance. By extension the model could describe variable or partly clouded sky conditions. The model will permit improvement in the prediction of the total solar radiation incident upon a surface of given tilt and orientation, such as that of a solar collector.

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