scholarly journals On the topographic bias and density distribution in modelling the geoid and orthometric heights

2018 ◽  
Vol 8 (1) ◽  
pp. 30-33 ◽  
Author(s):  
Lars E. Sjöberg
Keyword(s):  
Density Distribution ◽  
Mass Distribution ◽  
Geoid Height ◽  
Analytical Continuation ◽  
Orthometric Height ◽  
Gravimetric Geoid ◽  
Mountainous Regions ◽  
Imprecise Information ◽  
Topographic Bias ◽  
The Difference

Abstract It is well known that the success in precise determinations of the gravimetric geoid height (N) and the orthometric height (H) rely on the knowledge of the topographic mass distribution. We show that the residual topographic bias due to an imprecise information on the topographic density is practically the same for N and H, but with opposite signs. This result is demonstrated both for the Helmert orthometric height and for a more precise orthometric height derived by analytical continuation of the external geopotential to the geoid. This result leads to the conclusion that precise gravimetric geoid heights cannot be validated by GNSS-levelling geoid heights in mountainous regions for the errors caused by the incorrect modelling of the topographic mass distribution, because this uncertainty is hidden in the difference between the two geoid estimators.

scholarly journals On the topographic effects by Stokes’ formula

2014 ◽  
Vol 4 (1) ◽  
Author(s):  
L.E. Sjöberg
Keyword(s):  
Gravity Anomaly ◽  
Bouguer Anomaly ◽  
Gravity Anomalies ◽  
Geoid Height ◽  
Topographic Effects ◽  
Gravimetric Geoid ◽  
Bouguer Gravity ◽  
The Third ◽  
Stokes Formula ◽  
The Difference

AbstractTraditional gravimetric geoid determination relies on Stokes’ formula with removal and restoration of the topographic effects. It is shown that this solution is in error of the order of the quasigeoid-to-geoid difference, which is mainly due to incomplete downward continuation (dwc) of gravity from the Earth’s surface to the geoid. A slightly improved estimator, based on the surface Bouguer gravity anomaly, is also biased due to the imperfect harmonic dwc the Bouguer anomaly. Only the third estimator,which uses the (harmonic) surface no-topography gravity anomaly, is consistent with the boundary condition and Stokes’ formula, providing a theoretically correct geoid height. The difference between the Bouguer and no-topography gravity anomalies (on the geoid or in space) is the “secondary indirect topographic effect”, which is a necessary correction in removing all topographic signals.

scholarly journals A numerical test of the topographic bias

2018 ◽  
Vol 8 (1) ◽  
pp. 14-17 ◽  
Author(s):  
L.E. Sjöberg ◽  
M.S.S. Joud
Keyword(s):  
Density Distribution ◽  
Simple Formula ◽  
Numerical Test ◽  
Physical Geodesy ◽  
Gravity Anomalies ◽  
Analytical Continuation ◽  
External Potential ◽  
The Earth ◽  
Topographic Bias ◽  
The Common

Abstract In 1962 A. Bjerhammar introduced the method of analytical continuation in physical geodesy, implying that surface gravity anomalies are downward continued into the topographic masses down to an internal sphere (the Bjerhammar sphere). The method also includes analytical upward continuation of the potential to the surface of the Earth to obtain the quasigeoid. One can show that also the common remove-compute-restore technique for geoid determination includes an analytical continuation as long as the complete density distribution of the topography is not known. The analytical continuation implies that the downward continued gravity anomaly and/or potential are/is in error by the so-called topographic bias, which was postulated by a simple formula of L E Sjöberg in 2007. Here we will numerically test the postulated formula by comparing it with the bias obtained by analytical downward continuation of the external potential of a homogeneous ellipsoid to an inner sphere. The result shows that the postulated formula holds: At the equator of the ellipsoid, where the external potential is downward continued 21 km, the computed and postulated topographic biases agree to less than a millimetre (when the potential is scaled to the unit of metre).

scholarly journals The topographic bias in gravimetric geoid determination revisited

2019 ◽  
Vol 9 (1) ◽  
pp. 59-64
Author(s):  
Lars E. Sjöberg
Keyword(s):  
Density Distribution ◽  
Geoid Determination ◽  
The Other ◽  
Harmonic Potential ◽  
Gravimetric Geoid ◽  
Potential Bias ◽  
Computation Point ◽  
Density Distributions ◽  
Topographic Bias ◽  
Topographic Potential

Abstract The topographic potential bias at geoid level is the error of the analytically continued geopotential from or above the Earth’s surface to the geoid. We show that the topographic potential can be expressed as the sum of two Bouguer shell components, where the density distribution of one is spherical symmetric and the other is harmonic at any point along the normal to a sphere through the computation point. As a harmonic potential does not affect the bias, the resulting topographic bias is that of the first component, i.e. the spherical symmetric Bouguer shell. This implies that the so-called terrain potential is not likely to contribute significantly to the bias. We present three examples of the geoid bias for different topographic density distributions.

scholarly journals Comparing two years of Saharan dust source activation obtained by regional modeling and satellite observations

2012 ◽  
Vol 12 (10) ◽  
pp. 27667-27691
Author(s):  
I. Tegen ◽  
K. Schepanski ◽  
B. Heinold
Keyword(s):  
Regional Scale ◽  
Dust Emission ◽  
Saharan Dust ◽  
Strong Increase ◽  
Dust Source ◽  
Low Level ◽  
Mountainous Regions ◽  
Emission Fluxes ◽  
Low Level Jets ◽  
The Difference

Abstract. A regional-scale dust model is used to simulate Saharan dust emissions and atmospheric distributions in the years 2007 and 2008. The model results are compared to dust source activation events compiled from infrared dust index imagery from the geostationary Meteosat Second Generation (MSG) satellite. The observed morning maximum in dust source activation frequencies indicates that the breakdown of nocturnal low-level jets is responsible for a considerable number of dust source activation events in the Sahara. The comparison shows that the time of the day of the onset of dust emission is delayed in the model compared to the observations. Also, the simulated number of dust emission events associated with nocturnal low level jets in mountainous regions is underestimated in the model. The MSG dust index observations indicate a strong increase in dust source activation frequencies in the year 2008 compared to 2007, the difference between the two years is less pronounced in the model. The quantitative comparison of simulated dust optical thicknesses with observations at stations of the sunphotometer network AERONET shows, however, good agreement for both years, indicating that the number of observed dust activation events is only of limited use for estimating actual dust emission fluxes in the Sahara.

scholarly journals Comparing two years of Saharan dust source activation obtained by regional modelling and satellite observations

2013 ◽  
Vol 13 (5) ◽  
pp. 2381-2390 ◽  
Author(s):  
I. Tegen ◽  
K. Schepanski ◽  
B. Heinold
Keyword(s):  
Regional Scale ◽  
Dust Emission ◽  
Saharan Dust ◽  
Strong Increase ◽  
Regional Modelling ◽  
Dust Source ◽  
Low Level ◽  
Mountainous Regions ◽  
Low Level Jets ◽  
The Difference

Abstract. A regional-scale dust model is used to simulate Saharan dust emissions and atmospheric distributions in the years 2007 and 2008. The model results are compared to dust source activation events compiled from infrared dust index imagery from the geostationary Meteosat Second Generation (MSG) satellite. The observed morning maximum in dust source activation frequencies indicates that the breakdown of nocturnal low level jets is an important mechanism for dust source activation in the Sahara. The comparison shows that the time of the day of the onset of dust emission is delayed in the model compared to the observations. Also, the simulated number of dust emission events associated with nocturnal low level jets in mountainous regions is underestimated in the model. The MSG dust index observations indicate a strong increase in dust source activation frequencies in the year 2008 compared to 2007. The difference between the two years is less pronounced in the model. Observations of dust optical thickness, e.g. at stations of the sunphotometer network AERONET, do not show such increase, in agreement with the model results. This indicates that the number of observed dust activation events is only of limited use for estimating actual dust emission fluxes in the Sahara. The ability to reproduce interannual variability of Saharan dust with models remains an important challenge for understanding the controls of the atmospheric dust load.

TGFbeta1 induces a cell-cycle-dependent increase in motility of epithelial cells

1999 ◽  
Vol 112 (4) ◽  
pp. 447-454 ◽  
Author(s):  
D. Zicha ◽  
E. Genot ◽  
G.A. Dunn ◽  
I.M. Kramer
Keyword(s):  
Cell Cycle ◽  
Mass Distribution ◽  
Transforming Growth Factor Beta ◽  
Time Course ◽  
Transforming Growth Factor ◽  
Interference Microscopy ◽  
Response To Treatment ◽  
Gradual Onset ◽  
The Difference ◽  
Cycle Dependent

We have previously shown that addition of type 1 transforming growth factor-beta (TGFbeta1) to an exponentially growing population of mink lung CCl64 cells increases their average intermitotic time from 14.4 to 20.3 hours, predominantly by extending G1 from 7.5 to 13.5 hours. Here we have used the DRIMAPS system (digitally recorded interference microscopy with automatic phase-shifting) for obtaining data on cellular mass distribution, cell motility and morphology. We found no significant change in the cells' rate of mass increase following TGFbeta1 treatment, which implies that the treated cells attained a higher mass during their extended cell cycle and this was confirmed by direct measurement of cell size. However, the cells showed a dramatic motile response to treatment: TGFbeta1-treated cells had a significantly higher time-averaged speed of 36.2 microm hour-1 compared to 14.5 microm hour-1 for the control cells. The time course of the response was gradual, reaching a maximum mean speed of 52.6 microm hour-1 after 15 hours exposure. We found that the gradual onset of the response was probably not due to a slow accumulation of a secondary factor but because cells were dividing throughout the experiment and most of the response to TGFbeta1 occurred only after the first cell division in its presence. Thus, taking only those cells that had not yet divided, the time-averaged speed of treated cells (26.1 micrometer hour-1) was only moderately higher than that of untreated cells (14.9 micrometer hour-1) whereas, for those cells that had divided, the difference in speed between treated cells (45.1 micrometer hour-1) and untreated cells (14.1 microm hour-1) was much greater. Increased speed was a consequence of enhanced protrusion and retraction of the cell margin coupled with an increase in cell polarity. TGFbeta1 also increased the mean spreading of the cells, measured as area-to-mass ratio, from 3.2 to 4.4 micrometer2 pg-1, and the intracellular mass distribution became more asymmetric. The observations indicate that a G2 signal may be necessary to reach maximal motility in the presence of TGFbeta1.

scholarly journals Can We Measure H0 with VLBI Observations of Gravitational Images?

1988 ◽  
Vol 129 ◽  
pp. 207-208
Author(s):  
E. E. Falco ◽  
M. V. Gorenstein ◽  
I. I. Shapiro
Keyword(s):  
Time Delay ◽  
Mass Distribution ◽  
Velocity Dispersion ◽  
Gravitational Lens ◽  
Lens System ◽  
Relative Time ◽  
Surface Mass ◽  
A Value ◽  
Vlbi Observations ◽  
The Difference

We have used the relative positions and magnifications of the A and B images in the gravitational lens system 0957+561, obtained from VLBI observations, to constrain a model for the surface mass distribution of the lens. With measurements of the difference ΔτBA in propagation times associated with A and B (the “relative time delay”) and of the velocity dispersion of the main lensing galaxy, both to be obtained, our model will yield a value for H0 with an uncertainty of ∼ 20% due mainly to uncertainties in our assumptions.

scholarly journals A Numerical Study of the Analytical Downward Continuation Error in Geoid Computation by EGM08

2011 ◽  
Vol 1 (1) ◽  
pp. 2-8 ◽  
Author(s):  
L. Sjöberg ◽  
M. Bagherbandi
Keyword(s):  
Numerical Study ◽  
Analytical Continuation ◽  
Downward Continuation ◽  
The Pacific ◽  
Topographic Bias ◽  
Significant Difference ◽  
Topographic Potential ◽  
Zero Degree ◽  
High Degree ◽  
Geoid Computation

A Numerical Study of the Analytical Downward Continuation Error in Geoid Computation by EGM08Today the geoid can be conveniently determined by a set of high-degree spherical harmonics, such as EGM08 with a resolution of about 5'. However, such a series will be biased when applied to the continental geoid inside the topographic masses. This error we call the analytical downward continuation (DWC) error, which is closely related with the so-called topographic potential bias. However, while the former error is the result of both analytical continuation of the potential inside the topographic masses and truncation of a series, the latter is only the effect of analytical continuation.This study compares the two errors for EGM08, complete to degree 2160. The result shows that the topographic bias ranges from 0 at sea level to 5.15 m in the Himalayas region, while the DWC error ranges from -0.08 m in the Pacific to 5.30 m in the Himalayas. The zero-degree effects of the two are the same (5.3 cm), while the rms of the first degree errors are both 0.3 cm. For higher degrees the power of the topographic bias is slightly larger than that for the DWC error, and the corresponding global rms values reaches 25.6 and 25.3 cm, respectively, at nmax=2160. The largest difference (20.5 cm) was found in the Himalayas. In most cases the DWC error agrees fairly well with the topographic bias, but there is a significant difference in high mountains. The global rms difference of the two errors clearly indicates that the two series diverge, a problem most likely related with the DWC error.

scholarly journals Investigating the Impact of Digital Elevation Models on Sentinel-1 Backscatter and Coherence Observations

2020 ◽  
Vol 12 (18) ◽  
pp. 3016
Author(s):  
Ignacio Borlaf-Mena ◽  
Maurizio Santoro ◽  
Ludovic Villard ◽  
Ovidiu Badea ◽  
Mihai Andrei Tanase
Keyword(s):  
Remote Sensing ◽  
Laser Scanning ◽  
Digital Elevation Models ◽  
Shuttle Radar Topography Mission ◽  
Synthetic Aperture ◽  
Mountainous Regions ◽  
Aerial Laser Scanning ◽  
Digital Elevation ◽  
The Difference ◽  
The Impact

Spaceborne remote sensing can track ecosystems changes thanks to continuous and systematic coverage at short revisit intervals. Active remote sensing from synthetic aperture radar (SAR) sensors allows day and night imaging as they are not affected by cloud cover and solar illumination and can capture unique information about its targets. However, SAR observations are affected by the coupled effect of viewing geometry and terrain topography. The study aims to assess the impact of global digital elevation models (DEMs) on the normalization of Sentinel-1 backscattered intensity and interferometric coherence. For each DEM, we analyzed the difference between orbit tracks, the difference with results obtained with a high-resolution local DEM, and the impact on land cover classification. Tests were carried out at two sites located in mountainous regions in Romania and Spain using the SRTM (Shuttle Radar Topography Mission, 30 m), AW3D (ALOS (Advanced Land Observation Satellite) World 3D, 30 m), TanDEM-X (12.5, 30, 90 m), and Spain national ALS (aerial laser scanning) based DEM (5 m resolution). The TanDEM-X DEM was the global DEM most suitable for topographic normalization, since it provided the smallest differences between orbital tracks, up to 3.5 dB smaller than with other DEMs for peak landform, and 1.4–1.9 dB for pit and valley landforms.

Probing of the Wave Function of Shallow Donors and Acceptors by EPR in SiC Crystals with Changed Isotopic Composition

2005 ◽  
Vol 483-485 ◽  
pp. 507-510
Author(s):  
Marina V. Muzafarova ◽  
Ivan V. Ilyin ◽  
E.N. Mokhov ◽  
P.G. Baranov ◽  
B.Ya. Ber ◽  
...  
Keyword(s):  
Wave Function ◽  
Band Structure ◽  
Isotopic Composition ◽  
Density Distribution ◽  
Spin Density ◽  
Main Part ◽  
Shallow Donor ◽  
Line Broadening ◽  
Electronic Wave Function ◽  
The Difference

The conclusion which is drawn from the EPR line broadening and narrowing of the N shallow donor in an isotope enriched and non-enriched 4H-SiC and 6H-SiC crystals along with previous ENDOR results shows that the spin-density distribution over the C and Si nuclei differs between the 4H-SiC and 6H-SiC polytypes. The main part of the spin density in 4H-SiC is located on the Si sublattice. In contrast, in 6H-SiC the main part of the spin density is located on the C sublattice. An explanation for the difference in the electronic wave function of the N donor in 4HSiC and 6H-SiC can be found in the large difference in the band structure of two polytypes and in the position of the minima in the Brillouin zone.

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