Abstract:One of the limiting factors in the determination of gravity field solutions is the spatial sampling. Especially during phases, when the satellite repeats its own track after a short time, the spatial resolution will be limited. The Nyquist rule-of-thumb for mapping geopotential functions of a planet, also referred to as the Colombo-Nyquist rule-ofthumb, provides a limit for the maximum achievable degree of a spherical harmonic development for repeat orbits. We show in this paper that this rule is too conservat… Show more
“…1 (bottom). The density of the ground tracks of the satellites directly determines the achievable spatial and spectral resolution of the derived monthly gravity field (Weigelt et al 2013;Klokočník et al 2015 Fig. 1 GRACE monthly gravity fields available for this study (top; dark blue color indicates missing monthly gravity fields) and the maximum longitudinal spacings in the ground track of the GRACE-A satellite (bottom)…”
Section: Database Of Grace Monthly Gravity Fieldsmentioning
We combine the publicly available GRACE monthly gravity field time series to produce gravity fields with reduced systematic errors. We first compare the monthly gravity fields in the spatial domain in terms of signal and noise. Then, we combine the individual gravity fields with comparable signal content, but diverse noise characteristics. We test five different weighting schemes: equal weights, non-iterative coefficient-wise, order-wise, or field-wise weights, and iterative field-wise weights applying variance component estimation (VCE). The combined solutions are evaluated in terms of signal and noise in the spectral and spatial domains. Compared to the individual contributions, they in general show lower noise. In case the noise characteristics of the individual solutions differ significantly, the weighted means are less noisy, compared to the arithmetic mean: The non-seasonal variability over the oceans is reduced by up to 7.7% and the root mean square (RMS) of the residuals of mass change estimates within Antarctic drainage basins is reduced by 18.1% on average. The field-wise weighting schemes in general show better performance, compared to the order-or coefficient-wise weighting schemes. The combination of the full set of considered time series results in lower noise levels, compared to the combination of a subset consisting of the official GRACE Science Data System gravity fields only: The RMS of coefficient-wise anomalies is smaller by up to 22.4% and the non-seasonal variability over the oceans by 25.4%. This study was performed in the frame of the European Gravity Service for Improved Emergency Management (EGSIEM; http://www.egsiem.eu) project. The gravity fields provided by the EGSIEM scientific combination service (ftp://ftp.aiub.unibe.ch/EGSIEM/) are combined, based on the weights derived by VCE as described in this article.
“…1 (bottom). The density of the ground tracks of the satellites directly determines the achievable spatial and spectral resolution of the derived monthly gravity field (Weigelt et al 2013;Klokočník et al 2015 Fig. 1 GRACE monthly gravity fields available for this study (top; dark blue color indicates missing monthly gravity fields) and the maximum longitudinal spacings in the ground track of the GRACE-A satellite (bottom)…”
Section: Database Of Grace Monthly Gravity Fieldsmentioning
We combine the publicly available GRACE monthly gravity field time series to produce gravity fields with reduced systematic errors. We first compare the monthly gravity fields in the spatial domain in terms of signal and noise. Then, we combine the individual gravity fields with comparable signal content, but diverse noise characteristics. We test five different weighting schemes: equal weights, non-iterative coefficient-wise, order-wise, or field-wise weights, and iterative field-wise weights applying variance component estimation (VCE). The combined solutions are evaluated in terms of signal and noise in the spectral and spatial domains. Compared to the individual contributions, they in general show lower noise. In case the noise characteristics of the individual solutions differ significantly, the weighted means are less noisy, compared to the arithmetic mean: The non-seasonal variability over the oceans is reduced by up to 7.7% and the root mean square (RMS) of the residuals of mass change estimates within Antarctic drainage basins is reduced by 18.1% on average. The field-wise weighting schemes in general show better performance, compared to the order-or coefficient-wise weighting schemes. The combination of the full set of considered time series results in lower noise levels, compared to the combination of a subset consisting of the official GRACE Science Data System gravity fields only: The RMS of coefficient-wise anomalies is smaller by up to 22.4% and the non-seasonal variability over the oceans by 25.4%. This study was performed in the frame of the European Gravity Service for Improved Emergency Management (EGSIEM; http://www.egsiem.eu) project. The gravity fields provided by the EGSIEM scientific combination service (ftp://ftp.aiub.unibe.ch/EGSIEM/) are combined, based on the weights derived by VCE as described in this article.
“…The practical experience of gravity field recovery from various authors, however, does not support this rule (Weigelt et al, 2009(Weigelt et al, , 2013Visser et al, 2012 and many experiments performed in the Astronomical Institute, Ondřejov, at NOAA, Silver Spring and in Faculté des Sciences, de la Technologie et de la Communication). The rule looks too stringent.…”
Section: Introduction Motivation and Aim Of This Workmentioning
confidence: 71%
“…While these rules are solely based on the pattern of equator crossings (Wagner et al, 2006;Klokočník et al, 2008;Weigelt et al, 2009Weigelt et al, , 2013, the present work takes into account a possible latitude (and inclination) dependence. The authors here analyze the actual ground track patterns of CHAMP, GRACE and GOCE over all their available latitudes and then derive a more general rule for M max .…”
Section: Introduction Motivation and Aim Of This Workmentioning
confidence: 99%
“…The problem of spatial sampling has been studied repeatedly (Wagner et al, 2006;Klokočník et al, 2008;Weigelt et al, 2009) and simple rules have been derived to limit the maximum order for unconstrained solutions (inversions) for the gravity field parameters or their variations from observations of a single satellite. Here we work with the latest rule from Weigelt et al (2013) which distinguishes the maximum attainable order according to the parity of the two parameters defining the repeat orbit or orbital resonance, b the number of nodal satellite's revolutions in a nodal days (a, b co-prime integers, the ratio b/a irreducible). This rule, that the resolvable order (in a repeat near polar orbit) should be b for odd parity (b À a) and b/2 for even parity (b À a) orbits, arose from the discovery that the number of distinct and equally spaced equatorial crossings (ascending and descending passes) for odd parity (b À a) is 2b while for even parity orbits it is only b.…”
“…The quality of the gravity field models is not necessarily characterized by their spatial resolution, which is limited by the density of the ground track pattern during the corresponding time intervals (Weigelt et al, 2013), but by the error and signal content of the spherical harmonic coefficients (in the spectral domain), or equivalently, the grid values of geoid heights or quantities derived therefrom (in the spatial domain).…”
Abstract. Gravity field parameters are usually determined from observations of the GRACE satellite mission together with arc-specific parameters in a generalized orbit determination process. When separating the estimation of gravity field parameters from the determination of the satellites' orbits, correlations between orbit parameters and gravity field coefficients are ignored and the latter parameters are biased towards the a priori force model. We are thus confronted with a kind of hidden regularization.To decipher the underlying mechanisms, the Celestial Mechanics Approach is complemented by tools to modify the impact of the pseudo-stochastic arc-specific parameters on the normal equations level and to efficiently generate ensembles of solutions. By introducing a time variable a priori model and solving for hourly pseudo-stochastic accelerations, a significant reduction of noisy striping in the monthly solutions can be achieved. Setting up more frequent pseudo-stochastic parameters results in a further reduction of the noise, but also in a notable damping of the observed geophysical signals.To quantify the effect of the a priori model on the monthly solutions, the process of fixing the orbit parameters is replaced by an equivalent introduction of special pseudo-observations, i.e., by explicit regularization. The contribution of the thereby introduced a priori information is determined by a contribution analysis. The presented mechanism is valid universally. It may be used to separate any subset of parameters by pseudo-observations of a special design and to quantify the damage imposed on the solution.
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