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  • 1.
    Ågren, Jonas
    KTH, Superseded Departments, Infrastructure.
    Regional Geoid Determination Methods for the Era of Satellite Gravimetry: Numerical Investigations Using Synthetic Earth Gravity Models2004Doctoral thesis, monograph (Other scientific)
    Abstract [en]

    It is the purpose of this thesis to investigate different regional geoid determination methods with respect to their feasibility for use with a future GOCE satellite-only Earth Gravity Model (EGM). This includes investigations of various techniques, which involve different approximations, as well as the expected accuracy. Many, but not all, of these tasks are tested by means of Synthetic Earth Gravity Models (SEGMs). The study is limited to remove-compute-restore methods using Helmert condensation and to Sjöberg's combined approach (method with additive corrections).

    First, a number of modifications of Stokes' formula are tested with respect to their compatibility with a GOCE EGM having negligible commission error. It is concluded that the least squares modification method should be preferred.

    Next, two new point-mass SEGMs are constructed in such a way that the resulting models have degree variances representative for the full and topographically reduced gravity fields, respectively. These SEGMs are then used to test different methods for modified Stokes' integration and downward continuation. It is concluded that the combined method requires dense observations, obtained from the given surface anomalies by interpolation using a reduction for all known density anomalies, most notably the topography. Examples of other conclusions are that the downward continuation method of Sjöberg (2003a) performs well numerically.

    To be able to test topographic corrections, another SEGM is constructed starting from the reduced point-mass model, to which the topography, bathymetry and isostatic compensation are added. This model, which is called the Nordic SEGM, is then applied to test one strict and one more approximate approach to Helmert's condensation. One conclusion here is that Helmert's 1st method with the condensation layer 21 km below sea level should be preferred to Helmert's 2nd condensation strategy.

    The thesis ends with a number of investigations of Sjöberg's combined approach to geoid determination, which include tests using the Nordic SEGM. It is concluded that the method works well in practice for a region like Scandinavia. It is finally shown how the combined strategy may preferably be used to estimate height anomalies directly.

  • 2.
    Ågren, Jonas
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics. Lantmäteriet Swedish Mapping, Sweden.
    Engberg, L. E.
    Alm, L.
    Dahlström, F.
    Engfeldt, A.
    Lidberg, M.
    Improving the Swedish quasigeoid by gravity observations on the ice of Lake Vänern2014In: International Association of Geodesy Symposia, 2014, p. 171-177Conference paper (Refereed)
    Abstract [en]

    One of the key activities in Geodesy 2010, the Swedish strategic plan for geodetic activities during the period 2011–2020, is the restoration of the gravity network and data in order to improve the accuracy of the national quasigeoid model. One weak point has been that very few gravity observations have been available over Lake Vänern, Sweden’s largest lake. During the extremely cold winters 2010 and 2011, the ice became sufficiently thick to make ice observation of gravity. The main purpose of this paper is to present the 2011 ice gravity campaign, summarise the experiences made and investigate how much the new ice observations improve the computed quasigeoid model in the area. This is investigated under the assumption that a modern Earth Gravitational Model based on GRACE and GOCE is used. It is found that new ice measurements improve the quasigeoid with a RMS of about 2–3 cm in and around the lake with a maximum improvement of 7 cm.

  • 3.
    Ågren, Jonas
    et al.
    National Land Survey of Sweden.
    Kiamehr, Ramin
    KTH, School of Architecture and the Built Environment (ABE), Transport and Economics (closed 20110301), Geodesy (closed 20110301).
    Sjöberg, Lars Erik
    KTH, School of Architecture and the Built Environment (ABE), Transport and Economics (closed 20110301), Geodesy (closed 20110301).
    Numerical comparison of two strategies for geoid and quasi geoid determination over Sweden2007Conference paper (Refereed)
  • 4.
    Ågren, Jonas
    et al.
    Lantmäteriet (National Land Survey).
    Kiamehr, Ramin
    KTH, School of Architecture and the Built Environment (ABE), Transport and Economics (closed 20110301), Geodesy (closed 20110301).
    Sjöberg, Lars Erik
    KTH, School of Architecture and the Built Environment (ABE), Transport and Economics (closed 20110301), Geodesy (closed 20110301).
    Progress in the determination of a gravimetric quasigeoid model over Sweden2006Conference paper (Refereed)
    Abstract [en]

    One alternative to the traditional remove-compute-restore procedure that has hitherto been used to compute the Nordic geoid is to use the least squares modification method with additive corrections. This technique, which has been developed at the Royal Institute of Technology (KTH) in Stockholm, includes the least squares kernel modification together with topographic, downward continuation, atmospheric and ellipsoidal corrections.This paper presents the most recent results from an on-going joint project between KTH and Lantmäteriet (National Land Survey of Sweden), whose main purpose is to evaluate the KTH approach numerically and to compute a gravimetric quasigeoid model for Sweden. The work should also be viewed as being conducted under the umbrella of the working group for geoid determination of the Nordic Geodetic Commission (NKG). The evaluation is made using 108 high quality GPS/levelling height anomalies covering the major parts of Sweden except for the mountainous areas to the North West. After a 4-parameter fit, the most promising attempt achieves a RMS value for the residuals of 17 mm, which should be compared to the 28 mm RMS reached by the NKG 2004 model. It is concluded that the least squares modification method with additive corrections is a promising alternative for the future.

  • 5. Ågren, Jonas
    et al.
    Kiamehr, Ramin
    Zanjan University.
    Sjöberg, Lars Erik
    KTH, School of Architecture and the Built Environment (ABE), Transport and Economics (closed 20110301), Geodesy (closed 20110301).
    The new gravimetric quasigeoid model KTH08 over Sweden2009In: Journal of Applied Geodesy, ISSN 1862-9024, Vol. 3, no 3, p. 143-153Article in journal (Refereed)
    Abstract [en]

    The least squares modification of Stokes formula has been developed in a series of papers published in Journal of Geodesy between 1984 and 2008. It consists of a least squares (stochastic) Stokes kernel modification with additive corrections for the topography, downward continuation, the atmosphere and the ellipsoidal shape of the Earth. The method, developed at the Royal Institute of Technology (KTH) will here be denoted by the abbreviated name the KTH method.

    This paper presents the computational results of a new gravimetric quasigeoid model over Sweden (the KTH08 model) by employing the KTH method. Traditionally the Nordic Geodetic Commission (NKG) has computed gravimetric quasigeoid models over Sweden and other Nordic countries; the latest model being NKG 2004. Another aim of this paper is therefore to compare KTH08 and NKG 2004 quasigeoid models and to evaluate their accuracies using GNSS/levelling height anomalies. The rms fit of KTH08 in 196 GNSS data points distributed over Sweden by using a 1(4)-parameter transformation is 22 (20) mm. It is concluded that KTH08 is a significant step forward compared to NKG 2004.

  • 6.
    Ågren, Jonas
    et al.
    National Land Survey of Sweden.
    Kiamehr, Ramin
    KTH, School of Architecture and the Built Environment (ABE), Transport and Economics (closed 20110301), Geodesy (closed 20110301).
    Sjöberg, Lars Erik
    KTH, School of Architecture and the Built Environment (ABE), Transport and Economics (closed 20110301), Geodesy (closed 20110301).
    The Swedish geoid as evaluated by the method of least-squares modification with additive corrections2006Conference paper (Refereed)
  • 7.
    Ågren, Jonas
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    Errors in geoid and quasigeoid models as propagated from systematic uncertainties in the Digital Elevation Model2013Conference paper (Refereed)
  • 8.
    Ågren, Jonas
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning. Lantmäteriet, The Swedish Mapping, Cadastre and Registry Authority, Sweden .
    Sjöberg, Lars E.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Satellite Positioning.
    Investigation of gravity data requirements for a 5 mm-quasigeoid model over Sweden2014In: International Association of Geodesy Symposia, 2014, Vol. 141, p. 143-150Conference paper (Refereed)
    Abstract [en]

    When GNSS height determination improves in the future, users will ask for increasingly better geoid models. It is not unlikely that a standard error of 5 mm will more or less be required in a couple of years. The main purpose of this paper is to investigate the gravity data requirements to compute a Swedish gravimetric quasigeoid model to that order. The propagation of errors in the terrestrial gravity observations and the Earth Gravitational Model (EGM) are studied using both variance-covariance analysis in the spectral domain and least squares collocation. These errors are also checked by computing a new gravimetric quasigeoid model and comparing it with GNSS/levelling height anomalies. It is concluded that it will be possible to compute a 5 mm model over Sweden in the case that the gravity data set is updated to fulfil the following requirements: the resolution should be at least 5 km and there should be no data gaps nearby. Finally, the standard errors of the uncorrelated and correlated gravity anomaly noises should be below 0.5 and 0.1 mGal, respectively.

  • 9.
    Ågren, Jonas
    et al.
    KTH, Superseded Departments, Infrastructure.
    Sjöberg, Lars Erik
    KTH, Superseded Departments, Infrastructure.
    Comparison of some methods for modifying stokes' formula in the GOCE ERA2004Conference paper (Refereed)
    Abstract [en]

    The dedicated satellite gravity mission GOCE will drastically improve our knowledge of the long to medium wavelengths of the Earth's gravity field. In order to determine the finest details in regional geoid determination, however, we still have to utilise gravity data. It is the purpose of this paper to study three modifications of Stokes' formula numerically, using error propagations with simulated standard errors for the GOCE potential coefficients. The methods tested are the standard remove-compute-restore, the least squares, and the low-degree GOCE-only modifications. In the latter technique it is required that only GOCE information must influence the determination of the lowest degrees. It is concluded that of the modifications tested, the least squares method is most suitable to be used with a GOCE satellite-only model. This is the case also when pessimistic weights are used for the gravity anomalies. The main fault with the standard remove-compute-restore method is its sensitivity to long-wavelength errors in the gravity anomalies, while a very large truncation error is the most serious problem for the low-degree GOCE-only technique.

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