A Priori Gradients in the Analysis of Space Geodetic Observations
We introduce a static a priori gradient model (APG) based on a spherical harmonic expansion up to degree and order nine to describe the azimuthal asymmetry of tropospheric delays. APG is determined from climatology data of the European Centre for Medium-R
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J. Bo¨hm, L. Urquhart, P. Steigenberger, R. Heinkelmann, V. Nafisi, and H. Schuh
Abstract
We introduce a static a priori gradient model (APG) based on a spherical harmonic expansion up to degree and order nine to describe the azimuthal asymmetry of tropospheric delays. APG is determined from climatology data of the European Centre for MediumRange Weather Forecasts (ECMWF), and the refined model can be used in the analysis of observations from Global Navigation Satellite Systems (GNSS) and Very Long Baseline Interferometry (VLBI). Comparisons reveal that gradients estimated in GNSS analysis are mostly smaller than those provided by APG. This difference is also confirmed by station and source coordinate changes if APG is used in GNSS and VLBI analysis. Keywords
Tropospheric delay Tropospheric gradients VLBI GNSS APG
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Introduction
Azimuthal asymmetry of troposphere delays has to be taken into account in the analysis of space geodetic observations, e.g. from Global Navigation Satellite Systems (GNSS) or Very Long Baseline Interferometry (VLBI). This asymmetry can be due to systematic effects, e.g., a north–south oriented
gradient (see Fig. 17.1) is due to the larger extension of the troposphere above the equator, or due to random effects, like any change of weather patterns. Typically, north and east gradients, Gn and Ge (Eq. 17.1), are estimated with a resolution of 2–24 h to account for this asymmetry. Based on Davis et al. (1993) who set up a gradient model for the wet refractivity, MacMillan (1995) proposed to use DLða; eÞ ¼ DL0 ðeÞþ
J. Bo¨hm H. Schuh (*) Vienna University of Technology, Gußhausstraße 27-29, 1040 Vienna, Austria e-mail: [email protected]; [email protected] L. Urquhart University of New Brunswick, Fredericton, Canada P. Steigenberger Technische Universita¨t Mu¨nchen, Munich, Germany R. Heinkelmann Deutsches Geoda¨tisches Forschungsinstitut, Munich, Germany V. Nafisi Vienna University of Technology, Gußhausstraße 27-29, 1040 Vienna, Austria
þ mf ðeÞ cotðeÞ ½Gn cosðaÞ þ Ge sinðaÞ
(17.1)
to describe the troposphere delay DL(a,e) at azimuth a and elevation e, where DL0 denotes the symmetric part of the delay (Petit and Luzum 2010), and mf the mapping function. Usually, the hydrostatic mapping function is applied in the analysis of space geodetic observations. Chen and Herring (1997) proposed the model DLða; eÞ ¼ DL0 ðeÞþ 1 ½Gn cosðaÞ þ Ge sinðaÞ þ sinðeÞ tanðeÞ þ C
(17.2)
University of Tehran, Tehran, Iran University of Isfahan, Isfahan, Iran Z. Altamimi and X. Collilieux (eds.), Reference Frames for Applications in Geosciences, International Association of Geodesy Symposia 138, DOI 10.1007/978-3-642-32998-2_17, # Springer-Verlag Berlin Heidelberg 2013
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Fig. 17.1 Upper left (a): 5 5 east–west gradients. Lower left (b): 5 5 north–south gradients. Upper right (c): Spherical harmonic expansion up to degree and order 9 of north–south gradients (APG). Lower right (d): Residuals of north–south gradients, i.e. (b)(c)
an
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