Deflections of the vertical in The Netherlands derived from geodetic astronomical observations

In the period 1997-'99, geodetic astronomical observations were carried out at a number of geodetic stations of the (primary) triangulation network and GPS base network of the Rijksdriehoeksmeting (national geodetic datum). The objective of this project was to determine the deflection of the vertical at these stations in order to verify the gravimetric geoid and the Dutch triangulation network for (systematic) errors. At these geodetic stations, the astronomical latitude and longitude were simultaneous determined using a Zeiss Ni2 pendulum astrolabe (second-order field instrument) and applying the Gauss method, i.e. determining the astronomical latitude and longitude of a station by measuring the time of vertical transit of known stars. A pendulum astrolabe permits the observation of stars at equal altitudes. The orientation of these instruments is assured by a compensator pendulum which keeps the telescope horizontal. The time at which a star crosses the fixed wires of the reticle is visually determined by a permanent observer. In order to record the time, the observer uses a tapping key which is connected to an accurate quartz chronograph. The environmental parameters like temperature, barometric pressure and relative humidity, necessary to correct for variations in the atmospheric refraction, are measured by the observer's secretary using calibrated meteorological instruments.

Since the moments of vertical transit are determined visually, a (systematic) time error is introduced in the measurements due to the inability of the observer to determine the exact instant at which a star crosses the wires of the reticle. In order to determine the influence of this (personal) time error, similar observations were carried out at the beginning and at the end of the program of observations. The 'Sonnenborgh' observatory in Utrecht served as a reference station for these measurements. The astronomical longitude of the 'Sonnenborgh' observatory, with respect to Greenwich, was measured by using a first-order Wild T4 universal theodolite, equipped with an impersonal/self-registering micrometer. It was used as a refined astrolabe and set up on a brick observation pillar on the roof of the main building of the observatory. The telescope of the theodolite was fixed at a constant zenith distance (approximately 30°00'30"). Small variations in the adjusted zenith distance during the observations were recorded by a set of Horrebow-Talcott levels. The observed stars, crossing the field of view at about the centre point, were tracked by the hand-driven self-registering micrometer. Since only known stars located in the neighbourhood of the prime vertical (East-West vertical plane) were measured, the accuracy of obtained astronomical longitude is higher than the accuracy of the simultaneously determined latitude. For this reason, additional measurements were carried out at the 'Sonnenborgh' observatory, using a first-order Kern DKM3-A theodolite and applying the Sterneck method. This method determines the astronomical latitude by measuring the altitude of Polaris and other pole stars as well as the altitudes of known stars close to the southern half of the meridian in order to minimize some significant instrumental errors.

Accurate timekeeping plays a very important part in the determination of the astronomical longitude. In order to relate the measured times of vertical transit to the Universal Coordinated Time (UTC), time signals broadcasted by the German DCF77 transmitter in Mainflingen were recorded during the geodetic astronomical observations. In addition, a radio link was established between the NMi Van Swinden Laboratory (the national institute for standardization) and the 'Sonnenborgh' observatory allowing the comparison of the used quartz chronograph with the four standard caesium atomic clocks of the NMi Van Swinden Laboratory with a precision of a few microseconds.

In the summer and autumn of 1998, geodetic astronomical observations were carried out at six geodetic stations in The Netherlands using the above-mentioned Zeiss Ni2 astrolabe. The instrument sites were chosen as close as possible to the centre of these geodetic stations and were marked by stainless steel survey pins. The plane rectangular coordinates and orthometric heights of these instrument sites were determined by the Dutch Triangulation Service and the Survey Department of the Province of North Brabant in order to reduce the measured latitude and longitude to the centre and to compute the deflection of the vertical.

The deflection of the vertical is at any point of observation the angle between the local vertical and the spheroidal normal and can be resolved into two orthogonal components: the first component, denoted by x, is in the plane of the local meridian, the second component, h, is in the plane of the prime vertical. The local vertical (or plumb-line) is in the direction of the vector sum of the acceleration due to the Earth's gravitational field and the apparent acceleration due to the rotation of the Earth around its axis. In other terms, the vertical is perpendicular to the tangent plane of the equipotential surface of the Earth's gravity field at the point of observation. As a consequence, the deflection of the vertical depends on the actual form of the geoid as brought about by the Earth's irregularities of form and density. It depends also on the definition of the reference ellipsoid on which the geodetic coordinates are reckoned. The deflection of the vertical provides information about the geoidal slope: the direction of the deflection coincides with the direction of the maximum geoidal decline, and the magnitude of the deflection equals that of the gradient of the geoid. If the geographic (or astronomical) coordinates equal the geodetic coordinates, then the geoidal slope is equal to zero and the tangent plane of the geoid is, at this point, parallel to the tangent plane of the geodetic reference spheroid. The figure below (Figure 5) shows in blue the vectors of the deflection of the vertical, with respect to the European reference system ETRS89, supplemented with other geodetic stations in The Netherlands where geodetic astronomical measurements were carried out.

The mean external accuracy (1s) of the measured deflection in latitude (x) and longitude (h) is estimated to be <0".1 for the measurements which were carried out at the 'Sonnenborgh' observatory, 0".2 for the measurements which were carried out at the observatory of Leyden, and about 0".3 for the other geodetic astronomical stations. All astronomical observations are corrected for the polar motion, as published by the International Earth Rotation Service (IERS) in Paris, and refer to the conventional IERS celestial and terrestrial reference systems ICRS and ITRS. The final results are presented in Table 1 and Table 2. Table 1 lists the measured deflections of the vertical (x, h) with respect to the European reference system ETRS89, using GRS80 as reference spheroid, and with respect to the national datum of the Rijksdriehoeksmeting (RD1918). A brief description of the geodetic stations is provided in Table 2.

Table 1. Geodetic astronomical observations.

Table 2. Description of the geodetic stations.

The above described geodetic astronomical survey was carried out by 'De Koepel' foundation, situated at the 'Sonnenborgh' observatory in Utrecht, in collaboration with the Delft University of Technology and the Dutch Triangulation Service and with support of the Royal Netherlands Meteorological Institute (KNMI) and the Survey Department of the Province of North Brabant.

Related geodetic research at 'Sonnenborgh'
In the autumn of 1993, relative gravity measurements were carried out in one of the subterranean vaults of the old rampart 'Sonnenborgh' by the Delft University of Technology. The gravity was measured relative to the primary station 85 Delft using a LaCoste-Romberg gravimeter (model D, no. 59) belonging to the Royal Netherlands Meteorological Institute (KNMI). The orthometric height was determined by students of the University of Profesional Education in Utrecht. The final results are provided in Table 3. The measured gravity refers to the Netherlands Gravity datum 1993 (NEDZWA93), which is consistent with ISGN71, and the orthometric height refers to the Amsterdam Ordnance datum (NAP). The GRS80 normal gravity formula was used for the computation of the Bouguer anomaly and the topographic density was assumed to be 2.67 g/cm³.

Table 3. Gravimetric observations.

References

• Schreutelkamp, F.H., 'Astro-geodesie in Nederland - Controle van de gravimetrische geoïde met stermetingen', Geodesia 39, no. 10, p. 423-429 (1997);
• Schreutelkamp, F.H., G. de Jong en J.P. Hectors, 'Tijdsbepaling en tijdseinen', RB Electronica 67, no. 9, p. 26-29 (1998);
• Schreutelkamp, F.H., G. de Jong en J.P. Hectors, 'Hoe nauwkeurig zijn de tijdseinen?', Zenit 26, no. 1, p. 18-23 (1999);
• Schreutelkamp, F.H., 'Schietloodafwijkingen bepaald uit geodetisch-astronomische waarnemingen - Nederland dertig meter dichter bij Greenwich', Geodesia 42, no. 4, p. 155-162 (2000);
• Schreutelkamp, F.H., 'Analyse van historische geodetisch-astronomische waarnemingen - Oriëntering van de Bessel-ellipsoïde', Geodesia 42, no. 5, p. 203-209 (2000);
• Schreutelkamp, F.H., 'Is de Bessel-ellipsoïde scheef georiënteerd? - De rotaties in de transformatie tussen RD en ETRS verklaard', Geodesia 42, no. 6, p. 275-281 (2000);
• Schreutelkamp, F.H., 'De geoïde voor Nederland astrometrisch getoetst', Geodesia 43, no. 9, p. 404-411 (2001) (PDF file).
• Crombaghs, M.J.E., en A.J.T. de Bruijne, NLGEO2004 - Een nieuw geoïdemodel voor Nederland, Report AGI-GAP-2004-25, Adviesdienst Geo-informatie en ICT van Rijkswaterstaat, Delft (2004).

Recommend Internet sites

• Investigation of the Ni-2 astrolabe  (in Dutch)
• Bouguer gravity anomaly map of The Netherlands
• Geomagnetic observations in The Netherlands  (in Dutch)
• The geomagnetic field revealed  (paper in Dutch)
• The history of the Prime Meridian - Past and Present
• Deflections of the vertical in Switzerland
• The transportable digital zenith camera TZK2-D  (in German)
• Co-ordinate transformation between WGS84 and the national datum of the Rijksdriehoeksmeting (RD)  (paper in Dutch)
• Timekeeping in The Netherlands  (in Dutch)
• What time is it?
• Astronomy in The Netherlands

This page is maintained by ing. F.H. Schreutelkamp