Hydrological Influences on the Gravity Variations Recorded at

Hydrological Influences on the Gravity Variations Recorded at Bad Homburg Günter Harnisch, Martina Harnisch formerly Bundesamt für Kartographie und Geodäsie (BKG), Frankfurt a. M. Reinhard Falk Bundesamt für Kartographie und Geodäsie (BKG), Frankfurt a. M. Joint Workshop on Analysis of GGP Data and Environmental Influences Jena, March 27 - 31, 2006

Hydrological Influences on the Gravity Variations at Bad Homburg ● The gravimetric laboratory in the Bad Homburg Castle ● Processing of the gravity data (residual gravity) ● Influences of precipitation ● Groundwater influences and their correction ● Influences of air density variations ● Variation of the station height detected by GPS ● The TT 40 data series 1981 – 1984 ● Results, Conclusions

Bad Homburg v. d. Höhe Bad Homburg at the south-eastern slope of the Taunus Mountains Castle on a local height. White Tower 14 th century (oldest part). Archive wing 1679 - 1686 Gravimetric Laboratory since 1978 in the basement of the archive wing The laboratory is built in an isolated hut in the old “Apple Cellar”, with 2 rooms for AG and SG 1981 - 1984 data series with the TT 40, one of the first superconducting gravimeters Shallow pond about 14. 5 m below the gravimetric laboratory, area of the pond about 11000 m², max. depth 1 m Rough estimation of the gravity effect of the varying water level in the pond. From the viewpoint of AG influence can be neglected (Falk 1995).

Observation Sites around the Gravimeter Schlosskirche GPS 3 Groundwater gauges: ● Schlosskirche (Distance 110 m) ● Meiereiberg (Distance 200 m) ● Seulberg (Outside the figure, distance 3. 5 km) Rain gauge at the Castle Gardener‘s House Rain Gauge GPS antenna, at a wall, about 20 m high Gravimeter in the basement of the archive wing Castle Pond Meiereiberg GWR CD 030

The Groundwater Gauges and some Hydrological Background: 1. Schlosskirche (Distance about 110 m) Highly tensed aquifer in green schist. The strong variations of the groundwater level are caused by the formation of new groundwater in a higher situated area. This process depends on the sesonally varying vegetation. No formation of new groundwater during the vegetation period. No direct influence of precipitation is to be expected Mean groundwater level at 179. 49 m Begin of the data set 5. 2. 2004 2. Meiereiberg (Distance about 200 m) Aquifer also in green schist. No connection to the Schlosskirche aquifer. Influence of precipitation on the groundwater level is to be expected. Mean groundwater level at 171. 57 m Begin of the data set 26. 5. 2004 . 3. Seulberg (Distance about 110 m north-east) Green schist, weekly values since 9. 4. 1951 Mean groundwater level at 171. 801 m Instrumentation (Nr. 1 and 2): SEBA MDS Dipper II, sampling rate 1 hour

Groundwater Nearly the same behavior at the 3 groundwater gauges spread over more than 4 km Distance from the Gravimeter Sampling Rate Amplitude (peak to peak) 110 m 1 Hour (1. 376 ± 0. 006) m 200 m 1 Hour (0. 770 ± 0. 002) m 3. 5 km 1 Week (0. 572 ± 0. 016) m

Influence of Precipitation on the Groundwater Level Bad Homburg, 2004 - 2005 Spring: Influence of precipitation on the groundwater level exists Autumn: Precipitation has no influence on the groundwater level

Influence of Precipitation on the Groundwater Level The Examples show that the influence of precipitation on the groundwater varies with the seasons

Influence of Precipitation on the Groundwater Level Groundwater at the Meiereiberg: ● Amplitude 0. 67 m (Peak to Peak), only 48. 7 % of that at the Schlosskirche ● Influence of precipitation more clearly, as to be expected from the hydrological point of view

Precipitation. Rain Gauge at the Castle Gardener‘s House Modeled gravity effect of precipitation (Crossley u. a. 1998) i-1 Δgi = 2πGρ∑ rj (1 - exp (-(i-j)/τ1)) exp (-(i-j)/τ2) j=1 τ1 describes the infiltration of water into the ground („recharge time constant“) τ2 describes the gradual dry out of the ground („discharge time constant“) Both time constants depend on many physical, hydrological and biological parameters, which otherwise cannot be included in detail in a model for practical use. Other precipitation data are available from Bad Homburg Süd and the Airport Frankfurt a. M.

Influence of Precipitation on the Gravity Residuals Bad Homburg, 2004 - 2005 Modeled gravity effect of rain in relation to the residual gravity of the gravimeter GWR CD 030 Explanation of the residual gravity follows At Bad Homburg the influence of precipitation on the residual gravity is very weak.

Processing the Gravity Data (Residual Gravity) Recorded gravity Known disturbing Influences e. g. air density distribution, hydrological influences Tidal Analysis ● GWR CD 030 (L/U system) ● GGP_ISDC (e. g. corrected minute data) ● 36 WG, including LP, drift model (Tschebyscheff-polynomials) ● Channel 1: local air pressure ● Channel 2: polar motion, δ = 1. 16 Residual Gravity RG 1 Predicted tides (Sa: δ = 1. 16) and the local air pressure effect are subtracted from the gravity observations. Residual Gravity RG 2 Additionally the gravity effect of polar motion is eliminated Estimation of Disturbing Influences e. g. groundwater, precipitation ● Regression analysis ● Amplitude Ratio of long-period waves

Influence of Groundwater on the Residual Gravity Above: Influence included Below: Influence eliminated Groundwater regression coefficient r. GW(L) = 23. 0 nm s-2/m (GW „Schlosskirche“)

Seasonal Variations of the Vertical Air Density Distribution (Simon 2003) Fit of a sinusoidal wave with annual period (365. 25 days, red line) Amplitude (Peak to Peak) at Bad Homburg: (11. 23 ± 0. 13) nm s-2 The seasonal variations of the vertical air density distribution result in regular gravity variations which have to be considered if effects in the annual range are studied. The amplitudes at Moxa and Wettzell are nearly the same. Differences less than 1 nm s-2

Influence of Groundwater on the Residual Gravity Influence of air density anomalies corrected at first Above: Influence included Below: Influence eliminated Groundwater regression coefficient r. GW(L) = 29. 6 nm s-2/m (GW „Schlosskirche“)

GPS Observations at the Bad Homburg Castle Variations of the vertical component: some millimeters during the first year (red line) Large dispersion of the data points ! Reversed phase to the gravity residuals ? Explanation by thermal expansion of the wall ? Significant phase shift ?

TT 40, Bad Homburg 1981 – 1984 (Richter 1987) Amplitude Factor and Phase Lag of the Polar Motion Constituents Annual Wobble Chandler Wobble Hydrol. Corr. Phase Delta Phase NO 1. 52 29. 05 1. 42 22. 87 YES Results: 1. Groundwater Corrections smooth the Residual Gravity Delta 1. 55 20. 39 1. 51 12. 98 2. Groundwater correction influences mainly the phase values

Results, Conclusions ● The study presented here is the first such attempt at Bad Homburg ● The recorded graviy data are significantly disturbed by hydrological influences ● Groundwater influences are dominant in the long-time (annual) range ● Exact physically based modelling is nearly impossible because many observations and parameters of different kind from a large area had to be included ● Therefore regression models are preferred in which observations (e. g. groundwater) act as indicators, representing different components of the hydrological influences ● Pessimistic view: Hydrological influences as a limiting threshold of accuracy. Outlook ● Processing the data of the upper system of the gravimeter GWR CD 030 ● Continue the studies if more data are available, esp. the Meiereiberg gauge

Acknowledgements We thank - Peter Wolf (BKG Frankfurt), who maintained carefully the gravimeter, preprocessed its data and stored them into the GGP-ISDC, - Dr. Walter Lenz (Büro Hydrogeologie und Umwelt Gmb. H, Giessen), who gave valuable hints on the hydrologic regime in the region of Bad Homburg, - the Hessisches Landesamt für Umwelt und Geologie, Landesgrundwasserdienst, which made available the 50 years groundwater data from Seulberg, - the castle gardener Peter Vornholt, who made available his notes of precipitation in the neighborhood of the Bad Homburg Castle, - Peter Franke (BKG Frankfurt), who processed and made available the GPS-Data from the GPS-Station „Bad Homburg, Castle“).

Thank you for your attention

References Richter, B. , 1987. Das Supraleitende Gravimeter. Anwendung, Eichung und Überlegungen zur Weiterentwicklung. Dt. Geodät. Kommiss. , C 329, 126 p. Falk, R. , 1995. Abschätzung einer möglichen Beeinflussung des Schwerewertes des Absolutpunktes in Bad Homburg auf Grund von Wasserstandsschwankungen des Schloßteiches. [Potsdam], 10. 5. 1995, unpublished. Simon, D. , 2003. Modelling of the gravimetric effects induced by vertical air mass shifts. Mitt. Bundesamt Kartogr. Geodäsie, 21, 100 + XXXII p. J. Neumeyer et al. , 2004. Gravity reduction with three-dimensional atmospheric pressure data for precise ground gravity measurements. J. Geodynamics, 38 (2004), pp. 437 – 450. SEBA Hydrometrie Gmb. H. Datensammler MDS-Dipper II. http: //www. seba. de Deutscher Wetterdienst. Flughafen Frankfurt/Main. Klimadaten (Tageswerte). http: //www. dwd. de Crossley, D. J. , S. Xu , van Dam, T. , 1998. Comprehensive Analysis of 2 years of SG Data from Table Mountain, Colorado. Proc. 13 th Int. Symp. Earth Tides, Brussels, July 1997. Obs. Royal Belgique, Brussels 1998, pp. 659 – 668.

References (II) Harnisch, M. , Harnisch, G. , 2002. Seasonal Variations of Hydrological Influences on Gravity Measurements at Wettzell. Bull. d‘Inform. Marées Terrestres, Bruxelles 137, pp. 10849 - 10861 Harnisch, G. , Harnisch, M. , 2006. Hydrological influences in long gravimetric data series. J. Geodynamics, 41 (2006), pp. 276 – 287. Wilmes, H. et al. , 2006. A new data series observed with the remote superconducting gravimeter GWR R 038 at the geodetic fundamental station TIGO in Concepción (Chile). J. Geodynamics, 41 (2006), pp. 5 - 13.

Precipitation and Modeled Gravity Effect Bad Homburg Süd 10. 5. 2005 – 16. 2. 2006 Airport Frankfurt a. M. 1991 - 2005