2. 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

3. 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 TT40 data series 1981 – 1984 ●Results, Conclusions

4. 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 TT40, 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).

5. Schlosskirche GWR CD030 Meiereiberg Observation Sites around the Gravimeter Castle Pond GPS 3 Groundwater gauges: ● Schlosskirche (Distance 110 m) ● Meiereiberg (Distance 200m) ● Seulberg (Outside the figure, distance 3.5 km) Rain Gauge Rain gauge at the Castle Gardener‘s House GPS antenna, at a wall, about 20 m high Gravimeter in the basement of the archive wing

6. The Groundwater Gauges and some Hydrological Background: 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. 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 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

7. Groundwater 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 Distance from the Gravimeter Sampling Rate Nearly the same behavior at the 3 groundwater gauges spread over more than 4 km

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

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

10. 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

11. Δg i = 2πGρ∑ r j (1 - exp (-(i-j)/τ 1 )) exp (-(i-j)/τ 2 ) i - 1 j = 1 Modeled gravity effect of precipitation (Crossley u.a. 1998) Precipitation. Rain Gauge at the Castle Gardener‘s House Other precipitation data are available from Bad Homburg Süd and the Airport Frankfurt a.M. τ 1 describes the infiltration of water into the ground („recharge time constant“) τ 2 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.

12. Modeled gravity effect of rain in relation to the residual gravity of the gravimeter GWR CD030 Explanation of the residual gravity follows Influence of Precipitation on the Gravity Residuals Bad Homburg, 2004 - 2005 At Bad Homburg the influence of precipitation on the residual gravity is very weak.

13. Processing the Gravity Data (Residual Gravity) Recorded gravity Tidal Analysis Residual Gravity RG1 Residual Gravity RG2 Estimation of Disturbing Influences e.g. groundwater, precipitation Known disturbing Influences e.g. air density distribution, hydrological influences ● GWR CD030 (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 Predicted tides (Sa: δ = 1.16) and the local air pressure effect are subtracted from the gravity observations. Additionally the gravity effect of polar motion is eliminated ● Regression analysis ● Amplitude Ratio of long-period waves

14. Groundwater regression coefficient r GW (L) = 23.0 nm s -2 /m (GW „Schlosskirche“) Influence of Groundwater on the Residual Gravity Above: Influence included Below: Influence eliminated

15. Seasonal Variations of the Vertical Air Density Distribution (Simon 2003) 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. Fit of a sinusoidal wave with annual period (365.25 days, red line) The amplitudes at Moxa and Wettzell are nearly the same. Differences less than 1 nm s -2

16. Groundwater regression coefficient r GW (L) = 29.6 nm s -2 /m (GW „Schlosskirche“) Influence of Groundwater on the Residual Gravity Above: Influence included Below: Influence eliminated Influence of air density anomalies corrected at first

17. 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 ?

18. TT40, Bad Homburg 1981 – 1984 (Richter 1987) Hydrol. Corr. Annual Wobble Chandler Wobble DeltaPhaseDeltaPhase NO1.5229.051.4222.87 YES1.5520.391.5112.98 Amplitude Factor and Phase Lag of the Polar Motion Constituents 2. Groundwater correction influences mainly the phase values Results: 1. Groundwater Corrections smooth the Residual Gravity

19. Results, Conclusions Outlook ● Processing the data of the upper system of the gravimeter GWR CD030 ● Continue the studies if more data are available, esp. the Meiereiberg gauge ● 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 obser- vations 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.

20. Acknowledgements We thank - Peter Wolf (BKG Frankfurt), who maintained carefully the gravimeter, pre- processed its data and stored them into the GGP-ISDC, - Dr. Walter Lenz (Büro Hydrogeologie und Umwelt GmbH, Giessen), who gave valuable hints on the hydrologic regime in the region of Bad Homburg, - the Hessisches Landesamt für Umwelt und Geologie, Landesgrundwasser- dienst, 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“).

21. Thank you for your attention

23. 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 GmbH. Datensammler MDS-Dipper II. http://www.seba.dehttp://www.seba.de Deutscher Wetterdienst. Flughafen Frankfurt/Main. Klimadaten (Tageswerte). http://www.dwd.dehttp://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. 13th Int. Symp. Earth Tides, Brussels, July 1997. Obs. Royal Belgique, Brussels 1998, pp. 659 – 668.

24. 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 R038 at the geodetic fundamental station TIGO in Concepción (Chile). J. Geodynamics, 41 (2006), pp. 5 - 13.

25. Precipitation and Modeled Gravity Effect Bad Homburg Süd 10.5.2005 – 16.2.2006 Airport Frankfurt a.M. 1991 - 2005