Pure and Applied Geophysics

, Volume 175, Issue 5, pp 1755–1763 | Cite as

The Improved Hydrological Gravity Model for Moxa Observatory, Germany

  • A. Weise
  • Th. Jahr


The gravity variations observed by the superconducting gravimeter (SG) CD-034 at Moxa Geodynamic Observatory/Germany were compared with the GRACE results some years ago. The combination of a local hydrological model of a catchment area with a 3D-gravimetric model had been applied successfully for correcting the SG record of Moxa which is especially necessary due to the strong topography nearest to the SG location. Now, the models have been corrected and improved considerably by inserting several details in the very near surrounding. Mainly these are: the observatory building is inserted with the roof covered by a soil layer above the gravity sensor where humidity is varying, snow is placed on top of the roof and on topography (steep slope), and ground water is taken into account, additionally. The result is that the comparison of the corrected gravity residuals with gravity variations of the satellite mission GRACE, now using RL5 data, shows higher agreement, not only in amplitude but also the formerly apparent phase shift is obviously not realistic. The agreement between terrestrial gravity variations (SG) and the GRACE data is improved considerably which is discussed widely.


Superconducting gravimeter hydrology 3D gravity modeling local effects 

1 Introduction

Hydrological effects in gravity observations have been a subject of discussion for several decades, since the precision and repeatability is in the range of µGal. Repeated gravity campaigns, time lapse gravity, as well as time series are affected. One of the first reporting this effect, especially of soil moisture, was Bonatz (1967). Lambert and Beaumont (1977) found effects of ground water variations when seeking for tectonic gravity signals. Elstner et al. (1978) already used soil moisture measurements for estimation and correction of the effect of some 5 µGal (50 nm/s2). While at times, precipitation data had been used for statistical estimations, Mäkinen and Tattari (1988) predicted separately soil moisture and ground water effects applying the Bouguer plate model and could verify the calculated effect with repeated gravity observations. Over years, also statistical methods have been investigated, e.g. Braitenberg (1999) found in tiltmeter and extensometer data that the hydrological induced signal showed time variable correlations, which were not significant over longer periods or masked by other effects. Especially regarding repeated campaigns, same seasons are chosen for measurements to reduce the effect of hydrological impact. Hydrological effects can be amplified where strong topography occurs near the stations, for example at volcanoes (Jentzsch et al. 2004).

At the latest, general knowledge concerning seasonal changes of continental hydrology in gravity is widely spread since the GRACE project. Amongst others, this gives information about weak regions in continental hydrology models, e.g. with the ‘nulltest’ in arid regions (Hinderer et al. 2016). On the other hand, comparisons with terrestrial gravity observations from superconducting gravimeters (SG) show local effects at some stations. While Crossley et al. (2014) favor the Bouguer plate model for reduction of local hydrological effect where necessary at stations of superconducting gravimeters, in contrast, Weise et al. (2009, 2012) found that this holds only for flat and homogeneous surroundings like at Strasbourg station. But where strong topography leads to considerable effects physical modeling is needed, e.g. for stations like Moxa and Vienna. Naujoks et al. (2010) developed a successful correction model of local hydrological effect first combining hydrological and 3D-gravimetrical modeling for the SG station Moxa. After reduction the agreement of the SG time series with the result from GRACE for this region had been approved considerably (Weise et al. 2009, 2012).

During the last 3 years. the time series of the existing hydrological model were extended in period, and the combined hydrological–gravimetrical modeling could be clearly enhanced by inserting, especially some important details into the gravimetric model.

2 Hydrology Around Moxa Observatory

The hydrological situation around the Geodynamic Observatory Moxa is characterized by the fact that precipitation and topography cause mass movements above and below the sensor-level of the SG CD-34 (see Fig. 2 in Naujoks et al. 2010). In addition, different flow-paths are active for water transport from the hills to the valley and into the small creek Silberleite.

The local hydrological model of the catchment area of the creek Silberleite, around the observatory Moxa (see Fig. 4 in Naujoks et al. 2010) consists of hydrological responds units (HRUs) according to several soil parameters, discharging downhill along the given fluid paths. In front of the observatory building the runoff of the creek Silberleite is observed at the small weir (Fig. 1b). In addition, several divers installed in shallow drill-holes distributed over the model area are measuring soil moisture changes (Naujoks et al. 2010).
Fig. 1

a Strategy of hydrological modeling (after Eisner 2009), b small weir in front of the Geodynamic Observatory Moxa, where the runoff of the catchment area of the creek Silberleite is recorded

3 Hydrological Gravity Modeling

The hydrological modeling is based on the conceptual model J2000 (Krause 2001; Eisner 2009) and exemplarily shown for three horizons in Fig. 1a. The HRUs are defined according to different soil parameters, layers, permeability, drain information, and slope, among others. The variations of water content in the HRUs are modeled which cause density changes, due to three main storages: surface water (DPS), mid pore storage (MPS), and large pore storage (LPS), (s. Fig. 1a). Input data are temperature, precipitation, humidity, wind velocity, and radiation which together result in the input-storages defined by snowmelt (SM), precipitation (P), and throughfall (TF)/interception. The modeling provides the surface runoff (SQ), subsurface flow (SSQ), evapotranspiration (ET), and flow into groundwater (PERC). The main result of the model is the time dependent amount of stored water content (water column) in different water storages (layers) for all HRUs as time series. The final comparison of modeled vs. observed runoff gives an estimation of the quality of the modeling.

The main storages are large and middle pore storage, snow, interception storage, depression storage, quick and slow ground water storage. The temporal variation of the sum of all storages reflects seasonal variations in the range of 120–160 mm WC (mm water column, Fig. 2), with a maximum of 220 mm WC in 2011 due to extreme snow fall. The modeling period is 2004–2014.
Fig. 2

Temporal change of model content in water storages

In the next step, a 3D-gravity model was developed on the base of Bouguer gravity values and geological underground information (Naujoks 2008; Naujoks et al. 2010) using the software IGMAS (Schmidt et al. 2011) for describing the geological structures. Subsequently, the time series of the lateral distribution of water content, converted to density changes, go into the 3D-gravimetric modeling. Here, the units of different density are situated parallel to the topography, with a depth of 2–4 m for the soil layer which is underlain by a layer of 8–16 m where mainly the larger and long-term groundwater variation is supposed to take place. The direct vicinity of the observatory is much higher resolved (Fig. 3). The 3D-gravimetric model around the observatory (2 × 2 km2) has the SG in the center. The distance of the vertical planes is 5 m in the central part for high resolution of a few meters and increasing distances between the planes outwards. The model comprises 36 vertical planes connected by triangulation and 92 hydrological active units (Naujoks 2008).
Fig. 3

Improved realistic detail from gravimetric 3D-model of vertical plain through the observatory building

The most recent finding based on the work of Naujoks et al. (2010) is—beyond the correction of the conversion to density: the considerably more detailed modeling of the immediate SG-vicinity and observatory building is crucial and leads to improved results (Weise and Jahr 2015):
  • Roof:
    1. 1.

      snow is stored on the roof of the observatory and on the ground above the SG (Fig. 3),

    2. 2.

      with respect to the plastic cover soil humidity in the roof coverage is reduced to 30% (not zero),

  • building acts as a shield which leads to reduced variation of humidity in clefts beneath the observatory and SG, estimated with 10%,

  • topography next to the SG has been improved (especially steep slope),

  • geometry next to SG has been adapted more specific, including pillar height, thickness of basement, height of rooms, cover layer in the roof,

  • constant thickness of units next to the SG is set for exact conversion of water storage to density change,

  • slow ground water has been included (up to 30 mm WC seasonal). The equivalent density change has been included in the gravimetric model partly in the soil layer and partly in the deeper layer. The impact in the seasonal amplitude of gravity change at the SG site is about 20–30%. The apparent phase shift against the satellite data in former results vanished after including the slow ground water.

The results of the hydrological modeling are inserted into the gravimetric model by continuously changing densities dependent on the water content. In time steps of 1 h the gravity-effect due to water mass changes in the upper model units is calculated for the location of the SG resulting in the time series of the hydrological induced gravity effects for correction of the local hydrological effect in the SG recording.

4 Results: SG-Residuals and Comparison with GRACE

The result of the modeled gravity effect due to local hydrological variations (Fig. 4, total in blue) has the clear seasonal amplitude (peak-to-peak) of 30–45 nm/s2, up to 75 nm/s2 in the begining of 2011 caused by a high snow layer. Maxima in summer and minima in winter prove the dominating water masses above the SG sensor. The separation of particular contributions of the nearest areas (Fig. 4) demonstrates that the nearest area of <75 m radius is responsible for ~80% (red) of the local hydrological effect, whereof the most considerable and effective parts are the slope area above the observatory (~60%, green) and the roof (mostly snow, ~24%, brown) while the roof had not been considered before in the modelling of Naujoks et al. (2010).
Fig. 4

Contributions to local combined hydrological and 3D-gravimetrical modeling from several parts of the observatory surrounding, blue sum of the total modeled local hydrological gravity effect

Figure 5 illustrates the observed time series of gravity variations (monthly samples, black), reduced for tides, 3D atmospheric masses, and drift. The atmospheric correction from Atmacs (Atmospheric attraction computation service, ATMACS 2017) is used with the temporal resolution of 3- and 6-hourly samples which has been adapted to hourly samples by interpolation applying the local observed air pressure and an adapted regression coefficient. The reduced gravity variations are in the range of 20 nm/s2, up to maximum 57 nm/s2, without clear seasonal content. After subtracting the modeled local hydrological gravity effect (blue) the resulting gravity variations (red, monthly samples) show a seasonal signal in the range of 30–40 nm/s2 with maxima in winter and minima in summer as expected from water storage changes in global continental hydrology.
Fig. 5

Local hydrological effect 2004–2012 from combined hydrological and 3D-gravity modeling at the SG site (blue) with seasonal variations, SG-gravity residuals (monthly) observed (black) and after hydrological reduction (red)

We compare the SG residuals after reduction of local hydrological effect (red in Fig. 5) with gravity variations from the satellite mission GRACE for Moxa area which are computed according to Abe et al. (2012) using monthly sets (RL5) from JPL (Jet Propulsion Laboratory, Pasadena/California) and the spherical harmonic (SH) approach to the degree/order 120 (download from GFZ Information System and Data Center, ISDC,, see Abe et al. 2012). The deformation effect is added. The GRACE data are Gauss filtered with 1000 km radius, and additionally DDK1 anisotropic filter from Kusche (2007) was applied, both exemplarily as their suitability was demonstrated in Weise et al. (2012).

The general agreement (Fig. 6) of the corrected terrestrial gravity with gravity variations from GRACE for the Moxa area can be stated in magnitude and in phase and has been improved successfully against Naujoks et al. (2010). Partly agreeing structural details, e.g. with GRACE in winter 2007/8 and 2008/9 (double peaks) and with GLDAS in autumn 2010 and 2011, and in summer 2005, 2009 can support the similar origin of the signal. But also anomalous seasonal variations have to be ascertained, mainly from summer 2006 to 2007, and the minimum in summer 2008, with more slight extent in summer to autumn 2007. The reason is not clear, yet. All meteorological and gravity data have been checked. A most possible candidate could be the ground water in the hydrological modeling which still is a great challenge. Here, major work is still waiting to improve the underground information for modeling.
Fig. 6

Monthly gravity variations reduced for local hydrological effect (red; Fig. 5) compared for Moxa to the global hydrological model GLDAS (blue, hourly samples) and to satellite data from GRACE (RL5 JPL) which are Gauss filtered (R = 1000 km, dark green) and DDK1 anisotropic filter (light green, Kusche 2007) is applied

As the modeling and correction of the hydrological effect of the gravity record is mainly successful in the long-term range, we intended to check the possibility of realistic modeling in the short-term period range of hours to days. For several events of strong rain fall the modeling and correction has been checked, exemplarily shown for one event in Fig. 7. The single event is characterized by a nearly immediate and quick gravity decease and followed by a slower gravity increase nearly linear over 1–2 days. The almost immediate gravity decrease is due to the precipitation which increases soil humidity, which in Moxa occurs also and mainly above the gravity sensor.
Fig. 7

Example of short-term gravity changes after heavy rainfall with three modeled versions of the hydrological induced gravity effect

Modeling of the first start of simulated gravity decrease is basically agreeing in time, amplitude and in course of process. The subsequent gravity increase due to relaxation is too slow and delayed in the original modeled version (pink in Fig. 7). The main effective process in the model seems to be evaporation. The flow downhill should be driven by quick ground water. The orange model version shows that the flow of the ‘quick ground water’ downhill, which is not sufficiently fast in the model, could be increased, also by dividing the HRU at the slope. In the red model version the storage capacity of the quick ground water has been reduced, in the orange version, the amount of quick ground water is increased. Both experiments show that the dynamic is not sufficient in the model. Simulating the full dynamic of flow in the complex situation in the slope through weathered and fissured rock remains a big challenge. Still, there remains a lack of knowledge about the real flow path in the underground and its characteristics. One point is also the steepness of the slope where the realistic ground water modeling seems to be problematic.

5 Discussion and Conclusion

The main improvements against Naujoks et al. (2010) of modeling the local hydrological effect at Moxa observatory which is mainly caused by the near and strong topography are part of the 3D-gravimetric model: Snow on and humidity in the cover layer of the observatory roof above the SG, reduced storage changes beneath the observatory and the SG due to the building acting as a shield, improved geometry and topography nearest to the gravimeter sensor. Especially including the ground water which had been neglected before, lead to higher effects in the modeling and finally to more realistic amplitude in gravity compared to GRACE. With these improvements the agreement with the GRACE time series is considerably higher, not only in amplitude but also in phase which seemed to be a problem before. This enhancement is mainly regarding long-term gravity changes in the range of months and probably weeks. This result also supports the position, that terrestrial gravity mainly ‘sees’ the same temporal variation as satellites as GRACE do.

As discussed in Crossley et al. (2014) a certain part of the local effect which is representative for a larger region is included in the GRACE data and should, in best case, remain in or should be added to the terrestrial gravity record after subtraction of a local effect. This will be small for the area around Moxa observatory due to a thin soil layer on the rocks of “Thüringer Schiefergebirge”. We estimate, that the part subtracted from below the sensor is <5% of the whole modelled effect, and thus perhaps within the uncertainty. Up to now, it is not solved how to estimate a realistic value for the smooth effect representing a wider area and to be added after reduction of the local effect due to topography and an underground location of the SG. On the other hand, if we would leave out the part from below the SG in the reduction model we would neglect the fact that also the building is working as a shield. This point remains an open question in this work.

In the higher frequency range of days to hours the comparison of the hydrological effect from the model combination with the observed gravity time series from the SG shows on the one hand a certain improvement but on the other hand also the obviously limited possibilities of the modeling. Flow processes of high dynamics within the deeper underground and the slope next to and under the observatory seem to remain a big challenge to be modeled in a realistic way.



The investigations were carried out in the frame of the project JA-542-24-1, funded by the German Research Foundation (DFG), which is gratefully acknowledged. We also thank our project partners Daniel Hagedorn (PTB, Braunschweig) and Ronny Stolz (IPHT, Jena) and the colleagues from the Arbeitskreis Geodäsie/Geophysik for the fruitful discussions about the reduction of hydrological effects in SG recordings. Further, we thank Maiko Abe, GFZ Potsdam, for calculating the gravity variations of GRACE for Moxa location with all her expertise. To keep the Geodynamic Observatory Moxa running, the superconducting gravimeter SG-CD034 as well as all the components of weather and hydrology recordings, was guaranteed by Wernfrid Kühnel and Matthias Meininger; many thanks for doing this job in highest quality. We appreciate valuable suggestions improving the manuscript from two reviewers, one anonymous and N. Florsch.


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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Leibniz Institute for Applied GeophysicsHanoverGermany
  2. 2.Institute of GeosciencesFriedrich Schiller University JenaJenaGermany

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