# Gravity effect of water storage changes in a weathered hard-rock aquifer in West Africa: results from joint absolute gravity, hydrological monitoring and geophysical prospection

Basile Hector, Luc Séguis, Jacques Hinderer, M. Descloitres, J.M. Vouillamoz, M. Wubda, Jean-Paul Boy, Bernard Luck, Nicolas Le Moigne

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Basile Hector, Luc Séguis, Jacques Hinderer, M. Descloitres, J.M. Vouillamoz, et al. Gravity effect of water storage changes in a weathered hard-rock aquifer in West Africa: results from joint absolute gravity, hydrological monitoring and geophysical prospection. Geophysical Journal International, 2013, pp.10.1093/gji/ggt146. 10.1093/gji/ggt146. hal-00821181

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# Gravity effect of water storage changes in a weathered hard-rock aquifer in West Africa: results from joint absolute gravity, hydrological monitoring and geophysical prospection

Basile Hector,¹ Luc Séguis,² Jacques Hinderer,¹ Marc Descloitres,³ Jean-Michel Vouillamoz,³ Maxime Wubda,³ Jean-Paul Boy,¹ Bernard Luck¹ and Nicolas Le Moigne⁴

¹IPGS-EOST, CNRS/UdS, UMR 7516, 5 rue René Descartes, 67084 Strasbourg Cedex, France. E-mail: basile.hector@unistra.fr

²IRD/CNRS/UM2/UM1, UMR HydroSciences Montpellier, Place E. Bataillon, F-34095 Montpellier Cedex 5, France

³IRD/UJF-Grenoble-1/CNRS/G-INP – UMR LTHE, 08 BP 841 Cotonou, Benin

⁴Géosciences Montpellier, UMR CNRS/UM2 5243, Montpellier, France

Accepted 2013 April 9. Received 2013 April 8; in original form 2012 August 19

## SUMMARY

Advances in groundwater storage monitoring are crucial for water resource management and hydrological processes understanding. The evaluation of water storage changes (WSC) often involve point measurements (observation wells, moisture probes, etc.), which may be inappropriate in heterogeneous media. Over the past few years, there has been an increasing interest in the use of gravimetry for hydrological studies. In the framework of the GHYRAF (Gravity and Hydrology in Africa) project, 3 yr of repeated absolute gravity measurements using a FG5-type gravimeter have been undertaken at Nalohou, a Sudanian site in northern Benin. Hydrological data are collected within the long-term observing system AMMA-Catch. Once corrected for solid earth tides, ocean loading, air pressure effects, polar motion contribution and non-local hydrology, seasonal gravity variations reach up to 11 µGal, equivalent to a WSC of 260-mm thick infinite layer of water. Absolute temporal gravity data are compared to WSC deduced from neutron probe and water-table variations through a direct modelling approach. First, we use neutronic measurements available for the whole vertical profile where WSC occur (the vadose zone and a shallow unconfined aquifer). The RMSD between observed and modelled gravity variations is 1.61 µGal, which falls within the error bars of the absolute gravity data. Second, to acknowledge for the spatial variability of aquifer properties, we use a 2-D model for specific yield (Sy) derived from resistivity mapping and Magnetic Resonance Soundings (MRS). The latter provides a water content (θMRS) known to be higher than the specific yield. Hence, we scaled the 2-D model of θMRS with a single factor (α). WSC are calculated from water-table monitoring in the aquifer layer and neutronic measurements in the vadose layer. The value of α is obtained with a Monte-Carlo sampling approach, minimizing the RMSD between modelled and observed gravity variations. This leads to α = Sy/θMRS = 0.63 ± 0.15, close to what is found in the literature on the basis of pumping tests experiments, with a RMSD value of 0.94 µGal. This hydrogeophysical experiment is a first step towards the use of time-lapse gravity data as an integrative tool to monitor interannual WSC even in complicated subsurface distribution.

**Key words:** Time variable gravity; Hydrogeophysics; Hydrology; Africa.

## 1 INTRODUCTION

Water Storage Changes (WSC) in unsaturated soils and aquifers are a key variable for water resource management, yet still challenging to estimate (Scanlon *et al.* 2002; Healy & Scanlon 2010; Dubus & Dubus 2011). This is particularly true in the weathered hard-rock

basement of the Sudanian zone in West-Africa, where the total storage volume is low, but shows strong annual variations (MacDonald *et al.* 2012). There, urban development relies on the ability to provide enough fresh water along the year through high yield boreholes. These are still difficult to implement and the knowledge of local recharge is particularly important for their sustainability.
For instance, in the surroundings of the Nikki town in the hard-rock area of northern Benin, half of the boreholes drilled in 2011 were considered as dry (Direction Générale de l'Eau, Cotonou, personal communication, 2012), despite a high mean annual rainfall of 1300 mm. Furthermore, Achidi et al. (2012) found a 62 per cent success rate for water drillings in crystalline basement at the country scale, against up to 90 per cent for coastal sedimentary aquifers. Seasonal WSC is thus of critical concern in this highly sensitive area, and broadening the range of methods available to monitor this key variable is a major challenge.

There are numerous approaches for the evaluation of WSC that are usually based on distributed (or not) point measurements in one or several compartments responsible for WSC [i.e. top soil, vadose zone (VZ), water tables]. For instance, Time-Domain Reflectometry (TDR) is now widespread for water content monitoring, but has several limitations such as the small sampling volume (10⁻³ m³) of a single measurement and its limitation to the upper layers of the VZ. Deriving WSC from water-table monitoring strongly depends on the knowledge of the specific yield (Sy) parameter, and only provides WSC for the water-table fluctuation zone (WTFZ). Geophysical methods are often used to characterize underground structures for extending these point measurements. WSC at the field scale can be estimated by the interpolation of these point measurements, or by several methods such as water budget estimations or numerical modelling (Healy & Cook 2002; Scanlon et al. 2002). As noticed by Creutzfeldt et al. (2010b), Christiansen et al. (2011b) and several others, deriving WSC from limited point measurements is still an arduous task, despite recent developments that are often limited to the upper layers of the ground (spatial TDR measurements, high-precision lysimeters, cosmic ray neutron probes, etc.). This led some open space for the emerging hydrogravimetry method which allows to perform direct non-invasive monitoring that can be derived into integrative WSC estimations if other components affecting gravity are correctly removed (Pfeffer et al. 2011).

Water mass redistribution leads to variations in the Earth's gravity field, which can be measured by gravimeters. Superconducting Gravimeters (SGs) provide continuous relative gravity monitoring with very high accuracy (about 1 nm s⁻²). Apart from very recent developments on new SGs, they are drift-prone and can hardly be moved, which are their main drawbacks for hydrological studies. For further details on SGs, see for instance Goodkind (1999) and Hinderer et al. (2007). Spring-based gravimeters are lower accuracy (few µGal) relative gravimeters for field prospecting. They give access to spatial gravity variations with respect to a base station, and can thus provide spatiotemporal variations with repeated measurements (Naujoks et al. 2008; Jacob et al. 2010; Pfeffer et al. 2013). Their lower accuracy puts them on the edge of detection for many hydrological cases for which much care must be taken to achieve the best results, leading to a second drawback, the time consumption. However, they can be a powerful tool when used together with a SG or an absolute gravimeter (AG) as a base station. AGs have the advantage to be drift-free, allowing for monitoring gravity changes at long timescales, by repeating measurements without leaving the instrument at the same place. They give direct measurements of the earth gravity field with a 10–20 nm s⁻² (1–2 µGal) precision for the most accurate one, the FG5 model (Niebauer et al. 1995). The FG5 AG measures the successive positions of a free falling corner cube in a vacuum chamber, using a laser interferometer and an atomic clock. The actual gravity value along the direction of the local vertical is obtained for every drop.

Until recently, the hydrological signal has mainly been seen by the geodesy community as ‘noise’ to be removed from the SGs time-

series—often calibrated with absolute gravity measurements—to recover small geodynamics signals. Many site-specific hydrogravimetric studies can be found in the literature (e.g. Bower & Courtier 1998; Harnisch & Harnisch 2006; Imanishi et al. 2006; Kroner & Jahr 2006; Van Camp et al. 2006; Creutzfeldt et al. 2008; Longuevergne et al. 2009; Creutzfeldt et al. 2010a,b; Naujoks et al. 2010). However, only very few studies use AGs as field instruments for measuring temporal changes due to the redistribution of water (Jacob 2009; Pfeffer et al. 2011). This allows to investigate other areas than single SGs observatories without being affected by the drift and accuracy limitations of the microgravimeters.

Gravity measurements are often compared to hydrological monitoring, by calculating the gravity effect of these measured WSC in a direct modelling approach (Creutzfeldt et al. 2008; Jacob et al. 2008; Creutzfeldt et al. 2010a; Pfeffer et al. 2011). A few recent studies also successfully calibrated conceptual or physical hydrological models in a coupled hydrogeophysical inversion framework such as defined by Ferré et al. (2009) (see also Creutzfeldt et al. 2010b; Christiansen et al. 2011a,b). However, to successfully compare gravity data and hydrological monitoring, the hydrogravimetry method is also limited by the poor spatial extent of hydrological point measurements, and by the integrative character of gravity data. The latter requires some knowledge of the WSC of each compartment in the footprint area of the gravimeter. Very few studies consider the contribution of each layer, and the VZ is usually poorly or not documented (Christiansen et al. 2011b). Creutzfeldt et al. (2010a) presented the first study which comprehensively measured WSC in all relevant storage components, namely groundwater, saprolite, soil, topsoil and snow storage, and compared them to gravity measurements.

A usual byproduct of hydrogravimetric surveys is an estimation of the specific yield (Sy) parameter, as it relates water-table fluctuations (an observation easily available) to unconfined aquifer storage variations. This can be done for various levels of precision, using relative spring-based gravimeters (Montgomery 1971; Pool & Eychaner 1995; Gehman et al. 2009), absolute gravity data (Jacob et al. 2008; Pfeffer et al. 2011) or even GRACE (Gravity Recovery and Climate Experiment) satellite products (Shamsudduha et al. 2012). However, Creutzfeldt et al. (2010a) pointed out that ‘interpreting the regression coefficient [between gravity and water table level] in a physical way is problematic and only valid if the correlation between groundwater and other water storages can be neglected or the water mass variations in all other storages are small compared to the groundwater mass variation’. One may also add that the assertion is valid if WSC in other storages are known and their gravity effect can be calculated and removed from the regression analysis. At the field scale, Sy estimates are derived from classical hydrological experiments such as pumping tests or water budgets estimates. More recently, the emerging geophysical method of Magnetic Resonance Soundings (MRS) which determines a ‘MRS water content’ parameter (θMRS) was also used for estimating Sy (Healy & Cook 2002; Vouillamoz et al. 2005; Boucher et al. 2009). Comparing Sy obtained from pumping tests to θMRS, these authors observed lower Sy values with respect to θMRS, as summarized by the study of Vouillamoz et al. (2012) who found Sy/θMRS = 0.4 for a clayey sandstones aquifer in Northern Cambodia.

In this paper, we present an AG survey carried out in a tropical weathered hard-rock unconfined aquifer context of subhumid West Africa (Nalohou, Benin: 1.6056°E–9.7424°N) during 3 yr (2009–2011) using high accuracy FG5 measurements (four measurements a year). These measurements have been carried out in the framework of the GHYRAF (Gravity and HYdRology in Africa) project that
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Study area, measurement settings: gravimeters (FG5 and SG) and their shelters. Neutron probe borehole and observation well are respectively located 9 and 7 m to the FG5 location. The circle shows the 100-m radius zone of influence for gravity variations at the FG5 site. *Google Earth* image, 2010 February 4.</figcaption></figure>

aims at evaluating the ability of AGs to measure water storage varia-
tions in West Africa (Hinderer *et al.* 2009; Hinderer *et al.* 2012). This
project studies the strong seasonal monsoon signal within different
aquifers (sedimentary in Niger and weathered hard rock in Benin)
and climatic contexts (Sahelian and Sudanian zones). We also used
the intensive hydrological monitoring that has been carried out at
Nalohou site since 1992 in the frame of the AMMA-Catch long-
term observing system (www.amma-catch.org; Lebel *et al.* 2009),
which is an observatory of RBV (Réseau des Bassins Versants), the
French critical zone exploration network (rnbv.ipgp.fr). The data
are available upon request via the AMMA-Catch online database
(http://database.amma-international.org/).

The objective of this study is to compare absolute gravity mon-
itoring with seasonal WSC deduced from independent hydrologi-
cal data (neutronic measurements and water-table levels). This is
achieved through a direct modelling of the gravity variations in-
duced by WSC. First, we evaluate the observed gravimetric vari-
ations against an integrative WSC model obtained with neutronic
measurements from a single borehole that samples the whole pro-
file (from surface down to the lowest level of the water table).
Secondly, in order to take into account the spatial variability of *Sy*
in this weathered hard-rock context, we distinguish between two
layers to calculate the WSC: a shallow layer never saturated where
WSC are deduced from neutron probe (NP) measurements and a
deep layer where we use water-table data and a spatial distribution
of *Sy*. The 2-D model for *Sy* is obtained by coupling resistivity
mapping and MRS measurements that are scaled with a simple fac-
tor (α). The value of α is obtained with a Monte-Carlo sampling
approach, minimizing the RMSD between modelled and observed
gravity variations.

2 STUDY AREA

The Upper-Ouémé catchment in northern Benin (14 000 km²) is a
humid Sudanian area. It has been chosen for hydrological moni-
toring and accurate water budget estimations in the frame of the
AMMA-Catch multidisciplinary project. A dense monitoring net-
work dedicated to water redistribution processes studies has been
developed since 2003 on a small, embedded, microcatchment close

to the village of Nalohou (22.6 ha, Fig. 1), well suited for grav-
ity measurements (Hinderer et al. 2012). Mean annual rainfall is
1195 mm yr⁻¹ (over the period 1950–2004) at the Djougou weather
station—8 km from the Nalohou site—(Kamagaté et al. 2007) and
mean annual reference evapotranspiration is 1393 mm (over the pe-
riod 2002–2006 at the Djougou weather station; Séguis et al. 2011).
The Nalohou site has been equipped with observation boreholes
(water table and neutronic measurements) and complementary geo-
physical surveys (electrical methods, MRS) have been undertaken.
This contributed to some understanding of the prevailing hydrolog-
ical processes and first estimates of the hydrological budget terms:
the two main terms of the annual water budget are evapotranspi-
ration (75–90 per cent of total rainfall amount) and streamflow
(10–15 per cent). The residual term forms the interannual under-
ground water storage variation (Kamagaté et al. 2007; Guyot et al.
2009; Descloitres et al. 2011; Séguis et al. 2011).

The unconfined aquifer is located in a weathered layer 7–22 m thick (Kamagaté *et al.* 2007; Descloitres *et al.* 2011) over a fresh metamorphic basement (gneiss, micaschists, quartzites). Geological structures are north–south oriented, and the mean dip angle is 20° east. Regional soils are of ferruginous tropical leached type, but slightly vary depending on the topography and local basement. Groundwater recharge occurs by direct infiltration of rainfall water through the VZ during the rainy season.

The land cover in the vicinity of the gravimeter is governed by
crop (maize, sorghum, manioc and yam) and fallow rotations with
some remaining trees (Parkia biglobosa, vitellaria paradoxa, adan-
sonia digitata) kept for consumption purposes and a small cashew
trees (Anacardium occidentale) orchard. Fallow is composed by
trees (e.g. Isoberlinia Doka) and herbaceous cover, and the latter is
usually burnt at the beginning of the dry season.

FG5 measurements are undertaken within a 3 × 4 m² shelter,
close to another shelter for the SG. NP borehole and observation
well (OW) are respectively located 9 and 7 m to the FG5 location
(Fig. 1c). FG5 measurement site is located on the crest of a gentle
sloping hill as shown by contour lines (Fig. 1a).

Except for large towns (such as nearby Djougou), the socioeco-
nomical activity of the region is mainly rural, and the population
density is close to 30 inhabitants per km², with an annual growth
of 3.48 per cent (1992–2002; Direction des études démographiques 2003). As there is almost no irrigation (rain-fed crops) so far, water consumption is mainly domestic, through the use of village wells, and is negligible in the water budget (about 0.2 mm yr⁻¹, on a basis of 20l per inhabitant per day; Séguis et al. 2011).

## 3 HYDROMETEOROLOGICAL MONITORING

Rainfall is monitored by a tipping-bucket raingauge located 100 m away from the FG5 measurement site (Fig. 1a). Cumulative and daily rainfall are shown on Fig. 2b and exhibit the seasonal rainfall pattern characteristic of the West African monsoon with wet and dry seasons. About 60 per cent of the total annual amount falls between July and September (Kamagaté et al. 2007). The interannual variability of rainfall is very marked in this area (e.g. Le Barbé et al. 2002; Le Lay & Galle 2005), and explains the divergence of these annual rainfall amounts with the mean calculated over a longer period (see section Study area), especially for 2009 and 2010 which were two particularly wet years.

Water table is measured every 2 d in a 10 m-deep OW at about 7 m of the FG5 measurement site since 2009 March (Fig. 1c). Other OWs located in the surroundings show similar variations in amplitude and phase. WSC in the WTFZ (WSCₚ, [L]) are linked to water-table variations (Δh, [L]) through the specific yield Sy, using

$$WSC_p = Sy\Delta h. \qquad (1)$$

Water-table time-series is shown in Fig. 2a. Maximal water-table depth occurs at the end of June/early July and is 6.3 m in average. The increase of minimum storage from 2008 to 2010 is probably linked to an early start of the rainy season and high annual rainfall in 2009 and 2010 as shown in Fig. 2(b). The late onset of the

rainy season in 2011, after the wet year of 2010 is responsible for the drop in the minimum storage in 2011 June. These observations clearly show important interannual storage variations. Note that the thickness of the never-saturated VZ is about 1.7 m. From September to the following June, the groundwater depletion rate is regular and slow (12 mm d⁻¹). It has been shown that permanent groundwater does not drain into rivers through baseflow, instead groundwater depletion during the dry season (as in Fig. 2a) is more likely explained by root water uptake, even if deep drainage through fracture zones has not been discarded so far (Séguis et al. 2011). Another borehole located about 100 m from the gravimeter shows very similar water-table variations (less than 10 cm difference for the seasonal amplitude of about 4 m for the years 2009–2010, and much more, about 70 cm for the much drier year 2011—not presented in the study—and for which we suspect some problems). Another borehole also located about 100 m from the gravimeter, does exhibit similar water-table variations (less than 30 cm difference on the seasonal amplitude). This indicates that there are some small spatial variations of the water table, yet not directly linked to the topography or to a possible base level.

## 4 WATER STORAGE MONITORING

### 4.1 Method

About 9 m close to the OW is another 7.5-m deep borehole, but enclosed at its bottom, in which weekly measurements of soil moisture [θ, (%)] by NP are undertaken since 2009 March. For further details on NPs, the reader is referred to the IAEA training courses (IAEA 2003). Neutronic measurements are neutron counts measured in each layer of material and normalized by neutron counts acquired in the standard medium, that is, a water tank, giving counting rates (CR). Calibration is needed to transform these counting rates into

<figure><img src="image_3.png" /><figcaption>**Figure 2.** Hydrological data. (a) Water-table time-series. (b) Rainfall data: daily (blue) and cumulative (black). There is a gap in the rainfall data in 2011 May, but regional data show a deficit with respect to past years.</figcaption></figure>
soil moisture. Water contents were obtained by weighting drilling residuals from each depth (i.e. 0.15, 0.3, 0.5 m and every 0.5 m down to 7.5 m) during the drilling process to avoid any loss of water, and by further weighting these samples (about 100 cm³) after they have been dried in an oven. Dry bulk densities were obtained from gamma-probe measurements at same depths and were used to get volumetric water contents. After each drilling, a 63-mm diameter PVC access tube (enclosed at its bottom) was tight fitted into the borehole (65 mm diameter). The eventual thin gap between the tube and the surrounding soil was filled with fine drilling cuttings. NP measurements were undertaken immediately after the drilling, at the end of the day and the following day. This was done to check if there was no further evolution of the CRs after the drilling, may be due to the closing of some cavities around the access tube in soft areas. If none was detected, and no rain happened in between, the CR associated with the calibration was the mean of the three measurements. After calibration, WSC[L] are deduced from the NP moisture variations (Δθ) using the formula

$$WSC = l\Delta\theta, \qquad (2)$$

where l[L] is the investigated thickness (IAEA 2003).

Calibration curves are inferred from recent drillings of about 33 boreholes in 2011 April (dry season), and subsequent calibration drillings in following September (wet season), resulting in 775 (CR, θ) couples. These couples have been associated to three qualitatively defined textural classes based on drill logs analysis. The calibration curve has been inferred for each class, based on the assumption that in such a heterogeneous medium (weathered hard rock), equivalent physical properties can be defined for major units. The three different classes are: soil, lateritic layers and alterite. Classification of each layer has been undertaken qualitatively according colour and texture of cuttings (Fig. 3a).

Statistical parameters of the regression analysis for each class have been used to calculate error estimations on water storage variations, following an approach that takes into account covariance terms between horizons that have the same calibration curve (Vandervaere et al. 1994). The total variance σ²(WSC) of storage variations inferred from NP measurements between two dates is given by

$$\sigma^2(\text{WSC}) = \sigma_l^2(\text{WSC}) + \sigma_c^2(\text{WSC}) + \sigma_{\text{int}}^2(\text{WSC}), \qquad (3)$$

where σ_l²(WSC), σ_c²(WSC) and σ_{int}²(WSC) are the total variance on, respectively, the instrument measurement, the calibration and the integrative method used to interpolate between investigated depths (here we use the trapezoidal method).

NP calibration is based on a linear relationship between counting rates [CR(%)] and water content [θ(%)]:

$$\theta = a + CR \cdot b. \qquad (4)$$

## 4.2 Results

Calibration results are shown in Table 1. Corresponding regression analysis is shown in Figs 3(b)–(d) for each class. Only the borehole close to the gravimeter is used in this study because others are too recent and do not cover the time period of the study.

Soil moisture evolution is shown on Fig. 4, together with the water-table level and daily rainfall. High frequency variations (up to a few days) are not present because of the sampling rate of NP measurements (about 1 week, with some gaps). After a rain event, the top soil rapidly dries out, by evapotranspiration and infiltration. Top soil moisture increases when the first consequent rains fall and water-table rise when water infiltrates deep enough, with a time lag of up to 3–4 months (e.g. the increase in NP-derived

<figure><img src="image_4.png" /><figcaption>Figure 3. (a) Drilling log of the NP borehole and (b), (c) and (d) calibration regressions for each layer. Dotted lines represent the 1σ confidence interval.</figcaption></figure>
<table><caption>**Table 1.** Results of NP calibration for each class. *m* is the number of couples used for calibration, using the equation θ = *a* + *CR*·*b* + *eσ*(*CR*,θ) is the covariance between counting rates (*CR*) and moisture contents (θ), σ²() are variance terms for each parameter of the regression analysis and σ(*a*,*b*) is the covariance between *a* and *b*.</caption><thead><tr><th>Type</th><th>m</th><th>σ(CR,θ)</th><th>b</th><th>a</th><th>σ<sup>2</sup>(e)</th><th>σ<sup>2</sup>(b)</th><th>σ<sup>2</sup>(a)</th><th>σ(a,b)</th></tr></thead><tbody><tr><td>Soil</td><td>142</td><td>0.0058</td><td>3.15<sup>E</sup>-01</td><td>-1.20<sup>E</sup>-03</td><td>1.80<sup>E</sup>-03</td><td>6.76<sup>E</sup>-04</td><td>7.12<sup>E</sup>-05</td><td>-2.19<sup>E</sup>-04</td></tr><tr><td>Laterite</td><td>260</td><td>0.0045</td><td>3.71<sup>E</sup>-01</td><td>-5.54<sup>E</sup>-02</td><td>1.40<sup>E</sup>-03</td><td>4.65<sup>E</sup>-04</td><td>1.24<sup>E</sup>-04</td><td>-2.41<sup>E</sup>-04</td></tr><tr><td>Alterite</td><td>373</td><td>0.0078</td><td>3.51<sup>E</sup>-01</td><td>-5.83<sup>E</sup>-02</td><td>2.00<sup>E</sup>-03</td><td>2.36<sup>E</sup>-04</td><td>7.07<sup>E</sup>-05</td><td>-1.29<sup>E</sup>-04</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>**Figure 4.** Time-depth evolution of water content derived from NP monitoring. Solid black line is the water-table level and daily rainfall is shown on an independent axis.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 5.** NP derived WSC and associated date-to-date errors.</figcaption></figure>

storage in 2010 May has no obvious consequence on the water-table level). Noise in the data can be observed in the saturated zone, for which water content is supposed to remain constant. The upper part of the profile exhibits a higher water content, as can be expected from this weathered hard-rock basement context. During the dry season, storage variations in the WTFZ (i.e. below 1.7 m) are related to drainage process as evidenced by the analysis of suction data from nearby tensiometers. The two recession periods (from 2009 September to 2010 May and from 2010 September to 2011 July) produce seasonal WSC in the WTFZ of 117 and 125 mm, respectively. Once divided by the associated thickness, this gives average water content variations of 2.8 and 2.9 per cent, respectively. Because water content variations in the WTFZ during these recession periods are caused by drainage process, these values provide an estimate of vertically averaged *Sy* value at the NP location.

WSC shown on Fig. 5 are cumulative storage variations with respect to the first value that is set to 0. Error bars are calculated on

<table><caption>**Table 2.** Mean standard deviations of WSC from NP measurements: σ(WSC), σ₁(WSC), σₐ(WSC) and σint(WSC) are mean standard deviations on respectively the derived WSC, the instrument measurement, the calibration and the integrative method used to interpolate between investigated depths (here we use the trapezoidal method).</caption><thead><tr><th>σ(WSC)</th><th>σ₁(WSC)</th><th>σₐ(WSC)</th><th>σint(WSC)</th></tr></thead><tbody><tr><td>11.6 ± 10 mm</td><td>0.16 ± 4.10<sup>-3</sup> mm</td><td>0.6 ± 0.4 mm</td><td>11.6 ± 10 mm</td></tr></tbody></table>

a date-to-date storage variations basis. Standard deviation for WSC is in average 11.6 mm of equivalent water height when all possible couples of the time-series are analysed statistically, and is largely coming from the integration error (Table 2).

NP data show seasonal WSC (Fig. 5) ranging from about 150 mm for the wet season in 2010 to 250 mm in 2009. In this direct recharge context, the onset of the humid period is seen earlier in the NP data than in the water-table record.
# 5 RESISTIVITY AND MRS SURVEYS

For delineating structures of the subsurface in the surroundings of the gravimeter, Descloitre et al. (2011) have surveyed a 300 × 300 m² area using surface geophysical methods. To summarize this study, each geological formation and their respective weathered layers have been identified using a geological survey, resistivity methods and several MRS. Apparent resistivity mapping has been achieved using a Schlumberger array profiling survey with electrode spacing of 20 m, allowing to associate the mapping to the shallowest part of the aquifer. The apparent resistivity map is shown in Fig. 6. Apparent resistivity displays strips with a North–South orientation indicating roughly a 2-D spatial distribution of the corresponding weathered formations. Very clayey zones (conductive) are present jointly with more resistive ones, attributed to low weathered rocks. Because the water content is difficult to quantify with resistivity only, the strips have been investigated using MRS in order to characterize their MRS properties.

The MRS method is based on the property of the nuclei of the hydrogen atoms (protons) in water molecules to have a magnetic moment that can be excited with an alternative magnetic field generated by loop cable laid out on the surface. When the applied field is cut off abruptly, the protons go back to their initial position. Doing so, they generate a relaxation secondary magnetic field, recorded by the instrument. This is the measurement principle of MRS method detailed in numerous publications (see e.g. Legchenko & Valla 2002). The geophysical parameters derived after interpretation are the MRS water content, θ<sub>MRS</sub>, and the relaxation times, T<sub>2</sub>* and T<sub>1</sub>, versus depth. θ<sub>MRS</sub> is defined as the volume of water per unit volume with decay time constant higher than 30 ms (Legchenko et al. 2002). Signal from very clayey formations with too short decay time constants (bound water) are not recorded. θ<sub>MRS</sub> can give an estimate of the effective porosity, if dead-end and unconnected pores can be neglected (Lubczynski & Roy 2005). Both T<sub>2</sub>* and T<sub>1</sub> are linked to the mean pore size containing water (Kleinberg 1996; Kenyon 1997; Legchenko & Valla 2002). The location of MRS loops (8-shaped geometry due to noise removal procedure) is shown in Fig. 6. MRS show θ<sub>MRS</sub> values ranging from 1.5 to 10 per cent in the study area, enlightening the strong spatial heterogeneity

of the medium (Descloitre et al. 2011). Thus, it has been learnt
from this survey that *Sy* could vary a lot from place to place and
this spatial variation should be considered instead of a 1-D layered
subsurface while analysing the gravimeter signal.

6 GRAVITY MONITORING

Absolute gravity measurements were done on a concrete pillar of 1 m³, uncoupled with the shelter basement. The apparatus settings, measurements protocol and applied corrections are the same as presented by Pfeffer et al. (2011). Several series of data sets, each one consisting of 100 drops of the corner cube every 10 s, produce raw gravity values that are corrected for temporal effects, and averaged. Corrections include solid earth tides (tidal parameters from ET-GTAB software; Wenzel 1996), ocean loading (Schwiderski 1980), air pressure effects (using barometric *in situ* measurements, and a regression coefficient of −0.3 µGal hPa⁻¹) and polar motion contribution from pole positions given by the international earth rotation service, IERS (http://www.iers.org).

At short timescales, the earth can be considered as an elastic body,
hence WSC produce two main effects (Farrell 1972; Jacob 2009): (i)
a direct Newtonian effect from the attraction of masses, (ii) elastic
deformation. The latter implies two effects on the earth gravitational
field: a free-air effect from the radial displacement of the observation
point and global mass redistributions. In order to evaluate local WSC
(and compare results to local hydrological monitoring), we need to
correct gravity data for the non-local contribution. Following Pfeffer
et al. (2011), we evaluate large-scale effects using the Global Land
Data Assimilation System (GLDAS/Noah) model by Rodell et al.
(2004). We use soil moisture (from surface down to 2 m depth), snow
and canopy water outputs provided with 3 hr and 0.25° temporal and
spatial resolutions, and over all continental surfaces. The convolu-
tion of these global soil water content estimations with the Green's
functions for Newtonian and deformation responses on a spherical
non-rotating, elastic and isotropic (SNREI) Earth model gives the
total gravity variations (Boy & Hinderer 2006). These calculations,
together with atmospheric and oceanic loading, can be found in Boy
(2012) for the Global Geodynamics Project (GGP) sites, including

<figure><img src="image_7.png" /><figcaption>**Figure 6.** Geophysical data: apparent resistivity mapping and MRS measurements. Numbers are MRS water contents θ<sub>MRS</sub>. The circle shows the 100-m radius zone of influence for gravity variations at the FG5 site. MRS soundings are 8-shaped cable square loops.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Figure 7.** FG5 gravity data: raw (classical corrections applied) data in black, corrected for non-local contribution in red. Absolute values are obtained by adding 978033590.4 µGal. In background and light grey is water-table depth, plotted on an independent axe.</figcaption></figure>

Nalohou. Permanently ice-covered areas (Greenland, Alaska and mountain glaciers) have been masked out and the conservation of the total water mass has been enforced by adding/removing a uniform oceanic layer compensating any lack/excess of water over land. As described in Spratt (1982) or De Linage et al. (2007), the Green's functions have a Newtonian term (the direct attraction of the load) and an elastic, deformation-induced term. The former is also the sum of two contributions, local and global. The local term is equal to the Bouguer analytical expression (i.e. see eq. 5 in the next section). The contribution of continental water storage within a range of a several tens of kilometres around the station is negligible if we assume a thin layer load acting on a spherical earth. In this case, the water masses are at a similar height than the gravimeter, and the vertical attraction is almost null (Llubes et al. 2004). We correct gravity observations for the non-local contribution, by convolving the corresponding Green's functions with the outputs of the GLDAS/Noah global hydrology model.

Gravity measurements started in 2009 July, with a rate of four measurements per year. Dates have been selected according to the hydrological cycle: at the end of June and early July, the water table is the lowest. The corrected gravity values and associated standard deviation during 3 yr from 2008 July to 2011 July are presented in Fig. 7, together with their values corrected for the non-local hydrological component. As shown by a recent study in Niger, the local and non-local hydrology contributions are in phase, the non-local one being about 20 per cent of the total effect (Pfeffer et al. 2011). Hence, the correction for the non-local hydrology reduces the amplitude of gravity variations of local origin. In the background of Fig. 7 is shown the water-table depth, on an independent axis. This allows to roughly compare the phase of the two signals: when

groundwater recharge occurs (between July and September), there is a strong increase in gravity (around 10 µGal). One sees mainly the seasonal term since the lack of higher frequency gravity data sampling avoids finer comparisons.

## 7 GRAVIMETRICAL MODELING

Direct modelling of the gravitational effect of WSC ($\Delta g[LT^{-2}]$) can be achieved at first order by applying the 'Bouguer plate' model:

$$ \Delta g = 2\pi\rho GH, \qquad (5) $$

where $\rho$ is the density of water [$ML^{-3}$], $G$ is the gravitational constant [$L^3 M^{-1} T^{-2}$] and $H$ is the thickness of an infinite water layer [$L$]. This analytical expression can give satisfactory results in the case of a flat topography. In order to account for topographic effects, and for spatial heterogeneity of the specific yield, we use in this study a 3-D prisms model built from the prism equation provided by Leirião et al. (2009). The terrain has been discretized in prisms according to the topography using a local DEM (Digital Elevation Model) built from a network of points measured with differential GPS. The density of points is higher close to the gravimeter. DEM accuracy (Table 3) is derived from 1000 sets of control points randomly picked from the data set. In the region spanning 300 m around the SG, mean RMSD of DEMs with grid sizes varying from 5 to 20 m is about 0.1 m. The accuracy decreases with the spatial extent because of the lower density of points. Using this modelling approach, we simulated the effect of a 1-m thick layer of water distributed according to the topography, using $10 \times 10$-m$^2$ grid cells and obtained 44.5 µGal at the gravimeter measurement site. This

<table><caption>**Table 3.** DEM accuracy estimates. Mean and standard deviation values are calculated from 1000 sets of control points for each grid centered on the FG5 point.</caption><thead><tr><th>Grid size (m)</th><th>Spatial extent (m)</th><th>Data points</th><th>Control points</th><th>Mean (RMSD) (m)</th><th>Std (RMSD) (m)</th></tr></thead><tbody><tr><td>5</td><td>600</td><td>941</td><td>100</td><td>0.1</td><td>0.03</td></tr><tr><td>10</td><td>600</td><td>941</td><td>100</td><td>0.1</td><td>0.02</td></tr><tr><td>20</td><td>600</td><td>941</td><td>100</td><td>0.12</td><td>0.02</td></tr><tr><td>40</td><td>600</td><td>941</td><td>100</td><td>0.17</td><td>0.03</td></tr><tr><td>5</td><td>2000</td><td>2447</td><td>100</td><td>0.31</td><td>0.06</td></tr><tr><td>10</td><td>2000</td><td>2447</td><td>100</td><td>0.34</td><td>0.07</td></tr><tr><td>20</td><td>2000</td><td>2447</td><td>100</td><td>0.448</td><td>0.08</td></tr></tbody></table>
<figure><img src="image_9.png" /><figcaption>Figure 8. Ratio between the gravity effect of a 1 m layer of water in a disk centred on the FG5 with increasing radius and the gravity effect of a 1 m layer of water in a 2000-m diameter disk. Results are shown for different depths.</figcaption></figure>

is slightly more than the 42 µGal derived from the Bouguer plate analytical expression, implying a small role (about 6 per cent) of the topography with respect to a flat model. The effect of the topography, in this case, results in a higher gravity variation than for the Bouguer plate. This is because the gravimeter is located on top of a hill, and more masses than in the plane geometry are located ‘underneath’ the gravimeter, thus increasing the vertical component affecting the gravity measure. For instance, Creutzfeldt et al. (2008) found a higher value of 52 µGal for SG Wettzell observatory in Germany. The gravity effect of a 1-m thick layer of water at 1, 3 and 6 m deep with respect to the topography has been calculated with different grid sizes (5, 10, 20, 30 and 40 m) from the same DGPS data set. Discrepancies in gravity never exceed 2 per cent between all different grid sizes (largest discrepancies being between the 5 m and the 40 m). This very high accuracy obtained even with coarse grids is due to the very flat terrain, with almost no high frequency variations.

The 100-m footprint area of the gravimeter, such as shown on Fig. 1a, is calculated from the ratio between the gravity effect of a 1 m layer of water in a disk centred on the FG5 with increasing radius and the gravity effect of a 1 m layer of water in a 2000-m diameter disk. This is shown on Fig. 8. 90 per cent of the signal modelled up to a radius of 1000 m come from a disk of 40 m for the 1-m deep layer of water (2.5 m below the FG5), 60 m for the 3-m deep layer of water (4.5 m below the FG5), 80 m for the 5-m deep layer of water (6.5 m below the FG5) and 85 m for the 6-m deep layer of water. The 100 m radius corresponds to 92 per cent of the signal modelled up to a radius of 1000 m for the 5-m deep layer of water, which is about the average water-table level.

This model has been applied for the two goals of the present study: (i) to compare and cross-validate NP and FG5 data; (ii) to account for spatial heterogeneity of the specific yield.

## 7.1 Error assessment

In the following, the relevance of the fit between observed ($\Delta g_{FG5}$) and modelled ($\Delta g_m$) gravity variation is assessed using the RMSD equation

$$RMSD = \sqrt{\frac{\sum_{i=1}^{n}(\Delta g_{FG5,i} - \Delta g_{m,i})^2}{n}}, \quad (6)$$

where n is the number of available time steps.

Variances on observed absolute gravity values are obtained from the distribution of hourly set values for each experiment. Variances

on gravity variations are obtained from the summation of respective variances for consecutive data points.

# 8 JOINT ANALYSIS OF DATA SETS: METHODS

## 8.1 Comparison of NP and FG5 data

Because NP measurements are made in a single borehole, a 1-D geometry is applied in the first step of this modelling approach. Water content measurements by NP in the 0–7.5 m layer are uniformly applied for each grid cell of the model, accounting for topography. Let $G[WSC(t)]$ be the transformation of the storage variations through time to gravity variations. Hence,

$$\Delta g_m(\Delta t) = G[WSC_{NP(0-7.5m)}(t)], \quad (7)$$

where WSC$_{NP(0-7.5m)}(t)$ are the storage variations measured by NP through the whole vertical profile where storage variations actually occur, and $\Delta g_m$ is their modelled gravity effect. The latter is compared to FG5-derived gravity variations, and relevance of the fit is evaluated with the RMSD (eq. 6).

The instrument is protected by a 12 m² shelter. This modifies the local infiltration in the vicinity of the instrument (‘mask effect’), and consequently the lack of close infiltration has been evaluated. This mask effect is taken into account by considering two extreme cases, (i) no soil moisture variations underneath the shelter, or (ii) they are exactly the same as without shelter. The first case is obtained by subtracting to the total modelled signal the gravity effect from WSC occurring underneath the shelter.

One should keep in mind that FG5 measurements are spatially integrated, while NP produces point-measurements. The 1-D assumption made here can be inappropriate because 2-D structures have been evidenced with surface geophysics.

## Error assessment

The confidence interval on modelled gravity variations is simply calculated as the gravity effect of the NP-derived storage time-series; with $\pm 1\sigma$ uncertainty in NP values (as shown on Fig. 5, calculated using eq. 3).

## 8.2 2-D model for specific yield

The water-table fluctuations can be considered as representative over the 100 m radius around the FG5 site, as confirmed by the similarity exhibited by different water-table measurements carried out close to the site. Considering water-table fluctuations in the saturated zone of the model allows hence to account for spatial variability of the storage through $Sy$ mapping. For unconfined aquifers, mass variations in the saturated zone are directly linked to the specific yield. Its value and spatial distribution control the amount of water that produces gravity variations (Pool & Eychaner 1995). A 2-D model for $\theta_{MRS}$ is shown in Fig. 9. Cells size is 20 × 20 m² large in the vicinity of the gravimeter and 50 × 50 m² further away. Taking smaller cells had no influence, because of the relatively flat topography (see Section 7). Also, the resolution of resistivity mapping is not precise enough to describe a possible structure for $\theta_{MRS}$ at finer scales.

Numerous studies showed that $\theta_{MRS}$ is somewhat different from $Sy$ (Vouillamoz et al. 2005; Boucher et al. 2009; Vouillamoz et al. 2012) and rather close to the effective porosity, defined as the portion
<figure><img src="image_10.png" /><figcaption>Figure 9. 2-D model for θ<sub>MRS</sub> obtained through the spatialization of MRS water contents using resistivity mapping and geological observations. The circle shows the 100-m radius zone of influence for the FG5 gravimeter.</figcaption></figure>

of a medium that contributes to the flow and advective transport (Lubczynski & Roy 2005). Knowing this, we scaled the 2-D model by a factor α, using

$$S_y = \alpha \theta_{\text{MRS}}(x, y), \qquad (8)$$

where θ<sub>MRS</sub>(x, y) stands for the spatial distribution of the MRS water content.

Gravity variations from the WTFZ and the VZ are modelled by

$$\Delta g_m (\Delta t) = G [\Delta h \alpha \theta_{\text{MRS}} (x, y) + \text{WSC}_{\text{NP(VZ)}} (t)], \qquad (9)$$

where Δh is the water-table variations uniformly distributed according to the topography. It is then possible to optimize the α parameter (eq. 9) with respect to FG5 data, minimizing the RMSD (eq. 6).

It is also possible to derive a 1-D equivalent S<sub>y</sub> parameter, by adjusting a single value of S<sub>y</sub> over the whole area without taking into account the spatial variability. To derive a 1-D equivalent S<sub>y</sub> value is highly interesting for hydrological models, or for any further attempt to use gravity data as a proxy for water storage monitoring.

## 8.3 Error assessment

Variances on modelled gravity variations are estimated for the two contributing compartments (WTFZ and VZ). For the WTFZ, water-table measurements can be considered to be quite accurate. If we hypothesize an uncertainty of 1 cm on the reading, with an average S<sub>y</sub> value of 5 per cent, this leads to a 0.5 mm error on storage estimation, which is insignificant compared to NP measurements errors (as shown on Table 2). However, spatial variations of the water table in the vicinity of the gravimeter site are not taken into account in this study. As specified in Section 3, other boreholes exhibit similar variations, and discrepancies seem not to be correlated to spatial variations of θ<sub>MRS</sub>, as one could expect a correlation between water-table levels and S<sub>y</sub>. For the VZ (the 0–1.7 m layer), standard deviations on NP-derived storage variations are obtained using eq. 3. Then, their gravity effect has been calculated using the present model.

To get the best-fitting α value, a simple Monte-Carlo approach is adopted: 40 000 sets of (modeled VZ gravity contribution, observed FG5 data) scattered couples are randomly sampled within their distribution in both dimensions, assuming they are normally distributed. These distributions are defined by their mean values and standard deviations based on the error assessments of observed gravity variations and modelled VZ contributions. For each set, the contribution of the WTFZ is added by testing a range of α values. The best-fitting α for each set is found by minimizing the RMSD (eq. 6). We eventually obtain both the mean value and standard deviation of the resulting α distribution.

# 9 JOINT ANALYSIS OF DATA SETS: RESULTS

## 9.1 1-D model: cross-validation of NP and FG5 data

The first result of this study arises from the comparison of gravity data with direct water content measurements by NP in the 0–7.5 m layer (the whole profile where WSC occur), from which the gravity effect is calculated using the aforementioned model (Fig. 10). In this figure, as we are dealing with storage variations, each modelled time-series is vertically shifted with an offset that minimizes the distances to FG5 data points. When considering the mask effect of the shelter (i.e. no WSC underneath the shelter), the

<figure><img src="image_11.png" /><figcaption>Figure 10. FG5 data (red points with error bars) and gravity modelling of NP-derived storage variations (black line). Light black curves show the confidence interval at ±1σ. Dashed blue curve takes into account the mask effect of the shelter (i.e. no WSC underneath the shelter).</figcaption></figure>
calculation produces a time-series that remains most of the time within the error bars of the former (blue curve in Fig. 10). The comparison shows a fair agreement when considering respective error bars (RMSD = 1.61 µGal). Discrepancies between gravity measurements and the water storage model made out of point measurements can be related to the non-representativeness of the NP data (point measurements in a specific borehole) with respect to the larger zone ‘seen’ by the gravimeter. This is particularly true in case of strong local heterogeneities. Hence, the next step is to introduce the spatial distribution of θ<sub>MRS</sub>, known to be close to Sy.

## 9.2 2-D model and specific yield estimation

Fig. 11 shows the results of the 2-D model for specific yield (black curve), derived from MRS and resistivity mapping, assuming that θ<sub>MRS</sub> = Sy (i.e. α = 1). The gravity data, within their standard deviation, are not so well adjusted to the modelled water storage variations, particularly for the ‘wet’ point in 2010 and the two points in 2009 April and July. The black curve comes from the summation of two contributions, the VZ and the WTFZ. Relative contributions from the VZ and the WTFZ are 20 and 80 per cent, respectively, enlightening that now 80 per cent of the model does account for spatial heterogeneities of the specific yield. Furthermore, the underlying assumption

of spatial homogeneity in the upper (VZ) layer needs to be valid in a smaller area (see Fig. 8). The RMSD of the fit is 2.5 µGal, and associated scatter plot is shown on Fig. 12(a) (black points). Recent data from six other NP boreholes located within the 100 m radius of influence of the gravimeter indicated a mean seasonal amplitude in the VZ of 74 ± 10 mm for the 2011–2012 hydrological year. This standard deviation of 10 mm of equivalent water thickness corresponds to 0.44 µGal when using the linear relationship of 0.044 µGal mm⁻¹ (see Section 7). This is small compared to the seasonal signal, and to the RMSD of the fit, assuming little impact of using a single borehole for the VZ.

The WTFZ can produce the same contribution if we consider a uniform model of θ<sub>MRS_equ1-D</sub> = 0.07. This value is retrieved by assuming a homogeneous layer with a constant specific yield value in the WTFZ, and testing a range of values until the same curve as the one coming from the spatial model θ<sub>MRS</sub>(x, y) with α = 1 (Fig. 11) is qualitatively found (i.e. results with = 1 are exactly the same as when using a uniform layer with Sy = 0.07). This value can be seen as an averaged θ<sub>MRS</sub> within the footprint area of the gravimeter, somehow weighted by an inverse square distance function.

When using the 2-D model (eq. 9), it is thus possible to find the optimal α value, with respect to gravity data, by minimizing the RMSD (eq. 6). Results are shown on Fig. 11 (blue line) for the time-series, and on Fig. 12(a) (blue points) for the fit between

<figure><img src="image_12.png" /><figcaption>**Figure 11.** FG5 data (red points with error bars) and gravity modelling of hydrological effect: black and blue curves are the sum of the VZ contribution and the WTFZ contribution with respectively the spatialized θ<sub>MRS</sub>, with α = 1 (black), or with the best-fitting α value (blue).</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Figure 12.** (a) Scatter plot of gravity variations (model and data) for both the distributed model θ<sub>MRS</sub>(x, y) with α = 1 (black points) and the best-fitting α value (blue points) and respective error bars. (b) Distribution of optimized α values for the 40 000 sets of (modelled VZ gravity contribution, observed FG5 data) scattered couples.</figcaption></figure>
observed and modelled gravity variations. Blue points are closer to the $y = x$ line than black points, with a RMSD value of 0.94 µGal. They show a better agreement with FG5 data than both the spatial $\theta_{MRS}(x, y)$ ($\alpha = 1$) model and the 1-D uniform (NP) model.

The distribution of best-fitting $\alpha$ values following the Monte Carlo sampling scheme is shown on Fig. 12(b). Results seem normally distributed, and mean $\alpha$ value is 0.63 with a standard deviation of 0.15.

# 10 DISCUSSION

## 10.1 Storage variations

For the first time, gravity variations are compared to WSC measured by NP through the whole vertical profile, including the WTFZ. Integrative (100 m radius) gravity measurements show a good fit with modelled gravity from NP point measurements under the 1-D uniform assumption. Discrepancies between modelled and observed gravity variations (RMSD = 1.61 µGal) may arise from the strong heterogeneity of the investigated medium. The modelled shelter effect (no WSC underneath the shelter) provides a time-series that is very close to the unmasked one. Furthermore, because we focus on the seasonal scale (3 months sampling rate for the FG5 data), it is very likely that redistribution of water underneath the shelter occurs, minimizing this mask effect.

However, both time-series fit within their own error bars, providing us with a new validation of gravity data potential for hydrological studies. This validation of WSC quantification using absolute gravity data allows some comparisons with previous studies. For instance, daily gravimetric decrease rates during the dry season (derived from gravimetric measurement in September and January) are of about 0.05 – 0.08 µGal d⁻¹, that is to say, 1.1 – 1.8mm d⁻¹. This is in fair agreement with evapotranspiration values obtained during the dry season by scintillometry (Guyot et al. 2009), or by hydrological budget studies (Séguis et al. 2011) on this same study area, but with a microbasin wide (22.6 ha) spatial extent. Also, gravity data give us information about the interannual storage variations: minimum storage increased from 2008 to 2010 (1.7 ± 1.1µGal yr⁻¹), comparatively with water-table levels (Fig. 4), and resulting from 2 wet years.

## 10.2 Specific yield and MRS water content

An attempt to account for spatial heterogeneity of specific yield has been made on the basis of MRS and resistivity mapping. A single gravity time-series is in no way able to constrain such a spatial distribution. However, the lower RMSD value (Table 4) of this approach, with respect to the 1-D assumption, seems to confirm the interest of the method that combines hydrological data and geophysical survey for retrieving WSC.

Deriving the best-fitting $\alpha$ parameter means retrieving the $\alpha = Sy/\theta_{MRS}$ ratio for the footprint area of the gravimeter, somehow weighted by an inverse square distance function. Vouillamoz et al. (2005) for crystalline basement aquifers in Burkina Faso and Boucher et al. (2009) for sedimentary aquifers in SW Niger showed that $\theta_{MRS}$ was higher than $Sy$ obtained by pumping tests. The latter experiment has been confirmed by Pfeffer et al. (2011) when they compared MRS data and $Sy$ from gravity monitoring. This is because $\theta_{MRS}$ is an estimate of the effective porosity rather than specific yield (Lubczynski & Roy 2005). In the clayey weathered rocks of this study, effective porosity should be clearly higher than specific yield and thus $\theta_{MRS}$ higher than $Sy$ (Vouillamoz et al. 2012). These authors found $Sy/\theta_{MRS} = 0.4$ for a clayey sandstones aquifer in Northern Cambodia. We found that $Sy/\theta_{MRS} = 0.63 \pm 0.15$ thus confirming previous results. The 1-D equivalent $Sy$ value for each model are shown on Table 4, and are consistent with the best-fitting $\alpha$ value ($\alpha = Sy/\theta_{MRS} = 4.4/7 = 0.63$). Thus, a 1-D equivalent value of 4.4 per cent is to be kept for the footprint area of the gravimeter. This value can be compared to $Sy$ values derived from NP and water-table monitoring (see Section 4) during the two recession periods: 2.8 and 2.9 per cent, although these are only valid locally. Furthermore, both approaches have the limitation of producing a vertically averaged value, which has practical interests for hydrogeologists, but that may differ from the $Sy$ of single layers. This 1-D equivalent approach will serve further hydrological modelling, and will be employed to monitor groundwater storage from gravity data onsite.

## 10.3 Perspectives

Scarce absolute gravity data have proven to provide reliable estimations on both water storage variations and specific yield estimates when used jointly with complementary hydrological data. A SG is available on site since the summer of 2010 and provides us with a high precision (≈0.1 µGal) continuous time-series of gravity variations. Because of a strong initial drift in this relative gravimeter, data were not available for the timespan of this study. However, they will be used to achieve a precise monitoring of water storage variations, both at seasonal scale and short timescale (rainfall event). Also, microgravity relative measurements are currently undertaken to extend this data intercomparison to the small catchment surrounding the FG5 site. They will be used to infer spatiotemporal variability of recharge processes, and hopefully validating repeated microgravity measurements for hydrological processes studies at the catchment scale. They will also allow to further check the 2-D model of $\theta_{MRS}$ described in this study.

As gravity observations allow to recover seasonal storage variations, they can effectively be used for recharge monitoring. This study is currently undertaken, together with an analysis derived from these field experiments to recover the time variability of the specific yield. The field of hydrogravimetry proves to bring further

<table><caption>**Table 4.** RMSD, correlation coefficient and *p* value between observed and modelled gravity variations for each model, and 1-D equivalent $Sy$ for both the $\alpha = 1$ and the best-fitting $\alpha$ model.</caption><thead><tr><th>Model</th><th>1-D NP</th><th>2-D &theta;<sub>MRS</sub>(x, y)(&alpha; = 1)</th><th>2-D &alpha; = 0.63 &pm; 0.15</th></tr></thead><tbody><tr><td>RMSD (&mu;Gal)</td><td>1.61</td><td>2.50</td><td>0.94</td></tr><tr><td>Correlation coefficient</td><td>0.97</td><td>0.97</td><td>0.98</td></tr><tr><td>P Value</td><td>2 &times; 10<sup>-5</sup></td><td>7 &times; 10<sup>-6</sup></td><td>2 &times; 10<sup>-6</sup></td></tr><tr><td>1-D equivalent Sy (per cent)</td><td>-</td><td>7</td><td>4.4</td></tr></tbody></table>
insights for hydrologists by providing new kind of integrated obser-
vations, as long as non-hydrological components can effectively be
corrected from the signal.

11 CONCLUSION

In this study, absolute gravity data from FG5 monitoring have been
compared to modelled gravity variations derived from WSC mea-
surements by NP and water-table level. Gravity data have been
corrected for solid earth tides, ocean loading, air pressure effects,
polar motion contribution and non-local hydrology and residuals
are associated to local WSC and show seasonal variations of up to
11 µGal. This is somewhat higher than gravity variations deduced
from NP only and distributed according to the topography, using
a 0.1-m accuracy DEM. NP data have the advantage to investigate
the whole profile where WSC occur in this weathered hard-rock
basement context. Drawbacks of comparing NP data to gravity data
are the local character of the former, with respect to the integrated
nature of the second.

Spatial heterogeneities of the WTFZ were taken into account in the second part of this study, by scaling a factor of a 2-D model for θMRS on the basis of gravity residuals. This resulted in a significant decrease of the RMSD between gravity residuals and the modelled signal and thus militates for the proper modelling of the spatial distribution of WSC, especially in such heterogeneous medium.

ACKNOWLEDGEMENTS

This work has been performed within the frames of the ANR
GHYRAF project and the AMMA-CATCH observation system.
The authors would like to thank numerous people who helped to
achieve this work. Calvo M., Bernard J.D., and Tahirou Sarè for
FG5 measurements, Imorou I., Pagou E., Ouani T., Afouda S., for
hydrological acquisition, and Ferhat G. for topographic mapping.
We would also like to thank the project partners who allowed the
use of their infrastructure and provided valuable information and
advices. From the Direction Générale de l'eau (DG-Eau, Cotonou):
Gbodogbé J.C. and Zannou A., from the Abomey-Calavi university:
Yalo N. Creutzfeldt B. and another anonymous reviewer deserve a
special mention for the very complete and constructive review that
significantly helped to improve the present paper.

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