Olivier Stasse

Andreas Orthey

Mathieu Francesco Morsillo

Mathieu Geisert

Nicolas Mansard

Maximilien Naveau

Christian Vassallo

Airbus/future of aircraft factory HRP-2 as universal worker proof of concept

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Airbus/Future of Aircraft Factory HRP-2 as Universal Worker Proof of Concept. Abstract-In this paper, we present a preliminary proof of concept (PoC) aiming at introducing humanoid robots in an aircraft factory. The PoC was aiming at demonstrating the capacity of HRP-2 to deal with three aspects needed in a factory: reactivity to change in the environment, visual feedback and on-line motion generation. The limits reached in this PoC are here highlighted to draw some direction of research focused on the needs of Aircraft manufacturers.

Humanoid robot technology has reached a high level of maturity and now has been implemented on several high quality robots such as Asimo, Atlas, TORO or HRP-2. They have been long envisionned as universal worker which can be used in factory, this video present a PoC in this context.

I. FAST RE-PLANNING FOR MOVING OBSTACLE

AVOIDANCE

The setup of this scenario is depicted in Fig. 1. Using information provided by motion capture the robot is able to *This work was supported by the Airbus/Future of Aircraft Factory. 1 are with the CNRS, LAAS,7 av. du Colonel Roche, F-31400, Toulouse, France, Univ de Toulouse, LAAS, F-31400, Toulouse, France surname.name@laas.fr plan autonomously footsteps from its current location to the pylon engine. The pylon engine is the piece which connect the aircraft engine and the wing. This is where the robot has to perform his screwing motion. A human may move the toolbox such that it crosses the path of the robot. The robot is able to change its footsteps and avoid the toolbox.

The robot is searching over a set of pre-defined action set which are known to be feasible. The small foot-print of the action set allows for real-time planning search over a costfunction which includes a metric from the starting point to the robot current location and a metric from the robot current location to its final goal. This solution is currently based on the family of A* algorithms as proposed in the following papers [START_REF] Chestnutt | Motion Planning for Humanoid Robots[END_REF], [START_REF] Kuffner | A* for real-time foot-step planning[END_REF], [START_REF] Hornung | Anytime search-based footstep planning with suboptimality bounds[END_REF] with demonstrations on various humanoid robots such as ASIMO, HRP-2 or NAO. The method here is also based on our work published in [START_REF] Perrin | Fast humanoid robot collision-free footstep planning using swept volume approximations[END_REF]. More precisely, from a set of quasi static half-steps, the robot trajectory is speed up using an analytical pattern generator coupled with PQP to test if the trajectories are without collision.

The robot is able to plan very quickly a path from its current location to the final one as depicted in the bottom of the first sequence of the video. If the toolbox is put on the robot path and if the robot is three steps away it can avoid it. The three steps are a limitation related to the pattern generator which needs this information on the future. It is currently quite difficult to find in real-time a full wholebody trajectory which avoid obstacles and maintain the robot balance. The goal of this experiment showing the reactive capabilities of the system in this specific context has been reached.

A* approach are using a limited set of actions to simplify the problem solving. However in situation a bit more complex the robot tends to make unnecessary long sequence of steps because it is exploring only this limited sequence of actions. This was the main point of using a more aggressive approach proposed in [START_REF] Perrin | Fast humanoid robot collision-free footstep planning using swept volume approximations[END_REF]. In order to adapt more reactively the plan, the system would need a rather different control system for balancing. This is the subject of the second experience.

II. REACTIVE WALKING PATTERN GENERATOR

The balance control law of the robot takes as an input a velocity reference, and the system try to find footsteps such that the robot Center-Of-Mass is following as much as it can the velocity reference. In this PoC, two ways were tried to compute a reference velocity: visual servoing, and Euclidian distance between the object pose and the robot pose using a Motion Capture system. A more detailed description of the balance control law developed in the context of the French Research Project R-Blink is available in [START_REF] Herdt | Walking without thinking about it[END_REF]. A first experiment with this setup was realized in [START_REF] Dune | Vision based control for humanoid robots[END_REF].

In the video the robot is able to follow the position of the engine pylon given by the motion capture system in the frontal plan. This library was successfully used for the experiments described in [START_REF] Dune | Vision based control for humanoid robots[END_REF]. It was interesting to test it on a different HRP-2 to check the portability of the software.

Unfortunately if the ViSP library has been working quite well with the wooden mockup made by LAAS of the engine pylon, (as shown on the third section of the section) it did failed with the 3D-print provided by Airbus. The main reason is the lack of sharp edge in the back of the pylon. We tried various strategies such as including a Kalman Filter, introducing knowledge in the tracker, but it turns out to be easier to use the Motion Capture System. If this control law shows great promises, it needs further improvement in the robustness part to be used in a repeatable setup. Our current line of research is to improve the balance control by including resolved momentum control, and dynamic filter.

III. WHOLE BODY MOTION FOR SCREWING

The goal of this third behavior was to check whether or not if the humanoid robot HRP-2 is able to make the basic motion necessary to go towards positions allowing a screwing action on the engine pylon. Note that the robot assume that an extender of 10 cm is put at the extremity of the electric screwdriver.

The behavior realized was based on the stack of tasks [START_REF] Mansard | A versatile generalized inverted kinematics implementation for collaborative working humanoid robots: The stack of tasks[END_REF] a framework which is combining different control laws together and takes advantage of humanoid robots redundancy. Its software implementation has been used since 2006 to implement various demonstrators. The goal of the mathematical formulation is to enforce properties which make the control safer by checking strictly some limits, and still make possible to change dynamically the control and being efficient [START_REF] Escande | Hierarchical quadratic programming[END_REF].

In the frame of the PoC, the main point was to test the work space of the HRP-2 humanoid with a 3D print of an AIRBUS screwdriver. The robot was able to reach most of the positions in the frontal plane of the engine pylon. On the wood mockup we have been able to realize a behavior where the robot is visually tracking the point by a whole body motion without moving the feet. However the vision process did not work properly on the 3D-print, so we decide to switch to the Motion Capture instead. This is demonstrated in the third and fourth sequence of the video. It has to be notice that the transition between the points is not formally proved or checked. It worked because the robot is highly redundant and we did not push the robot to the limit. Trying to reach the screws at the top of the engine pylon will need probably planning trajectories. During the process we tested our control in acceleration to improve the behavior of the system.

The behavior was very much improved but we found one problem in our solver when the task is a posture. For this reason we came back to the usual kinematic control.

In addition we have tested very high gain showing that the robot is able to go up to 1.6s between the transitions. But the momentum involved by this fast motion has to be taken into account at a higher level and cannot be recovered by the current robot stabilizer. For this reason, we kept a rather low gain for the robot and we are currently in the process of improving it. Finally we noted that when the robot is lowering down, it is close to self-collision. This can be fixed using self-collision avoidance, but call for a deep interaction between planning and control. This is especially true when using vision. A slight drift in rotation may prevent the convergence of the controller to a screwing point.

IV. CONCLUSION

The robot HRP-2 is able to evolve in an environment with moving objects such as a toolbox pushed by a human. We have shown that using a localization system, it is possible to walk but also to make the robot perform whole body motion with one control architecture. The current limitation of the system is the complexity of the environment and the large space of possible motion for the robot. Still for the current setup on which we agree for the PoC, the current techniques seem applicable. It is however possible to improve the speed of the robot, and try the next level where the robot is really trying to perform the screwing action. We are looking forward to continue this line of action and try more challenging environment, and motion.

O. Stasse 1 1 Fig. 1 .

 111 Fig. 1. Situation of the experiment: The robot has to go in the vicinity of the pylon engine depicted in blue while avoiding the red moving toolbox ;

ACKNOWLEDGEMENT

We gratefully acknowledge S. Boria and B. Duprieux from Airbus/Future of the Aircraft Factory for their help and support.


P Genthon
email: pierre.genthon@ird.fr

Hector
email: bhector@unistra.fr

A Luxereau
email: luxereau@mnhn.fr

M Descloitres
email: marc.descloitres@ird.fr

H Abdou

M Bakalowicz
email: michel.bakalowicz@gmail.com

Groundwater Recharge by Sahelian Rivers : Consequences for Agricultural Development. Example from the Lower Komadugu Yobe River (Eastern Niger, Lake Chad Basin)

Keywords: aquifer recharge, irrigated pepper farming, groundwater modeling, sustainable development, Lake Chad Basin, Komadugu Yobe

In the Sahel region, temporary rivers and ponds constitute green spaces of welfare where sustainable development requires parsimonious management of water resources. The Komadugu Yobe (KY) valley in Eastern Niger is presented here as an example case of recent agricultural development based on irrigated pepper cropping. Piezometric maps indicate there that the river recharges the upper quaternary aquifer. A simplified numerical model allows to quantify the exchanges between the river on the aquifer, based mainly on exploration geophysics data and three piezometric records, covering between 1 and 3 years of our 4 years modeling period. Recharge at the valley axis is modeled with a linear river coefficient constant for each hydrological year. The main findings are that: (i) during dry years, the river is disconnected from the aquifer and separated from it by a layer of unsaturated medium, (ii) however, this effect can be reversed, such as during the 2010-2011 wet year or after the Sahelian drought event of the 1980s and 1990s, (iii) the infiltration rate from the river amounts to 30 to 40% of its total discharge and to at least four times the abstraction for pepper irrigation along its 150 km lower course at the Niger-Nigeria boundary, which implies that neither the aquifer recharge nor the river discharge are at risk due to the present agricultural development. Similar modeling near temporary river axes could provide some help in water resource management in the Sahel.

Introduction

Water availability is a key factor for the sustainable development of Sahelian societies [START_REF] Cheo | Vulnerability of water resources in northern Cameroon in the context of climate change[END_REF]Babamaajii and Lee 2014). In several instances they can rely on groundwater mainly recharged in the past [START_REF] Taylor | Groundwater and climate in Africa-a review[END_REF][START_REF] Macdonald | Quantitative maps of groundwater resources in Africa[END_REF]) and from which the present renewal rate can be estimated [START_REF] Scanlon | Global synthesis of groundwater recharge in semiarid and arid regions[END_REF], generally by geochemical methods [START_REF] Edmunds | Paleoclimate and groundwater evolution in Africa: implications for adaptation and management[END_REF]). In the northern Sahel, rivers, ponds and lakes constitute green spaces of relative welfare where the production activities rely on both surface water and groundwater [START_REF] Tarhule | Adaptation to the dynamics of rural water supply from natural sources: a village example in semi-arid Nigeria[END_REF]. Local water budgets are needed for estimating the water resource available for sustainable development [START_REF] Carter | Shallow groundwater in the northeast arid zone of Nigeria[END_REF]. Numerical modeling of groundwater/surface water interaction may help to understand the effect of climate changes [START_REF] Engelhart | Surface and subsurface conceptual model of an arid environment with respect to mid-and late Holocene climate changes[END_REF], to assess the consequences of various management scenarios [START_REF] Feng | Groundwater simulation using a numerical model under different water resources management scenarios in an arid region of China[END_REF]) and to solve possible future conflicting uses. Flowing at the eastern part of the boundary between Niger and Nigeria, the Komadugu Yobe (KY) is a sahelian temporary river which drains into Lake Chad (Fig. 1). This region was strongly impacted by the Great African Drought, which began during the 1970s and is considered as one of the most significant climatic events worldwide [START_REF] Hulme | Climatic perspectives on Sahelian dessiccation: 1973-1998[END_REF]. Local people have achieved strong adaptation to the drought effects almost without external help [START_REF] Mortimore | Farmer adaptation, change and 'crisis' in the Sahel[END_REF][START_REF] Mortimore | Adapting to drought in the Sahel: lessons for climate change[END_REF]). In the KY area they mostly substituted fishing and rainfed agriculture (pearl millet) with sweet pepper cropping irrigated with surface water, however with minor abstraction of groundwater (Luxereau et al. 2011). There are concerns on the sustainability of the development of this area given the limited water resource, the climate variability and the limited size of the pepper market. Several models have been developed at the scale of the uppermost quaternary aquifer of the Lake Chad, as part of the PhD works of [START_REF] Leblanc | Use of GIS and remote sensing for water resources management of large semiarid regions[END_REF], [START_REF] Gaultier | Recharge et paléo-recharge d'une nappe aquifère libre en milieu sahélien (Niger Oriental). Approches géochimiques et hydrodynamiques[END_REF], Zairi (2008) who took into account the variable climatic forcing and in [START_REF] Boronina | Application of AVHRR imagery and GRACE measurements for calculation of actual evapotranspiration over the Quaternary aquifer (Lake Chad basin) and validation of groundwater models[END_REF] who focused their work on evapotranspiration and on the infiltration budget. [START_REF] Candela | Groundwater modelling with limited data sets: the Chari-Logone area (Lake Chad Basin, Chad)[END_REF] aimed to provide a user friendly model for the water planners of this area. One common conclusion of these models is that the Yobe River and the Lake Chad constitute presently the main recharge zones for the aquifer. However the poor coverage of their dataset, both in time and space and the resulting poor spatial resolution of the models produce large uncertainties in the water budget in the Yobe -Lake Chad area. Since 2005, thanks to a series of research projects additional data have been gathered in this area regarding (i) the changes of livelihood of local population since the African Drought and the development of irrigated agriculture (ANR/Biodivalloc ANR/Plantadiv and EC2CO/Repas projects), (ii) the structure and hydraulic properties of the quaternary aquifer, from exploration geophysics, direct sampling and piezometric data (IRD/Lake Chad, EC2CO/Repas, and ANR/Ghyraf programs). The KY will therefore be considered as an example case for assessing the water budget of a combined river aquifer system in the Sahelian area. A conceptual model focused on the KY is proposed, and then a numerical model with a hundred meter spatial resolution is built near the city of Diffa. The first part of the present paper is devoted to the surface water changes in the Yobe River and the Lake Chad since the 1970s. The second one is devoted to the quaternary aquifer, its structure from exploration geophysics and fluctuations of water table, and finally to the outline of the resulting conceptual model. The third one discusses the results of numerical modeling of the response of the uppermost aquifer to the river flow regime and consequences for the water budget and the reaction of the river to drought events. Some hints on the sustainability of the development are given in conclusion. Detailed informations on the livelihood of local population and its changes triggered by the Drought are given in Online Resource 1, and additional information on the model, its optimization and validation can be found in Online Resource 2.

Surface water

The Komadugu Yobe River (KY) originates in the wet highlands of the Jos Plateau in Nigeria. It flows through several wetlands before its entry in Niger and then is meandering over nearly 150 km in the Kadzell plain before reaching the Lake Chad (Fig. 1). The Kadzell plain itself is believed to have constituted the bed of the Megalake Chad that covered nearly 350 000 km 2 during the African Humid period nearly 6000 years ago [START_REF] Leblanc | Reconstruction of Megalake Chad using shuttle radar topographic mission data[END_REF]). The KY is a non-steady river at the decadal to millennial timescale; significant changes in its course since 1950 are reported by Martinsson ( 2010) and a fossil valley of the KY can be seen 40 km northward of the present one. The present valley is 1 to 5 km wide and characterized by numerous abandoned meanders. The main source of data for the hydrology of the KY is the "Direction de l'Hydraulique" located in Diffa and the SIEREM database [START_REF] Boyer | SIEREM an environmental information system for water resources. 5 th World FRIEND Conference[END_REF]. There are several gauging stations along the course of the KY in Niger (Tam, Bagara, Geskerou, Bosso) but Bagara, situated 5 km upstream Diffa is by far the most complete. The annual rainfall on its watershed was computed from both rain gauges and satellite data, with a weight shifting from rain gauges data before 2000 toward satellite data later on, using the method assessed for the whole Lake Chad hydrologic basin by [START_REF] Bastola | Temporal extension of meteorological records for simulation modeling of Lake Chad Basin (Africa) using satellite rainfall data and reanalysis datasets[END_REF]. Rainfall (Fig. 2a) exhibits the same rupture as the one noted in the West African Sahelian record by Le [START_REF] Barbé | Rainfall variability in West Africa during the years 1950-90[END_REF] and [START_REF] Mahé | 1896-2006 sahelian rainfall variability and runoff increase of sahelian rivers[END_REF]; the 1970s and especially the 1980s are marked by severe droughts. However, there is almost complete recovery of rainfall since the 2000s, as noted by [START_REF] Lebel | Recent trends in the Central and Western Sahel rainfall regime (1990-2007)[END_REF] for the whole Eastern Sahel. The annual discharge of the KY appears to be mainly controlled by rainfall. It has been severely impacted by the drought of the 1970s and 1980s, but this impact was only transitory and discharges during recent years are comparable to those of the humid years of the 1960s (Fig. 2a). Some characteristic hydrographs of the KY at Bagara are displayed on Fig. 2b. The water level rises sharply at the onset of flow, generally between mid-June and the beginning of July. The wettest years present a second rise of water level at the end of the high flow period. All hydrographs are characterized by an abrupt drop of the level at the end of the flow period which indicates very little discharge from the aquifer during low flow. The influence of the major dams of Tiga and Challawa [START_REF] Barbier | Upstream dams and downstream water allocation; the case of the Hadejia-Jama'are floodplain, northern Nigeria[END_REF] built in 71-74 and in 90-92 on the upper tributaries of the KY is hardly detected in the hydrographs. However some large isolated peaks of discharge such as in 1998, 2001 and 2003 might be attributed to the management of these dams, since the discharge seems disproportionate with respect to the rainfall anomaly. The Lake Chad is characterized by its large sensitivity to climate: Its northern pool, the only one to which people from Niger have access, was dried repetitively during the African Drought. Since the 1990s, the drought has alleviated and water has returned in the northern pool, but without reaching the level of the 1960s. More details on the hydrology of the Lake Chad can be found in [START_REF] Olivry | Reverse phenology and dryseason water uptake by Faidherbia Albida (Del.) A. Chev. in an agroforestry parkland of Sudanese west Africa[END_REF], while a discussion focused on the region of the mouth of the KY is given in Luxereau et al. (2011). Due to the lesser availability of water from the Lake Chad local people had to turn toward the KY, which induces a larger dependency to the KY hydrological regime.

Groundwater with emphasis on the uppermost quaternary aquifer

The Quaternary aquifer near Diffa

The KY valley overlies a series of superposed aquifers in the Lake Chad sedimentary basin [START_REF] Leduc-Pnud | Les ressources en eau du département de Diffa, Diffa, Direction de l'Hydraulique[END_REF]. The uppermost quaternary aquifer is hydraulically isolated from lower aquifers by more than 100 m thick Pliocene clays [START_REF] Greigert | Atlas des eaux souterraines de la République du Niger. Etat des connaissances[END_REF]Schneider and Wolf 1992). Its hydraulic properties have been discussed by [START_REF] Greigert | Atlas des eaux souterraines de la République du Niger. Etat des connaissances[END_REF], Schneider and Wolf (1992), [START_REF] Leduc-Pnud | Les ressources en eau du département de Diffa, Diffa, Direction de l'Hydraulique[END_REF] and [START_REF] Eberschweiler | Monitoring and management of groundwater resources in the Lake Chad Basin: mapping of aquifers water resource management -final report[END_REF]. It is nearly 80 m thick in the region of Diffa and consists mainly of silty sands alternating with sand or clayey layers of limited extension [START_REF] Gumnior | Late Quaternary river development in the southwest Chad Basin : OSL dating of sediments from the Komadugu paleoflooplain (Northeast Nigeria)[END_REF]. We have now a precise knowledge of the uppermost 10 m of this aquifer thanks to the nearly 50 auger holes drilled and analyzed by Le Coz (Le Coz 2010;[START_REF] Coz | Multiple-point statistics for modeling facies heterogeneities in a porous medium: the Komadugu-Yobe alluvium, Lake Chad Basin[END_REF]. They consist of silty sand with clayey lenses of a mean 200 m lateral extension and a 2 m mean thickness. It results that the semipermeable layers are not connected between each other and that there is continuity in the quaternary aquifer, which can therefore be modeled as a single aquifer with averaged transport properties. These data allow better understanding of the connection between the river and the shallow aquifer. As an example, the four logging profiles near the Bagara school well (see location on Fig. 3) are displayed on Fig. 4a. A coarse sandy layer is generally present at the base of boreholes drilled across the whole aquifer for drinking water supply and it is suspected to produce a significant part of the yield of the borehole. The pumping tests carried out in these boreholes indicate transmissivity values ranging from 10 -3 m 2 s -1 to 2.8 10 -2 m 2 s -1 . On the other hand hydraulic conductivity estimates at the scale of the whole aquifer provided by groundwater numerical models range from 10 -6 to 10 -5 m/s with the highest conductivity near the river [START_REF] Leblanc | Use of GIS and remote sensing for water resources management of large semiarid regions[END_REF][START_REF] Gaultier | Recharge et paléo-recharge d'une nappe aquifère libre en milieu sahélien (Niger Oriental). Approches géochimiques et hydrodynamiques[END_REF]Zairi 2008). An exploration geophysics survey including Magnetic Resonance Sounding (MRS) and Time Domain Electromagnetism (TDEM) was achieved in 2008 on a 12 km long profile across the KY valley with an additional single point near the Bagara elementary school (Fig. 3) situated 6 km East of the profile. Magnetic Resonance Sounding (MRS) provides an estimate of the free water content through the saturated part of the aquifer as well as an estimate of grain size distribution related to the permeability of the aquifer [START_REF] Legchenko | Nuclear magnetic resonance as a geophysical tool for hydrogeologists[END_REF]. MRS water content is considered as an estimate of the effective porosity of silty and sandy aquifers. Time Domain Electromagnetism (TDEM) produces electrical resistivity soundings (Fitterman and Steward 1986). Combining informations from MRS and TDEM allows differentiating between clayey and silt layers. Clayey layers have low free water content (despite they contain bound-water undetectable by MRS) and low electrical conductivity, while silt and sand layers are characterized by both detectable MRS water content and a higher electrical resistivity [START_REF] Guérin | Geophysical surveys for identifying saline groundwater in the semi-arid region of the central Altiplano, Bolivia[END_REF]Descloitres et al. 2013). The whole exploration geophysics survey is published in a separate paper (Descloitres et al. 2013). It shows that: (a) the thickness of the KY aquifer ranges from 30 to 60 m tending to decrease at the borders of the KY valley and the aquifer is limited at depth by high electric conductivity clayed layers; a second conductivity drop is observed at 70-80 m, which is attributed to massive Pliocene clays, (b) the mean porosity of the aquifer is 20-25 % in the valley decreasing to 15% outside (c) high porosity (up to 30%) and high permeability layers are observed locally at the base of this aquifer; they could correspond to the coarse sand levels noted in several borehole technical reports, (d) however MRS permeability estimates cannot be reconciled with those deduced from pumping tests. The Bagara sounding (Fig. 4b) shows a sharp decrease of both the electrical resistivity and the MRS water content near 50 m depth, which correspond to the clayed layers at the base of the quaternary aquifer, a mean MRS water content of 25% in the aquifer and a second drop of the resistivity near 90 m corresponding to the massive Pliocene clays. It is therefore characteristic of the KY valley.

Water level

The region of Diffa lies in the Northern Sahel area and therefore suffers from a 9-month dry season during which people not living near the KY have to rely on groundwater. Water levels were therefore measured early and piezometric maps are available since the 1960s, mainly as BRGM (the French Geological Survey) unpublished reports, which are summarized in [START_REF] Greigert | Atlas des eaux souterraines de la République du Niger. Etat des connaissances[END_REF]. Further discussions on the properties of the quaternary aquifer and on piezometric maps can be found in UNESCO (1972), IWACO (1985), [START_REF] Leduc-Pnud | Les ressources en eau du département de Diffa, Diffa, Direction de l'Hydraulique[END_REF], [START_REF] Carter | Shallow groundwater in the northeast arid zone of Nigeria[END_REF], [START_REF] Leduc | Evolution des resources en eau dans le département de Diffa, Bassin du Lac Tchad, Est Niger[END_REF], Boronina and Ramillien (2005), [START_REF] Candela | Groundwater modelling with limited data sets: the Chari-Logone area (Lake Chad Basin, Chad)[END_REF] and in the unpublished theses of [START_REF] Leblanc | Use of GIS and remote sensing for water resources management of large semiarid regions[END_REF], [START_REF] Gaultier | Recharge et paléo-recharge d'une nappe aquifère libre en milieu sahélien (Niger Oriental). Approches géochimiques et hydrodynamiques[END_REF]Zairi (2008). The map included in Fig. 1 is redrawn after Zairi ( 2008) and includes a large set of new data on the southern rim of the KY in Nigeria. On this map the KY valley appears as a piezometric ridge surrounded by two depressions. This indicates that the KY constitutes a present zone of recharge for the quaternary aquifer, and therefore that without recharge by the river, the water level will flatten below the KY valley and will tend toward the level of the two piezometric depressions. The groundwater resource appears therefore at risk if the infiltration from the KY would decrease significantly. Continuous piezometric records are extremely scarce. The Direction de l'Hydraulique in Diffa monitors 14 wells located at less than 5 km from the KY on a monthly basis but with several missing data. The standard deviation of the measurements was considered as a proxy for the annual water level variability in the wells. Fig. 5a shows that it decreases rapidly away from the river. This standard deviation is nearly 0.9 m close to the river and is less than 0.3 m at distances larger than 2 km. However, due to the lack of continuity in the data record, these data cannot be used for quantitative modeling. Moreover, a 4 year long dataset including near monthly measurements and dating back from 1994 was found for the Assaga well in Gaultier's thesis [START_REF] Gaultier | Recharge et paléo-recharge d'une nappe aquifère libre en milieu sahélien (Niger Oriental). Approches géochimiques et hydrodynamiques[END_REF]). The Assaga well is located 15 km downstream Bagara and 170 m away from the river axis. The Bagara elementary school well, nearly 800 m away from the river (Fig. 3) constitutes the most continuous record with some data back from 1995 (Fig. 5c). Measurements are interrupted in 1997 and resume after 2005 with an offset of more than one meter. This could result from a change in reference level, since the well is cased with concrete rings constituting a nearly 1 m high edge. Since the 2000s the school benefits from tap water and the well is no more used. Our sensors were stolen in 2008 but the near periodicity of the water level allowed us to interpolate an approximate curve (dotted line) during the missing months. A piezometric profile was set up at the end of 2008 perpendicularly to the river. It consists of 3 auger holes (P1-3) drilled at 50 m, 290 and 600 m from the river axis (Fig. 3) which were monitored weekly over a 1yr duration. P2 and P3 are located in a non cultivated areas and P1 is inside an irrigated pepper plot. The water level records (Fig. 5b,c,d) indicate a yearly signal with amplitude decreasing away from the river, from nearly 2 m at P1 to 1 m at P3 and Bagara. The minimum level occurs near mid-July, just when the KY begins to flow while the maximum takes place in January when the KY stops flowing. The water level seems therefore controlled by the KY regime and not by rainfall.

Gravity is sensitive to water level changes since it involves mass displacements. Gravity data are shown to provide a porosity estimate for an aquifer, when combined with water level measurements (Hinderer et al 2011). Here FG5 absolute gravity measurement gathered at Bagara (Fig. 5d) led to a porosity of 0.2, however with a large uncertainty. Since the porosity estimate derived from the gravity measurements is the same that the one measured with MRS, it will be used as a strong constraint in further modeling. [START_REF] Leduc | Estimation de la recharge de la nappe quaternaire dans le nord-ouest du bassin du lac Tchad (Niger oriental) à partir de mesures isotopiques[END_REF]. Adjustment of groundwater models led [START_REF] Leblanc | Use of GIS and remote sensing for water resources management of large semiarid regions[END_REF] and [START_REF] Gaultier | Recharge et paléo-recharge d'une nappe aquifère libre en milieu sahélien (Niger Oriental). Approches géochimiques et hydrodynamiques[END_REF] to adopt a negative recharge -due to evapotranspiration -of a few mm/yr on the Kadzell plain. However, the KY itself is considered as the main zone of recharge of the aquifer, with a mean estimated recharge rate of 1.2×10 6 m 3 /yr and a minor supply from Lake Chad of 0.2×10 6 m 3 /yr [START_REF] Gaultier | Recharge et paléo-recharge d'une nappe aquifère libre en milieu sahélien (Niger Oriental). Approches géochimiques et hydrodynamiques[END_REF]). Recently, Le [START_REF] Coz | Modeling increased groundwater recharge due to change from rainfed to irrigated cropping in a semiarid region[END_REF] starting from the properties of superficial sediments (Le Coz 2011) proposed numerical modeling of infiltration and conclude that the infiltration rate below irrigated plots could amount to 0.3 m/yr. Numerous ponds, which consist mainly of abandoned meanders (Fig. 3) are filled by rainwater and water from the KY during the rainy season. Since their bed is mainly constituted by clay material, these ponds cannot take part to the recharge. 3.3.2 Vegetation uptake. Several species of tree and shrub of the Sahel have been shown to be able to extract groundwater up to several tens meter depth [START_REF] Canadell | Maximum rooting depth of vegetation types at the global scale[END_REF]. These species include Prosopis juliflora, several Accacia species, Fahiderbia albida (gao) and Azardirachta indica (neem) which are common in the Diffa area. Various transpiration values, generally deduced from sap flow measurements have been reported in the literature for these species [START_REF] Brenner | Transpiration from a neem windbreak in the Sahel. In: Soil water balance in the Soudano-Sahelian zone[END_REF][START_REF] Khanzada | Groundwater uptake and sustainability of acacia and prosopis plantations in southern Parkistan[END_REF]Roupsard et al. 1999) which have been averaged by us to 1.5 mm/d under the canopy. For a tree coverage of 5% deduced from Google Earth images of this region this corresponds to a 0.075 mm/d transpiration value. The tree coverage can be locally much more than 5%, for example at the NE border of the city of Bagara, but we have checked that the groundwater models used here were sensitive to the tree coverage at the scale of the model rather to its local changes. [START_REF] Boronina | Application of AVHRR imagery and GRACE measurements for calculation of actual evapotranspiration over the Quaternary aquifer (Lake Chad basin) and validation of groundwater models[END_REF] deduced from AVHRR satellite data a much higher value of 0.5 mm/d near Bagara during the dry season, however with a coarse resolution of 1 km × 1 km, which can be modified by the neighboring pixels located above the free water still remaining in a pond on the riverbed.

Transient models of the quaternary aquifer

4.1. Modeling approach 4.1.1. The conceptual model. The piezometric map shows that the KY is a major recharge zone for the quaternary aquifer and agriculture is concentrated in the KY valley, which led us to considered a conceptual model focused on the KY valley (Fig. 6a). According to this model, the quaternary aquifer is recharged at the bed of the KY, and groundwater flow is directed symmetrically toward the two piezometric depressions located north and south. The quaternary aquifer is considered as a 50 m flat layer either with constant properties, or including a 2m thick higher permeability basal layer. This aquifer overlies the Pliocene clays which are considered as unpervious. It is recharged by the KY at its axis. Given the lack of data on the riverbed properties, the relationship between the recharge flux Q in , the altitude of the river surface hr and that of the water table h, is kept as simple as possible, i.e. linear and characterized by a single river coefficient C :

Q in =C × (hr-hb) h < hb (1) Q in =C × (hr-h) h > hb
(2) When the hydraulic head in the aquifer is below the river bed, the water flux is directed toward the aquifer and proportional to the height of the KY above its bed, while when the hydraulic head is above the river bed Q in can be either positive or negative. Equation (2) allows therefore the aquifer to take part to the river discharge during low flow. The coefficient C is adjusted for each hydrologic year [START_REF] Rushton | Representation in regional models of saturated river-aquifer interaction for gaining/losing rivers[END_REF]. This is clearly an approximation since the relationship between Q in , hr and h is known to be often nonlinear [START_REF] Sophocleous | Interactions between groundwater and surface water: the state of the science[END_REF]. Indeed, more sophisticated models of the river aquifer interaction are possible (Delft et al., 2011;[START_REF] Shanafield | Aquifer response to surface water transience in disconnected streams[END_REF][START_REF] Min | The spatial variability of streambed vertical hydraulic conductivity in an intermittent river, northwestern China[END_REF]), but they would require data which are not available in the context of data scarcity in the sahelian area. A symmetry condition is assumed at the KY axis, which allows to consider only the northern border of the river. At the northern boundary of the model, the water table is not sensitive to yearly to decadal changes induced by the river (Fig. 4a), the hydraulic head is constant and the hydraulic gradient defines the flow escaping from the aquifer Q out . A constant flux, Q evap is extracted from the aquifer by the vegetation according to the previous section. 4.1.3. Numerical model. The quaternary aquifer is modelled as 50 m × 6.5 km × 8 km horizontal volume including one or two different layer with a finite differences 100 m × 100 m uniform grid (Fig. The model is calibrated against water levels observed at P2, P3 and Bagara, P1 being excluded, as it is located inside an irrigated plot. The following parameters are calibrated : the hydraulic conductivity and porosity of the aquifer, the river coefficient C for each hydrological year, and an offset between P1-3 and the riverbed corresponding to errors in the leveling surveys. First simulations with a no flow surface boundary condition were not able to reproduce the water level at the Bagara well, and especially the nearly 90 mm decrease between the minimum levels in July 2008 and July 2009. All models include therefore the vegetation uptake of 0.075 mm/d discussed in section 3.3.

Adjustment of model parameters

First models with a constant hydraulic conductivity led to a value of 4.3 10 -4 m/s (see Online Resource 2), i.e. at least one order of magnitude larger than previous estimates derived from large scale groundwater models of this area, unrealistic for silty sediments and more than one order larger than the estimate obtained by Le Coz et al. (2010) for superficial sediments. This led us to suspect that this high permeability was partly standing for the coarse sand layer observed at the base of several boreholes and for the higher permeability zones deduced by Descloitres et al. (2013) from MRS data. Then, the refined model with a 2 m thick basal high permeability layer is adopted. The adjusted permeabilities are 1.7 10 -5 m/s and 10 -2 m/s, for the upper and lower layers. The porosity is 0.2 and the river coefficients are 10, 8.7, 7.6 and 12×10 -6 m/s for the years 2007-2008 to 2010-2011 (Fig. 7). The standard deviation between measured and observed water levels is 0.12 m. River coefficients display a good regression (R 2 =0.96) when plotted against the mean height of the river during the flow season, which gives some confidence on the physical consistency of the model and will allow to estimate the unknown C. The reader is referred to Online Resource 2 for a detailed comparison between the one layer and the 2-layer models, a validation of the model against previous data at the Assaga well and a sensitivity study on the model parameters. The sensitivity study shows that the error bars on either river coefficients or hydraulic conductivities were corresponding to a 1.6 multiplicative factor, i.e. that any variables, say C 0 should be considered within the [0.4× C 0 ,1.6× C 0 ] uncertainty range.

Effect of recharge under irrigated plots.

Part of the irrigation water returns to the aquifer under irrigated plots, especially since they are located near the river where the water level is only a few meters below the surface. We have therefore included a 0.3 m yearly recharge, which is the mean recharge given by Le [START_REF] Coz | Modeling increased groundwater recharge due to change from rainfed to irrigated cropping in a semiarid region[END_REF]. This recharge was assumed to take place at a constant rate during the irrigation period, i.e. during 7 months between mid-June and mid-January. This distribution in time of the recharge could be easily refined, taking into account both the results of Le [START_REF] Coz | Modeling increased groundwater recharge due to change from rainfed to irrigated cropping in a semiarid region[END_REF] and the agricultural calendar for pepper exposed in the Online Resource 1. The additional recharge is assumed to occur below a 200 m band along the KY, which was measured on the different images provided by Google Earth. Extrapolating these 200 m on both banks of the KY and on a length of 150 km of the KY between Tam and Bosso will result in a 6000 ha irrigated pepper surface, which roughly correspond to the estimate given in Online Resource 1. Simulations from the resulting adjusted model show similar agreement with data as the model with no infiltration (standard error=0.12m) with the following river coefficients 9.3, 5.9, 5.8, 9.4×10 -6 ms -1 , and a 3 cm change in the adjusted leveling error. The adjusted porosity and permeabilities were the same as those of the previous section. Interestingly, the only changed parameters are those which directly control the infiltration rates, i.e. the river coefficients. The mean difference of 20% between the infiltration coefficients suggests that the irrigation recharge would represent nearly 20% of the volume infiltrated from the KY. Hence the infiltration budget of the river is not significantly changed by the introduction of infiltration, since there is 20% less infiltration at the river axis but 20% additional infiltration along the 200 m irrigated band. Given the minor effect introduced by irrigation return flow on the water budget, we did not attempt to model more precisely the distribution in time of this recharge.

Implications for the water budget of the KY and of the quaternary aquifer.

The annual uptake from the KY due to infiltration through its bed can be estimated from the river coefficients adjusted in our models. For each kilometer, the infiltration uptake is 0.87×10 6 m 3 /yr for the 2010-2011 wet year, and 0.53×10 6 m 3 /yr for the 2009-2010 driest year in our 4 yr simulation period. Considering that the distance between Tam at the entry of the KY in Niger and Bosso at its mouth is nearly 150 km and extrapolating our results over this distance would predict an infiltration uptake on the northern rim of the KY of 130×10 6 m 3 /yr for a humid year and of 79×10 6 m 3 /yr for a dry year. This constitutes a significant part of the total discharge of the river, comprised between 400 and 900×10 6 m 3 /yr for the last ten years. These results seem reasonable with respect to the decrease of discharge commonly observed for the KY between Tam and Bosso. However the lack of continuous datasets at these hydrological stations does not allow to confirm the infiltration balance of the KY from discharge data. It should therefore be considered that these estimates suffer from a 60% uncertainty resulting from the uncertainty on the river coefficients themselves (see Online Resource 2). The annual abstraction by irrigation can be roughly estimated by considering a total irrigated surface of 6 000 ha, with an annual water need of 600 mm identical to that of sweet pepper (Dorrendos and Kassam 1979). This would require an annual uptake of 36×10 6 m 3 /yr, which is still negligible with respect to the total discharge of the KY. However, this constitutes a significant part of the water infiltrated from the KY. These estimates are several orders of magnitude larger than those of [START_REF] Gaultier | Recharge et paléo-recharge d'une nappe aquifère libre en milieu sahélien (Niger Oriental). Approches géochimiques et hydrodynamiques[END_REF] (1.2×10 6 m 3 /yr) or even [START_REF] Leduc-Pnud | Les ressources en eau du département de Diffa, Diffa, Direction de l'Hydraulique[END_REF] (5×10 6 m 3 /yr) and [START_REF] Leblanc | Use of GIS and remote sensing for water resources management of large semiarid regions[END_REF] (6.5×10 6 m 3 /yr). However, they are consistent with the 1.6 m/km observed slope of the water table in the quaternary aquifer; the difference between the present model and the previous ones relies on the adopted permeability in the aquifer. As in the previous model, the permeability was constrained by the need to sustain the piezometric depression in the Kadzell, it seems that the permeability values obtained here hold for KY valley only and not for the whole Kadzell area.

Tentative extrapolation for future scenarios for the KY regime

Assessing the consequences of climatic changes should include wet years and dry years given the uncertainties on climatic models for the region [START_REF] Druyan | Review of studies of 21 th -century precipitation trends over West Africa[END_REF]. We forced therefore the model with 5 humid years, which are modeled as the 2010-2011 year, followed by five dry years modeled as the 1973-1974 year, and again 5 humid years. The 1973-1974 hydrological year is the driest one for which quantitative detailed data are available. The river coefficient for 2010-2011 is the adjusted one, while the 1973-1974 one has been obtained by extrapolation from the linear relationship between adjusted river coefficients and the mean height of the KY during its flow season. This leads to a 3.5×10 -6 ms -1 river coefficient. It is shown in Fig. 8 that five successive dry years resulted in a nearly 2 m drop of the water table near the KY axis. The hydraulic head at the river axis shows that water infiltrating from the KY must then flow through a 3 m unsaturated zone, for which the permeability could become extremely low and the river coefficient of 3.5×10 -6 ms -1 could be overestimated. However, the water table is able to recover almost completely after 5 yrs. It should be emphasized that these results are strongly dependent on the adopted river coefficient model and that using the river coefficient of the year 2010-2011 after the four dry year is probably an overestimate. If we consider that the river coefficient is controlled by the thickness of the non-saturated zone under the river, the coefficient of dry years should be kept for the wet years following the drought. In such case, the recovery of the groundwater level would be less than 1 m at the river axis and is nearly 0.5 m at the Bagara well. Hence there could be a serious risk for a permanent and irreversible drop-down of the groundwater storage. The river coefficient for 73-74 is also poorly constrained, as it results from extrapolation. If we use instead the value of 7.6×10 -4 m 2 s -1 , which is the lowest adjusted river coefficient value, obtained for the much wetter year 2009-2010, the groundwater level drop is only 1 to 1.5 m near the KY, and the recovery is almost complete after five wet years.

Conclusion

The Northern Sahel area generally lacks any active permanent hydrological network and groundwater constitutes there a key resource for development. Sensitivity of this resource to climate and to anthropic disturbances should be assessed to foster sustainable development. The KY area may serve as an example case due to its recent population growth and agricultural development in the immediate border of the river. It is shown here that even with scarce data the water budget of the river and the aquifer can be estimated from numerical modeling of groundwater flow. The model relies on groundwater monitoring, mainly on a 1 yr period, at various distances of the river. It is strengthened by exploration geophysics data, namely by TDEM and MRS. It requires in addition that an approximate piezometric map is available at a larger scale for providing boundary conditions. The model results rely on a poor data coverage, both in space and in time, which is a common situation in remote African regions. They should be therefore considered as first estimate to be refined as soon as further data are available. The hydraulic head in the aquifer is lower than the water level in the KY during all simulations. As a consequence the quaternary aquifer is not able to sustain the low flow discharge of the KY. Nonreversible disconnection of the aquifer from the river could result from decreasing infiltration rates through an unsaturated porous medium of increasing thickness. The present water level in the aquifer shows however that the aquifer was able to catch up with the KY level after the drought of the 80s and the 90s. The model proposed here indicates that this should also occur even after applying the 73-74 level of the KY during 5 successive years, although with large uncertainties resulting from the simplified aquifer/river coupling with a constant C. During the study period, the infiltration from the KY toward the aquifer was between 160×10 6 m 3 /yr and 260×10 6 m 3 /yr, which constitutes a significant part of the total discharge of the KY, ranging from 400 to 900×10 6 m 3 /yr. The total amount of water needed for irrigation of pepper plots can be estimated to 36×10 6 m 3 /yr. This indicates that the present state of agricultural development is sustainable regarding the available amount of surface water and groundwater. Non sustainability may however arise due to exhaustion of soil or the persistence of pesticides or fertilizers in the environment. Since major uncertainty relies on the coupling between the river and the aquifer we suggest focusing further studies on this topic. A series of ponds remain in the riverbed after the flow season. Their connection with the aquifer can be questioned given the importance of these ponds for irrigation after the flow season. Moreover recharge of the aquifer could be optimized with small dams. To further generalize the method applied here to the KY valley, we suggest that integrated water resource management in the Sahelian area should consider the role of temporary rivers, and should involve data gathering and analysis on their immediate surroundings.

Aknowledgements : The research presented in this paper has been funded by the Ghyraf ANR project, the REPAS CNRS/INSU EC2CO project and the IRD LAC TCHAD project. Nathalie Rouché is thanked for her help with the SIEREM database, François Delclaux for kindly providing the rainfall data, Gilbert Ferhat for his help with the leveling, Mathieu le Coz for sharing his experience on the permeability of the KY aquifer, and the whole IRD team in Niamey for logistic support.

ONLINE RESOURCE 1 LIFESTYLE OF POPULATIONS AND ACCESS TO WATER

Change of livelihood with the Drought

More than 60 % of the inhabitants of the Eastern Niger area are sedentary kanuri-speaking farmers and fishers. The livelihood of local populations is controlled by access to water: the north is devoted to herding, while in the south rainfed and irrigated agriculture are practiced with uncertain yield due to the large interannual rainfall variability of the Sahel climate. Before 1975, i.e. before the drought, the populations living on the border of the Lake Chad and the KY enjoyed a privileged situation where both fishing and irrigated farming were practiced in addition to rainfed agriculture. The main activity was fishing, which provided both a healthy food and cash income from sales of dried or smoked fish in Nigeria. Big fishes from the Lake Chad could also be found in the KY up to Tam. Rainfed pearl millet was farmed on sandy soils and irrigated farming was restricted to the lowlands near the Lake Chad and in the KY valley; onions, local eggplants, barley and wheat were grown. Rice was grown on clayey soils in the lowest plots, which were naturally flooded. Recession flood farming involved kassava, sweet potatoes, sorghum, cowpeas, squash and cucumbers. However, farming was a minor occupation and fishing was the main pillar of the local economy. Rainfed agriculture severely decreased since the drought and presently only 20 % of the food needs are now covered (USAID FEWS Net Project, 2005). Despite the fact that local early varieties such as moro (80-90 days cycle) or buduma (60 days cycle) are cultivated, pearl millet farming has progressively receded. Fishing is now restricted to the (rare) years when the Lake Chad returns in Niger and in some villages such as Bosso and Tam. Moreover, the diversity and size of fishes have severely decreased. While rice, sorghum and cowpeas persist, these crops are of minor importance. Today, irrigated sweet pepper is the main source of income in the region and the so-called "red gold" induces a relative wealth in the Diffa region, where the poverty rate was close to 18% in 2010 against 60 % in the whole Niger (Rep. du Niger, 2010).

The success story of sweet pepper cropping in the KY

Irrigated sweet pepper is a new crop which was introduced by local traders from Nigeria in the Eastern Diffa region in 1955-1956. Thanks to well-known ancient irrigation techniques, it was adopted rapidly as a minor cash crop. Its geographical extension was limited until 1985, when the government of Niger and NGOs began to develop small irrigation programs. Then the pepper crop extended eastwards in the KY valley, reached Bosso in the 1990s and began recently to be cultivated on the Lake Chad shore. It is now estimated that pepper covers between 4 000 and 8000 ha (nearly 65% of the total irrigated area) and provides work for at least 25 000 people. Almost every inhabitant of the borders of the KY, including migrant farmers and a noticeable part of the urban population (and even employees of the state, of the local administration and of NGOs) is involved in producing, transforming or trading pepper. The annual yield is estimated to be 10 000 t corresponding to a total income to 5 to 6 billion FCFA (0.76 to 0.91 M€) by [START_REF] Prêt | Etude sur l'impact de la production et de commercialisation du poivron dans les revenus des ménages de la région de Diffa[END_REF], AUDEC (2006) and [START_REF] Barhouni | Etude de marché des produits agro-pastoraux dans la région de Diffa[END_REF]. The cropping calendar is governed by the KY: pepper is sewed in nursery 40 days before the estimated arrival of the KY and is watered by rain and by irrigation until transplantation, which occurs at the actual arrival of the river, in June-July in Tam and later during July in Bosso. This offers to the people of Tam the advantage of an early first harvest, which they usually sell quickly as fresh pepper (i.e. not dried). Afterwards, plants are irrigated according the growth of the plant and to the evapotranspiration rate ; twice a week after transplantation, up to once a day in October when temperature is at its maximum, once a week or less when the temperature declines until January. Irrigation uses motored pumps to convey water from the nearby river or from ponds located in its abandoned meanders. The pumps are placed on the border of the river and water is distributed to the different plots by a system of narrow earth canals. In order to limit water leakage by infiltration from these canals pepper plots are generally concentrated on a narrow band along the KY. However, some of them are located more than 1 km away and the farmers must use two motored pumps, one of them being installed at mid distance. It is generally estimated that irrigation needs of pepper amount to 500 to 600 mm (Dorrenbos and Kassam, 1979). Irrigation stops when the river stops flowing and harvesting has to stop soon when irrigation is not possible. There is less insecurity in places such as Diffa, where undulations of the river bed define permanent ponds, from which water can be pumped after the flow period of the KY. Their connection to groundwater is still to be assessed. Depending from the cultural calendar, the KY regime and the localization of the plot, 5 to 7 successive harvests are allowed and pepper is mostly dried and sold in Nigeria. Harvest operations are exclusively reserved for women, with compensation in pepper. Sweet pepper can be very profitable; however producers are always at risk. In 2009, the KY stopped flowing at the end of December in Bosso, between the first and the second harvest. Furthermore, this crop requires an initial input of 0.8 Mcfa/ha (1220 €) for fertilizers, pesticides and gasoline for the motored pumps, for a gross income of 1.2 Mcfa /ha (1830 €), obtained later at the harvest. Income inequalities are partly based on quality and surface of the plots as well on the ability of the producers to mobilize saving to buy inputs. Poorest producers may be involved in cycle of successive loans which lead them to sell their plots and work for bigger land owners (Luxereau and Diara, 2009;Luxereau et al., 2011). Moreover after 25 years of intensive agriculture, plots near the river suffer from soil exhaustion, which requires more fertilizers, and from pest infestations which require chemical control; both expenditures can alter the budget of producers. Moreover fertilizers and pesticides can be harmful to groundwater. Finally, new lands, away from the KY are now converted to pepper, with water either collected from the river with a system of intermediate pumps and reservoirs or from boreholes drilled in the quaternary aquifer, with serious risks of soil salinization due to the higher content of dissolved species in groundwater.

with an offset for P1-P3 of -0.58 m. The standard deviation between modeled and observed hydraulic heads is 0.12 m.

Sensitivity study

There is a strong coupling between hydraulic conductivity and the river coefficients as shown in equation ( 1), assuming that the Dupuit approximation is valid, the river follows a straight line and that the aquifer is at steady state: / (1) where x is the coordinate perpendicular to the river axis, h is the hydraulic head, C is the river coefficient at the riverbed, H the mean height of the river above the water level in the aquifer (CH is therefore the flux of water introduced into the aquifer by the river) and K is the hydraulic conductivity of the aquifer. It results that the C/K ratio, only can be inversed from . A sensitivity study has therefore been achieved, starting from the case of Fig. OR2.1. 1), the line C/K=1 would correspond to the value 1. Fig. OR2.2 displays in contrast an ellipsoid shaped minimum with maximum elongation along the C/K=1 line. The dark blue area corresponds to f/f 0 <2, and allows a 1.6 ratio either on C or on K. Estimating that f/f 0 =2 clearly exceeded the limit of a reasonable adjustment of the data led us to consider that our permeability and infiltration coefficients were determined within a 1.6 multiplicative factor.

Two layers versus one layer

The adjusted hydraulic conductivity value for the one layer model of section 1 is one order of magnitude larger than previous estimates derived from large scale groundwater models of this area and unrealistic for silty sediments. It is also more than one order larger than the 1.2 10 -5 m/s value obtained for the hydraulic conductivity of the superficial sediments from infiltration experiments with simulated rainfall (Le Coz, 2010). This led us to suspect that this high hydraulic conductivity was partly standing for the coarse sand layer observed at the base of several boreholes and for the higher permeability zones deduced by Descloitres et al. (2013) from MRS data. This led us to additional runs with a 2-layer sedimentary structure. As a rule of thumb piezometric data control the transmissivity of the whole aquifer and any combination of hydraulic conductivities producing the same transmissivity could lead to a satisfactory fit of the data. So we chose to introduce a 2 m thick basal layer with hydraulic conductivity of 10 -2 m/s (coarse sand) which produces an adjusted permeability of 1.7 10 -5 m/s for the 48 upper meters of the aquifer, i.e. close to the hydraulic conductivity measured at the surface by Le Coz (2010). Our data are however not sensitive to the thickness and position of the high hydraulic conductivity layer, as long as it lies at depth in the aquifer and cannot act as a short circuit between the river and the piezometers. On the other hand, as the total transmissivity of the aquifer is unchanged, our hydraulic conductivity results cannot be reconciled with those obtained from models developed at the scale of the whole quaternary aquifer. The adjusted porosity is still 0.2 and the river coefficients are now 10, 8.7, 7.6 and 12×10 -6 ms -1 for the years 2007-2008 to 2010-2011, while the offset of P1-3 is -0.54 m. The river coefficients display a good regression (R 2 =0.96) when plotted against the mean height of the river during the flow season, which give some confidence on the physical consistency of the model and will allow estimating unknown C. It results that if the constant hydraulic conductivity model cannot be discarded from the water level data, the second model, relying on a high permeability basal layer is much more consistent with other informations on the aquifer. It will be therefore kept as the preferred solution.

Comparison with previous data at the Assaga well

A series of nearly monthly measurements lasting from 1994 to 1998 for both the water level in the Assaga well and the level of the KY at Bagara can be found in the [START_REF] Gaultier | Recharge et paléo-recharge d'une nappe aquifère libre en milieu sahélien (Niger Oriental). Approches géochimiques et hydrodynamiques[END_REF] is the KY level. The Assaga well is located at a distance from the KY between those of P1 and P2.

The Assaga well is located within a meander of the KY at distances of 170 m and 430 m from the river on both sides of the meander, in an intensively cropped pepper area. This situation is therefore somewhat between those of P1 and P2. Keeping the basal high permeability layer and the irrigation recharge of 0.3 m/yr, the model has been forced with the 1994-1998 data of the KY levels, however keeping the geometry of the KY near P1-3. This approximation is justified by the proximity of Assaga well from the river, which makes it rather insensitive to the details of the shape of the river. The Assaga well has not been leveled, and it appears that its height, as given in the Gaultier's thesis ( 2004) is deduced from the topographic maps of the region, which can result in a several meters uncertainty and allows only relative height comparisons with the model. The 95-96 hydrologic year is a dry year and the three other years are average. The river coefficients have been estimated by interpolation of results of the previous section. Fig. OR2.3 shows that the water levels observed at Assaga are in fair agreement with those simulated for P1 and P2, in particular for the water drop after the 1995 dry year and its recovery during the 2 following years It appears therefore, that in spite of the numerous approximations made in the model parameters, our model can provide some reasonable estimates of the groundwater level fluctuation outside its calibration period.

Sensitivity to changes of K and C

Decrease of permeability outside the KY valley. Exploration geophysics results suggest a lower hydraulic conductivity outside the KY valley. As the model is focused on the valley area, this will impact the boundary conditions of the model. As noted in section 4.1 of the main paper, yearly changes of the river axis do not propagate to the boundaries of the model. Therefore the modeling results are not sensitive to the boundary conditions; actually, they are mostly sensitive to the initial hydraulic head distribution, which are deduced from piezometric maps. However, it should be noted that longer simulations, for example those dealing with the present climate change should take into account the permeability distribution outside the KY valley.

Changes of C during the KY flow period.

It is expected that the constant river-aquifer coefficient C will stand for a lower coupling between the KY and the aquifer at the beginning of the flow period, when the aquifer is separated from the KY by a thick non saturated layer of low permeability and for a more efficient coupling at the end of the flow period. A variable C would induce a slower rise of the water level in the aquifer at the beginning of the flow period, which will be mostly observed on the boreholes close to the river. However, we expect that the amplitude of water level changes in the aquifer will be controlled by the total infiltrated flux, and therefore by the mean value of C. A variable C would therefore not impact strongly the water budget results, once the total amplitude of water level change is fitted to available data.

Fig. 1 .

 1 Fig. 1. The Komadugu Yobe (KY) river and its tributaries. The piezometric map, displayed as thin grey level curves evidences two depressions on both sides of the KY near Diffa and a piezometric ridge under the KY. The red square is centered around the study area near the city of Diffa.

Fig. 2 .

 2 Fig. 2. Flow regime of the KY; a: comparison of the annual discharge of the KY and rainfall over its catchment area; b: comparison of the water level of the KY at the Bagara station during the 1960s, for a dry year (73-74) and during recent years

Fig. 3 .

 3 Fig. 3. The KY valley near Diffa with the location of the piezometers, well and geophysical measurement points used in this study. The blue heavy line correspond to the modeled area

Fig. 5 .

 5 Fig. 5. Piezometric data near the KY; a: standard deviation of the water level in the different wells monitored by the "Direction de l'Hydraulique" as function of their distance to the KY; b: one year of piezometric measurement on the P1-P3 profile; c: data from the Bagara school well. The main sinusoidal interannual cycle is indicated in pink. Note the offset of about 1 m between 1996 and 2000; d: enlargement of the modeled period. Gravity data with the vertical scale are adjusted for a 0.20 porosity aquifer

  Fig.6b). The equation of flow are solved with the Modflow open source package for which both the set of equations and the numerical resolution method can be found in(Harbaugh and McDonald 1996a, b). Pmwin provides a free user-friendly interface for Modflow(Chiang and Kinzelberg 2005). These softwares, as they can be freely distributed, are well suited for low income countries such as Niger. The model is calibrated with 4 years of the KY daily water level observations, beginning in July 2007 and ending in June 2011. The 2008-2011 duration corresponds to our data coverage and the year 2007 is used to damp the difference between our initial condition and the actual head distribution.

Fig. 6 .

 6 Fig. 6. The model. a: conceptual model drawn perpendicularly to the river axis. The river recharges the aquifer at its axis; water is extracted from groundwater by sahelian vegetation and the slope of the water table defines the flux escaping at the northern boundary. b: the finite difference grid with a 100 m uniform grid spacing in both direction. The river is at the base of the grid (in light brown) and the grey area at the base of figure is not modeled. The orange line is the northern boundary condition.

Fig. 7 .

 7 Fig. 7. Comparison of modeled (thin lines) and observed hydraulic heads (heavy lines) for the adjusted 2-layers model of the upper quaternary aquifer. The water level of the KY is in brown. Data from Bagara are in red and from P2 and P3 in green and blue, respectively. The hydraulic head in the aquifer at the KY axis is indicated by the curve in cyan. The adjusted parameters are: K= 1.7 10 -5 m/s for uppermost 48 m and 10 -2 m/s for the 2 m thick basal layer, φ= 0.20, C1-4= 10, 8.7, 7.6, and 12×10 -6 m/s. The standard deviation between modeled and observed hydraulic heads is 0.12 m

Fig. 8 .

 8 Fig.8. Water level at the P1-3 and Bagara wells during a theoretical KY hydraulic regime change (upper brown curve). The color code of the curves is the same as in Fig.7

  Fig. OR2.2 shows the ratio of the actual objective function by the minimal objective function of the case of Fig. OR2.1 as a function of the Log of the hydraulic conductivity and the Log of river coefficients. In this figure, all four C coefficients of Fig. OR2.1 are multiplied by the same value. If our case study was fully depicted by equation (

Fig. OR2. 2 .

 2 Fig. OR2.2. Sensitivity of the optimized solution to the hydraulic conductivity and the infiltration coefficients. The ratio of the actual objective function over the one of the case of Fig. OR2.1 is pictured as a function of the multiplicative factors of the hydraulic conductivity and infiltration coefficients The values of C 0 and K 0 refer respectively to the hydraulic conductivity and infiltration coefficients of the case of Fig. OR2.1. All the infiltration coefficients are multiplied by the same value.

  thesis and are displayed in Fig. OR2.3.

Fig. OR2. 3

 3 Fig. OR2.3 Comparison of observed water levels in the Assaga well (red crosses) with those simulated for the P1 (magenta), P2 (green) and P3 (blue) wells. The brown curve

SUPPLEMENTARY MATERIAL ON MODEL ASSESSMENT

Results obtained with a one-layer model

First simulations were aimed at assessing the sensitivity of our observations to the different model parameters. This led us to choose to invert the following parameters: the permeability and porosity of the aquifer (K and φ), river coefficients at the bottom of the river for each hydrological year, and an offset corresponding to the leveling error between P1-3 and the riverbed. The best fitting model (Fig. OR2.1) was obtained with the Fmincon optimization function of Matlab and the rms of the difference between modeled and observed water level values at P2, P3, and Bagara as objective function. We have also verified that our results were not dependent on the optimization method by checking also least squares and thermal annealing with similar results. The stability of the solution was checked by adding a random gaussian noise of standard deviation of 0.1 m to the data. The maximun water level at the end of 2008 was hardly reproduced either on P2, P3 and Bagara. This could be a consequence of errors in the initialization of the model and could only be improved in future models if longer time series become available. Moreover, it was difficult to fit simultaneously Bagara P2 and P3, and even P2 and P3 simultaneously. This was interpreted as an effect of the simplifications introduced in the models. In particular, it appears in Fig. OR2.1 that the simulated water level in P3 and especially in P2 is similar in shape to the KY height curve, which is a consequence of the simulation of infiltration at the riverbed with a single river coefficient. Other sources of errors arise from heterogeneities in the riverbed and in the permeability field. The modeled hydraulic head at the river axis remains below the riverbed during most of the simulation time. This indicates that infiltration occurs through a non-saturated zone of variable thickness for which the transport properties are poorly accounted for by a single coefficient since processes in the vadose zone are known to be non-linear. The adjusted river coefficient commensurate with the mean level of the KY.