Emeric Guéguen
email: emeric.gueguen@insa-rennes.fr

Matthieu Crussière
email: matthieu.crussiere@insa-rennes.fr

Jean-Franc ¸ois Hélard
email: jean-francois.helard@insa-rennes.fr

An OFDM-CDMA scheme for High Data Rate UWB applications

Keywords: UWB, MB-OFDM, MC-CDMA, SS-MC-MA

In this paper, we investigate a new waveform for UWB systems obtained by the combination of Orthogonal Frequency Division Multiplex (OFDM) and Code Division

Multiple Access (CDMA). The proposed system, called Spread Spectrum -Multi-Carrier -Multiple Access (SS-MC-MA) turns out to be a judicious solution to combat frequency selectivity and narrowband interferers, and to manage the coexistence of several users and piconets. It is shown that the addition of a degree of freedom brought by the spreading component of SS-MC-MA allows to optimize jointly the assignment of the number of used codes and coding rates in order to make the system more robust. Through simulations, it is demonstrated that the new system can outperform Multi-Band OFDM Alliance (MBOA) for low data rates and is able to provide wider range of rates.

I. INTRODUCTION

Ultra Wide Band (UWB) radio systems are today acknowledged as high potential solutions for Wireless Personal Area Networks (WPAN). The novelty of these systems lies in the possibility of non regulated access to the spectral resource leading to a flexible use of the radio channel for an important number of applications.

In 2002, the Federal Communications Commission (FCC) regulated UWB systems by imposing a spectral mask to limit the transmission power [START_REF]First report and order, revision of part 15 of the commission's rules regarding ultra-wideband transmission systems[END_REF]. According to the FCC regulation, a signal must have a minimum bandwidth of 500 MHz or a bandwidth to central frequency ratio above 0.2 to be considered as UWB. The power spectral density (PSD) should also not exceed -41.3 dBm/MHz. The UWB channel, running from 3.1 to 10.6 GHz, is frequency selective and considered as almost invariant in time. Proposed UWB systems must not disturb existing narrowband systems, such as Wireless Local Area Network (WLAN) 802.11a standard at 5 GHz for example.

Following that, the Institute of Electrical and Electronics Engineers (IEEE) initiated a standardization process, referred to as task group 802.15.3a, to define a high data rate physical layer for WPAN. The last three years have hereby seen the emergence and the confrontation of two approaches: a pulse radio solution using Direct Sequence -Code Division Multiple Access (DS-CDMA) ternary codes supported by UWB Forum, and a multi-carrier multi-band solution based on Orthogonal Frequency Division Multiplex (OFDM). The latter has been proposed by the Multi-Band OFDM Alliance (MBOA) consortium and is currently promoted by the main actors of the general public and component industries [START_REF] Batra | Multi-Band OFDM physical layer proposal for IEEE 802.15 task group 3a[END_REF].

In section II, this paper presents the main parameters of the MBOA solution. After a critical analysis of this solution section III the interest of adding a CDMA component to the MB-OFDM waveform. In section IV, the principle of the new waveform called Spread Spectrum -Multi-Carrier -Multiple Access (SS-MC-MA) is presented. Particularly, SS-MC-MA offers for the future WPAN good performance and great flexibility for the resource allocation between users of a same piconet. This new UWB system is then described in section V and the comparison of the performances obtained with the MBOA solution and the SS-MC-MA system is presented in section VI. Finally, section VII concludes the paper.

II. THE MBOA SOLUTION

The MBOA consortium proposes to divide the available band into 14 sub-bands of 528 MHz, as illustrated in Fig. 1. Each of these sub-bands allows the transmission of an OFDM signal, obtained from a 128-point Inverse Fast Fourier Transform (IFFT). Most of the UWB studies focus on the first mode which clusters the first three sub-bands from 3.1 to 4.8 GHz. The multi-user management within a piconet is based on Time Division Multiple Access (TDMA) by using a Time-Frequency Code (TFC). At a given moment, each user then occupies one of the three sub-bands of mode 1 [START_REF] Batra | Multi-Band OFDM physical layer proposal for IEEE 802.15 task group 3a[END_REF]. The signal, sampled during the analog-to-digital conversion, has a limited bandwidth of 500 MHz, leading to low-cost components and power consumption reduction. However, the use of TFC translates into frequency hopping from one subband to another at each OFDM symbol. Hence, each user benefits from the frequency diversity brought by the three sub-bands in mode 1. In addition, considering that each user occupies a given sub-band only one third of the time, it is possible to optimize the transmitted power while respecting the PSD mask imposed by the FCC. Lastly, it is also advised to plan the cohabitation of 4 piconets in a same environment.

Transmitted data rates in each sub-band essentially depend on the coding rate, as the modulation applied to the different subcarriers of the OFDM multiplex is a quadrature phaseshift keying (QPSK). Data rates, from 53. [START_REF] Muquet | Cyclic prefix or zero padding for wireless multicarrier transmission?[END_REF] and its conjugate symmetric are transmitted into the same OFDM symbol by one subcarrier and its "mirror" subcarrier respectively. This way, the frequency diversity is exploited into each sub-band at the cost of a division by 2 of the useful transmitted data rate. Moreover, for modes corresponding to data rates from 53.3 Mbit/s to 200 Mbit/s, a time spreading of 2 is applied. It consists in the transmission of the same information during 2 consecutive OFDM symbols in order to take advantage of a better frequency diversity, due to the joint application of the TFC. All OFDM parameters of the MBOA solution are detailed in [START_REF] Batra | Multi-Band OFDM physical layer proposal for IEEE 802.15 task group 3a[END_REF]. One of the main difference compared to a classical OFDM system is the use of a zero padding (ZP) guard interval instead of the traditional cyclic prefix (CP). Indeed, CP is replaced by trailing zeros. Details of this operation are well explained in [START_REF] Muquet | Cyclic prefix or zero padding for wireless multicarrier transmission?[END_REF]. ZP allows one to obtain a spectrum with fewer ripples in the useful band than with a traditional CP. Thus the signal can take the exact shape of the PSD mask [START_REF] Batra | Multi-Band OFDM physical layer proposal for IEEE 802.15 task group 3a[END_REF].

To summarize, the MBOA solution offers some advantages for high data rate UWB applications, such as the signal robustness against the channel selectivity and the efficient exploitation of the signal energy received within the prefix duration. The main argument of multi-carrier modulation in general is often quoted in favour of the MBOA solution, when one compares it with the competitive DS-CDMA solution. The latter can actually hardly make use of all the received energy, the number of the RAKE fingers being compulsorily limited for complexity reasons. However, the MBOA solution is relatively limited in a multi-user and multi-piconet context. Particularly, when the only three first sub-bands of the first mode are considered, conflicts immediately appear at the addition of a fourth user within a piconet, whereas scenarios going

III. THE CDMA COMPONENT ADD INTEREST

Recent studies have proposed to add a CDMA component to the MBOA solution in order to improve the system robustness or the resource sharing between several users [START_REF] Park | Performance of UWB DS-CDMA/OFDM/MC-CDMA system[END_REF]. This spreading component essentially allows to organize the access of several users to a common resource. Taking into account the UWB channel characteristics, frequency selectivity and slow time variations in indoor environment, spreading is generally performed along the frequency axis, leading to a Multi Carrier-CDMA (MC-CDMA) waveform. The symbols of all users are transmitted by all the subcarriers as depicted in Fig. 2, the spreading code length L c being lower or equal to the subcarrier number N p of the OFDM multiplex.

Compared to the "traditional" MBOA solution, and beyond a greater facility in the resource sharing, the MC-CDMA system also presents a better robustness against channel frequency selectivity ( [START_REF] Park | Performance of UWB DS-CDMA/OFDM/MC-CDMA system[END_REF], [START_REF] Schmidt | Ultra wideband transmission based on MC-CDMA[END_REF]) and improves the UWB signal robustness against narrowband interferences. This last point is fundamental for uncontrolled access to the spectral resource. In [START_REF] Park | Performance of UWB DS-CDMA/OFDM/MC-CDMA system[END_REF] however, authors suggest to use an MC-CDMA signal with a bandwidth B w = 1.58 GHz, equivalent to 3 sub-bands of the MBOA signal, which leads to an highly increase of the sampling frequency of the analog-to-digital conversion.

IV. A NEW WAVEFORM FOR MULTI-BAND UWB : THE SS-MC-MA

By applying a spreading code and a multi-access component, we propose in this paper an SS-MC-MA waveform [START_REF] Cariou | A novel uplink transmission system based on MIMO frequency hopping SS-MC-MA for the future wireless cellular networks[END_REF], which is new for UWB applications and offers better performance and more flexibility in the resource management.

A. SS-MC-MA principle

SS-MC-MA can be viewed as a multi-block system compared to the classical MC-CDMA system, since the spectrum is divided into "blocks" of several subcarriers. The SS-MC-MA solution, illustrated in Fig. 2, consists in assigning to each user a specific set of subcarriers according to a Frequency Division Multiple Access (FDMA) approach. Code dimension L c can then be exploited for an adaptive resource optimization and sharing (modulation type, data rate, . . . ). Spreading in the frequency domain leads to diversity gain and, as it is the case of MC-CDMA, improves the signal robustness against narrowband interferers. With an SS-MC-MA signal, symbols are transmitted simultaneously on a specific subset of subcarriers by the same user and undergo the same distortions. Self-interference (SI) which then replaces the Multiple Access Interference (MAI) obtained with MC-CDMA signals, can be easily compensated for by mono-user detection with only one complex coefficient per subcarrier.

B. SS-MC-MA advantages

Let us consider the case of the MBOA standard in mode 1 (Fig. 1).

1) Case of three or less users: The SS-MC-MA system allows the allocation of a 528 MHz sub-band for each user. This system offers the same performance and advantages as MC-CDMA to which a simplicity is added for the channel estimation in reception. In fact, with SS-MC-MA a given subcarrier is distorted by only one channel, the one of the user associated with this subcarrier. At contrary, with an MC-CDMA system, each subcarrier is corrupted by the different channels of different users, which increases considerably channel estimation complexity. In that case, each user has to estimate the response of many channels all over the total available bandwidth.

2) Case of more than three users: In the MBOA solution, conflicts appear from 4 users and could cause information losses. In the SS-MC-MA case, the code dimension could be exploited to share a same 528 MHz sub-band between 2 or even 3 users if necessary. In that case, the generated signal within a given block corresponds to an MC-CDMA signal, but with a limited number of users per block (2 or even 3).

More generally, in a multi-piconet context, the possibility of easily modifying the number of spreading codes assigned to a given user in a given piconet, allows the SS-MC-MA scheme to offer a more flexible and efficient dynamic resource sharing than the MBOA solution does.

V. THE NEW UWB SYSTEM

A. System studied

The proposed system is based on the MBOA solution. Fig. 3 introduces the MBOA transmission chain in continuous lines and, in dashed lines, the functions that are added to obtain an SS-MC-MA waveform. These functions are mainly the Hadamard Transform ("Fast Hadamard Transform": FHT) at the transmitter and the inverse transform (IFHT) at the receiver. In addition, Minimum Mean Square Error (MMSE) single user detection is applied.

The spreading factor L c is chosen equal to 16 and the number of useful subcarriers is reduced from 100 to 6 × 16 = 96 for each OFDM symbol. This means that 4 more guard subcarriers are added.

B. Signals expression

In the MBOA solution case, the signal generated at the output of the IFFT expresses:

S OFDM (t) = +∞ i=-∞ n=+NST/2 n=-NST/2 X n (i)p c (t -iT CP ) × e j2πn∆F(t-iTCP ) (1)
where ∆ F , N ST and T CP represent the subcarriers spacing, the total number of used subcarriers and the spacing between two consecutive OFDM symbols, respectively. X n (i) is a complex symbol belonging to a QPSK constellation and is transmitted by subcarrier n during the ith OFDM symbol. It represents a data, a pilot or a reference symbol. p c (t) is a rectangular window defined by:

p c (t) = 1 0 ≤ t ≤ T FFT 0 T FFT ≤ t ≤ T FFT + T CP + T GI (2)
In the SS-MC-MA case, complex symbols are converted into P parallel symbols D l (i) (with P ≤ L c ) which are transmitted by the same L c subcarriers. P then represents the load, and is namely equal to L c in the full load case and to L c /2 in the half load case. The waveform is the same as previously, but the complex symbol X m (i) which is transmitted by the mth subcarrier (m varying from 1 to L c = 16, with m = n modulo( 16)) of a block of L c = 16 subcarriers bound by the same spreading codes of length L c can be express by:

X m (i) = P l=1 D l (i)c l,m (3)
where

C l = [c l,1 ... c l,m ... c l,L ]
is the lth Walsh-Hadamard orthogonal spreading code and D l (i) represents the P complex symbols, belonging to a QPSK constellation and which are transmitted by the block of L c subcarriers considered during OFDM symbol i. In reception, as in the classical OFDM system case, mono-user detection is simply realized at the output of the FFT by one complex multiplication per subcarrier. MMSE detection technique is considered leading to coefficients: where h n,i and γ n,i represent the complex channel response and the signal to noise ratio for subcarrier n of symbol i respectively.

g n,i = h * n,i |h n,i | 2 + 1 γn,i (4)

C. UWB channel modeling

The channel model used in the MBOA and SS-MC-MA chain is the one adopted by the IEEE 802.15.3a channel modelling sub-committee to evaluate the UWB physical layer performance. This channel model results from Saleh-Valenzuela model for indoor application [START_REF] Saleh | A statistical model for indoor multipath propagation[END_REF]. This ray based model takes into account clusters phenomena highlighted during channel measurements. Mathematically, the impulse response of the multipath model is given by:

h k (t) = X k M k m=0 P k p=0 α k (m, p)δ (t -T k (m) -τ k (m, p)) (5)
where X k is the log-normal shadowing for the kth channel realization, α k (m, p) and τ k (m, p) are the gain and the delay of path p of cluster m respectively, and T k (m) is the delay of cluster m. Table II gives the mean excess delay τ m and the root mean square delay spread τ rms for the 4 channel models CMi. In the Line Of Sight (LOS) configuration, transmitter and receiver antennas are in direct visibility, contrary to the Non Line Of Sight (NLOS) configuration.

The channel is modelled in the time domain, and is normalized in mean energy for each realization. 100 different realizations are used for each CMi, one realization being applied along a whole frame duration.

D. Choice of the spreading code

To reduce the SI, spreading sequences or codes are chosen orthogonal. In presence of a multipath channel, the orthogonality between signals is broken and an SI term appears. It is shown that some combinations of spreading codes could increase or decrease the SI power. Thus, [START_REF] Nobilet | Spreading sequences for uplink and downlink MC-CDMA systems: PAPR and MAI minimization. 2 nd Special Issue on Multi-Carrier Spread-Spectrum and Related Topics -European Trans[END_REF] proposed a method to minimize this SI which consists of a judicious subgroup selection of N u spreading sequences. These methods are used in this study to select the spreading codes.

VI. SYSTEMS PERFORMANCES

Firstly, the performance of the MBOA system has been estimated for UWB channel CM1. In simulations, frames of 150 OFDM symbols are used, and one different channel realization is applied on each new frame. Fig. 4 exhibits the results obtained in the ideal case of perfect channel estimation for rates ranged from 53.3 to 480 Mbit/s. It appears that the Similar results not presented herein have been obtained with channel CM4 leading to the same conclusions, except that a performance floor can appear at high SNR for high data rates, i.e. for high channel code rates. This performance degradation can simply be understood noticing that the GI length is smaller than the delay spread of CM4 [START_REF] Maret | Ultra-wideband MBOA PHY layer performance analysis and enhanced issues (IST MAGNET project)[END_REF].

Let us now focus on the performance obtained with the proposed SS-MC-MA system on channel CM1. The simulation configurations are similar to those used with MBOA, even if the total number of subcarriers N ST is henceforth 118 instead of 122 to take into account the spreading component, the guard and pilot subcarriers. Consequently, the transmission bandwidth becomes equal to 490.87 MHz instead of 507.37 MHz. Via the assignment of a given number P of spreading codes and the choice of the coding rate, it is possible to obtain many different data rates. Table III introduces the code number/coding rate pairs that lead to SS-MC-MA data rates very close to the MBOA ones. As it will be detailed in the following, these pairs correspond to the best choices, among other possible solutions, in term of BER results. The additional degree of freedom brought by the ability to select a given number of spreading codes allows to reach the target rates without applying the conjugate symmetric function nor the time spreading. Fig. 5 exhibits the results obtained for the data rates of table III. It is shown that SS-MC-MA with R=1/3 clearly outperforms MBOA, whereas the two systems MBOA and SS-MC-MA with R=1/2 gives quasi similar results. This behavior is consistent with the conclusions already drawn in other studies [START_REF] Ibars | Comparing the performance of coded multiuser OFDM and coded MC-CDMA over fading channels[END_REF] that tends to show that hybrid OFDM/CDMA systems perform at best for low coding rates (e.g. 1/3). In that case, the diversity brought by the spreading function leads to a substantial performance increase while the SI effect remains limited. At the contrary, for high coding rates, the diversity gain is almost completely reduced by the performance degradation caused by the SI.

To emphasize on the performance gain at low data rate, Fig. 6 exhibits comparative results of the two systems. The plotted curves give for each targeted data rates the E b /N 0 required to obtain a BER equal to 10 -4 . Two coding rates, 1/2 and 1/3 are considered with SS-MC-MA, and the number P of spreading codes is mentioned near each marker. Firstly, it is clear that a coding rate of 1/3 should be exploited with SS-MC-MA for data rates lower than 200 Mbit/s as already introduced in table III. As expected from the previous conclusions, SS-MC-MA (R=1/3) outperforms MBOA for data rates lower than 200 Mbit/s. These results essentially highlight that the MBOA solution based on TSF and conjugate symmetric is not efficient. On the other hand, for R=1/2 the proposed system performs very close to MBOA, however providing a wider range of rates due to the high flexibility brought by the joint assignment of the number of used codes and coding rates.

VII. CONCLUSION

In this paper, we proposed a new waveform for UWB systems based on the combination of OFDM and CDMA which is called SS-MC-MA. The main interest of this solution is a better resource allocation in multi-user and multi-piconet as well as a better robustness against frequency selectivity and narrowband interferers. With SS-MC-MA, the addition of a degree of freedom brought by the spreading component allows to optimize jointly the assignment of the number of used codes and coding rates. Particularly, it has been shown that the optimized new system outperforms MBOA for low data rates and is able to provide wider range of rates. These improvements could be obtained without increasing the system complexity in comparison with the reference MBOA solution since the transmission chain only requires the addition of an Hadamard transform function.

Fig. 2 .

 2 Fig. 2. Data distribution of different users for MC-CDMA and SS-MC-MA systems

Fig. 6 .

 6 Fig.6. Required E b /N 0 to obtain a BER=10 -4 on CM1

  to 480 Mbit/s, are listed in TableI. For certain modes, each complex symbol

	Mode 1	Mode 2	Mode 3	Mode 4	Mode 5
	Band 1	Band 2	Band 3	Band 4	Band 5	Band 6	Band 7	Band 8	Band 9	Band 10	Band 11	Band 12	Band 13	Band 14
	3432 3960 4488	5016	5544 6072 6600 7128 7656 8184 8712 9240 9768 10296	f (MHz)
			Fig. 1. Channels distribution for MBOA solution
							TABLE I
						MBOA DATA RATES
	Data	Modulation	Coding	Conjugate	Time		Coded
	rate					rate		symmetric	spreading	bits per
	(Mbit/s)					(R)		input		factor	OFDM
									to IFFT		(TSF)	symbol
	53.3		QPSK		1/3		Yes			2		100
	80			QPSK		1/2		Yes			2		100
	110		QPSK		11/32		No			2		200
	160		QPSK		1/2		No			2		200
	200		QPSK		5/8		No			2		200
	320		QPSK		1/2		No			1		200
	400		QPSK		5/8		No			1		200
	480		QPSK		3/4		No			1		200

TABLE III POSSIBLE

 III DATA RATES WITH SS-MC-MA

	Data rate	Modulation	Coding Rate	Load	Coded bit
	(Mbit/s)		(R)	P	per symbol
	51.2	QPSK	1/3	4	48
	76.7	QPSK	1/3	6	72
	115.1	QPSK	1/3	9	108
	153.6	QPSK	1/3	12	144
	192	QPSK	1/2	10	120
	307	QPSK	1/2	16	192
	409	QPSK	2/3	16	192
	460	QPSK	3/4	16	192
	rate couples 53.3-110 Mbit/s and 80-160 Mbit/s give closed
	results. This shows that the conjugate symmetric does not
	improve performance as well as expected for data rates 53.3
	and 80 Mbit/s.

ACKNOWLEDGMENT

The authors would like to thank France Télécom R&D/RESA/BWA which supports this study within the contract 461 365 82.


Pierre Maillot

Sébastien Ferré

Peggy Cellier

Mireille Ducassé

Franck Partouche
email: franck.partouche@gendarmerie.interieur.gouv.fr

FORMULIS: Dynamic Form-Based Interface For Guided Knowledge Graph Authoring

Knowledge acquisition is a central issue of the Semantic Web. Knowledge cannot always be automatically extracted from existing data, thus contributors have to make efforts to create new data. In this paper, we propose FORMULIS, a dynamic form-based interface designed to make RDF data authoring easier. FORMULIS guides contributors through the creation of RDF data by suggesting fields and values according to the previously filled fields and the previously created resources.

Introduction

Manual acquisition of RDF data requires an effort either from contributors or from Semantic Web experts. In systems based on contributors' efforts, such as WebProtégé [START_REF] Tudorache | WebProtégé: A collaborative ontology editor and knowledge acquisition tool for the web[END_REF], the contributors have to learn Semantic Web principles, and how to use the specialized interfaces based on these principles. In systems based on Semantic Web experts' efforts, such as ActiveRaUL [START_REF] Sahar Butt | ActiveRaUL: A Web form-based User Interface to create and maintain RDF data[END_REF] or OntoWiki [START_REF] Frischmuth | OntoWiki -an authoring, publication and visualization interface for the data web[END_REF], the data input interfaces are easier to use, but have to be set up by the experts. In case of data evolution, contributors depend on experts to adapt the interface.

In this paper, we propose FORMULIS, a system that offers the user-friendliness of forms while guiding users with dynamic suggestions based on existing data. The contribution is threefold. First, the forms can be nested as deeply as necessary. Hence, it is possible to create at once several related entities, linked by property paths, by building nested descriptions. Second, the forms need no set up by experts because their content is based on SEWELIS suggestions [START_REF] Hermann | An interactive guidance process supporting consistent updates of RDFS graphs[END_REF]. Fields and values are suggested by taking into account all the fields and values already entered in the base and in the current form, hence offering dynamic and accurate suggestions. Last but not least, the forms can be extended with new fields and new sub-forms at any time, according to user needs and data evolution, with a simple click. New forms can also be created for new classes of resources.

FORMULIS has been used in a real setting. Six forensic experts from the forged ID unit of the document department of IRCGN4 put into a knowledge base the description of thirty five forged Portuguese ID cards seized during a police operation. That experiment was successful despite experts having no knowledge of the Semantic Web, different level of expertise in forged ID detection, and different specialties. All were able to produce good quality data.

FORMULIS: Guided RDF Authoring Through Forms

FORMULIS aims at facilitating RDF authoring without knowledge of RDF by proposing a familiar interface, forms, and by dynamically suggesting values from current and previous inputs. On the one hand, graph-based data representations tend to become quickly illegible with the size of the graph and text-based notations, such as Turtle, need prior knowledge to be understood. On the other hand, forms are a common interface for data input. FORMULIS generates a data-driven form-based interface for the production of RDF data.

Interaction loop. At each iteration, the system computes suggestions to fill the form further, and the user selects one suggestion. The form is initially empty, and it is progressively filled through interaction steps, until it is judged complete by the user. Suggestions are computed with the help of the query relaxation and query evaluation mechanisms of SEWELIS [START_REF] Hermann | An interactive guidance process supporting consistent updates of RDFS graphs[END_REF]. This requires first to translate the partially-filled form into an initial query that is supposed to retrieve the possible values for the field under focus, given the already filled fields. Query relaxation of that initial query is in general necessary to ensure the existence of results. In order to propose legible suggestions, those results have then to be rendered as form elements, i.e. user interface widgets and controls. Finally, each time a user selects an element or activates a control, the form is modified by filling a field, adding a field, inserting a nested form, etc. From there, a new interaction step can start.

Nested forms and their RDF counterpart. A form F in FORMULIS is composed of an RDF class C, a resource URI R, and a set of RDF properties p 1 , . . . , p n , along with their sets of values V 1 , . . . , V n . Class C (e.g., dbo:Film) determines the type of the resource being described, and resource R (e.g., dbr:Corpse Bride) determines its identity. Each property p i (e.g., dbo:director) defines a field of the form. Each field may have one or several values. Indeed, unlike tabular data, the RDF data model allows a resource to have several values for the same property, and it is therefore important to account for this in RDF editing tools. An example about films is the property dbo:starring relating films to actors. A field value can be one of: void, i.e. the field has not yet been filled ; a literal, e.g. a string ; an RDF resource already present in the knowledge base (e.g., dbr:Tim Burton) ; or a nested form to create and describe a new RDF resource. Those definitions of forms and field values exhibit the recursive nature of forms in FORMULIS, which allows for cascading descriptions of resources. User interface. Figure 1 shows an example of nested form, as it is displayed in the user interface of FORMULIS. In this example, the form is used to create the description of the film "Corpse Bride". The first step done by the user was to choose "Film" among the available classes in order to get the initial form to create a new film. The suggested fields of the initial form are based on the description of existing films in the base. The user interface follows the classical layout of a form with each field labeled by a property of the described resource. In frame (A), the "director" and "release date" are filled with RDF resources, respectively the URI labeled "Tim Burton" and the literal "2005". Note that RDFS labels are used to display URI in forms. Frame (B) shows two nested forms: one for the description of a new person as "music composer" of the current film ("Danny Elfman"), and another for the description of his birth place ("United States"). In frame (C), the resource labeled "Helena Bonham Carter" has been entered as starring in the movie. In another field for the "starring" property, the user is given six suggestions corresponding to actors that have been starring in movies similar to "Corpse Bride", either because they were also directed by "Tim Burton", released in 2005 and/or starring "Helena Bonham Carter". Below those suggestions, the user is also given the possibility to create a new resource ("New element"), or to ask for more suggestions by not taking into account the previously filled fields ("More general").

Suggestions. In order to suggest values for a field, we need to translate the form to a SPARQL query that retrieves existing values for that field in the knowledge base. Suppose that the user has set the focus on the "starring" field in Figure 1 because she wants to get suggestions for the actors of the film. We could retrieve all values of the "starring" property in the base, using query: SELECT ?v WHERE {?x dbo:starring ?v}. However, this would make suggestions unspecific. We make suggestions dynamic and more accurate by taking into account all filled fields. The principle is to generate a SPARQL query whose graph pattern is the current description: SELECT ?v WHERE {?x a dbo:Film; dbo:director dbr:Tim Burton; dbo:releaseDate "2005"; dbo:musicComposer [a dbo:Person; dbo:birthPlace [a dbo:Country]]; dbo:starring dbr:Helena B Carter, ?v.}.

That query is sent to SEWELIS for relaxation and evaluation.

Cold start. In the case of an empty base or a new class, the creation of the first instance of the new class requires the creation of a new form and its fields, in addition to entering field values. That first instance is enough to generate the forms for the following instances. The user can also extend generated forms with new fields, as it can be seen in Figure 1 at the bottom of each form ("New line").

Demo

The demo will show that the accuracy of suggestions improves when more fields are filled, and when more resources are put in the knowledge base. That accuracy will be shown by the suggestions of values reflecting patterns commonly found in data, for example the fact that actor Johnny Depp is often starring with Helena B. Carter in films directed by Tim Burton. Participants will be given the opportunity to enter the description of recent movies, starting from DBpedia films. The demo will also show the cold start case with the creation of new forms. FOR-MULIS is available in beta version at http://servolis.irisa.fr:8080/formulis/.

Fig. 1 .

 1 Fig. 1. Screenshot of FORMULIS during the creation of a film directed by Tim Burton using the DBpedia vocabulary, with parts in dotted frames for explanation purposes.

This work is partially supported by ANR project IDFRAud (ANR-14-CE28-0012)

"Institut de Recherche Criminelle de la Gendarmerie Nationale", Forensic Sciences Institute of the French Gendarmerie.


Charles N Baroud
email: baroud@ladhyx.polytechnique.fr

Jean-Pierre Delville
email: jp.delville@cpmoh.u-bordeaux1.fr

François Gallaire

Régis Wunenburger

Thermocapillary valve for droplet production and sorting

Keywords: numbers: 47, 61, -k, 47, 55, dm

Droplets are natural candidates for use as microfluidic reactors, if active control of their formation and transport can be achieved. We show here that localized heating from a laser can block the motion of a water-oil interface, acting as a microfluidic valve for two-phase flows. A theoretical model is developed to explain the forces acting on a drop due to thermocapillary flow, predicting a scaling law which favors miniaturization. Finally, we show how the laser forcing can be applied to sorting drops, thus demonstrating how it may be integrated in complex droplet microfluidic systems.

Microfluidic droplets have been proposed as microreactors with the aim to provide high performance tools for biochemistry. Individual drops may be viewed as containing one digital bit of information and the manipulation of a large number of slightly differing drops would allow the testing of a large library of genes rapidly and with a small total quantity of material [1]. In microchannels, drops are produced and transported using a carrier fluid [2] and typical channel sizes allow the manipulation of volumes in the picoliter range. Surfactant in the carrier fluid prevents cross-contamination of the drops through wall contact or fusion [3,4]. However, while the geometry of the microchannel may be used to determine the evolution of drops and their contents [3][4][5], the implementation of real lab-on-a-chip devices hinges on the active control of drop formation and its evolution, which remains elusive.

In this letter, we remedy the situation by demonstrating experimentally how a focused laser can provide precise control over droplets through the generation of a thermocapillary flow. In doing so, we develop the first theoretical model of a droplet subjected to localized heating, yielding a general understanding of the forces acting on the drop and a scaling law which favors miniaturization. A carrier fluid is still used for the formation and transport of drops but the effects of geometry are augmented with a local thermal gradient produced by the laser beam, focused through a microscope objective inside the microchannel.

Indeed, moving drops with heat has been a preoccupation of fluid mechanicians since the initial work of Young et al [6]. Although originally motivated by microgravity conditions where surface effects are dominant [6,7], microfluidics has opened up a new area where bulk phenomena are negligible compared to surface effects. Recently, thermal manipulation of drops or thin films rest-ing on a solid substrate has received the attention of the microfluidics community either through the embedding of electrodes in the solid [8,9] or through optical techniques [10][11][12]. However, the physical mechanisms in the transmission of forces when the liquid touches a solid wall are fundamentally different from the case of drops suspended in a carrier fluid, away from the boundaries [13]. The latter case has received little attention despite the advantages that microchannels offer over open geometries.

Our experimental setup consists of a microchannel fabricated using soft lithography techniques [14]. Water and oil (Hexadecane + 2% w/w Span 80, a surfactant) are pumped into the channel at constant flowrates, Q water and Q oil , using glass syringes and syringe pumps. Channel widths are in the range 100 -500 µm and the height h is in the range 25 -50 µm. Local heating is produced by a continuous Argon-Ion laser (wavelength in vacuum λ Ar + = 514 nm), in the TEM 00 mode, focused inside the channel through a ×5 or ×10 microscope objective to a beam waist ω 0 = 5.2 or 2.6 µm, respectively. The optical approach can be reconfigured in real-time and it allows the manipulation inside small microchannels with no special micro-fabrication. The absorption of the laser radiation by the aqueous phase is induced by adding 0.1% w/w of fluorescein in the water.

A surprising effect is observed when the water-oil interface reaches the laser spot: In the cross-shaped microchannel of Fig. 1, we produce water drops in oil through the hydrodynamic focusing technique in which two oil flows pinch off water droplets at the intersection of the channels. In the absence of the laser, drops of water are produced in a steady fashion and are transported along with the oil down the drain channel, as shown in Figs. 1(a)-(c). When the laser is illuminated, however, the oil-water interface is blocked in place as soon as it crosses the beam. While the typical drop pinching time is τ d ∼ 100 ms in the absence of the laser, we find that we can block the interface for a time τ b which may be of several seconds, as shown in Figs. 1(d)-( ding is completely inhibited and the volume in the water tip increases until the viscous stresses finally break it off.

The drop thus produced is larger, since it has been "inflated" by the water flow.

In the microchannel shown in Fig. 2, we measured the variation of the blocking time τ b with respect to laser power and forcing position. We observe that τ b increases approximately linearly with the power, above an initial threshold, showing a weak position-dependence of the laser spot. Furthermore, the inset of Fig. 2 shows that the droplet length L varies linearly with τ b , as expected from mass conservation at constant water flowrate L = L 0 +τ b Q water /S, L 0 being the droplet length without laser and S ≃ (125 × 30) µm 2 the channel cross section. The best linear fit to the data gives an effective water flowrate Q water = 0.028 µL/min, close to the nominal value 0.03 µL/min, showing that the water flowrate remains controlled even in presence of the laser forcing. Thus, the optical forcing provides a tunable valve which provides control over droplet timing and size. Similar blocking is observed in a T geometry or if the flows are driven at constant pressure. However, the blocking is only obtained when the light is absorbed, here by using a dye.

We visualize the convection rolls produced by the heating by placing tracer particles in both fluids, as shown in Fig. 3(a) for a drop that is blocked in a straight channel. For pure liquids, the direction of Marangoni flow along the interface is directed from the hot (low surface tension) to the cold (high surface tension) regions. However, the flows in our experiments point towards the laser along the interface, indicating an increase of surface tension with temperature. This is consistent with previous studies that have shown a linear increase of surface tension with temperature in the presence of surfactants [16][17][START_REF]concentration reduced the efficiency of the blocking; a detailed exploration of surfactant effects will be addressed in a future study[END_REF].

One important constraint for practical applications is the amplitude of the temperature rise. Since the materials used in this study have similar thermal properties (thermal diffusivity D th ∼ 10 -7 m 2 s -1 , thermal conduc- tivity Λ th ∼ 0.5 Wm -1 K -1 ), we estimate the maximum temperature in the flow by modeling the heating produced by a laser absorbed in a single fluid phase [START_REF] Gordon | [END_REF], assuming thermal diffusion as the only energy transport mechanism. Considering the measured optical absorption of our water/dye solution α th = 117.9 m -1 , and assuming that the temperature 100 µm away is fixed by the flowing oil at room temperature, we find ∆T ≃ 12 K for the temperature rise at the laser focus for a beam power P = 100 mW. The temperature gradient is steep near the focus, with the temperature dropping to 5 K at 20 µm from the beam spot. However, note that given the typical flow velocity (U ∼ 1 mm/s) and the characteristic length scale over which thermal diffusion occurs (L = 100 µm), the thermal Peclet number P e = U L/D th is comparable to unity. Thus, our calculation overestimates the actual overheating.

The force generated by the convective flow on a droplet is investigated through the depth-averaged Stokes equations, since our channels have a large width/height aspect ratio [20]. The detailed modeling will be discussed in a subsequent publication; here we limit ourselves to the main features: a circular drop of radius R is considered in an infinite domain and the flow due to the Marangoni stresses is evaluated. Assuming a parabolic profile in the small dimension (h) and introducing a streamfunction for the mean velocities in the plane of the channel, the depth averaged equations, valid in each fluid, are

1 r ∂ ∂r r ∂ ∂r + 1 r 2 ∂ 2 ∂θ 2 1 r ∂ ∂r r ∂ ∂r + 1 r 2 ∂ 2 ∂θ 2 - 12 h 2 ψ = 0, (1)
where the depth-averaged velocities may be retrieved from u θ = -∂ψ/∂r and u r = 1/r(∂ψ/∂θ). The kinematic boundary conditions at the drop interface (r = R) are zero normal velocity and the continuity of the tangential velocity. The normal dynamic boundary condition is not imposed since the drop is assumed to remain circular, which is consistent with our experimental observations, Fig. 3a. Finally, the tangential dynamic boundary condition, which accounts for the optically-induced Marangoni stress, is

µ 1 r ∂ ∂r u 1 θ r -µ 2 r ∂ ∂r u 2 θ r = - γ ′ r dT dθ , (2)
where µ 1,2 are the dynamic viscosities and u 1,2 θ are the velocities in the drop and the carrier fluid, respectively. γ ′ = ∂γ/∂T is the surface tension to temperature gradient, which is positive in our case.

For simplicity, we approximate the steady state temperature distribution using a Gaussian form T (x, y) = ∆T exp[-((x -R) 2 + y 2 )/w 2 ], where ∆T is the maximum temperature difference between the hot spot and the far field and w corresponds to the size of the diffused hot spot, which is significantly larger than ω 0 [START_REF] Gordon | [END_REF]. The equations are nondimensionalized using ∆T as temperature scale, R as length scale, Rγ ′ ∆T as force scale and R(µ1+µ2) γ ′ ∆T as time scale, the remaining nondimensional groups being the aspect ratio h/R, the nondimensional hot spot size w/R and the viscosity ratio μ = µ 2 /(µ 1 + µ 2 ).

A typical predicted flow field solving the above numerical formulation is shown in Fig. 3(b), in which the four recirculation regions are clearly visible. The velocity gradients display a separation of scales in the normal and tangential directions, as observed from the distance between the streamlines in the two directions. Indeed, it may be verified that the velocities vary over a typical length scale h/R in the normal direction, while the tangential length scale is given by w/R. Along with this flow field, we compute the pressure field, as well as the normal (σ r r = 2μ ∂ ūr ∂ r ) and tangential σrθ = μ 1 r ∂ ūr

∂θ + ∂ ūθ ∂ r -ūθ r
viscous shear stresses in the external flow. Their projections on the x axis, shown in the inset of Fig. 3(c), are then summed and integrated along θ to yield the total dimensionless force ( F ) on the drop. Note that the global x component of the force is negative and therefore opposes the transport of the drop by the external flow. The y component vanishes by symmetry and the integral of the wall friction may be shown to be zero since the drop is stationary. Numerically computed values of F R/h are shown by the isolated points in Fig. 3(c) as a function of w/R, for different values of the aspect ratio h/R. The points all collapse on a single master curve, displaying a nondimensional scaling law F ∝ wh/R 2 , for small w/R.

The dimensional form of the force can be obtained, for small h/R and w/R, by considering the three contributions separately and noting that the velocity scale in this problem is imposed by the Marangoni stress. Using the separation of scales along the azimuthal and radial directions, Eq. 2 becomes (µ

1 + µ 2 ) U h ∼ ∆T γ ′ R R
w , where the '∼' is understood as an order-of-magnitude scaling. This yields the characteristic tangential velocity scale

U ∼ ∆T γ ′ µ 1 + µ 2 h w . (3)
The force due to the tangential viscous shear is then obtained by multiplying σ rθ ∼ µ 2 U/h by sin θ ≃ w/R and integrating on the portion w × h of the interface,

F t ∼ µ 2 U h w R wh = µ 2 µ 1 + µ 2 ∆T γ ′ hw R . (4)
The force due to the normal viscous shear can be shown to scale like F n ∼ h R F t and is therefore negligible. The pressure force, on the other hand, derives from a balance between the pressure gradient and the radial second derivative of velocity. In the present circular geometry, similar scaling arguments yield a law for the contribution of the pressure force F p , which follows the same scaling as F t , resulting in the same scaling law for the total force F . A rigorous derivation (to be published elsewhere) yields the final form of the force including the prefactor:

F = -2 √ π µ 2 µ 1 + µ 2 ∆T γ ′ hw R . ( 5
)
This expression is represented (once nondimensionalized) by the straight line on Fig. 3(c) and agrees very well with the numerically computed values.

The physical value of the force for a typical experiment is estimated by taking µ 1 = 10 -3 Nm -2 s (water), µ 2 = 3µ 1 (hexadecane), and extracting γ ′ ∼ 1 mNm -1 K -1 from Ref. [17]. This yields a force on the order of 0.1 µN, which is of the same order as the drag force on a drop in a large aspect ratio channel [21], thus confirming that thermocapillary forcing can indeed account for the blocking. Note that the force we calculate is several orders of magnitude larger those generated from electric fields [22] or optical tweezers [23].

This blocking force may be applied at different locations in a microchannel by displacing the laser spot. In particular, we demonstrate the sorting of drops, a fundamental operation in the implementation of lab-on-a-chip devices. Drops are formed, as above, in a cross-junction and arrive at a symmetric bifurcation, carried by the continuous phase. In the absence of laser forcing, the drops arriving at the bifurcation divide into two equal parts [5], Fig. 4(a). When the laser is applied, the wateroil interface is asymmetrically blocked on the right hand side while the left hand side continues to flow, Fig. 4(b). Above a critical laser power (approximately 100 mW for the present configuration), the drop is blocked long enough that it is completely diverted through the left hand channel [15]. Drops may therefore be sorted by accordingly selecting the laser position.

In summary, we have experimentally and theoretically demonstrated the efficiency of laser-driven blocking of water-in-oil drops. The theoretical treatment brings out two length scales, h/R and w/R. While h and w can be thought of as determining the typical scales for velocity variations in the radial and azimuthal directions, R enters the force scaling as a local radius of curvature rather than the actual size of the drop. It is therefore not surprising that the blocking force should increase as R decreases. On the other hand, the drag force due to the external flow scales as R 2 [21], implying that the laser power necessary to counterbalance the drag quickly decreases with the drop size. This, along with the rapidity of viscous and thermal diffusion while thermal inertia is reduced, all lead to laws favorable to miniaturization. The generality of the process provides a practical new way for acting on individual droplets, at any location, while working inside the robust environment of the microchannel.

FIG. 1 :

 1 FIG. 1: Microfluidic valve: In a cross-shaped microchannel, the oil flows from the lateral channels and the water enters through the central channel. (a)-(c) In the absence of laser forcing, drops are shed with a typical break-off time [(b) to (c)] of 0.1 s. (d)-(f) When the laser is applied, the interface is blocked for several seconds, producing a larger drop. In image (e), the evolution of the neck shape is shown through a superposition of 100 images (2 s). Exit channel width is 200 µm. Operating conditions are: Qwater = 0.08 µL/min, Qoil = 0.90 µL/min, beam power P = 80 mW and beam waist ω0 = 5.2 µm.

FIG. 2 :

 2 FIG. 2: (color online) Dependence of the blocking time τ b on laser power and position (indicated in the picture) for Qwater = 0.03 µL/min and Qoil = 0.1 µL/min, ω0 = 2.6 µm. Inset: Rescaled droplet length L/L0 vs. the blocking time (laser position •), where L0 is the droplet length without the laser. The dashed line is a linear fit, ignoring the outlier at τ b = 0.75 s.

FIG. 3 :

 3 FIG. 3: (color online) (a) Overlay of 100 images from a video sequence showing the motion of seeding particles near the hot spot. Note that the motion along the interface is directed towards the hot spot. (b) Streamfunction contours obtained from the depth-averaged model described in the text. Dashed and continuous contours indicate counterclockwise and clockwise flows, respectively. (c) Rescaled nondimensional force F R/h plotted as a function of w/R for various aspect ratios h/R for μ = 3/4. The straight line corresponds to the dimensional scaling derived in the text. The inset shows the x-component of the distribution along the azimuthal direction of the pressure, normal and tangential shear stresses, where the solid circle is the reference zero. Their sum yields the total force. Channel width in part (a) is 140 µm. h/R = 0.2, w/R = 0.5 for parts (b) and (c)inset.

FlowFIG. 4 :

 4 FIG. 4: Sorting drops: (a) Without laser forcing, a drop at a bifurcation divides into approximately equal daughter droplets. (b) When the laser forcing is applied, the drop advance in the right hand channel is blocked so the whole drop is diverted into the left channel. Main channel width is 200 µm and the operating conditions are Qwater = 0.02 µL/min, Qoil = 0.2 µL/min, and ω0 = 5.2 µm.

We acknowledge help from Julien Buchoux, David Dulin and Emilie Verneuil.

This work was partially funded by the CNRS PIR "Microfluidique et Microsystèmes Fluidiques", the Conseil Régional d'Aquitaine, and the convention X-DGA.


M Van Camp

O De Viron

J P Avouac

Separating climate-induced mass transfers and instrumental effects from tectonic signal in repeated absolute gravity measurements

 The signature of climate-induced interannual mass transfers on repeated absolute gravity measurements is estimated everywhere in the world  Instrumental artefacts should be taken into account and mitigated as much as possible.

 In most cases, the uncertainty is estimated to ~5 nm/s²/a after 10 yearly campaigns

Abstract 150 words

We estimate the signature of the climate-induced mass transfers in repeated absolute gravity measurements based on satellite gravimetric measurements from the GRACE mission. We show results at the globe scale, and compare them with repeated absolute gravity (AG) time behavior in three zones where AG surveys have been published: Northwestern Europe, Canada and Tibet.

For 10 yearly campaigns, the uncertainties affecting the determination of a linear gravity rate of change range 3-4 nm/s²/a in most cases, in absence of instrumental artefacts. The results are consistent with what is observed for long term repeated campaigns. We also discuss the possible artifact that can results from using short AG survey to determine the tectonic effects in a zone of high hydrological variability. We call into question the tectonic interpretation of several gravity changes reported from stations in Tibet, in particular the variation observed prior to the 2015 Gorkha earthquake.

Introduction

Absolute gravimeters (AG), by construction, suffer no time drift; this makes them most appropriate to measure long-term surface gravity changes, which might reflect either vertical ground motion or mass redistribution. AGs have for example been used to monitor slow vertical ground displacements [START_REF] Mazzotti | Crustal uplift and sea level rise in northern Cascadia from GPS, absolute gravity, and tide gauge data[END_REF]Djamour et al., 2010;[START_REF] Van Camp | Repeated absolute gravity measurements for monitoring slow intraplate vertical deformation in western Europe[END_REF]Zerbini et al., 2007] and Glacial Isostatic Adjustment [START_REF] Lambert | Long-term monitoring by absolute gravimetry: tides to postglacial rebound[END_REF][START_REF] Steffen | Present rate of uplift in Fennoscandia from GRACE and absolute gravimetry[END_REF][START_REF] Mazzotti | Absolute gravity calibration of GPS velocities and glacial isostatic adjustment in mid-continent North America[END_REF][START_REF] Sato | Gravity and uplift rates observed in southeast Alaska and their comparison with GIA model predictions[END_REF]. It has also been used to study mass redistribution by erosion [START_REF] Mouyen | Erosion effects assessed by repeated gravity measurements in southern Taiwan[END_REF] and crustal tectonics [START_REF] Mouyen | Investigating possible gravity change rates expected from long-term deep crustal processes in Taiwan[END_REF]. Intriguing measurements of gravity changes in Tibet have been recently reported [START_REF] Sun | Gravity and GPS measurements reveal mass loss beneath the Tibetan Plateau: Geodetic evidence of increasing crustal thickness[END_REF] found evidences for a gravity decrease at three stations, which they interpreted as the signature from a long term thickening of the Tibetan plateau and Chen et al. [2015] reported a gravity increase, which they attribute to preseismic processes associated to the 2015, Mw 7.8 Gorkha earthquake.

Such tectonic interpretation should be considered with caution in view of the possible effect of non-tectonic causes, in particular surface hydrology, on absolute gravity measurements and instrumental artefacts. Yi et al. [2016] showed that the signal observed prior to the Gorkha earthquake by Chen et al. [2015] is most probably due to a local hydrological effect unrelated to the earthquake itself.

Gravity measurements are indeed extremely sensible to local water storage changes, which depends on very local geologic and climatic conditions, e.g. rock porosity, vegetation, evaporation, and runoff rates [ Van Camp et al., 2006a;[START_REF] Jacob | Absolute gravity monitoring of water storage variation in a karst aquifer on the larzac plateau (Southern France)[END_REF]Creutzfeldt et al., 2010a;[START_REF] Lampitelli | Hydrological effects on gravity and correlations between gravitational variations and level of the Alzette River at the station of Walferdange, Luxembourg[END_REF]; the associated gravimetric signature often exceeds the tectonic effects, and consequently induces non negligible time correlated signature in the gravity time series [ [START_REF] Van Camp | Characterizing long-time scale hydrological effects on gravity for improved distinction of tectonic signals[END_REF]. Hydrological effects are observed locally from AG measurements but also at the regional or global scale from satellite gravimetric measurements or GPS geodetic measurements [e.g. [START_REF] Bettinelli | Seasonal variations of seismicity and geodetic strain in the Himalaya induced by surface hydrology[END_REF], Blewitt et al., 2001;[START_REF] Chanard | Modeling deformation induced by seasonal variations of continental water in the Himalaya region: Sensitivity to Earth elastic structure[END_REF][START_REF] Ramillien | Global time variations of hydrological signals from GRACE satellite gravimetry[END_REF][START_REF] Van Dam | Crustal displacements due to continental water loading[END_REF].

Separating the instrumental artifacts and the contribution of surface hydrology from tectonic processes in the AG measurements is thus a major challenge. A better understanding and quantification of these effects, as well as of instrumental artifacts, is in our view a prerequisite to any tectonic interpretation of an AG survey. Hereafter, we first discuss instrumental artifacts and next discuss hydrological effects based on satellite gravimetric measurements and comparison with local AG observations in a few areas.

Instrumental artefacts

When different AGs are used in the same study, inter-instrument differences should be taken into account, as done for example by [START_REF] Lambert | Long-term monitoring by absolute gravimetry: tides to postglacial rebound[END_REF]2013b], or included in the uncertainty budget [START_REF] Sato | A geophysical interpretation of the secular displacement and gravity rates observed at Ny-Alesund, Svalbard in the Arctic-effects of post-glacial rebound and present-day ice melting[END_REF][START_REF] Mémin | Secular gravity variation at Svalbard (Norway) from ground observations and GRACE satellite data[END_REF][START_REF] Palinkas | Analysis of the repeated absolute gravity measurements in the Czech Republic, Slovakia and Hungary from the period 1991-2010 considering instrumental and hydrological effects[END_REF]. Intercomparison campaigns [e.g. [START_REF] Van Camp | Uncertainty of absolute gravity measurements[END_REF][START_REF] Francis | Results of the European Comparison of Absolute Gravimeters in Walferdange (Luxembourg) of November 2007[END_REF][START_REF] Francis | The European Comparison of Absolute Gravimeters 2011 (ECAG-2011)[END_REF][START_REF] Francis | CCM.G-K2 key comparison[END_REF][START_REF] Jiang | The 8th International Comparison of Absolute Gravimeters 2009: the first Key Comparison (CCM.G-K1) in the field of absolute gravimetry[END_REF][START_REF] Schmerge | Results of the first North American comparison of absolute gravimeters, NACAG-2010[END_REF][START_REF] Vitushkin | Results of the Sixth International Comparison of Absolute Gravimeters ICAG-2001[END_REF] showed that differences between FG5 and JILAg gravimeters are commonly of the order of 100-150 nm/s² . A difference as large as 461 nm/s² was reported for one of the A10 instruments that participated in the ICAG-2001 intercomparison [START_REF] Vitushkin | Results of the Sixth International Comparison of Absolute Gravimeters ICAG-2001[END_REF]. In other comparisons, systematic and random errors of A10 gravimeters ranged between 70 and 220 nm/s² [START_REF] Jiang | Final report on the Seventh International Comparison of Absolute Gravimeters (ICAG 2005)[END_REF][START_REF] Van Camp | Uncertainty of absolute gravity measurements[END_REF][START_REF] Francis | The European Comparison of Absolute Gravimeters 2011 (ECAG-2011)[END_REF][START_REF] Francis | CCM.G-K2 key comparison[END_REF].

Concurrently, the uncertainty due to the setup of the AG instrument should be taken into account. This noise results from instrumental setup-dependent offsets and can be due for example to middling alignment of the instrument, errors in height measurement, slight perturbations due to transportation or different instrument-floor couplings. For an FG5, the sources of uncertainties can be represented by a normal random distribution, with a standard deviation of 16 nm/s² [ [START_REF] Van Camp | Uncertainty of absolute gravity measurements[END_REF]. In some circumstances, larger, isolated systematic errors due to instrumental setup may occur. For example, an error in the laser frequency can induce a shift in gravity of 270 nm/s²; a malfunctioning or not calibrated clock is also possible (2 nm/s²/mHz for an FG5 instrument), etc. (for a comprehensive review of errors see [START_REF] Niebauer | A new generation of absolute gravimeters[END_REF]). This is difficult to detect but can be mitigated by sufficiently repeating the AG measurements. Finally, other possible artefacts like building construction or soil sealing around the gravity station may modify gravity significantly.

Separating hydrological effects from tectonic signal

Separating hydrological signature from tectonic signal in AG data can be done if either (1) the hydrological signal is known with a precision sufficient to allow subtraction of the hydrology signature from the AG data, (2) one disposes from sensors with a response to hydrological load and tectonic effect different from that of the AG, or (3) the space-time behavior of the two signals differs to such an extent that it is possible to use data processing technique to separate them. The third method is most often not practical because of the sparsity in time and space of AG data. Method 2 requires disposing of additional data of a different kind.

Method 1 requires precise independent information about hydrology. Estimating subsurface water storage changes is notoriously complex, and it is even more so at the very local scale, where the gravity transfer function is the most sensible. [START_REF] Lambert | Long-term monitoring by absolute gravimetry: tides to postglacial rebound[END_REF] succeeded in that estimation using a single-thank soil moisture model, but this method is not easily transposable. Such a modeling of hydrogeological effects requires comprehensive investigations and costly in situ instrumentation for ground water measurements [Creutzfeldt et al., 2010a;2010b], which cannot be performed at each gravity station. In addition, correction of the hydrology signature by applying global hydrological models such as the Global Land Data Assimilation System [GLDAS, [START_REF] Rodell | The global land data assimilation system[END_REF] or European Re-Analysis [ERA, [START_REF] Uppala | The ERA-40 re-analysis[END_REF], or space-based observations from the Gravity Recovery and Climate Experiment [GRACE, Wouters et al., 2014] is not adequate, given their limited time and space resolution.

Ground water storage is indeed heterogeneous in space and variable in time at scales below the spatial and temporal resolution of GRACE, preventing one from retrieving local hydrological effects [ [START_REF] Van Camp | Characterizing long-time scale hydrological effects on gravity for improved distinction of tectonic signals[END_REF]2014].

Separation of the causes of temporal variations of AG measurements and precise correction of hydrogeological effects is thus not possible in most cases. Based on the spectral content of modelled hydrogeological effects and of SG time series, [START_REF] Van Camp | Repeated absolute gravity measurements for monitoring slow intraplate vertical deformation in western Europe[END_REF] investigated the hydrological effects on repeated gravity measurements. They showed that the time required to measure a gravity rate of change of 1 nm/s²/a at the 1 level was of the order of 10 years but highly dependent on the location, assuming continuous, hourly sampled gravity time series at the existing SG stations. In case of repeated absolute gravity measurements, the continuity of measurements is broken, and the setup noise must be taken into account. Presently, the easiest and only practical way to mitigate hydrological effects in AG measurements is to perform measurements at the same epoch of the year -the impact of seasonal variations is then minimized and, for a sufficiently long time period, interannual variations average out. This procedure is only approximate due to long-term variability of the hydrological signal and to possible long term drift of groundwater storage. The addition of superconducting gravimeter (SG) information mitigates the error in the estimation of gravity rates of change caused by the presence of long period, interannual, and annual signals in the AG data [ [START_REF] Van Camp | Improving the determination of the gravity rate of change by combining superconducting with absolute gravimeter data[END_REF], but this remains unpractical. However, global models, as GRACE or GLDAS, can meaningfully be used to investigate the spatiotemporal behavior of the hydrological signal, and gather information about the possible magnitude of the hydrological signature.

Since 2002, GRACE has provided long enough time series to be used as in the study of [START_REF] Van Camp | Characterizing long-time scale hydrological effects on gravity for improved distinction of tectonic signals[END_REF]. Unlike most of the global hydrological model, GRACE integrates the whole ground water content, from the saturated and unsaturated zones, producing a reliable tool to estimate water storage changes. Hence, keeping in mind that the local effects can significantly modify the water storage change signal both in phase and amplitude [ [START_REF] Camp | The quest for a consistent signal in ground and GRACE gravity time series[END_REF], GRACE can be used as a proxy in order to estimate the space-time variability of water storage changes in different climatic and hydrogeological contexts on repeated gravity measurements. This is done below by simulating repeated AG measurements performed once a year.

Space-time variability of hydrological effects on surface gravity measurements

We use monthly GRACE mass concentration (mascon) solutions from JPL [Watkins et al., 2015;[START_REF] Wiese | JPL GRACE Mascon Ocean, Ice, and Hydrology Equivalent Water Height RL05M.1 Filtered[END_REF]. The solutions are expressed on a 0.5 by 0.5 degree grid, though the actual resolution is closer to 2 degrees. As we want to avoid the influence of possible slow tectonic processes, a 1 st -degree polynomial estimated at each point over the whole GRACE area, was removed, to avoid the influence of possible slow tectonic processes.

In this study, we only consider the Newtonian effects on the AG measurements. The deformation effect caused by the surface mass loading can be corrected using Global Navigation Satellite System (GNSS) observations [Zerbini et al., 2007] and, after 5 years, is at the mm/a level [Santamaría-Gómez and [START_REF] Santamaría-Gómez | Geodetic secular velocity errors due to interannual surface loading deformation[END_REF], equivalent to 3 nm/s²/a.

The equivalent water height is converted into gravity signal, in nm/s², using the Bouguer factor of 4.2 nm/s² for 1 cm of water height equivalent, which has been shown to be an excellent approximation [Creutzfeldt et al., 2008]. Then, we computed the Allan standard deviation [START_REF] Allan | The statistics of atomic frequency standards[END_REF], i.e. the averaged squared differences between successive averages performed over a given time interval as a function of the interval length.

𝜎 𝑦 2 (𝜏) = 1 2 〈(𝑦 ̅ 𝑛+1,𝜏 -𝑦 ̅ 𝑛,𝜏 ) 2 〉,
where the averages 𝑦 ̅ 𝑛+1,𝜏 are computed over the interval 𝜏.

This statistics quantifies the impact of the timescale 𝜏 on the variability of the signal. This was done on each grid cell everywhere on land but Antarctica and Greenland, for which there is no solution of the JPL mascon.

The Allan deviations of the gravity signature are calculated for time intervals of 12 months over three zones where several studies reporting on repeated AG measurements were published (Figure 1): Northwestern Europe (Belgium and western Germany; Van Camp et al.

[2011], results extended to 2014 by the authors), Canada-Northern USA [START_REF] Lambert | Long-term monitoring by absolute gravimetry: tides to postglacial rebound[END_REF]2013a;2013b;[START_REF] Mazzotti | Absolute gravity calibration of GPS velocities and glacial isostatic adjustment in mid-continent North America[END_REF] and Southeast Asia (Tibet; [START_REF] Sun | Gravity and GPS measurements reveal mass loss beneath the Tibetan Plateau: Geodetic evidence of increasing crustal thickness[END_REF]; Chen et al.

[2016]). This is also done at time intervals of 1, 3, 6 and 60 months for the whole world (Figure 2). Note that the color scale has been saturated to allow a better visibility. In the supporting information, Figures S1 show other zones not discussed in this paper: Central Asia, South America, Africa and Oceania. Figure S2 provides the distributions shown on Figures 1 andS1.

The figures indicate that, in most of the cases, we can expect a standard deviation in the range 10-25 nm/s² for measurements repeated once a year, due to interannual climate dynamics.

In other words, even when performing the measurements at the same moment every year, the 95% confidence interval for the interannual gravity variability, for example due to hydrologicalrelated surface load variations, is typically in the interval 20-50 nm/s².

Northwestern Europe

In Northwestern Europe, Belgium and western Germany lie in a zone where GRACE indicates a 12-month Allan standard deviation of 7 nm/s². Adding up the AG setup noise, one obtains 17.5 nm/s². This uncertainty compares with the one deduced from our repeated AG measurements that provide standard deviations ranging 16-24 nm/s².

To better estimate this effect, as well as the influence of the number of repeated AG measurements on the trend estimate, we simulated yearly measurements performed 2, 3, 5 and 10 times, for durations of 2, 3, 5 and 10 years by randomly picking data from the GRACE mascon solution.

To estimate the variability of the trend, we randomly pick 5,000,000 places in the area of interest and starting dates (distributed from 30 days before to 30 days after October, 1); then we compute the trend obtained from the GRACE models for those places. October 1 st is chosen because most of the yearly AG measurements relevant for this study are acquired around that time of the year. Concurrently to the interannual mass variability effects, the instrumental setup noise is taken into account by adding a normal random variable with a standard deviation of 16 nm/s². Table S1 provides a standard deviation averaged on the zones shown on Figures 1 andS1.

We also made similar simulations at the AG stations, for which we picked randomly 100,000 sets of N dates, around October 1st, distributed over D years (N, D= 2, 3, 5 and 10, D≥N). For the resulting time series, we estimate the standard deviation of the GRACE time series closest to the station. We end up with an average standard deviation of 1.5±0.3 nm/s²/a after 10 years of yearly measurements, which compares well with the actual average standard deviation of 1.6±1.4 nm/s²/a reported at the 9 AG stations (see Table 2 in [START_REF] Van Camp | Repeated absolute gravity measurements for monitoring slow intraplate vertical deformation in western Europe[END_REF]). Considering that GRACE does not represent precisely the space-time mass distribution near the stations, and that the experimental setup is not exactly that reproduced in our test, we consider that the results of this simulation are close enough to observation to be convincing and to validate our approach.

Table S1 shows that, everywhere in the world, at least 5 AG measurements are needed over a 10 year period to achieve an uncertainty smaller than 10 nm/s²/a at the one sigma level.

This becomes less than 5 nm/s²/a, provided one measurement is performed each year.

Canada, northern USA

In North America, the AG stations from the study of Lambert et al. [2013a;2013b] and [START_REF] Mazzotti | Absolute gravity calibration of GPS velocities and glacial isostatic adjustment in mid-continent North America[END_REF] lie in a zone where GRACE indicates a 12-month Allan deviation ranging 5 nm/s² (Priddis, Alberta) to 37 nm/s² (Wausau, Wisconsin). Taking into account the AG setup noise of 16 nm/s², one obtains 28-40 nm/s², which compares with the uncertainties of yearly repeated AG measurements that provide standard deviations ranging 25-37 nm/s² (digitized data from the Figures 3a-3e in Lambert et al. [2005]). After 10 years, the uncertainties on the slopes range 1-3 nm/s²/a, which agrees with [START_REF] Mazzotti | Absolute gravity calibration of GPS velocities and glacial isostatic adjustment in mid-continent North America[END_REF] reporting on uncertainties ranging 1-4 nm/s²/a.

Southern Tibet

In southern Tibet, Chen et al. [2016] reported on gravity differences of -21, 62, 70 and 407 nm/s², at 4 stations, based on measurements performed first in October 2010 or August 2011, and repeated once in July 2013. However, this zone experiences strong loading effects from seasonal water storage changes and hydrological changes over the longer term [Chanard et al., 2015;[START_REF] Hao | Vertical crustal movement around the southeastern Tibetan Plateau constrained by GPS and GRACE data[END_REF][START_REF] Rodell | Satellite-based estimates of groundwater depletion in India[END_REF]. The 12-months Allan standard deviations, which indicate the interannual variability, are 26, 17, 17, 21 nm/s² at Naqu, Lhasa, Shigatse and Zhongba, respectively. There are large differences in monsoon rainfall between July-August (about 120 mm of water per month in Lhasa) and October (10 mm of water per month), which can induce additional hydrological effects at the 20 nm/s² level, according to the 1-month Allan deviation. To account for this variability, another simulation of the uncertainty affecting the slope estimate was performed. This includes the setup noise, considering 60 days before and after October 1 (Table S2). We end up with standard deviations of 32, 24, 20 and 28 nm/s²/a at Naqu, Lhasa, Shigatse and Zhongba, respectively. This is enough to account for the claimed gravity changes at all stations but Shigatse.

Note that the monsoon effects can dramatically be amplified by local hydrogeological effects such as floods in valleys, response of local aquifers, lakes, endorheic lakes and alluvial plains; or mudflows, landslides and deposits, which may play an important role, especially in the Tibetan rugged terrain. This cannot be observed directly by GRACE, and requires local investigation, as done for example by [START_REF] Mouyen | Erosion effects assessed by repeated gravity measurements in southern Taiwan[END_REF]. the observed signal: the reported differences affecting FG5 and JILAg instruments range up to 134 nm/s², and up to 461 nm/s² for A10 gravimeters. In particular, Francis et al. [1995] report on results from JILAg 3 and 5 instruments used by [START_REF] Sun | Gravity and GPS measurements reveal mass loss beneath the Tibetan Plateau: Geodetic evidence of increasing crustal thickness[END_REF]: difference of about 100 nm/s² is observed between the two instruments, and unrealistic trends in Brussels (300 nm/s² in 6 years) and Membach (eastern Belgium, 100 nm/s² in 3 years) could never be confirmed later on

[ [START_REF] Van Camp | Repeated absolute gravity measurements for monitoring slow intraplate vertical deformation in western Europe[END_REF]. Hence, the tectonic interpretations of [START_REF] Sun | Gravity and GPS measurements reveal mass loss beneath the Tibetan Plateau: Geodetic evidence of increasing crustal thickness[END_REF] and Chen et al.

[2016] are questionable in our opinion, especially when the still experimental JILAg and early FG5 instruments are taken into account. A detailed discussion on the offsets and uncertainties of JILAg and early FG5 gravimeters are given by [START_REF] Palinkas | Analysis of the repeated absolute gravity measurements in the Czech Republic, Slovakia and Hungary from the period 1991-2010 considering instrumental and hydrological effects[END_REF]. Moreover, in Lhasa, the trend is the average of two trends recorded at two different places, 800 m apart. Differences in the gravity response to local hydrogeological effects at sites only 40 meters apart have been reported to be as large as 100 nm/s² within a few months [START_REF] Mikolaj | Portable superconducting gravimeter in a field enclosure: first experiences and results[END_REF]. Hence, averaging two trends, including one determined on only three measurements, is questionable.

Other zones

As shown by the Tables S1 andS2, in most of the cases, one needs at least 5 repeated AG measurements during 10 years to achieve an uncertainty on the determination of a trend lower than 10 nm/s²/a, at the one-sigma level. This decreases down to 3-4 nm/s² if the 10 yearly measurements are performed. On the other hand, it is hopeless to achieve a precision better than 20 nm/s²/a, if only 3 measurements are performed during 3 years. Given that measurements are usually not performed at exactly the same date of the year, degrees of freedom of +/-30 and +/-60 days were taken into account. The 60 days cases are slightly noisier, but the increase remains under the 10% level. However, those GRACE-inferred estimates represent average values in the geographic zones shown on Figures 1 andS1. They do not represent local phenomena, where hydrogeological effects may affect gravity at the 100-150 nm/s² level, sometimes within a few hours [ Van Camp et al., 2006b;[START_REF] Meurers | Correcting superconducting gravity timeseries using rainfall modeling at the Vienna and Membach stations and application to Earth tide analysis[END_REF]. Our results can thus be considered as a lower bound of the climate-induced mass transfer uncertainty.

Conclusions

The ground water content inferred from GRACE mascon JPL solutions was used to estimate the time variations of hydrological signals in repeated absolute gravity measurements.

This was done everywhere in the world, and the results are discussed in three zones where papers report on repeated AG measurements: Northwestern Europe, Canada and Tibet. Taking into account the instrumental setup noise, different time intervals (2, 3, 5, 10 years) and different numbers of AG campaigns [START_REF] Watkins | Improved methods for observing Earth's time variable mass distribution with GRACE using spherical cap mascons[END_REF]3,5,10), we estimate uncertainties affecting the determination of a linear gravity rate of change. For 10 yearly campaigns, performed during the same epoch of the year, an average uncertainty ranging 3-4 nm/s²/a can be achieved in most of the cases, in the absence of instrumental artefacts and of strong local hydrogeological effects.

The results are consistent with the amplitude of observed gravity changes on long term repeated campaigns, provided the measurement were performed with the same instrument. This allows extrapolating our simulation at different locations in the world. They invite care regarding the interpretation of results from short campaigns, and even more so in area prone to fluctuations of hydrology and mass redistribution by surface processes. Poor calibration of the gravimeters may dramatically affect this result. We draw attention on the possible offsets which can significantly influence the repeated AG measurements when different instruments are used.

Finally, in this study, a linear trend was removed from the GRACE time series. points of the selected area, and repeated to sum up to 5 000 000 simulated experiment on the areas shown on Figures 1 andS1. As the gravity measurements cannot be performed exactly at the same day of the year, the simulations allow the measurements to happen randomly from 30 before to 30 days after October, 1. In all case an instrumental setup noise of 16 nm/s² is included.

Figure 1 .

 1 Figure 1. Allan deviations of the hydrological effects on repeated gravity measurements, at the

Figure 2 .

 2 Figure 2. Allan deviations of the hydrological effects on repeated gravity measurements in the

  That paper reports on repeated AG measurements in Taiwan where the observed gravity changes range -410 to +2850 nm/s², induced by landslides and sediment accumulation triggered by a typhoon. Given the large AG changes at Shigatse station do not coincide with any signal in the GRACE data, we believe, likeYi et al. [2016] that it must reflect a local effect related either of hydrology or mass redistribution by surface processes.[START_REF] Sun | Gravity and GPS measurements reveal mass loss beneath the Tibetan Plateau: Geodetic evidence of increasing crustal thickness[END_REF] also reported repeated measurements in Tibet at three stations, performed between 1990 and 2008 at the same epoch of the year: Lhasa (4 and 3 measurements on two different points, -19.7 nm/s²/a), Kunming (6 measurements, -14.2 nm/s²/a) and Dali (10 measurements, -4.1 nm/s²/a). Combining the hydrological effects and the setup noise, we obtain uncertainties on the trend of 3, 9 and 2 nm/s²/a, considering that measurements were made within ±30 days around October 1. Lhasa and, possibly, Dali may have experienced a gravity rate too large (above the two-sigma level) to relate to climate dynamics. However, in these two studies in Tibet, different instruments were used.[START_REF] Chen | Gravity increase before the 2015 Mw 7.8 Nepal earthquake[END_REF] made use of at least two different absolute gravimeters (one FG5 and one A10), while[START_REF] Sun | Gravity and GPS measurements reveal mass loss beneath the Tibetan Plateau: Geodetic evidence of increasing crustal thickness[END_REF] used 5 different ones in Lhasa, 2 in Kunming and 4 in Dali. This induces instrumental artefacts at a level that can reach

Introduction

  This supporting information contains maps of zones which are not directly discussed in the main paper: South America, Central Asia, Africa and Oceania. FigureS2provides the distributions shown on Figures1 and S1.The tables S1 and S2 provide detailed uncertainties on the determination of the gravity rate of change as a function of the geographic area, the duration of the measurements and the number of measurements.

Figure S1 .

 S1 Figure S1. Allan deviations of the hydrological effects on repeated gravity measurements, at the

Figure S2 .

 S2 Figure S2. Box and whisker plots of the Allan standard deviations shown on Figures 1 and S1:

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Table S2 .

 S2 Same as TableS1but allowing the measurements to be performed up to 60 days

	D Duration (years) N Number of measurements
	World	3	5	10
	10	9	5	3
	5	14	9	-
	3	18	-	-
	2	-	-	-
	Europe
	10	9	5	3
	5	14	9	-
	3	19	-	-
	2	-	-	-
	Southeast Asia
	10	14	7	4
	5	21	14	-
	3	29	-	-
	2	-	-	-
	North America
	10	10	5	3
	5	17	11	-
	3	21	-	-
	2	-	-	-
	South America
	10	10	6	4
	5	16	10	-
	3	21	-	-
	2	-	-	-
	Central Asia
	10	10	5	3
	5	16	10	-
	3	21	-	-
	2	-	-	-
	Africa
	10	10	5	3
	5	16	11	-
	3	20	-	-
	2	-	-	-
	Oceania
	10	9	5	3
	5	14	9	-
	3	18	-	-
	2	-	-	-

527

before and after October 1.

Acknowledgments and Data

The data used in the references, tables and supplements and repository at http://podaac.jpl.nasa.gov/dataset/TELLUS_GRACE_MASCON_CRI_GRID_RL05_V1. We thank Reinhard Falk (BKG) and Michal Mikolaj (GFZ Potsdam), two anonymous reviewers and the editor Andrew Newman for fruitful discussions. The work of OdV was supported by the Institut Universitaire de France, and by the CNES as an exploitation of the GRACE space gravity mission.

Table S1. Standard deviation (in nm/s²/a) of a linear trend due to the hydrological effects as 517 inferred from GRACE, on repeated gravity measurements, performed 2, 3, 5 and 10 times.

518

When relevant, the simulation is done for durations of 2, 3, 5 and 10 years. The standard 519 deviation is obtained by averaging the standard deviations of GRACE observed at all the data