P Ailliot

E Frénod

V Monbet

Long term object drift forecast in the ocean with tide and wind

Keywords: Averaging method, Two scale modeling, Monte Carlo simulation, Wind time series, Ocean forecasting, Object drift

In this paper, we propose a new method to forecast the drift of objects in near coastal ocean on a period of several weeks. The proposed approach consists in estimating the probability of events linked to the drift using Monte Carlo simulations. It couples an averaging method which permits to decrease the computational cost and a statistical method in order to take into account the variability of meteorological loading factors.

Introduction

Drift of things in the ocean is potentially dangerous for human activities and marine ecosystems. For instance, drifting containers may cause serious accidents in the event of collision with ships and oil spills may have very negative impacts especially in coastal areas. In this paper, we investigate a new method to forecast the drift of an object in near coastal ocean on a period of several weeks.

The motion of a drifting object on the sea surface is the net result of a number of forces acting upon it (water currents due to tide wave, atmospheric wind, wave motion, wave induced currents, gravitational force and buoyancy force). It is possible to estimate the drift trajectory given information on the local wind, the surface current, and the shape and the buoyancy of the object. For instance, in order to estimate the position of lost containers, the safety-and-rescue services generally use short-term meteorological forecasts as forcing of an hydrodynamic model of drift (see Daniel et al. [5]). It is usual in such problems to consider several possible buoyancy and drift properties for the object since these features are not known precisely in most cases. An uncertainty on the initial conditions (position and time) may also be taken into account (see Hackett et al. [START_REF] Hackett | Forecasting the drift of things in the ocean[END_REF]).

Since we are interested in longer periods of time in the present study, we cannot directly use meteorological forecasts to estimate the object trajectory. Then the drift forecast has to be led out in terms of probability. This will be done using a Monte Carlo method, which makes it possible to estimate the probability of some scenarios linked to the object's trajectory, like the probability of being in a given point at a given time or the probability of running aground in given areas, for example. It consists in computing the object trajectories corresponding to a large number of meteorological time series representative of the climatology on the considered area. Because of the variability of the meteorological conditions, it is necessary to compute a large number of trajectories in order to get reliable estimates of the quantities of interest. Hence we are faced with two problems.

At first, as the existing data sets describe the meteorological conditions only on the few last decades, it is necessary to be able to simulate new realistic meteorological time-series. For this, we have used stochastic models. More precisely, it is assumed that these time series can be decomposed as the sum of two components, the first one that describes the meteorological conditions at a synoptic scale and the second one that represents fluctuations at the smaller scale. Then, the synoptic component is simulated with a non-parametric resampling algorithm proposed by Monbet, Ailliot and Prevosto [START_REF] Monbet | A survey of stochastic models for sea state parameters[END_REF], and the short-term component with an Autoregressive model.

Secondly, we have to compute the corresponding object trajectories, which oscillate with tide, in a reasonable computational time. Indeed, the trajectory of a drifting object submitted to tide wave currents and currents generated by other meteorological factors, is essentially composed by a trend and oscillations due to the tide, which have a small period with respect to the time period of interest (several weeks). Due to these high frequency oscillations, the numerical integration of the considered system is generally time consuming. So that it is convenient to split the estimation of the displacement of the object in two steps: first, we calculate the trend which is of low computational cost thanks to the lack of oscillations and then we reconstruct the oscillation around the trend. For this, we apply the Averaging Method developed by Frénod [START_REF] Frénod | Application of the averaging method to the gyrokinetic plasma[END_REF] in order to identify the averaged fields governing the trend and the oscillating operators allowing the reconstruction of the real object trajectory from the trend. As far as we know, this method has never been used before in the metocean field.

In order to check the validity of the proposed methodology, we consider a situation with deterministic currents and negligible wave effects and we study a simplified model where the acceleration of the floating object is equal to the sum of the acceleration of the water (due to the wave tide and a perturbation of smaller order which represents other water currents) and the difference between the wind speed and the object velocity. This model is described more precisely in the second section. Then, in the third section, we present the basic ideas of the Averaging Method and we compare computational cost of this method with the one which consists in integrating the real trajectory directly. In Section 4, we validate our method using numerical experiments. First, the models of the meteorological forcing fields (tide wave, perturbation and wind) are specified. Then, the accuracy of the Averaging Method is checked on the basis of numerical comparisons. Finally, in Section 5 the methodology is illustrated with an example in which the probability of running aground is estimated for an academic domain.

Model

The model on which we shall implement the method evoked above is a very simplified model for large time drift in ocean, above continental shelf in strong tide zone, of an almost completely submerged object submitted to wind. This model is extracted from exhaustive scaling analysis for large time floating object drift which we shall present in a forthcoming paper.

In short, the evolution of the position X(t) = X(t; x, v) ∈ R 2 and the velocity V(t) = V(t; x, v) ∈ R 2 of the considered object, having x and v as initial position and velocity, is given by:

dX dt = V, (2.1)
dV dt = d dt m(t, X)) + Λ(w(t, X) -V) = ∂m ∂t (t, X) + ∇m(t, X) V + Λ(w(t, X) -V), (2.2)
where m ≡ m(t, x) is the ocean velocity field and w ≡ w(t, x) the wind velocity field. ∇m stands for the Jacobian matrix of m. This equation says nothing but that the object is submitted to the sea water acceleration and to the wind force quantified by a constant Λ. The time scale t on which we want to observe the drift phenomenon is about 3 months and the object is submitted to tide oscillations whose period T is about 12.5 hours. Then a small parameter ε appears in our problem: the ratio T t tide period on observation time scale. The magnitude of ε is about 1/200. We consider that the velocity measurement of the object, wind and water are all done with the same unit: v. The observation length scale l, which has to be the characteristic length of continental shelf, is about several hundred kilometers. This length has to be compared with the characteristic distance T v the water covers during a tide period, which is of some kilometers. It seems then reasonable to consider that the ratio T v l is also about ε. Having those scale considerations at hand, we introduce the following rescaled variables t ′ , x ′ and v ′ expressing time, position and velocity in unit t, l and v

t = tt ′ , x = lx ′ and v = vv ′ , (2.3) the rescaled trajectory (X ′ (t ′ ; x ′ , v ′ ), V ′ (t ′ ; x ′ , v ′ )) defined by lX ′ (t ′ ; x ′ , v ′ ) = X(tt ′ ; lx ′ , vv ′ ), vV ′ (t ′ ; x ′ , v ′ ) = V(tt ′ ; lx ′ , vv ′ ), (2.4)
and the rescaled fields m ′ and w ′ defined by

vm ′ (t ′ , x ′ ) = m(tt ′ , lx ′ ), vw ′ (t ′ , x ′ ) = w(tt ′ , lx ′ ). (2.5)
We consider that the sea velocity writes

m ′ (t ′ , x ′ ) = M(t ′ , t T t ′ , x ′ ) + εN(t ′ , t T t ′ , x ′ ) = M(t ′ , t ′ ε , x ′ ) + εN(t ′ , t ′ ε , x ′ ), (2.6)
where M(t ′ , t ′ ε , x ′ ) ∈ R 2 is the rescaled sea water velocity exclusively due to the tide wave. It is supposed to be regular. Considering its dependency with respect to the oscillating time variable, we suppose that

θ ′ → M(t ′ , θ ′ , x ′ ) is a 1-periodic function satisfying M(t ′ , θ ′ , x ′ ) dθ ′ = 0 where M(t ′ , θ ′ , x ′ ) dθ ′ = 1 0 M(t ′ , θ ′ , x ′ ) dθ ′ . The field εN(t ′ , t ′ ε , x ′ ), where N(t ′ , θ ′ , x ′ ) is also 1-periodic in θ ′ ,
is the sea water velocity perturbation induced by meteorological factors. As concerns the wind velocity field, we consider that w ′ also involves two time scales, i.e.,

w ′ (t ′ , x ′ ) = W(t ′ , t ′ ε , x ′ ). (2.7)
Nonetheless, wind time series bring out as unrealistic considering a periodic dependency of W(t ′ , θ ′ , x ′ ) with respect to θ ′ . In practice, we only consider that, for any t ′ and x ′ , it admits an average value

W(t ′ , θ ′ , x ′ ) dθ ′ which actual definition is discussed later on.
Finally, we may deduce the equation satisfied by the rescaled trajectory and involving the rescaled fields. Removing the ′ , this equation, which is the model on which we shall implement our method, reads:

dX dt = V, (2.8
)

dV dt = 1 ε ∂M ∂θ (t, t ε , X) + ∂M ∂t (t, t ε , X) + ∂N ∂θ (t, t ε , X) + ∇M(t, t ε , X) V + W(t, t ε , X) -V +ε ∂N ∂t (t, t ε , X) + ∇N(t, t ε , X) V .
(2.9)

Notice that system (2.8)-(2.9) is rescaled, and that, in it, every variable and field characteristic scale is of order 1.

Clearly, the model under consideration is too simplistic to be used for operational applications. Nevertheless, it contains most of the physical ingredients of drift of object in the ocean: joint action of sea and wind, two time scales, possibility of using not so unrealistic sea velocity fields. Moreover, it seems to be relatively straightforward to incorporate a realistic sea velocity in it, with a tide period that weakly evolves with time and to apply it in a real geographical geometry. Hence, the validity of the methodology we present in this paper is not limited by the simplifications we consider.

Asymptotic analysis

Having the goal of using the Monte Carlo Method to estimate the probability of events linked to the trajectory of the drifting object in mind, we need to compute the object trajectory for a large number of wind conditions. The solution (X, V) contains 1 ε -frequency oscillations. Then, solving (2.8)-(2.9) directly by numerical methods forces the use of a very small time step. For instance, if the explicit Euler scheme is used, since the characteristic size of the left hand side of (2.9) and of its gradient are about 1 ε and the size of its time derivative is about 1 ε 2 , the classical error estimate yields, for a time step ∆t small enough, an error about

∆t ε 1 + ∆t ε 1 ∆t ∼ ∆t ε e 1 ε . (3.1)
Hence, if we want to obtain a precision about ε 2 a time step ∆t about ε 3 e -1 ε is needed. This is really too small for operational applications. Hence we shall write an expansion of (X, V) and find non oscillating equations satisfied by the terms of this expansion. This way, the previously evoked constraint imposed on the time step vanishes.

It is an easy game to see that system (2.8)-(2.9) enters the framework of an oscillatory-singularly perturbed dynamical system

d dt   X V   = a(t, t ε , X, V) + εa 1 (t, t ε , X, V) + 1 ε b(t, t ε , X, V), (3.2)
very close to the one studied by Frénod [START_REF] Frénod | Application of the averaging method to the gyrokinetic plasma[END_REF] which originates from gyrokinetic plasma questions (see also Poincaré [17], Krylov and Bogoliubov [START_REF] Krylov | Introduction to Nonlinear Mechanics[END_REF], Bogoliubov and Mitropolsky [START_REF] Bogoliubov | Asymptotical Methods in the Theory of Nonlinear Oscillations[END_REF], Sanders and Verhulst [START_REF] Sanders | Averaging methods in nonlinear dynamical systems[END_REF], Schochet [START_REF] Schochet | Fast singular limit of hyperbolic PDEs[END_REF], Frénod and Sonnendrücker [START_REF] Frénod | Homogenization of the Vlasov equation and of the Vlasov-Poisson system with a strong external magnetic field[END_REF][START_REF] Frénod | Long time behavior of the two dimensionnal Vlasov equation with a strong external magnetic field[END_REF][START_REF] Frénod | The Finite Larmor Radius Approximation[END_REF], Frénod and Watbled [START_REF] Frénod | The Vlasov equation with strong magnetic field and oscillating electric field as a model for isotop resonant separation[END_REF] and Frénod, Raviart and Sonnendrücker [START_REF] Frénod | Asymptotic expansion of the Vlasov equation in a large external magnetic field[END_REF] for presentations of methods allowing to remove time oscillations).

With very little changes we may apply the results it contains to deduce that

X(t) = X 0 (t, t ε ) + εX 1 (t, t ε ) + . . . , V(t) = V 0 (t, t ε ) + εV 1 (t, t ε ) + . . . , (3.3)
where oscillating functions X 0 , V 0 , X 1 and V 1 are linked to non oscillating functions Y 0 , U 0 , Y 1 and U 1 by

X 0 (t, θ) = Y 0 (t), (3.4) V 0 (t, θ) = M(t, θ, Y 0 (t)) + U 0 (t), (3.5)
and

X 1 (t, θ) = Y 1 (t) + θ 0 M(t, σ, Y 0 (t)) dσ, (3.6) V 1 (t, θ) = {∇M(t, θ, Y 0 (t))}{Y 1 (t) + θ 0 M(t, σ, Y 0 (t)) dσ} + U 1 (t) + N(t, θ, Y 0 (t)) -N(t, 0, Y 0 (t)) + θ 0 W(t, σ, Y 0 (t)) - W(t, ς, Y 0 (t)) dς dσ - θ 0 M(t, σ, Y 0 (t)) dσ. (3.7)
Then Y 0 , U 0 , Y 1 and U 1 are the solution to

dY 0 dt = U 0 , (3.8
)

dU 0 dt = W(t, θ, Y 0 ) dθ -U 0 , (3.9
)

dY 1 dt = {∇M(t, θ, Y 0 )}{ θ 0 M(t, σ, Y 0 ) dσ} dθ + U 1 + N(t, θ, Y 0 ) dθ -N(t, 0, Y 0 ) + θ 0 W(t, σ, Y 0 ) - W(t, ς, Y 0 ) dς dσ dθ - θ 0 M(t, σ, Y 0 ) dσdθ - θ 0 ∇M(t, σ, y 0 ) dσdθ {U 0 } - θ 0 ∂M ∂t (t, σ, y 0 ) dσdθ, (3.10
)

dU 1 dt = ∇W(t, θ, Y 0 )dθ {Y 1 } + ∇W(t, θ, Y 0 ) θ 0 M(t, σ, Y 0 ) dσ dθ - {∇M(t, θ, Y 0 )}{ θ 0 M(t, σ, Y 0 ) dσ}dθ + U 1 + N(t, θ, Y 0 ) dθ -N(t, 0, Y 0 ) + ( θ 0 W(t, σ, Y 0 ) dσ -θ W(t, σ, Y 0 ) dσ) dθ - θ 0 M(t, σ, Y 0 ) dσdθ + ∇N(t, 0, Y 0 ) - ∇ θ 0 W(•, σ, •) dσ -θ W(•, σ, •) dσ (t, Y 0 ) dθ + θ 0 M(t, σ, Y 0 ) dσdθ {U 0 } + ∂N ∂t (t, 0, Y 0 ) - ∂ θ 0 W(•, σ, •) dσ -θ W(•, σ, •) dσ ∂t (t, Y 0 ) dθ + θ 0 ∂M ∂t (t, σ, Y 0 ) dσdθ, (3.11)
equipped with initial conditions Y 0 (0) = x, U 0 (0) = v, Y 1 (0) = 0 and U 1 (0) = 0.

As said previously, this result may be inferred from [START_REF] Frénod | Application of the averaging method to the gyrokinetic plasma[END_REF]. It may also be deduced by expanding fields and functions in (2.8) and (2.9) in a correct way. This is done formally in the Appendix. Equations (3.4) and (3.5) mean that the order 0 trajectory does not oscillate and that the 0 order velocity is the tide velocity added with a non oscillating velocity U 0 which is generated by wind. Wind acts on U 0 only through its averaged value. This is translated in (3.9). By the way, notice that since the average value of M is 0, equations (3.8)-(3.9) only involve the average wind. As concerns order 1 terms, the situation is more complex. First since θ 0 M(t, σ, Y 0 (t)) dσ may be interpreted as the position of a sea water particle placed in Y 0 (t) at the beginning of a tide cycle (θ = 0), equation (3.6) means that the order 1 position is this water particle position plus a non oscillating function Y 1 (t). Regarding the terms (3.7) contains, the first one describes the way the space variation of the tide velocity acts, the second one is the non oscillating part of the velocity. The third and fourth terms quantify the action of the sea velocity perturbation. Concerning the next term, we need to remember that the action of the averaged value of the wind velocity is taken into account in order 0 equation (3.9). Then we notice that W(t, σ, Y 0 (t)) -W(t, ς, Y 0 (t)) quantifies the wind action around its averaged value at each time of a tide cycle. Hence

θ 0 W(t, σ, Y 0 (t)) -W(t, ς, Y 0 (t)
)) dς dσ is the cumulated action of the wind around its averaged value. This quantity acts at order 1. The last term of (3.7) can be interpreted as the previous one recalling that the mean value of the sea velocity is 0. It is hard to give intuitive explanations for the evolution equations (3.10)- (3.11). We only notice that they involve mean value of non-linear interactions between fields which quantify the mean joint action of sea and wind. This non intuitive quantification is made possible thanks to the asymptotic analysis presented in [START_REF] Frénod | Application of the averaging method to the gyrokinetic plasma[END_REF] and in the Appendix.

The characteristic size of the right hand sides in (3.8)-(3.11) are 1. Hence, to get the same precision about ε 2 , with the same Euler scheme using (3.3)-(3.11) to compute (X, V), in place of using (2.8)-(2.9) as evoked in the beginning of this section, the needed time step ∆t is about ε 2 . Comparing this with the value ε 3 e -1 ε found in the beginning of the section, despite the heavy form of (3.8)- (3.11), this is an appreciable gain even more so given that our probabilistic forecast method needs numbers of simulations for numbers of wind time series.

Concerning the validity of the expansion (3.3), if W(t, θ, x) was a regular function, periodic with respect to θ, asymptotic expansion (3.3) could be rigorously justified, applying [START_REF] Frénod | Application of the averaging method to the gyrokinetic plasma[END_REF], by the following inequality

sup t∈[0,1] X(t) -X 0 (t, t ε ) ≤ cε, sup t∈[0,1] X(t) -X 0 (t, t ε ) -εX 1 (t, t ε ) ≤ cε 2 , (3.12)
sup

t∈[0,1] V(t) -V 0 (t, t ε ) ≤ cε, sup t∈[0,1] V(t) -V 0 (t, t ε ) -εV 1 (t, t ε ) ≤ cε 2 , (3.13)
which would be true for ε small enough and for a constant c independent of ε, where • stands for the Euclidean norm in R 2 .

As we cannot consider the wind time series to have this form, we will estimate the error using numerical experiments. This is done in the next section: several realistic wind time series are simulated using a method described in Monbet et al. [START_REF] Monbet | A survey of stochastic models for sea state parameters[END_REF] and the corresponding error is calculated for each of them. For this, we have to decide how the average values are to be computed. If the way is clear for fields linked to M or N, for which we simply take dθ = 1 0 dθ, the situation is more obscure for wind linked fields. For them, we will take as averaged value at time t the mean value on the interval centered in t and with length p, i.e.

W(t, θ, x) dθ = 1 p t+p/2 t-p/2 W(s, s ε , x) ds, (3.14)
for a parameter p that has to be adjusted experimentally. As concerns the integrals in θ of the wind linked fields, they have to be replaced by integrals respecting V 1 (t, t ε ) = U 1 (t) when t ε is an integer, which is a constraint imposed by the Averaging Method. Hence, we replace

θ 0 W(t, σ, x) dσ |θ= t ε by t ε[ t ε ] W(s, s ε , x) ds, (3.15)
where [ t ε ] stands for the integer part of t ε . Those choices have also to be experimentally validated.

Numerical validation

We begin this section by introducing the sea velocity fields and briefly presenting the stochastic method used to generate the wind time series. Then, the expansion (3.3) is validated by numerical experiments. More precisely, several wind time series are generated. Then, for each of them, we compute the real trajectory using (2.8)-(2.9) and compare it to the trajectory obtained with expansion (3.3) and the following equations.

Metocean fields

Let us first describe the metocean fields that have been used in our numerical experiments. Regarding the rescaled ocean velocity induced by the tide wave and its perturbation, we have chosen the following simple parametric fields:

M(t, θ, x) = (2 + sin(6πt)) x 1   sin(2πθ) + 1 4 sin(4πθ) 1 2 sin(2πθ)   , (4.1)
N(t, θ, x) = (2 + cos(6πt)) x 2   sin(2πθ) sin(2πθ)   , (4.2)
where x 1 and x 2 are the first and second components of x.

The trajectories associated with the field

  sin(2πθ) + 1 4 sin(4πθ) 1 2 sin(2πθ)
  are non circular loops which remind those we can observe in Nihoul [START_REF] Nihoul | Modelling of marine system[END_REF] or Salomon and Breton [START_REF] Salomon | An atlas of long-term currents in the Chanel[END_REF]. The velocity field M is this simple vector field modulated by a time and position dependency in order to see the influence of time derivative and gradient on the object trajectory. N is also a simple field which gradient is orthogonal to the one of M.

In order to simulate realistic wind time series, we have assumed that they can be decomposed as the sum of two components, e.g W(t, t ε , x) = W Lt (t, x) + W st ( t ε , x) where • W Lt (t, x) represents the wind evolution at a synoptic-scale, e.g at the scale of the high-and low-pressure systems. The typical dimension of these systems ranges approximately from 1000km and 2500km and their duration is a couple of days to at most a couple of weeks.

• W st ( t ε , x) represents the small scale evolution of the wind (e.g mesoscale and microscale winds). This scale includes phenomena such as thunderstorms, squall lines, land and sea breezes... Such a decomposition is discussed more precisely by Breckling (see Breckling [START_REF] Breckling | The Analysis of Directional Time Series: Applications to Wind Speed and Direction[END_REF] and [START_REF] Ailliot | Modèles autorégréssifs a changements de régimes makovien[END_REF]). Different methods have been proposed in the literature to simulate realistic wind time-series at the synoptic scale (see Monbet, Ailliot and Prevosto [START_REF] Monbet | A survey of stochastic models for sea state parameters[END_REF] and references therein). In this study, we have first assumed that the wind W Lt (t, x) is homogeneous in space; i.e. W Lt (t, x) = W Lt (t) for all x and t, what seems realistic according the size of the domain which is supposed to be about some hundred kilometers. Then, we have used a non-parametric resampling method to simulate the process W Lt (t), namely the Local Grid Bootstrap algorithm proposed by Monbet, Ailliot and Prevosto [START_REF] Monbet | A survey of stochastic models for sea state parameters[END_REF]. This method has already been validated on various datasets, and it was found that it can successfully be used to simulate realistic wind time series. In the present study, it has been calibrated on a dataset which describes the wind condition during the summer at a point of coordinates (46.25 N, 1.67 W ), located near the French Atlantic coast. It describes the synoptic wind conditions during the last 20 years recorded every ∆t 1 = 6 hours.

Then, in order to simulate the small scale variations, we have used an Autoregressive model. More precisely, for simplicity reasons, we have first assumed that this field is homogeneous in space. This assumption is unrealistic and could be refined later on. Then, we have assumed that, for

k ∈ N * , W st (k∆t 2 ) = aW st ((k -1)∆t 2 ) + E(k∆t 2 ) (4.3)
where {E(k∆t 2 )} k∈N * denotes a zero-mean Gaussian white noise with covariance matrix σ 2 I 2 . In practice, we have simulated this small-scale component with a time-step ∆t 2 = ε/100. This consists in giving the wind value every 4 min approximately, and the parameters a and σ have been chosen such that the process W st has a memory of a few hours and such that the standard deviation of its marginal distribution represents approximately 10% of the one of the process W. Finally, the procedure described above makes it possible to simulate the processes W Lt (t) and W st ( t ε ) for t ∈ k∆t 1 and t ε ∈ k∆t 2 , respectively. The values of these processes for other values of t have been calculated by linear extrapolation. An example of simulated wind time-series is given in Figure 2.

Numerical results

In order to validate the asymptotic expansion given in the previous section, we have computed the solutions of (2.8)-(2.9) and of (3.3)- (3.11) for N = 100 artificial wind time series. Let us denote Xi , Vi , X0 i , V0 i , X1 i , V1 i , for i ∈ {1, ..., N }, the corresponding numerical approximations of X, V, X 0 , V 0 , X 1 and V 1 , respectively. We have tested different algorithms to solve these ODEs, and the best results have been obtained with an explicit Runge-Kutta (4,5) formula. In practice, we have used the Maltlab's function ode45 which is based on an explicit Runge-Kutta (4,5) formula, the Dormand-Prince pair [START_REF] Dormand | A family of embedded runge-kutta formulae[END_REF]. In the numerical results given hereafter, we have used ε = 1/50. This choice makes it possible to compute the solutions of the system (2.8)-(2.9) with a good precision in a reasonable computational time, and permits also easier graphics representations. We have used x i = (1, 1) and v i = (0, 0) as initial values.

In Table 1, the norms of error in object position and velocity for order 0 and 1 expansions are given. Let us discuss more precisely the results obtained with ǫ = 1/50. It shows that the asymptotic expansions obtained with p = ε/10 (corresponding to an interval of 40 min), p = ε/2 (corresponding to an interval of 6h15min) and p = ε (corresponding to an interval of 12h30min) are about 5ε 2 worth, and close to each other. For comparison, we also compute the solution to system (3.3)-(3.11) when the wind is null, and we also found an error equal to 0.0022 ≈ 5ε 2 . For p = 4ε (corresponding to an interval of 2 days), the error is significantly higher. As concerns the computational coast, it decreases as p increases, so that a good compromise seems to use ε/2 ≤ p ≤ ε; i.e. the wind at a synoptic scale. Such a value of p permits to compute the solutions of the system (3.3)-(3.11) with a good precision in a computational time significantly lower than the one corresponding to the system (2.8)-(2.9). For instance, if an Euler scheme is used, the exact system (2.8)-(2.9) requires ε = 1 50 Speed (order 0) Speed (order 1) Position (order 0) Position (order 1)

p = ε 10 0.
t∈[0,1] Vi (t) -V0 i (t) (second column), sup t∈[0,1] Vi (t) -V0 i (t) -ε V1 i (t) (third column), sup t∈[0,1] Xi (t) -X0 i (t) (forth column) and sup t∈[0,1] Xi (t) -X0 i (t) -ε X1 i (t) (fifth column
) for different values of p. The last line for ε = 1 50 gives the error for a zero wind field.

about 1000 more iterations than the approximate system (3.3)-(3.11) to achieve the same accuracy. And, for the problem considered in this paper, an iteration of the exact system is 20 less expensive in terms of computational time. But this last remark is not general since the computational time highly depends on the nature of the tide and current fields M and N : here they are modeled by a quite simple analytical formula.

In Figure 1, we have plotted the object trajectory associated with the wind time series shown on the top of Figure 2, using p = ε/2. More precisely, the solid line represent X computed by directly solving (2.8)-(2.9). The dashed line represents the average trajectory Ŷ0 + ε Ŷ1 obtained solving (3.8) and (3.10). We can see that this averaged trajectory follows nicely the trend of X. Then reconstructing X0 and X1 using (3.4) and (3.6), we have represented the trajectory X0 + ε X1 in dotted line. The superimposition with X seems to be almost perfect. In order to go further in the result analysis, we turn to Figure 2. On the top of this figure, we have shown the wind as a function of time. The second figure represents, in dashed line, the average trajectory of the position of the first component and, in solid line, the first component of the trajectory itself. We can see on this trajectory not only the long term trend but also the two time periodic phenomena in game: tide oscillations (rapid oscillations) and tide coefficient amplitude (modulated amplitude). Finally, the last plot exhibit ε 2 -order error (here ε = 1/50 = 2. 10 -2 , then 10 -3 = 2.5 ε 2 ). Moreover, we can see that this error function is a periodic function with modulated amplitude. This spurs us thinking that we could improve the accuracy of the reconstructed trajectory, if it is needed, considering the next terms in the expansion of X and V. Figure 3 shows the first component of the average wind, the average velocity (dashed line) and the velocity itself (solid line). The third plot shows the error on the velocity. This figure permits to visualize the action of the wind on the averaged velocity, which first increases and then decreases.

In order to make our numerical validation more convincing, we also made simulations for varying ε. In Table 2, the norms of the error on object position and velocity for order 0 and 1 expansions are given for ε = 1/100 and ε = 1/25 . The errors are proportional to ε for order 0 and to ε 2 for order 1 as it was expected from the theory.

t∈[0,1] Vi (t) -V0 i (t) (second column), sup t∈[0,1] Vi (t) -V0 i (t) -ε V1 i (t) (third column), sup t∈[0,1] Xi (t) -X0 i (t) (forth column) and sup t∈[0,1] Xi (t) -X0 i (t) -ε X1 i (t) (fifth column) for different values of p.
5 Application: long term forecast of an object's drift with Monte Carlo Method

In the previous section, we have shown that the expansion of the trajectories of an object in near coastal ocean submitted to wind makes it possible for us to compute quickly good approximation of this trajectory. It is then possible to make this computation for a large number of synthetic wind time series, and thus deduce the probability of a given scenario (this may be the probability of presence in a given area, of collision or of running aground, for example).

As an example, in this section we compute a running aground probability. More precisely, we have fixed an arbitrary coast line, e.g. the circle of center (1, 1) and radius 0.3 and we have focused on the running aground of the object on this coast. We have generated one thousand wind time series with the same stochastic model as in the previous section and have also used the same sea velocity fields. We have computed the thousand associated trajectory. For this, we have used the method described in the previous sections, based on asymptotic expansion (3.3). The methodology is illustrated in Figure 4 where one hundred of the thousand trajectories are drawn. Proceeding this way, we have obtained enough trajectories to get reliable estimates of the quantities of interest. First we can deduce an estimation of the probability of running aground by calculating the percentage of trajectories that reach the circle in the time interval [0, 1]. We found 64.3%. Then we can estimate the probability that the object runs aground in a given area. The obtained results are shown in Figure 5. On the left, we have plotted a wind rose which shows the joint repartition of direction and intensity. The length of each bar is proportional to the proportion of wind having a direction around the direction the bar indicates. The bars are then shared into four subbars which lengths are proportional to the proportion of wind having the corresponding magnitude. We can see that the wind is generally blowing from the north. The second histogram must be read in the following way. The length of each bar is proportional to the proportion of trajectories that run aground around the point of the coast which is in the bar direction. We then see that the proportion of running aground trajectories has a maximum around the South-South-West of the coast line.

Conclusion

In this paper, we have explored a method to make probabilistic forecasts of long term drift, in near coastal ocean, of object submitted to tide and wind. The method is based on generating a large number of realistic wind time series and, for each of them, to compute the associated object trajectory. The probabilities of trajectory linked events may then be estimated using this large number of trajectory realizations. In order to achieve this goal, we have used a method proposed by Monbet, Ailliot and Prevosto [START_REF] Monbet | A survey of stochastic models for sea state parameters[END_REF] to generate realistic wind time series and the Averaging Method based on an asymptotic expansion of trajectory of Frénod [START_REF] Frénod | Application of the averaging method to the gyrokinetic plasma[END_REF] to remove tide oscillations and compute quickly the object's trajectory. This method has allowed us to compute the probability for an object to run aground on an academic domain.

The quality of the results are good enough for us to contemplate going further in exploring this new methodology. Among the things to do in order to achieve the objective of computing operationally events probabilities in real coastal areas we wish to broach the following.

First, we will present a complete scale analysis of a coupled system Shallow Water Equations -Newton Principle modeling the joint running of ocean and drifting object. The aim is to identify several regimes under interest such as "storm regime in coastal zone" or "stillness above continental shelf" and so on, and the corresponding equations. This would give a way to compute the sea velocity fields M and N, M being exclusively due to tide wave and N to meteorological factors. Notice also that N could be divided into two parts: one linked to pressure variations and another linked to wind. Those aspects would then have to be incorporated in a software in order to access the fields M and N. Then we shall study the abilities of the method presented in the present paper to fit to pseudo-periodic fields M and N. We are optimistic because the method already works well with pseudo-periodic wind fields. The realism of the synthetic wind time series used as input of the numerical model could also be improved. In particular, the space-time model proposed by Ailliot, Monbet and Prevosto [START_REF] Ailliot | An autoregressive model with time-varying coefficients for wind fields[END_REF] could be used to simulate non-homogeneous wind fields. Finally, the method could be implemented on real coastal areas.

Figure 1 : 3 Figure 2 :

 132 Figure 1: Example of object's trajectory (two-dimensional phase plane plot). Solid line: X, Dotted line: X0 + ε X1 , Dashed line: Ŷ0 + ε Ŷ1 . ε = 1/50, p = ε/2.

Figure 3 :

 3 Figure 3: Example of object's speed (time series plot)(Top: smoothed zonal wind component (p = ǫ/2), Second: first component of zonal object's speed (Solid line: V, Dashed line: Û0 + ε Û1 ), Third: zonal error V -V0 -ε V1 ). ε = 1/50, p = ε/2

Figure 4 :

 4 Figure 4: Object's trajectory corresponding to 100 synthetic wind time series and corresponding running aground points(*)

Figure 5 :

 5 Figure 5: Repartition of the wind (left) and of the running aground points (right)

Table 1 :

 1 1115 [0.1115,0.1116] 0.0460 [0.0454,0.0467] 0.0174 [0.0173,0.0174] 0.0023 [0.0021,0.0029] Mean value, minimum and maximum values (mean [min, max]) of the errors sup

	p = ε 2	0.1118 [0.1113,0.1134] 0.0460 [0.0448,0.0473] 0.0174 [0.0173,0.0174] 0.0024 [0.0021,0.0032]
	p = ε	0.1125 [0.1108,0.1168] 0.0460 [0.0441,0.0488] 0.0173 [0.0171,0.0174] 0.0026 [0.0020,0.0047]
	p = 4ε 0.1192 [0.1102,0.1280] 0.0542 [0.0438,0.0691] 0.0174 [0.0166,0.0196] 0.0065 [0.0024,0.0144]
	W ≡ 0	0.1115	0.0096	0.0174	0.0022

Table 2 :

 2 Mean value, minimum and maximum values (mean [min, max]) of the errors sup

		0557 [0.0557,0.0557] 0.0292 [0.0270,0.0358] 0.0086 [0.0085,0.0086] 0.0011 [ 0.0011,0.0014]
	p = ε 2	0.0558 [0.0554,0.0563] 0.0294 [0.0270,0.0362] 0.0086 [0.0085,0.0086] 0.0012 [0.0010,0.0015]
	p = ε	0.0560 [0.0552,0.0574] 0.0296 [0.0273,0.0363] 0.0085 [0.0084,0.0086] 0.0013 [0.0010,0.0020]
	p = 4ε	0.0595 [0.0552,0.680]	0.0355 [0.0304,0.0516] 0.0086 [0.0082,0.0098] 0.0026 [0.0010,0.0072]
	ε = 1 25	Speed (order 0)	Speed (order 1)	Position (order 0)	Position (order 1)
	p = ε 10	0.2254 [0.2249, 0.2257] 0.1143 [0.1022 ,0.1418] 0.0358 [0.0358,0.0359] 0.0046 [0.0040,0.0057]
	p = ε 2	0.2254 [0.2226,0.2277] 0.1142 [0.1017,0.1410] 0.0358 [0.0357,0.0359] 0.0045 [0.0039,0.0058]
	p = ε	0.2257 [0.2201,0.2310] 0.1142 [0.1011,0.1379] 0.0358 [0.0356,0.0360] 0.0044 [0.0037,0.0069]

Acknowledgements

We would like to thank the referees for their pertinent comments and suggestions. We would also like to thank Junko Murakami who has kindly accepted the task of proofreading the manuscript and improving our poor english.

A Appendix : Computations leading (3.4) - (3.11) In this Appendix we formally lead the asymptotic expansion that gives equations (3.4) - (3.11).

First, if we define Y(t) and U(t) so that X(t) = Y(t), (A.1)

and inserting those in (2.8) and (2.9), we deduce

Then, we assume that Y and U may be expanded in the following way:

) being 1-periodic with respect to θ to be defined latter. Using those asymptotic expansions in (A.1) and (A.2) yields (3.4) and (3.5). Using again (A.5) and (A.6) in (A.3) and (A.4), expanding every functions using a Taylor expansion yields

where + • • • contains every terms being of order greater than 1 in ε.

Identifying the terms of order 0 in ε gives

Integrating those equations with respect to θ from 0 to 1, we obtain (3.8) and (3.9). Once this is done, equations (A.9) and (A.10) yield

and then (3.6) and (3.7).

Looking now at the terms of order 1 in ε in (A.7) and (A.8), after replacing A 1 , B 1 , dY 0 /dt and dU 0 /dt by their expressions, results in two equations. Those equations, when integrated in θ, lead in a heavy but straightforward way (3.10) and (3.11).


Jos Baeten

Pascal Estraillier

Claude Kirchner

Alexandre Moatti

Laurent Romary

Open Access in Japan -a multi-institutional perspective

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Open Access in Japan -a multiinstitutional perspective

Scientific information and open access -an introduction and an overview of the context in France and Europe

The wide dissemination of research results is an essential component of a prosperous development of science and technology. The legacy of the scientific publishing landscape, created in the print era, as well as the prospect that the wide deployment of information technologies may lead to a simplified dissemination of research assets, have made necessary for researchers, libraries and all institutions involved in higher education and research to contribute to an in-depth evolution of the scientific communication processes.

Without drawing a complete history of the open access movement here, we can identify some major milestones, which have lead to the current situation:  Dramatic increase in journal subscription costs in the 90"s (so called "serial crisis");  Setting of the first publication repositories with arXiv in 1994, following several year of pioneering dissemination of digital papers on ftp sites, mailing lists etc.;  Emergence of the Open Access movement stating that scientific content, seen as a public good, should be freely accessible and re-used. We can mention here the Berlin declaration issued in 2004 and signed by many scientific organisations worldwide2 :  Further deployment of institutional, thematic or national repositories worldwide (see Romary &Armbruster, 2006) contributing to the expansion socalled green Open Access3 :  Rise of new publishing models based on the payment by authors of an Article Processing Charge (APC) in order to make the paper available online at the time of publication (part of what is named gold Open Access4 ).

Behind the notion of public good, we can also mention the importance of scientific, institutional or national sovereignty, whereby publicly funded research should lead to productions that remain within the remits of their producers. This has direct consequences at various levels: preservation of authors" copyright, setting up reliable infrastructures, defining publication cots in accordance to clear services provided by third parties (as opposed to the current non-competitive publication market), with the objective of increasing the capacity of public actor carry out their assessment or strategic planning duties in full independence 5 .

In Europe, despite isolated attempts to favour the publishing business 6 , green open access has taken up strongly and in particular France has developed a national Some institutions such as Inria or CWI have managed to go even further by mandating researchers to deposit publications within their repositories. Such mandates are usually linked to annual assessment, whereby the papers in the repositories are taken as the sole source for reporting by researchers or research teams.

Initiatives are also taking place to develop new publishing models that decouple the notion of publication, understood as the dissemination of the content publicly online, from the peer-reviewing process. We can mention here the Episciences initiative (See Berthaud et al. 2014) in France that offers an environment for implementing so-called overlay journals on top of existing publication repositories.

Open access is also one element in global reshaping of the dissemination of research results from a wider perceptive. The issue has for instance been high up on the political agenda of the G8, with its Open Data charter 8 , and the underlying copyright issues (re-usability, for instance for text and data mining) is an essential component of the European Union copyright reform 9 .

Main objectives

The main objectives for the European delegation during this series of meeting were the following ones:

 Understand the situation of open access in Japan, in particular to identify factors for change in this domain;  Compare the main issues in Japan with the political and technical settings in France and at CWI;  Identify some possible collaboration themes that would allow our countries to develop better and stronger open access policies in the future.

Contextual information

The Japanese academic landscape is based upon a large group of 774 universities (86 national universities, 83 public universities and a majority of 605 private universities). At a political level, three main institutions are in charge of the higher education and research policies: MEXT: Ministry of Education, Culture, Sports, Science and Technology) and two funding agencies: JST: Japan Science and Technology Agency and JSPS: Japan Society for the Promotion of Science.

The stay was organised in two complementary types of meetings:

 series of discussions with institutional actors, among which Prof.Harayama, the above-mentioned institutions and the NII management;  workshops dedicated to specific communities of interest and stakeholders.

CSTI (Council for Science, Technology and Innovation)

Yuko Harayama is an Executive Member of the CSTI at the Cabinet Office. The CSTI has been seminal in producing an important report in March 2015 aiming at defining a national policy in the domain of open access to scientific result. In this context our delegation had the opportunity to exchange some core ideas with Prof.Harayama. The main topics addressed during this meeting were the following one:

 Importance of scientific sovereignty and to define ways of mastering the dissemination of scholarly result;  The possibility to go towards a more pro-active policy in the domain of scientific article deposit in publication repositories, taking the examples of the ambitious deposit mandate policies of Inria and CWI;  The necessity to experiment new scientific publishing models based on public platforms;  International collaboration between Japan and Europe in the above-mentioned themes.

MEXT (Ministry of Education, Culture, Sports, Science and Technology)

"MEXT has started to work with JST to introduce mandatory rule for scientists to publish their papers and data sets open accessible attached to public funds. "

In particular, MEXT originated an open access mandate for all PhD theses in Japan in March 2013 through the institutional repository of the PhD awarding institution.

From an infrastructural point of view, MEXT finances the technical support provided by NII concerning scientific publication platform and in particular the work carried out on journal management environments and publication repositories.

JSPS (Japan Society for the Promotion of Science)

There are 3 funding agencies in total in Japan, two under the auspices of the Ministry of Higher Education and Research (MEXT): JSPS and JST, one under the auspices of the Ministry of Industry (MITI): NEDO. Among the three the JSPS, established in 1932, represents the biggest one with a budget of around 2 billion Euros per year.

The meeting took place in presence of MakotoAsashima, executive director of JSPS, and was the opportunity to have an in-depth discussion on open access issues in relation to the forthcoming report by CISTI due in March 2015.

In the domain of scientific information and open access, the JSPS has had several programs to encourage the move of scholarly society journals from print to electronic, as well as specific support for gold open access publication. It should be noted that current plans do not integrate any specific support for green open access.

A specific discussion took place concerning the opportunity to better coordinate open access issues within the GRC (Global Research Council). G8, ANR

JST (Japan Science and Technology Agency)

JST provided us a series of questions that served as a basis of discussions and allowed us to better understand their current topics of interest. We provide specific details about the corresponding interaction.

A specific debate took place during the meeting on the compatibility between the development of open access journal and the role of depositing papers in publication repositories. A consensus actually emerged to understand that the necessity of mandating deposit in public repositories remains when papers are being published within open access journals, in order to ensure that a reference corpus of scientific publications be maintained by governmental institutions. The debate also addressed to related aspects:

 The role of publication repositories for the early (pre-peer review) dissemination of scholarly manuscripts, with the possibility of both getting quick and efficient community feedback on scientific results, but also to take precedence since such manuscripts can serve, for instance, as prior art during patent examination. In the case of papers that are not further published (or refused) in traditional journals, it appears that keeping these records are essential to maintain a rich scholarly background for future research;  The danger of (probably ephemeral) private platforms such as Academia or Research Gate offering hosting services for scholarly papers and which bring in the risk of even more fragmentation of our scientific assets. For countries like Japan (with Jairo cloud) or France (with HAL) where there exist a national publication repository strategy, a stronger information campaign should deter scientists from using such platforms to record their productions.

JST expressed their interest in stronger collaboration schemes between Japan and Europe on publication platforms and supported the idea that specific links with the developments carried out within NII should be established.

NII (National Institute of Informatics)

Beyond its core mission as a research institution in the domain of computer science (with 80 permanent researchers), NII plays a central role in the Japanese scientific information landscape since it is in charge of implementing and operating the main national information infrastructures for universities in Japan. If we were to compare to the French situation, it groups together missions that are spread across ABES (central catalogue), CCSD (national repository HAL), Persée (digitisation of scholarly journals in human sciences) and INIST (provision of subscribed content).

An early program initiated between 2004 and 2007 provided initial support for the implementation of institutional repositories within up to 70 universities:

 NII-ELS is a platform dedicated to the online delivery of digitized legacy journals from scholarly societies in Japan (thus close to the scope of Persée). It hosts the content of 109 journals but does not really offer the service of a publication platform. It seems the content is about to move to J-stage;  JAIRO Cloud is a centralized digital research object repository, allowing not only universities to implement publication portals within it, but also offering research data archiving and publication facilities.

Besides, NII provides targeted services concerning publishers" copyright policies (SCPL -Society Copyright Policies in Japan, similar to SHERPA/ROMEO) or assessment of repository downloads (ROAT -Repository Output Assessment Tool).

We consider NII as a model for future scientific information infrastructure where technical support is strongly coupled with research activities (for instance in the domain of text and data mining or visualisation).

Library and information science workshop

The workshop provided a comprehensive overview of the situation in various (public and private) universities in Japan as well as an overview of the current organisational and technical issues at a national level.

There are as a whole 1486 University libraries (289 national, 129 public and 1068 private) in the academic sector. From an organisational point of view, several consortia are relevant for the management of scientific information in Japanese universities:

 JCCUL, Japanese Coordinating Committee for University Libraries. It has signed in 2010 an agreement with NII in scientific information for the higher academic sector;  JUSTICE (Japan Alliance of University Library Consortia for E-Resources) is the equivalent organisation to Couperin 10 in France in that it is in charge of the negotiations with publishers, with the difference that its activities do not comprise the setting up of centralised subscription consortia ("groupement de commande" for Couperin). JUSTICE currently has a membership of 516 libraries in close collaboration with the NII;  DRF (Digital Repository Federation) groups together institutional repository initiatives (150 members). DRF is a member organisation to COAR (Confederation of Open Access Repositories). This structure seems to evolve into the Institutional Repository Promotion Committee, set in 2013 between NII and university libraries;  Finally, SCREAL Standing committee for research in academic libraries.

The Japanese libraries have altogether the quite large budget of 21 831 million Yens dedicated to subscriptions with a total number of 4970 journal titles. The recent drop of the Yen exchange rate, coupled with an increased VAT applied to subscriptions and a global reduction in University library budget dramatically impacts on the capacity to keep to this budget. The current consequence is a tendency to abandon the big deal model in favour of the identification of relevant title portfolio within each university.

The institutional repository (IR) landscape was until now extremely fragmented with a large network of 370 university repositories that has steadily (hita-hita, cf. Tsuchide et alii, 2013) increased over the years. They are mainly operated by the university libraries and comprise an impressive number of items (1 400 000) as of 2014. NII has played strong role in this development by first supporting several university repository projects and recently by offering a centralised repository service (JAIROcloud) where Universities can develop their own portal, in a setting which is quite equivalent with what we have in France with HAL11 . Most of the institutional repositories have a "everything welcome policy" (for instance in Chiba), whereby the aim of the platform is to host all types of scholarly productions, comprising reports, grey literature at large, theses, wide public articles, posters etc. in complement to research article in the narrow sense of the term.

University bulletins (or Kiyo), mainly in the social and human sciences domain, represent a majority of the content of these institutional repositories12 . This reflects the fact that IRs are not seen as a tool for providing open access to otherwise published material but more of a document repository for locally generated documents (texts or data). The deposit mandate on PhD thesis can be also seen from this perspective.

Universities begin to have difficulties in keeping their maintenance budget for their local institutional repositories, which may lead to a step-by-step switch to JAIRO. Beyond the budget aspects we see numerous advantages to this, based on our experience with HAL: coherent meta-data description, connection to national authority files, quicker take up of new technologies (e.g. visualisation and data mining) and better connection with international initiatives (cf. [START_REF] Romary | Beyondinstitutionalrepositories[END_REF]; https://hal.inria.fr/hal-00399881).

As a general conclusion, we have observed a strong independence of each university, with in general a low political support to institutional repositories at University management level. Institutional repository contents are also very heterogeneous, and it is hardly foreseeable that Universities will issue OA mandates in the future, not even strong requirements. Of course the national request made for PhD theses ensures at least that most of them are available in the repositories.

Researchers' workshop

Several projects and institutions were presented, and a broad exchange of views took place about these projects, that were either in the field of exact sciences as well as human sciences (in particular: digital humanities). Among the latter, we can cite the projects of the Japanese Association of Indian and Buddhist Studies13 , the Japanese Association for Digital Humanities (www.jadh.org), the Japanese Association for Religious Studies (www.jpars.org), or the Research Institute for Sustainable Humanosphere, Kyoto University (http://www.rish.kyoto-u.ac.jp/), or the Digital Silk Road Project, one of the pioneers (http://dsr.nii.ac.jp , since 2001).

The National Diet Library, responsible in Japan for legal deposit of books and reviews, presented also its projects; in France, it is not the Diet Library but the BibliothèqueNationale de France which is in charge of legal deposit 14 . The questions of legal deposit of the Web sites (that is implemented in France by a law of 2007), as well as the legal deposit under electronic format (which is a different question, not available in France) have been discussed.

The question of research data (scientific "big data") has also been raised; the Japanese delegation gave the interesting example of the preservation of records for unique scientific phenomenon, like eclipses or big earthquakes. This is part of Japanese implication in the international Research Data Alliance (www.rdalliance.org).Japan Science and Technology Agency (JST) curates data centres in several scientific realms, dedicated to this mission of research data preservation.

Several points arose during the discussion between the French delegation and the Japanese institutes, among which:  The possibility of having digital humanities projects better known by a larger public, for example through Wikipedia (systematically indexing these projects on the related Wikipedia pages; in the other way, also releasing iconography from research institutes for Wikipedia pages).  The possibility of associating a larger public to some digital projects: for example transcription of historical manuscripts by internet users; or "participative science" (in botanic, in astronomy, etc.) where scientific data coming from non-researchers is aggregated to complement and enrich research data as well as programs.

Contextual analysis

For many years, the favourable exchange rate between the Yen and the Dollar, in which most subscription contracts were set up, has attenuated the effects of the serial crisis in Japan and created a feeling of wealth with regards the private scholarly publishing sector. This has resulted in the negotiation of numerous big deals between Japan academia and publishers and also a particularly strong dedication to the newly introduced Gold open access model, as compared to what has been experienced in Europe. The recent devaluation of the Yen, coupled with an increase of the VAT rate on foreign products has completely changed the perspective on publishing cost and the actual role of private publishing in the dissemination of scientific information.

The Tōhoku earthquake and tsunami in 2011 has also had an important impact on the role of the government and governmental agencies with regards scientific research.

Whereas most of the national institutes for instance were quite autonomous in defining their research priorities, the dramatic consequences of the tsunami has awaken the Japanese authorities to the necessity to define strong research priorities in such domains as energy, environment or information technology. This in turn has created a favourable background for a stronger national policy in the scientific information domain.

From an academic point of view, the development of scientific information policies in Japan have been subordinated to three main important factors:

 The fragmentation of the university landscape with 774 universities as a whole and the importance of the private sector (605 private universities as opposed to 86 national and 83 public universities);  The central role of scientific societies, which have maintained a specific portfolio of scientific journals. This has induced specific initiatives towards the corresponding publishing sector, for instance in terms of publication platforms;  A strong autonomy of Japanese universities, and within them of Professors, which lies at the root of the current fragmentation of the publication repository landscape so far, but also slowed down various initiatives towards more concerted actions in the open access domain.

In the recent years, Japan has seen a dramatic growth in the number of open access repositories within its universities and research organisations. With 388 repositories, which reflect the fragmented academic landscape in Japan, there are currently great discrepancies in actual coverage, technical developments and prospect for sustainability across these platforms 15 . Another important issue is the reduced coverage of these repositories in terms of real scientific publications (around 15% of journal 16 articles). Kiyos (departmental bulletins) represent more than a half of the content, with also an increasing importance of PhD theses (4,4%) thanks to the national deposit mandate. The PhD mandate, which explicitly refers to the IR of the awarding institution has also contributed to the fragmentation of the landscape: no specific national service has been set in place, as is the case in France with STAR and TEL17 , and the European portal DART18 .

The relation to commercial publishers is very specific in Japan with a very high budget that seems to reflect that commercial publishers have tend to see Japan as a "Poule aux oeufsd"or"19 : 260 M€ (to compare to the subscription budget in France: 80 M€), which has also been amplified by a strong Gold open access policy. One factor here is the central role for national journals with two additional issues:

 The specific language issue, whereby gold open access and often associated with the need of advanced copy-editing in English;  The absence of a real policy for new quality assessment factors, with the journal citation index remaining a major reference in Japan;

Conclusions -Perspectives

Over the week"s discussions that took place between Japanese and European colleagues, it has become clear that there is a need to a closer collaboration between us all in order to go towards a more ambitious scientific information policy that would favour the open access dissemination of both publications and data. In particular, very similar views have been shared concerning the need to take over again the sovereignty over scientific information, and consequently identify public policies and infrastructures that would ensure that the scientific common good is not exclusively given away to the private sector. The objective is both to be able to provide a better dissemination of scientific results, but also to offer the possibility to implement new services (indicators, data mining) based upon a comprehensive pool of scientific content.

Several concrete domains have been identified, which could be the basis of future collaborations:

 Sharing our principles and the way we communicate towards scientific communities. In particular, we need to have a better coordination of our information concerning the risks of gold open access;  Compare our technical It has become clear for instance that NII and Inria have a very similar role in their being at the intersection of computer science research and scientific information services development.  Creating better communication channels between our institutions and in particular our library networks (Couperin in France, JUSTICE in Japan) about the various negotiations and agreements that are taking place with private publishers, concerning: subscription deals, gold open access deals and specific licencing agreements (re-use and data mining). This could lead to the identification of bilateral coordination when facing major hurdles in future negotiations;  Developing strategies to strengthen the role of digital librarians and data scientist with the perspective to increase the sustainability and re-use of the digital scientific content that will be produced in the future. The importance of such new professional profiles has been identified by both sides as crucial to scientific information policies in the digital world;  Coordinate the evolution of the copyright legal landscape in order to favour access and re-use of scientific content;

There are clearly lessons to learn for the French scholarly landscape. The Japanese example tells us in particular the danger of having a fragmented publication repository landscape and French Universities such as Strasbourg or Bordeaux should look at the consequences of developing and maintain their own platforms. From a political point of view, the deposit mandates of Inria and CWI have clearly been seen as examples that should followed step by step (hita-hita again…) by various university libraries.

Participants au premier workshop (28 Janvier 2015)

Crédit photo : Ambassade de France au Japon Une délégation réunissant des experts français dans le domaine de l"Open Access, sujet clé à l"échelle mondiale pour le monde de la recherche, a été invitée par le Service pour la Science et la Technologie à venir au Japon du 27 au 30 Janvier 2015. Cette mission visait à rencontrer l"ensemble des parties prenantes pour faire un point complet sur la situation au Japon en matière d"Open Access et d"envisager de possibles collaborations.

L'Open Access -un nouveau modèle pour la recherche scientifique mondiale

L"Open Access ou « Libre Accès » consiste en la mise à disposition immédiate, gratuite et permanente sur Internet des publications scientifiques issues de la recherche et de l"enseignement. Ce mouvement, initié dans les années 90, a pris de l"ampleur ces dernières années face au pouvoir de pression grandissant des éditeurs de revues scientifiques et leur mainmise sur les données, soulevant des questions sur la souveraineté numérique des pays.

Renforcer la coopération franco-japonaise

La délégation française, coordonnée par l"Inria (Institut national dans le domaine des sciences du numérique, a pu à cette occasion rencontrer les responsables de différentes institutions japonaises impliquées sur le sujet de l"Open Access : le MEXT (Ministry of Education, Culture, Sports, Science and Technology), la JSPS (Japan Society for the Promotion of Science), la JST (Japan Science and Technologyagency), le NII (National Institute of Informatics), et également le Dr Yuko Harayama, membre exécutif du CSTI (Council for Science, Technology and Innovation). Deux ateliers de travail, l"un réunissant des représentants de bibliothèques universitaires, le second les scientifiques japonais impliqués sur ce sujet, sont venus compléter ces entretiens. Les discussions ont notamment porté sur :

-Les plans existants de souscription aux revues scientifiques et de licenses nationales (coûts, services associés comme l"archivage et l"exploration de données, ou « data mining »). -La politique existante et la position japonaise sur la question des modèles « Gold Open Access » où les auteurs paient pour la publication de leur article, « Green Open Access » où les auteurs déposent une copie de leurs articles sur une page personnelle ou une archive ouverte, ou encore les modèles hybrides. -Plus particulièrement sur le modèle « Green Open Access », l"état actuel de déploiement d"archives ouvertes (et la politique menée pour encourager les chercheurs à y déposer leurs publication) et de plateformes d"évaluation et à contenu éditorial (épi-journaux, « overlay journals »..) -La politique en matière d"accès libre aux données de la recherche :

infrastructures et recommandations au niveau national pour la mise à disposition libre des données de recherche.

De nouvelles possibilités de collaboration, pour la synchronisation d"archives et de plateformes, le développement des services associés, mais également pour l"échange de bonnes pratiques en vue de sensibiliser les chercheurs, ont été mises en valeur. A l"issue de cette mission, un rapport fournira un état des lieux sur le statut actuel de l"Open Access au Japon et ces perspectives de collaboration.

Contact : Mme Evelyne ETCHEBÉHÈRE, attachée pour les Sciences et Technologies de l"Information et de la Communication à l"Ambassade de France.

  Still, there are several positive factors that are likely to help Japan taking a leading role in the open access movement:  The dramatic growth of open access repositories in Japan in the recent year, despite the fragmentation effect we have already mentioned created a real culture of repository management in Japan as well as a factor for higher collaboration between Japanese university libraries;  The centralisation role of NII and in particular the recent deployment of JAIRO cloud 20 or the provision of a national journal management platform is likely to create in the very close future a very strong and coherent infrastructure at the service of forthcoming open access policies 21 ;  Mandate (PhD) MEXT has started to work with JST to introduce mandatory rule for scientists to publish their papers and data sets open accessible attached to public funds. [Source MT]  The strong influence of library networks (cf. the pioneering role of Universities such as Chiba)

  publication repository platform: HAL 7 .At national level, the French Minister for Research has issued in January 2013 a strong statement on open access to scholarly results, where the archiving of publications in open access repositories, and in particular the HAL national platform, has been given priority, in complement to the definition of new viable editorial and business model for scientific publishing.

http://openaccess.mpg.de/Berlin-Declaration

green open access can be defined as the free dissemination of scholarly papers by authors themselves

green open access can be defined as the free dissemination of scholarly papers by the publishing platforms where the article has been submitted.

for instance without relying on the sole Journal Impact Factor

See for instance the infelicitous proposal in:

http://www.couperin.org

As opposed to France where major universities have chosen to have their IR portal developed within HAL, JAIRO Cloud initially took up within smaller universities which could not afford deploying their own IR environment.

Kiyos are also disseminated using the CiNii service from NII (http://ci.nii.ac.jp)

www.jaibs.jp

In universities such as KeiO (KOARA repository) with a specific policy, the rate can reach 40%, with a clear impact on visibility.

https://tel.archives-ouvertes.fr/STAR

http://www.dart-europe.eu

ガチョウと黄金の卵

JAIRO cloud now hosts 60% of all IR in Japan, in particular from smaller universities with limited in-house implementation resources.

A typical example is Chiba University, a precursor in the domain of setting up an institutional repository and associated overlay services, which now experimenting a switch to JAIRO cloud.

http://www.ambafrance-jp.org/Compte-rendu-Mission-d-experts

Acknowledgements

We are much thankful to two essential persons that have made our visit to Tokyo possible. First, EvelyneEtchebehere from the French embassy has been seminal in identifying the need for such a visit, providing the corresponding financial and logistic support and finally managing to have some essential doors open. Second, SyunTutiya from the National Institution for Academic Degrees and University Evaluation, who provided most of our contact persons in Japan and identified the

participant lists have been moved at the end of this report as annexes. http://pubman.mpdl.mpg.de/://hal.archives-ouvertes.fr 8 https://www.gov.uk/government/publications/open-data-charter/g8-open-datacharter-and-technical-annex 9 From Julia

Annexes

 (1985)in mathematics of the University of Minnesota (USA). He worked at the Technical University of Delft (1983Delft ( -1984)), at the Centre for Mathematics and Computer Science (CWI) in Amsterdam (1984-1985 and 1989-1991) and at the University of Amsterdam (1985)(1986)(1987)(1988)(1989)(1990)(1991), before getting appointed in 1991 as full professor of computer science at the TechnischeUniversiteit Eindhoven (TU/e).

As of October 2011, he is general director of CWI in Amsterdam, keeping a part-time professorship at TU/e. As of January 2015, this part-time professorship is replaced by one at the Institute of Logic, Language and Computation of the University of Amsterdam.

He is well-known as a researcher in formal methods, in particular in process algebra and its applications. To date, he supervised 29 Ph.D. degrees. He was scientific director of the national research school Institute for Programming research and Algorithmics (1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004), dean of the department of Mathematics and Computer Science of the TU/e (1996-1999 and 2002-2004), and initiated the Embedded Systems Institute in Eindhoven (1996). He chairs the steering committee of the CONCUR conferences and is a member of the KHMW (Royal Holland Society of Arts and Humanities). Recently Claude Kirchner has also been involved in the set-up of the FUN (France UniversitéNumérique) French gouvernemental MOOC initiative and was an organizer of the DagstuhlPerpective Workshop on MOOCs (http://www.dagstuhl.de). He is member of numerous scientific advisory committees, member of the committee for ethical research in digital science in France (CERNA) and president of Inria"s Institutional Review Board (COERLE), président of the CCSD (Centre pour la Communication ScientifiqueDirecte) steering committee.

AlexandreMoatti, 55 ans, estingénieur en chef des Mines (Conseilgénéral de l'économie, de l'industrie et des technologies, ministère de l'Industrie) et parallèlementchercheurassocié à l'université Paris-VII-Diderot (laboratoired'histoire des sciences et des techniques sphere UMR 7219

17:10 Closing

Citizen science in France is just emerging (like in Japan).

Press release from the French embassy 22

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Compte-rendu : Mission d'experts français sur l'Open Access

Une mission d"experts français portant sur l"« Open Access » a été organisée du 27 au 30 Janvier 2015 à Tokyo, par le service pour la Science et la Technologie de l"ambassade de France au Japon.

Une mission d"experts français portant sur l"« Open Access » a été organisé du 27 au 30 Janvier 2015 par le service pour la Science et la Technologie de l"ambassade de France au Japon.