Daniil Ryabko
email: daniil@ryabko.net

ASYMPTOTIC STATISTICAL ANALYSIS OF STATIONARY ERGODIC TIME SERIES

It is shown how to construct asymptotically consistent efficient algorithms for various statistical problems concerning stationary ergodic time series. The considered problems include clustering, hypothesis testing, change-point estimation and others. The presented approach is based on empirical estimates of the distributional distance. Some open problems are also discussed.

INTRODUCTION

Statistical problems involving time-series data arise in a variety of modern applications, including biology, finance, network analysis, etc. These applications often dramatically violate traditional statistical assumptions imposed on time series. This applies not only to parametric models, but even to assumptions that are often considered nonparametric, for example that the data points are independent or that the time series have limited memory, or that the processes mix sufficiently fast and so on.

Here I summarize some recent work on statistical analysis of time series where the only assumption on the time series is that they are stationary ergodic. No independence or mixing-type assumptions are involved.

The considered problems are hypothesis testing, clustering, the two-and thre-sample problems, and change point estimation. The main results establish asymptotically consistent algorithms for the considered problems. The consistency results follow from the simple fact that the so-called distributional distance [START_REF] Gray | Probability, Random Processes, and Ergodic Properties[END_REF] can be estimated based on sampling; this contrasts previous results that show that the d distance can not (in general) be estimated for stationary ergodic processes [START_REF] Ornstein | How sampling reveals a process[END_REF]. For more details on these results see [START_REF] Ryabko | Clustering processes[END_REF][START_REF] Ryabko | Nonparametric statistical inference for ergodic processes[END_REF][START_REF] Ryabko | Discrimination between B-processes is impossible[END_REF][START_REF] Ryabko | Testing composite hypotheses about discrete ergodic processes[END_REF][START_REF] Khaleghi | Multiple change-point estimation in stationary ergodic time-series[END_REF].

PRELIMINARIES

Let A be an alphabet, and denote A * the set of tuples ∪ ∞ i=1 A i . In this work we consider the case A = R; extensions to the multidimensional case, as well as to more general spaces, are straightforward. Distributions, or (stochastic) processes, are measures on the space (A ∞ , F A ∞ ), where F A ∞ is the Borel sigma-algebra of A ∞ . When talking about joint distributions of N samples, we mean distributions on the space

((A N ) ∞ , F (A N ) ∞ ).
For each k, l ∈ N, let B k,l be the partition of the set

A k into k-dimensional cubes with volume h k l = (1/l) k (the cubes start at 0). Moreover, define B k = ∪ l∈N B k,l and B = ∪ ∞ k=1 B k . The set {B × A ∞ : B ∈ B k,l , k, l ∈ N} generates the Borel σ-algebra on R ∞ = A ∞ . For a set B ∈ B let |B| be the index k of the set B k that B comes from: |B| = k : B ∈ B k .
We use the abbreviation X 1..k for X 1 , . . . , X k . For a sequence x ∈ A n and a set B ∈ B denote ν(x, B) the frequency with which the sequence x falls in the set B.

ν(x, B) := 1 n-|B|+1 n-|B|+1 i=1 I {(X i ,...,X i+|B|-1 )∈B} if n ≥ |B|, 0 otherwise. A process ρ is stationary if ρ(X 1..|B| = B) = ρ(X t..t+|B|-1 = B)
for any B ∈ A * and t ∈ N. We further abbreviate ρ(B) := ρ(X 1..|B| = B). A stationary process ρ is called (stationary) ergodic if the frequency of occurrence of each word B in a sequence X 1 , X 2 , . . . generated by ρ tends to its a priori (or limiting) probability a.s.:

ρ( lim n→∞ ν(X 1..n , B) = ρ(B)) = 1.
Denote E the set of all stationary ergodic processes.

Definition 1 (distributional distance). The distributional distance is defined for a pair of processes ρ 1 , ρ 2 as follows (e.g. [START_REF] Gray | Probability, Random Processes, and Ergodic Properties[END_REF])

d(ρ 1 , ρ 2 ) = ∞ m,l=1 w m w l B∈B m,l |ρ 1 (B) -ρ 2 (B)|,
where w j = 1/j 2 .

(The weights in the definition are fixed for the sake of concreteness only; we could take any other summable sequence of positive weights instead.) In words, we are taking a sum over a series of partitions into cubes of decreasing volume (indexed by l) of all sets A k , k ∈ N, and count the differences in probabilities of all cubes in all these partitions. These differences in probabilities are weighted: smaller weights are given to larger k and finer partitions. It is easy to see that d is a metric. We refer to [START_REF] Gray | Probability, Random Processes, and Ergodic Properties[END_REF] for more information on this metric and its properties.

The methods below are based on empirical estimates of the distance d:

d(X 1 1..n1 , X 2 1..n2 ) = ∞ m,l=1 w m w l B∈B m,l |ν(X 1 1..n1 , B) -ν(X 2 1..n2 , B)|, (1)
where

n 1 , n 2 ∈ N, ρ ∈ S, X i 1..ni ∈ A ni .
Although the expression (1) involves taking three infinite sums, it will be shown below that it can be easily calculated (see Section 4).

ASYMPTOTIC CONSISTENCY RESULTS

The consistency results are based on the following statement, which is quite easy to derive from the definition of ergodicity (or from Birkhoff's ergodic theorem).

Lemma 1 ( d is consistent). Let ρ 1 , ρ 2 ∈ E and let two samples x 1 = X 1 1..n1 and x 2 = X 2 1..n2 be generated by a distribution ρ such that the marginal distribution of X i 1..ni ρ i is stationary ergodic for i = 1, 2. Then lim n1,n2→∞ d(X 1 1..n1 , X 2 1..n2 ) = d(ρ 1 , ρ 2 ) ρ-a.s.

The three-sample problem

The first problem we consider is the three-sample problem, also known as process classification. Let there be given three samples

X = (X 1 , . . . , X k ), Y = (Y 1 , . . . , Y m ) and Z = (Z 1 , . . . , Z n ).
Each sample is generated by a stationary ergodic process ρ X , ρ Y and ρ Z respectively. Moreover, it is known that either

ρ Z = ρ X or ρ Z = ρ Y , but ρ X = ρ Y .
We wish to construct a test that, based on the finite samples X, Y and Z will tell whether

ρ Z = ρ X or ρ Z = ρ Y .
The proposed test chooses the sample X or Y according to whichever is closer to Z in d. That is, we define the test G(X, Y, Z) as follows. If d(X, Z) ≤ d(Y, Z) then the test says that the sample Z is generated by the same process as the sample X, otherwise it says that the sample Z is generated by the same process as the sample Y. The statement is easy to derive from Lemma 1. Note that X, Y, Z are not required to be independent. All we need is that the distributions are stationary ergodic (more formally, the distribution generating the three sequences is arbitrary except for the fact that the marginals are stationary ergodic).

Time-series clustering

A more general but closely related problem is time-series clustering. We are given N samples x 1 , . . . , x N , where each sample x i is a string of length n i of symbols from A:

x i = X i 1..ni .
Each sample is generated by one out of k different unknown stationary ergodic distributions ρ 1 , . . . , ρ k ∈ E. Thus, there is a partitioning I = {I 1 , . . . , I k } of the set {1..N } into k disjoint subsets I j , j = 1..k {1..N } = ∪ k j=1 I j , such that x j , 1 ≤ j ≤ N is generated by ρ j if and only if j ∈ I j . The partitioning I is called the target clustering and the sets I i , 1 ≤ i ≤ k, are called the target clusters. Given samples x 1 , . . . , x N and a target clustering I, let I(x) denote the cluster that contains x.

It is required to partition the index set {1..N } in such a way that as the length of each sequence grows the partitioning coincides with the target clustering from some time on with probability 1. Such an algorithm is called asymptotically consistent. In other words, when the sequences are long enough, we have to group together those and only those sequences that were generated by the same distributions.

This can be done as follows. The point x 1 is assigned to the first cluster. Next, find the point that is farthest away from x 1 in the empirical distributional distance d, and assign this point to the second cluster. For each j = 3..k, find a point that maximizes the minimal distance to those points already assigned to clusters, and assign it to the cluster j. Thus we have one point in each of the k clusters. Next simply assign each of the remaining points to the cluster that contains the closest points from those k already assigned. One can notice that the described algorithm just one iteration of the k-means algorithm, with socalled farthest-point initialization and using the distance d. Theorem 2. The described algorithm is strongly asymptotically consistent provided ρ i is stationary ergodic for each i = 1..k.

Change-point estimation

Next we consider the change-point problem. The sample

Z = (Z 1 , . . . , Z n ) consists of two concatenated parts X = (X 1 , . . . , X k ) and Y = (Y 1 , . . . , Y m ), where m = n -k, so that Z i = X i for 1 ≤ i ≤ k and Z k+j = Y j for 1 ≤ j ≤ m.
The samples X and Y are generated independently by two different stationary ergodic processes with alphabet A = R. The distributions of the processes are unknown. The value k is called the change point. It is assumed that k is linear in n; more precisely, αn < k < βn for some 0 < α ≤ β < 1 from some n on.

It is required to estimate the change point k based on the sample Z.

Note that we do not assume that the single-dimensional marginals before and after the change point are different, as is done almost exclusively in the literature on this problem. We are in the most general situation where the timeseries distributions are different, i.e. the change may be only in the long-range dependence.

For each t, 1 ≤ t ≤ n, denote U t the sample (Z 1 , . . . , Z t ) consisting of the first t elements of the sample Z, and denote V t the remainder (Z t+1 , . . . , Z n ).

Define the change point estimate

k : A * → N as fol- lows: k(X 1 , . . . , X n ) := argmax t∈[αn,n-βn] d(U t , V t ).
The following theorem establishes asymptotic consistency of this estimator. Theorem 3. For the estimate k of the change point k we have

1 n | k -k| → 0 a.s.
where n is the size of the sample, and when k, n -k → ∞ in such a way that α < k n < β for some α, β ∈ (0, 1) from some n on.

This result can be extended [START_REF] Khaleghi | Multiple change-point estimation in stationary ergodic time-series[END_REF] to multiple change points and unknown α and β, although the algorithm becomes much more sophisticated.

Impossibility results: the two-sample problem and its implications

For the problems considered above we have relatively simple algorithms that are asymptotically consistent under most general assumptions. What is more, the proofs of consistency (although mostly omitted here) are quite simple as well. From this one can get the impression that asymptotic consistency results are very easy to obtain and probably they hold for all other interesting problems as well. This is not the case. The first example is another classical statistical problem: homogeneity testing, also known as the two-sample problem. We are given two samples X = (X 1 , . . . , X n ) and Y = (Y 1 , . . . , Y n ) generated by two stationary ergodic distributions ρ X and ρ Y . We want to tell whether they were generated by the same or by different distributions, that is, whether ρ X = ρ Y . We are willing to settle for a rather weak asymptotic result. Say a two-sample test L(X, Y ), that takes two samples and outputs 0 or 1, is asymptotically consistent if EL → 1 as n → ∞ if ρ X = ρ Y and EL → 0 otherwise. Moreover, we can further assume that the samples are binary-valued and there is no dependence between X and Y . This does not help: Theorem 4. There is no asymptotically consistent twosample test.

This result holds even if we additionally require ρ X and ρ Y to be B-processes [START_REF] Ryabko | Discrimination between B-processes is impossible[END_REF], contrasting earlier results of Ornstein and Weiss for this class of processes [START_REF] Ornstein | How sampling reveals a process[END_REF]. The proof (omitted here) relies on a counterexample which is a limit of hidden Markov processes with a countably infinite state space, using a method similar to that of [START_REF] Ryabko | Prediction of random sequences and universal coding[END_REF].

As a consequence of this negative result, we can also derive impossibility results for some generalizations of the problems considered above.

Corollary 1. Under the assumptions of theorems 2 and 3 respectively, there is no asymptotically consistent clustering algorithm when the number of clusters is unknown, and there is no asymptotically consistent change-point detection algorithm.

Hypothesis testing

Some of the problems considered above, as well as many other interesting problems, cab be formulated in the following way. Consider two sets H 0 and H 1 which are subsets of the set of all stationary ergodic processes, and let there be given a sample X 1 , . . . , X n generated by a stationary ergodic process distribution ρ. We want to tell whether ρ ∈ H 0 or ρ ∈ H 1 . The problem arises to characterize those pairs (H 0 , H 1 ) for which this is possible in some asymptotic sense, that is, whether asymptotically consistent tests exists. It turns out that the distributional distance can be used to answer this question to a considerable extent.

To define the notion of consistency we use for this problem, recall that Type I error is said to occur if the test says "1" while the sample was generated by the distribution from H 0 . Type II error occurs if the test says "0" while H 1 is true. In many practical situations, these errors may have very different meaning: for example, this is the case when H 0 is interpreted as that a patient has a certain ailment, and H 1 that he does not. In such cases, one may wish to treat the errors asymmetrically. Also H 0 can often be much simple than the alternative H 1 , for example, H 0 can be a simple parametric family, or it may consist of just one process distribution, while H 1 can be the complement of H 0 to the set of all stationary ergodic processes.

Call a test consistent if, for any pre-specified level α ∈ (0, 1), any sample size n and any distribution in H 0 the probability of Type I error (the test says H 1 ) is not greater than α, while for every distribution in H 1 and every α the Type II error is made only a finite number of times with probability 1, as the sample size goes to infinity.

Recall that a stationary process can be represented as a mixture of stationary ergodic processes, that is, as a measure on the set E (see, e.g., [START_REF] Gray | Probability, Random Processes, and Ergodic Properties[END_REF]). The set E is not closed with respect to the distributional distance, but the set S of all stationary process distributions is. The following theorem utilizes these facts. Its proofs relies in addition on some other nice properties of the metric space (S, d); see [START_REF] Ryabko | Testing composite hypotheses about discrete ergodic processes[END_REF] for the proof and [START_REF] Gray | Probability, Random Processes, and Ergodic Properties[END_REF] for the properties of (S, d).

Theorem 5. There exists a consistent test for H 0 against H 1 if H 0 has probability 1 with respect to ergodic decomposition of every distribution from the closure of H 0 , where the closure is with respect to the distributional distance d. Conversely, if there is a consistent test H 0 against H 1 then H 1 has probability 0 with respect to ergodic decomposition of every distribution from the closure of H 0 .

The necessary and sufficient conditions coincide if H 1 is the complement of H 0 to the set E of all stationary ergodic process distributions: Corollary 2. There exists a consistent test for H 0 against H 1 := E\H 0 if and only if H 1 has probability 0 with respect to ergodic decomposition of every distribution from the closure of H 0 .

COMPUTATIONAL COMPLEXITY

While the definition of empirical distributional distance d involves taking infinite sums, in can be calculated not only in finite time but efficiently. To see this, first observe that in d all summands corresponding to m > n (where n is the min length of x 1 , x 2 ) are 0. In the sum over l (cube size) all the summands are the same from the point where each cube has at most one point in it. This already makes computations finite. Moreover, even though the number of cubes in B m,l is exponential in m and l, at most 2n cubes are non-empty and these are easy to track (across different values of cube size l) with a tree structure. Thus, d can be calculated as is (in a naive way) in time O(n 2 s log n) where s is the minimal non-zero distance between points. This can be further reduced: the summands for m > log n and for l such that each cube less than log n points have no chance to have consistent estimates and only contribute (a negligible part) to the error. Thus, it is only practical to truncate the sums at log n; since all the theoretical results presented here are asymptotic in n, it is easy to check that they still hold with this modification of d. The computational complexity of d becomes O(n polylog n). For more information on implementation of the resulting algorithms see [START_REF] Khaleghi | Online clustering of processes[END_REF]. The latter work also provides some empirical evaluations of the clustering algorithm described here, as well as theoretical results for the online version of this problem.

OUTLOOK

Here we mention some interesting open problems for future research. First, the characterisation of those hypotheses for which consistent tests exist is so far incomplete: the necessary and sufficient conditions coincide only in the case when H 1 is the complement of H 0 (cf. Theorem 5 and the corollary). Furthermore, one can consider other notions of consistency of tests, both weaker and stronger ones, such as requiring both probabilities of error to converge to 0, or requiring both errors to be bounded uniformly. An interesting statistical problem that we did not consider here is independence testing. Given two samples it is required to test whether they were generated independently or not. Given the negative result of Theorem 4, one could think that this problem is also impossible to solve. However, Theorem 5 implies that it is, in fact, possible. Finding an actual test (possibly using d) is an interesting open problem.

Theorem 1 .

 1 The described test makes only a finite number of errors with probability 1, when |X|, |Y | and |Z| go to infinity.

ACKNOWLEDGMENTS

This work was supported by Ministry of Higher Education and Research, Nord-Pas-de-Calais Regional Council and FEDER through the "Contrat de Projets Etat Region (CPER) 2007-2013," the ANR projects Explora (ANR-08-COSI-004) and Lampada (ANR-09-EMER-007), by the European Community's Seventh Framework Program (FP7/2007-2013) under grant agreement 270327 (project CompLACS) add Pascal-2.


Estimating population size of the red swamp crayfish (Procambarus clarkii) in fish-ponds (Brenne, Central France)

Procambarus clarkii, fish-ponds, mark-recapture, population size estimation

The red swamp crayfish, Procambarus clarkii, was discovered in 2007 in the "Parc naturel régional (PNR) de la Brenne" (France). Ten colonized sites have been identified in the park to date, including two new sites discovered in 2011. The present study aims at establishing a protocol suitable for estimating the population size of P. c l a r k i i b yt h eu s eo faC a p t u r e -M a r k -Recapture (CMR) technique in a chain of five connected fish-ponds. Results show different cohorts of individuals among seasons and fish-ponds. However, trapping effort was not efficient enough to obtain an accurate estimate of the population size of this species in a fish-pond larger than 2-3 ha. On the other hand, the adopted protocol appeared useful to assess, in smaller fish-ponds, the effect of intensive trapping and other control methods on P. c l a r k i i populations.

RÉSUMÉ

Estimation de la taille de populations d'écrevisse de Louisiane (Procambarus clarkii) dans des étangs de pisciculture (Brenne, Central France)

Mots-clés :

Procambarus clarkii, étangs, marquagerecapture, taille de la population L'écrevisse de Louisiane, Procambarus clarkii, a été récemment découverte (2007) dans le "Parc naturel régional (PNR) de la Brenne" (France). Dix foyers d'infestation sont à présent identifiés dans le parc, dont deux très récemment (2011). La présente étude a pour but d'établir un protocole efficace pour estimer la taille des populations de P. c l a r k i i par la technique de Capture-Marquage-Recapture (CMR), au niveau de 5 étangs piscicoles organisés en chaine. Les résultats montrent différentes cohortes d'individus variant selon les saisons et selon les étangs. L'effort de piégeage effectué dans cette étude s'avère insuffisant pour des étangs supérieurs à 2 ou 3 ha. Pour les étangs de plus petite taille, un tel protocole semble être plus adapté et permettrait d'évaluer l'impact du piégeage intensif et autres méthodes de contrôle sur les populations de P. c l a r k i i .

INTRODUCTION

According to [START_REF] Strayer | Alien species in fresh waters: ecological effects, interactions with other stressors, and prospects for the future[END_REF], the strong ecological effects of freshwater alien species 1 can be divided among five different groups: consumers, fishes, aquatic plants, diseases, and decapods that act as powerful omnivores. Indeed most invasive decapods are nonindigenous crayfish species (NICS), which often have strong direct and indirect ecological negative impacts, on the food web of many ecosystems [START_REF] Lodge | Nonindigenous crayfishes threaten North American freshwater biodiversity: Lessons from Europe[END_REF]. Native to north-eastern Mexico and south-central USA [START_REF] Hobbs | An illustrated checklist of the American crayfishes (Decapoda: Astacidae, Cambaridae, Parastacidae)[END_REF], the red swamp crayfish Procambarus clarkii is now widespread and abundant across the world [START_REF] Gherardi | Crayfish invading Europe: the case study of Procambarus clarkii[END_REF]. After having been introduced for the first time in 1973 into a European country (southern Spain) [START_REF] Habsburgo-Lorena | Present situation of exotic species of crayfish introduced into Spanish continental waters[END_REF], this NICS is currently present in 15 European countries [START_REF] Holdich | A review of the ever increasing threat to European crayfish from non-indigenous crayfish species[END_REF].

Most P. c l a r k i i 's populations are present in Spain, Italy and France. In France, the first population was recorded in 1988 in Charente-Maritime department, since then, it has spread through most of the hydrographic basins of this department. The strongest geographical expansion of P. c l a r k i i occurred in the period 2001[START_REF] Gherardi | Crayfish invading Europe: the case study of Procambarus clarkii[END_REF][START_REF] Collas | Note technique de la situation des écrevisses en France résultants des enquêtes nationales réalisées entre 1977 et 2006 par le Conseil Supérieur de la Pêche[END_REF]. Everywhere, this NICS appears to be a very strong competitor with the native crayfish, being highly aggressive and generally resistant to diseases, with some exceptions [START_REF] Edgerton | Understanding the causes of disease in European freshwater crayfish[END_REF]. Procambarus clarkii can withstand extreme environmental conditions (review in [START_REF] Gherardi | Understanding the impact of invasive crayfish[END_REF]a n d is able to colonize varied ecosystems. It is continuously in the process of colonizing new departments, new watersheds, and of eliminating indigenous crayfish species (ICS) and other species of conservation concern. Due to its invasive potential, P. c l a r k i i is now present in 61 departments of metropolitan France [START_REF] Collas | Note technique de la situation des écrevisses en France résultants des enquêtes nationales réalisées entre 1977 et 2006 par le Conseil Supérieur de la Pêche[END_REF].

Impacts of its proliferation are catastrophic for the invaded ecosystems. [START_REF] Geiger | Impact of an introduced Crustacean on the trophic webs of Mediterranean wetlands[END_REF] have synthesized evidence of the ecological impacts the species has on the trophic food webs of Mediterranean wetlands, and how it changed their structure and functioning. Its success as an invader is facilitated by high reproductive output, short development time, and a flexible feeding strategy. As a consequence of its omnivorous feeding habit, it affects both lower and higher trophic levels, by grazing on macrophytes and preying on macroinvertebrates, and has a role as an important food source for several vertebrate species. In addition to being a vector of the crayfish plague, due to its short life-history, rapid growth, burrowing activities and high population density, it can adversely impact the aquatic environment (Rodriguez et al., 2003(Rodriguez et al., , 2005;;G h e r a r d i ,2006; [START_REF] Gherardi | Invasive crayfish in Europe: the impact of Procambarus clarkii on the littoral community of a Mediterranean lake[END_REF][START_REF] Souty-Grosset | Synthèse des connaissances scientifiques sur les écrevisses exotiques en Europe, Faire face à Procambarus clarkii et aux écrevisses invasives[END_REF].

Identified for the first time in 2007 in the "Parc naturel régional de la Brenne" (Central France), P. c l a r k i i has very quickly caused severe problems. It has colonized various environments and dug burrows in the banks of ponds, particularly fish-ponds. This resulted in biological imbalances for the affected ecosystem and difficulties to control populations. To date ten infestation sites have been identified, including two discovered very recently (in 2011). Many trapping campaigns of P. c l a r k i i are planned by both park officers and owners of fish-ponds.

However, to be able to assess the effects of control methods on populations of this species, it is first necessary to define the appropriate technique for estimating the population size of P. c l a r k i i in fish-ponds of different sizes and at different seasons.

While many studies have been conducted to obtain an estimate of animal abundance, such as amphibians [START_REF] Pellet | Estimation de l'effectif d'une population isolée de salamandres tachetées (Salamandra salamandra) par une approche bayesienne[END_REF] and reptiles [START_REF] Koller | Étude et estimation de l'effectif de Couleuvres vipérines (Natrix maura) et de Couleuvres tesselées (N. tessellata) dans le Lavaux[END_REF], estimating the population size of decapod crustaceans, particularly crayfish, remains very difficult to undertake and produce reliable mixed results, depending on the crayfish species and habitats.

There are many descriptions of monitoring methods in the literature -perhaps because each biotope appears unique and demands a different methodology [START_REF] Somers | Variable trappability of crayfish associated with bait type, water temperature and moon phase[END_REF].

However, the Capture-Mark-Recapture (CMR) method has been efficient for estimating the population size of crayfish (see the review of [START_REF] Nowicki | Monitoring crayfish using a mark-recapture method: potentials, recommendations and limitations[END_REF]. [START_REF] Acosta | Effective sampling area: a quantitative method for sampling crayfish populations in freshwater marshes[END_REF] used CMR techniques for monitoring the density of Procambarus alleni in Florida Everglades and demonstrated the efficacy of this technique for sampling crayfish populations in flooded marsh habitats. Da [START_REF] Silva | Population size estimation of the exotic crayfish Procambarus clarkii (Girard) (Crustacea, Decapoda, Cambaridae) in the Alfredo Volpi City Park, São Paulo, Brazil[END_REF] estimated the size of an established population of P. c l a r k i i in an artificial pond in São Paulo, Brazil, by the means of CMR techniques and applied the Schumacher and Eschmeyer's method for population size determination [START_REF] Krebs | Ecological Methodology[END_REF]. They showed that estimates should be performed over no longer than three weeks.

This not only seems to be a fairly adequate time period for estimating the population size of a

Figure 1

Chain of fish-ponds, with presence/absence of P. clarkii. Fish-ponds are represented with , the ponds with , the traps between two fish-ponds with , traps for the session 1 (March) with and additional traps for the sessions 2 and 3 (April and June-July) with .

Represents fish-pond with crayfish, fish-pond with few crayfish and without crayfish.

closed population of crayfish but would also guarantee that, even if one or more specimens molted, ecdysis would not likely occur twice for the same adult during this short three-week period. These methods were also applied to indigenous crayfish (Astacus astacus)( M a g u i r e et al., 2004).

The aim of the present study was to understand whether CMR techniques are effective in fish-ponds. We also conducted a study of P. c l a r k i i population's characteristics with the aim of characterizing the different cohorts of individuals.

MATERIALS AND METHODS

> STUDY AREA

A chain of five linked fish-ponds located in the south of the Brenne Park offers an unusual opportunity to analyze the efficacy of CMR techniques (Figure 1). A fish-pond is an area of standing water, shallow (1.5 m on average), equipped with a floodgate. The smaller fish-ponds in Brenne cover 1-3 ha and the largest spread over 180 ha. Fish-ponds are emblematic of the Brenne, called "the land of thousand fish-ponds". There are over 4000 fish-ponds today. They are organized in chains; they empty into each other within the same watershed.

This chain studied here is 'simplified' as compared to other chains in the centre of the park where very numerous fish-ponds are linked. The five fish-ponds studied are all connected by ditches, which allow checking movements of crayfish between fish-ponds by placing traps between them. The three fish-ponds located furthest upstream in the chain (fish-pond 1 (2 ha), fish-pond 2 (3 ha) and fish-pond 3 (13 ha)) are affected by the presence of P. c l a r k i i , whereas fish-pond 4 (3 ha) is in a very early stage of colonization and fish-pond 5 (4 ha) is unaffected until now (Figure 1).

> CRAYFISH TRAPPING AND CAPTURE-MARK-RECAPTURE (CMR)

A total of 40 cylindrical traps with two entrances and a place to put bait (length: 65 cm, diameter: 35 cm, mesh size: 5 mm), were positioned in fish-ponds and in their connecting ditches, as well as in nearby ponds. Bait consisted of pieces of carp. Traps were lifted after 24 h, following [START_REF] Bellanger | Cahier des charges standard pour l'étude méthodologique des populations d'écrevisses autochtones en Rhônes-Alpes, Diagnostic du milieu et des populations d'écrevisses à pieds blancs, Recherche du déterminisme de répartition et des causes de régression[END_REF]. This relatively short period of trapping was necessary to avoid cannibalism, injuries and decreased numbers of trapped crayfish, due to competitive exclusion by dominant crayfish.

Water temperature was measured 10 cm below the surface during each field campaign. Field sessions began in March 2010 with 1 trap•ha -1 . Trapping effort proved to be insufficient for a reliable estimate of population size, so the density of traps was increased to 1.5 traps•ha -1

for sessions 2 and 3, in April and June-July 2010, respectively.

To assess the size of P. c l a r k i i 's population in each fish-pond, the CMR technique was chosen.

Each caught crayfish was sexed, weighed and measured (total length, from the telson to the tip of the rostrum). The sex ratio is computed as number of males over the total number of individuals.

The first capture was followed by three recaptures over two weeks of experimentation. All individuals were marked with coloured varnish on the cephalothorax (Figure 2). Each fishpond corresponded to a different color varnish, which allowed us to recognize the fish-pond of provenance of each crayfish subsequently trapped, but not individually. CPUE (Catch Per Unit Effort) was calculated as the number of crayfish caught per trap within 24 h.

The french law prohibits releasing the individuals in water, transporting them live or using them as bait. For scientific reasons in this study, caught individuals were not killed each time but exceptionally at the end of the last session, and not between sessions in order to work on the same population. However, eggs and larvae from berried females were removed before returning the female to the water.

> DATA ANALYSIS

Population size in each fish-pond was estimated using the program MARK (developed by White and Burnham in 1999: CA-Visual Objects 2.0 Standard Application) by creating a matrix of presence/absence in excel which was transferred to the software. The "closed captures" model was tested, as each population was assumed to be closed, i.e. crayfish were assumed not to migrate from one fish-pond to another. We also used the MARK software to test another model "Jolly-Seber" that, on the contrary, assumed an open population [START_REF] Bourgault | Techniques de capture et de marquage des micromammifères[END_REF].

In order to compare different methods of estimating numbers of individuals, we used paired Student's t-tests to compare estimates from one session to another and population models (open or closed population). When the data were not normally distributed or when the variances were not homogeneous, the Wilcoxon test was applied using the software "R commander" (Version 1.4-5).

RESULTS

> ESTIMATES OF POPULATION SIZE

Ta b le s I-III show the estimated size of P. c l a r k i i 's population obtained using the software MARK; estimates varied according to different field campaigns. Sessions 1 and 3 revealed the greatest numbers of trapped individuals, reflecting more pertinent results. The coefficient of variation (CV) is an index of the accuracy of our estimates. When this ratio is between 0-15%, the estimate (Nt) is reliable for the fraction of the population sampled. A capture probability (pC) of 30% or more is also required to be considered a good estimate. In Tables I andIII,theCV was lower for session 3 (4-10%). For fish-pond 1, pC was constant. Fish-pond 2hadapC of 23% in session 1, but a recapture probability (pR) less than 11%, meaning that either an effect of traps occurs or our trapping effort is insufficient. For this reason, trapping effort was increased (to 1.5 traps•ha -1 ) in sessions 2 and 3. Nevertheless, the probabilities of catches were always low, with a pC of only 1% in session 2 (fish-pond 3) and 7% in session 3.

Concerning fish-pond 4, only one individual was captured during the sessions, so no estimate was calculated. No crayfish were caught in fish-pond 5.

Estimates obtained with open and closed models did not differ significantly (Student's t-test, session 1: p = 0.66, session 2: p = 0.44, session 3: p = 0.25).

> COHORTS OF INDIVIDUALS AND SEX-RATIO

The three sessions differed for the groups of individuals, sex ratios and, in some cases, between sites (Tables IV-VI).

Sex ratio was biased towards males in one site and biased towards females in another site in the same session (Tables IV-VI), for example between fish-ponds 1 and 2. Figures 345show cohorts of individuals caught during the 3 sessions for the fish-pond 3. Fourteen % of berried females were captured in session 1 vs. 3% captured in session 2 and 0% in session 3. The sex ratio was also different, being in favor of females in session 1 but in favor of males in the other sessions. Besides, the number of individuals caught differed between sessions.

Despite the increased trapping effort in sessions 2 and 3, only 37 individuals were captured during the first capture in the second session, against 234 in session 1 and 680 individuals in session 3 (Figures 345). Equivalent differences were also observed in fish-ponds 1 and 2.

> CATCH PER UNIT EFFORT (CPUE)

CPUE gives an average number of individuals per trap during each session. The fluctuations in the average number of individuals per trap followed seasonal variations (Figure 6), ranging from 17.5 individuals in March to 5.5 individuals in April and 32.7 individuals in June in fishpond 3. A decreased CPUE was observed in each fish-pond in April, despite the rise in surface water temperatures.

> TOTAL CRAYFISH-CATCHES

A total of 706 crayfish were captured in fish-pond 1, 1572 in fish-pond 2, 3916 in fish-pond 3 and only 1 in the fish-pond 4, totaling 6 194 P. c l a r k i i captured in the chain of fish-ponds during the three sessions (Tables IV-VI). The sex ratio was 51.3% of males and females comprising 1.1% of berried female.

Mean body length (rostrum-telson) of captured individuals was 10.5 cm for a mean body weight of 33.15 g. The smallest individual captured measured 5 cm and weighed 3 g (fishpond 2 in July, session 3). The largest individual was 14.9 cm long, the heaviest weighed 106 g (fish-pond 3 in March, session 2).

The number of eggs per berried female averaged 90, with a maximum of 339 eggs (session 1, fish-pond 3).

DISCUSSION

Baited traps and mark-recapture techniques are commonly used to estimate the population size of crayfish, excluding juveniles, which cannot be captured due to the large mesh size [START_REF] Maguire | Estimation of noble crayfish (Astacus astacus L.) population size in the velika Paklenica stream (Croatia)[END_REF]; indeed, we caught only crayfish larger than 5 cm. The marking technique that we adopted was suitable to have an estimate during a short period (to avoid loss of marks). Similar techniques have been used in other studies on the same species, as in Brazil by Da [START_REF] Silva | Population size estimation of the exotic crayfish Procambarus clarkii (Girard) (Crustacea, Decapoda, Cambaridae) in the Alfredo Volpi City Park, São Paulo, Brazil[END_REF]. The estimate we obtained shows changes between sessions, which may suggest the intervention of a seasonal effect in the population size. It would be preferable to conduct trapping in late winter (with rising temperatures) and summer (with high temperatures) to possibly detect periods of increased activity of crayfish. Also, during the 3rd session marked crayfish were captured in the ditches between fish-ponds, which indicated that crayfish can migrate from one fish-pond to another, at least during June-July. This proves that it is important to control the whole chain. Session 2 appeared to be not useful in this study, because of the low numbers of individuals caught compared to the two other sessions (Figure 6, CPUE). The number of crayfish captured decreased despite the increase in trapping effort (trap density from 1 to 1.5 ha -1 ).

Several berried females were captured during session 1 (March), but only one during session 2 (April). In France, P. c l a r k i i is considered to reproduce from June to September, except in southwestern France where it reproduces from May to December [START_REF] Nepveu | Jeu de fiches descriptives des espèces animales exotiques et indigènes susceptibles de proliférer dans le bassin Artois-Picardie : Procambarus clarkii[END_REF]B a l d r y , 2007).

Few juveniles (defined as <6 cm of lenght), were captured during all sessions and in all sites.

Cohort analysis (Figures 345) shows that juveniles were present mostly during session 3 and in small frequencies (3%). As said above, this result may be biased by the larvae passing through the mesh of the traps. Capture probability (pC) was not sufficiently high in all sessions. For fish-pond 1, pC was low but constant. The lowest pC was obtained for fish-pond 3 during session 2 (less than 1%): this fish-pond is used for angling and the bait used by fishermen may attract crayfish, being thus a possible source of disturbance.

Cohorts of individuals can differ, depending on either session or fish-pond (Tables IV-VI).

These differences may explain the different estimates of numbers that were most relevant at sessions 1 and 3. Sex ratio differed between fish-ponds, as a probable function of sampling periods. A study conducted in an Italian lake [START_REF] Dörr | Biology of Procambarus clarkii (Girard, 1852) in Lake Trasimeno[END_REF] revealed changes in P. c l a r k i i 's sex ratio over 11 months of observation. In April, they found that sex ratio was in favor of females, in contrast to the results of our study in which sex ratio was most often in favor of males. However, a sex ratio biased towards males was seen in June-July. [START_REF] Scalici | Population structure and dynamics of Procambarus clarkii (Girard, 1852) in a Mediterranean brackish wetland (Central Italy)[END_REF] discussed the difficulties encountered in explaining such variability in sex ratio, as reproduction, incubation, burrowing and recruitment could all differ among introduced populations [START_REF] Scalici | Structure and dynamics of an invasive population of the red swamp crayfish (Procambarus clarkii) in a Mediterranean wetland[END_REF]L i g a s ,2008). Similarly, [START_REF] Ligas | Population dynamics of Procambarus clarkii (Girard, 1852) (Decapoda, Astacidea, Cambaridae) from southern Tuscany (Italy)[END_REF] observed that in southern Tuscany the sex ratio of a P. c l a r k i i population was extremely variable both geographically and seasonally. We have seen that sex ratio varies among fish-ponds in the same period and among periods in the same fish-pond. Besides, our study has shown that each fish-pond has its peculiarities. It is therefore necessary that trapping should be made several times at different seasons and different sites.

To conclude, trapping effort was not suitable in all the fish-ponds here analyzed, particularly in the case of the larger fish-ponds. Nevertheless this study adds some interesting results

demonstrating the plasticity of P. c l a r k i i . If trapping effort were to be increased, the protocol would be more suited to small fish-ponds (surface water < 2 ha), while in large fish-ponds it may be necessary to increase considerably the numbers of traps, with concomitantly increased problems in monitoring.

2( 1 )

 1 Université de Poitiers, Laboratoire Écologie & Biologie des Interactions, Équipe Écologie Évolution Symbiose, UMR CNRS 7267, 40 avenue du Recteur Pineau, 86022 Poitiers Cedex, France (2) Parc naturel régional de la Brenne, Maison du Parc -Le Bouchet, 36300 Rosnay, France

Upstream

Figure 2

 2 Figure 2Location of individual tags.

  Figure 3Trapped crayfish during the first session in the fish-pond 3. Cohorts of individuals and sex-ratio S-r: number of male over the total number ofindividuals. f = female; m = male; bf = berried female; total = total caught individuals.

  Figure 5Individuals caught during the third session in the fish-pond 3. With the same legend and jf = juvenile female; jm = juvenile male.

Table I

 I Estimates of population size, first period (18 to 30 March 2010) with a trap density of 1 ha -1 .

		MARK software	SE	CI	CV	Capture
		Population	(standard	(confidence	(coefficient	probability pC (%)
	Fish-ponds	estimate (Nt)	error)	interval 95%) variation %)	Recapture
		closed captures				probability pR (%)
	Fish-pond 1	Nt = 185	40	130-292	22	pC = 12
	(2 ha)
	Fish-pond 2 (3 ha)	Nt = 452	54	377-597	12	pC = 23 pR = 11
	Fish-pond 3	Nt = 2569	206	2209-3021	8	pC = 8
	(13 ha)

Table II

 II Estimates of population size, second period (19 to 28 April 2010) with a trap density of 1.5 ha -1 .

		MARK software	SE	CI	CV	Capture
		Population	(standard	(confidence	(coefficient	probability
	Fish-ponds	estimate (Nt)	error)	interval 95%)	variation %)	pC (%)
		closed captures
	Fish-pond 1	Nt = 253	53	178-393	21	pC = 10
	(2 ha)
	Fish-pond 2	Nt = 828	210	526-1379	25	pC = 5
	(3 ha)
	Fish-pond 3	Nt = 9488	3505	4786-19 265	37	pC = 1
	(13 ha)
	Table III
	Estimates of population size, third period (28 June to 9 July 2010) with a trap density of 1.5 ha -1 .
		MARK software	SE	CI	CV	Capture
		Population	(standard	(confidence	(coefficient	probability
	Fish-ponds	estimate (Nt)	error)	interval 95%)	variation %)	pC (%)
		closed captures
	Fish-pond 1	Nt = 952	37	885-1029	4	pC = 14
	(2 ha)
	Fish-pond 2	Nt = 3546	298	3025-4197	8	pC = 7
	(3 ha)
	Fish-pond 3	Nt = 24611	2330	20 495-29 669	10	pC = 7
	(13 ha)

Table IV -

 IV VITotal crayfish catches with different cohorts of individuals and the sex-ratio. With f = female; m= male; bf = berried female; jf = juvenile female; jm = juvenile male; total = total captured individuals. Sex-ratio: number of male over the total number of individuals.

	Fish-pond 1	1st capture	1st recapture			2nd recapture			3rd recapture		To t a l	Sex-ratio
	Session 1	10 f	4m	10 f	15 m	2bf	10 f		8m		3bf	16 f	8m		1bf	87	0.40
	Session 2	7f	11 m	12 f	27 m	10 f		23 m		1jf	8f		8m		107	0.64
	Session 3	58 f	60 m	92 f	51 m	1jm	67 f	63 m	4jm	1jf	49 f	63 m	1jm	2jf	512	0.47
	Fish-pond 2		1st capture		1st recapture			2nd recapture		3rd recapture	To t a l Sex-ratio
	Session 1	37 f	79 m	1bf	30 f	40 m		3bf 52 f		31 m	1bf	40 f		39 m	353	0.54
	Session 2	12 f	38 m	17 f	32 m	11 f		35 m	2jm	7f	17 m	2jf	173	0.72
	Session 3	99 f 139 m 16 jm 12 jf 117 f 164 m 21 jm 22 jf 78 f 82 m 24 jm 24 jf 96 f 108 m 29 jm 15 jf 1046	0.56
	Fish-pond 3		1st capture		1st recapture			2nd recapture		3rd recapture	To t a l Sex-ratio
	Session 1	127 f	74 m	33 bf 100 f	46 m	13 bf 180 f		70 m	16 bf 169 f	71 m	4bf 903	0.29
	Session 2	15 f	21 m	1bf	46 f		49 m		97 f	68 m	55 f		57 m	409	0.48
	Session 3	316 f 344 m 7jm 13 jf 311 f 345 m 17 jm	4jf	281 f 326 m 13 jm	1jf	253 f 355 m 16 jm 2jf 2604	0.55

ACKNOWLEDGEMENTS

We thank the whole team of the "Parc naturel régional de la Brenne" and especially the Park officers for their help during our field investigation. Thanks are also due to the staff of "Réserve Naturelle Nationale de Chérine" and particularly to Zoey Owen-Jones for giving advice concerning the MARK software. We are indebted to Julian D. Reynolds for his helpful suggestions towards improvement of this paper.


Cécile Bessou
email: cecile.bessou@cirad.fr

Simon Lehuger

Benoit Gabrielle

Bruno Mary

Benoît Gabrielle

Using a crop model to account for the effects of local factors on the LCA of sugar beet ethanol in Picardy region, France

Keywords: Biofuel, Ethanol, Sugar Beet, Local LCA, Greenhouse Gases, Agricultural Practices, Process-based Model, CERES-

Background. The results of published Life Cycle Assessments (LCAs) of biofuels are characterized by a large variability, arising from the diversity of both biofuel chains and the methodologies used to estimate inventory data. Here, we suggest that the best option to maximize the accuracy of biofuel LCA is to produce local results taking into account the local soil, climatic and agricultural management factors.

Methods. We focused on a case-study involving the production of first-generation ethanol from sugar beet in the Picardy region in Northern France. To account for local factors, we first defined three climatic patterns according to rainfall from a 20-year series of weather data. We subsequently defined two crop rotations with sugar beet as a break crop, corresponding to current practice and an optimized management scenario, respectively. The six combinations of climate types and rotations were run with the process-based model CERES-EGC to estimate crop yields and environmental emissions. We completed the data inventory and compiled the impact assessments using Simapro v.7.1 and Ecoinvent database v2.0.

Results. Overall, sugar beet ethanol had lower impacts than gasoline for the abiotic depletion, global warming, ozone layer depletion and photochemical oxidation categories. In particular, it emitted between 28 and 42% less greenhouse gases than gasoline. Conversely, sugar beet ethanol had higher impacts than gasoline for acidification and eutrophication due to losses of reactive nitrogen in the arable field. Thus, LCA results were highly sensitive to changes in local conditions and management factors. As a result, an average impact figures for a given biofuel chain at regional or national scales may only be indicative within a large uncertainty band.

Conclusion

. Although the crop model made it possible to take local factors into account in the life-cycle inventory, best management practices that achieved high yields while reducing environmental impacts could not be identified. Further modelling developments are necessary to better account for the effects of management practices, in particular regarding the benefits of fertiliser incorporation into the topsoil in terms of nitrogen losses abatement. Supplementary data and modelling developments also are needed to better estimate the emissions of pesticides and heavy metals in the field.

Introduction

The development of renewable energy sources has recently been fostered and promoted as an alternative to the use of fossil resources to mitigate greenhouse gas (GHG) emissions and climate change worldwide [START_REF] Ipcc | Summary for Policymakers[END_REF].

While no single renewable energy source may claim to be the perfect solution, it is their best combination in relation to local resources that may lead to a carbon neutral energy mix. Among these renewable sources, biofuels have been largely promoted worldwide. In Europe, the renewable directive (2009/28/EC, European Commission 2009) aims at substituting 10% of its fossil fuel consumption for transport with biofuels by 2020. In order to be eligible for this share and to benefit from fiscal incentives, biofuels should comply with a set of sustainability criteria, including minimum GHG savings of 35% compared to equivalent fossil fuels. These criteria were imposed to ensure a net benefit in terms of environmental impacts with biofuels, following the controversy on their life-cycle GHG emissions [START_REF] Quirin | CO 2 Mitigation through Biofuels in the Transport Sector. Status and Perspectives[END_REF][START_REF] Farrell | Ethanol Can Contribute to Energy and Environmental Goals[END_REF].

Life Cycle Assessment (LCA) is the most commonly-used framework to assess the environmental impacts of products throughout their life cycle, since its holistic approach makes it possible to avoid pollution trade-offs across the life-cycle stages or impacts. However, the complexity of biofuel chains has evidenced some limits of this methodology, in particular because system boundaries are variable across studies, and because the assumption that emissions are proportional to inputs is often violated for field emissions. These emissions result from complex biogeochemical processes that are strongly dependent on local soil, climatic and management factors. For instance, the emissions of nitrous oxide (N 2 O), a gas with a global warming potential 298 times larger than CO 2 [START_REF] Forster | Changes in Atmospheric Constituents and in Radiative Forcing[END_REF]), depend on a number of the above-mentioned factors and are therefore highly variable at the plot scale [START_REF] Parkin | Soil microsites as a source of denitrification variability[END_REF][START_REF] Mosier | Nitrous oxide emissions from agricultural fields: Assessment, measurement and mitigation[END_REF][START_REF] Farquharson | Concepts in modelling N 2 O emissions from land use[END_REF]. As a consequence, the linear regression model used in the IPCC Tier 1 (2006) estimation method, which only accounts for soil N input rates should only be expected to provide an order of magnitude for these emissions, associated with a wide uncertainty band (-70% to +300%;IPCC, 2006). Also, many studies on biofuel chains are focused on specific impacts (e.g. global warming) rather than the range of impacts that may be potentially addressed by LCAs [START_REF] Quirin | CO 2 Mitigation through Biofuels in the Transport Sector. Status and Perspectives[END_REF][START_REF] Blottnitz Von | A review of assessments conducted on bio-ethanol as a transpotation fuel from a net energy, greenhouse gas, and environmental life cycle perspective[END_REF], thus conveying an incomplete picture of biofuels sustainability. Finally, given the expanding demand for biofuels and the limited available land area, concerns have risen that biofuels may lead to land use changes, whose impacts

are not yet fully assessed within the classical (attributional 1 ) LCA framework [START_REF] Reinhard | Global environmental consequences of increased biodiesel consumption in Switzerland: consequential life cycle assessment[END_REF]. Because of all these limitations of LCA, confusion and controversy arose on the environmental interest of biofuels [START_REF] Crutzen | N 2 O release from agro-biofuel production negates global warming reduction by replacing fossil fuels[END_REF][START_REF] Fargione | Land Clearing and the Biofuel Carbon Debt[END_REF]Bessou et al. 2010a).

Assessing the environmental impacts of a biofuel chain with enough accuracy so that a decision can be made with respect to the above-mentioned sustainability criteria requires: 1) the definition of common system boundaries and methodological choices; and 2) a reduction of the uncertainty of inventory data, which may be achieved by more accurate emission models. There are currently ongoing international projects seeking to harmonize the LCA methodology (PAS2050 by BSI 2008; ISO 14067 2 ; ILCD by European Commission-JRC-1 An attributional LCA is a descriptive LCA assessing the impacts of an added produced Functional Unit = FU (status-quo + FU) without considering the changes induced by this added FU as it is done in a consequential or change-oriented LCA (FU + consequential modifications of the initial state due to the added FU). 2 ISO 14067 still under-development IES 2011), while past studies have dealt with system boundaries for biofuel chains [START_REF] Quirin | CO 2 Mitigation through Biofuels in the Transport Sector. Status and Perspectives[END_REF][START_REF] Farrell | Ethanol Can Contribute to Energy and Environmental Goals[END_REF]. Other studies also used agro-ecosystem models to generate input data for the life-cycle inventory, thereby reducing the uncertainty of emissions from agricultural fields [START_REF] Gabrielle | Life-cycle assessment of straw use in bio-ethanol production: a case-study based on deterministic modelling[END_REF][START_REF] Langevin | Inclusion of the variability of diffuse pollutions in LCA for agriculture: the case of slurry application techniques[END_REF]. Nevertheless, these model outputs were either specific to a set of particular sites (for the latter studies) or related to country averages in terms of management data (JRC 2008;[START_REF] Smeets | Contribution of N(2)O to the greenhouse gas balance of first-generation biofuels[END_REF]). When dealing with biofuels, data representative from the feedstock supply area should be sought.

Our objective was hence to produce such a 'local LCA' for first generation ethanol from sugar beet, and to test the sensitivity of its results to changes in local environmental or management factors. We used the Picardy region in Northern France as a case-study, involving sugar beet as a feedstock. Sugar-beet has been produced on a large scale for decades in this area. To account for in the effect of local factors, we simulated crop growth and N emissions to the environment with the dynamic agro-ecosystem model CERES-EGC [START_REF] Gabrielle | Process-based modeling of nitrous oxide emissions from wheat-cropped soils at the subregional scale[END_REF].

This works addresses regional variations and data quality but does not address inconsistency in system boundary and the linearity assumptions imposed on the parameters not modelled.

Material and Methods

Goal and system boundary

The aim of this study was to conduct a full-blown attributional Life Cycle Assessment of the production and combustion of first-generation ethanol from sugar beet. We compared ethanol from sugar beet with its fossilbased equivalent, gasoline, to examine the benefits of substituting the latter with bio-ethanol, however strictly in an attributional framework. System boundaries were Well-to-Tank, i.e. including all flows of resources, energy and pollutants from the extraction of raw materials up to ethanol dehydration. The chosen functional unit was 1 MJ of biofuel energy content, using the low heating value (LHV) of ethanol. This was calculated from the potential energy that would be delivered by the fuel at the refinery gate if its combustion in the car engine was complete. Since we focused here on the impacts of biofuel production and more specifically on its agricultural feedstock, we did not include the steps of fuel blending and distribution to the filling station, as both would be similar between the two fuels. Energy embedded in farm machinery and capital equipment was included. On the contrary, the caloric intake and transportation of farm workers were not included [START_REF] Farrell | Ethanol Can Contribute to Energy and Environmental Goals[END_REF]. Missing reliable inventory data prevented a complete inventory of some packaging, enzyme and yeast inputs for the fermentation processes. In terms of land use, we considered that sugar-beet was grown on existing crop land, so that no land-use changes occurred (PAS2050 by BSI 2008). From an attributional perspective, we assessed the impacts of producing sugar beet ethanol without accounting for any possible displacement of other crops to compensate for the resulting reduction in sugar production. This approach was in accordance with the underlying assumption that there is an over-production of sugar in this region, as a result of the sugar reform in the European Union. We did not account for biogenic CO 2 fixation and emissions since no emissions from land use change were considered. The system boundaries for the two fuel chains are presented Figure (1).

The system was extended to take into account savings due to the substitution by co-products as recommended by LCA-ISO standards (ISO 14044:2006). Over the year, sugar beet ethanol is produced from different raw materials: sugar-beet juice and fermentation slurry during the campaign (in the 3 months following the harvest of sugar-beet crops), and syrup and slurry during the remaining time interval (inter-campaign). The inputs and outputs of the refinery-distillery processes were calculated based on the mass balances of the processes from raw material to the various final products over the year. The co-products of sugar beet ethanol considered included pulp, lime-carbonation residue, vinasse and sugar. For each of these co-products, alternative chains were designed according to local practices and the expertise of professionals from the region. The avoided production of mineral fertilisers was calculated based on the chemical composition of co-products and their mineralization rates, depending on the site and time of spreading [START_REF] Decloux | Interest of electrodialysis to reduce potassium level in vinasses. Preliminary experiments[END_REF][START_REF] Itb | Revue technique sur la culture de betterave en France[END_REF]. The equivalent of pulp was silage maize, given the close dry matter contents (around 25% DM) and low protein values of the two products that leads farmers to use them indifferently in feeding rations (Comité National des Co-Produits/ADEME 2002).

In state of the art of sugar beet sugar-and-ethanol production plants in France, sugar represents the main output.

For the allocation between sugar and ethanol, we intrinsically used a mass-based procedure through the mass balance calculation. It is justified by the fact that the only locally-available substitute for sugar involved the same sugar-beet chain. Given this case, the use of system expansion and from mass-based allocation would give the same results.

Temporal and geographical scopes

LCA typically provides a "snapshot" of the studied systems at a given point in time. Here, the reference period for the data related to industrial processes was the 2000-2010 time interval, i.e. involving state-of-the-art technologies currently in use at commercial level. No prospective scenarios involving possible near-term improvements over these technologies in terms of energy efficiency or pollution abatement were analysed. In particular, we did not consider any possibility of capturing fermentation-derived CO 2 . The reference period for agricultural productions was the 1988-2009 time interval to account for sufficient climate variability in the modelling work. Crop management data were representative of a more recent period running from 2000 to 2010.

The agricultural production site considered was the INRA Agro-Impact experimental station at Estrées-Mons in the Picardy region (49°80'N, 3°60'E), where the mean annual precipitation and air temperature are 667 mm and 9.6°C respectively (Guérif et al. 1996). The size of the experimental site is 170 ha. The annual total sugar beet area represents 15 ha. The soil is an Orthic Luvisol (FAO, 1998), which represents 20% of the arable soils in this region [START_REF] Gagnaire | Une approche économique, énergétique et environnementale du gisement et de la collecte des pailles et d'une utilisation pour les filières éthanol[END_REF]. In order to better capture the emission variability due to the local production factors, climatic and agricultural management data were collected from this station over 21 years. In this area, sugar beet is a common break crop rotated with wheat and maize. None of these crops are usually irrigated.

Life cycle inventory of the agricultural production

Sugar beet cropping system

Field emissions are linked to physico-chemical and microbial transformations in soils. They can be classified as direct or indirect according to their occurrence in the causal chain from the application of agricultural inputs to the final impacts incurred. For instance, primary emissions of leached nitrate are defined as direct field emissions, whereas N 2 O emissions ensuing from this primary emitted nitrate but occurring beyond the agricultural field itself are considered indirect. Field emissions are related to reactive compounds either applied to the field as fertilisers and pesticides, or originating from the mineralization of crop residues. Most fieldapplied fertilisers and pesticides are managed over one crop cycle. However, some fertilisers such as lime may be managed at the crop rotation level. In our case study, lime was managed over a 4-crop rotation, hence one fourth of the input rate and spreading costs were allocated to sugar beet.

In order to account for all field emissions, we considered sugar beet as part of the sugar beet-winter wheatmaize-winter wheat rotation, which is common in the area. This rotation was implemented and monitored at the study site for more than 20 years. We simulated this rotation with CERES-EGC during the 1988-2009 time period, meaning that each run consisted of 5 repetitions of the rotation. To obtain an occurrence of sugar-beet for all individual years of the 1988-2009 period, we shifted the starting year from 1988 to 1991, resulting in four model runs. For all crops, residues were incorporated by deep ploughing. Emissions due to residue mineralization and nitrate leaching were allocated to each crop of the rotation by considering that N mineralization was the main source of inorganic N in between two growing seasons. We first defined the time interval for this allocation as the period running from the sowing of the crop of interest to the first fertiliser application on the following crop. In terms of tillage, each crop was thus allocated the incorporation of its harvest residues. Since the studied rotation included some 8 months of bare soil between wheat harvest and the sowing of sugar beet or maize, we allocated part of this bare soil period to these spring crops. This discrimination resulted in a final splitting of the whole rotation into four one-year periods, starting and stopping on February 15th each year. N-inputs were calculated from a balance of crop requirements and supply from soil, including residue returns from the preceding crops. Hence, the green residues from sugar beets left in the field after harvest were not considered as a co-product of ethanol in the LCA.

The current crop rotation is not optimal in terms of soil cover. Introducing a cover crop between winter wheat and sugar beet, for instance, may reduce the bare soil period by some 85 days [START_REF] Itb | Revue technique sur la culture de betterave en France[END_REF]. This cover crop is thereby expected to reduce N-losses by taking up N prior to the winter drainage period, and to make it available to the following crop after the cover crop has been ploughed in. The combined effect of cover crop on reducing nitrate leaching and increasing efficiency of N-uptake by the crops can be significant over the years [START_REF] Constantin | Cumulative effects of catch crops on nitrogen uptake, leaching and net mineralization[END_REF]. N-losses may be further reduced by adjusting fertiliser N management. In particular, the soil incorporation of the first fertiliser N application together with the seeds can save as much as 15 kg N ha -1 yr -1 (ITB 2002). Beside our baseline scenario of the current rotation, we hence tested an "optimized rotation", consisting of 2 aspects: 1) the introduction of a cover crop within the rotation between winter wheat and sugar beet or maize; and 2) the incorporation of N inputs upon sowing allowing the above mentioned savings of 15 kg N ha -1 yr -1 in both sugar beet and maize fields. In the study, we extended the cover crop, i.e. mustard, from August 15 until January 5, i.e. 144 days, so that it would be killed by the frost without requiring herbicides. The consequences for sugar-beet were accounted for through the resulting decrease of N losses between February 15th and the sowing in April as simulated by the crop model. The costs of cover crop establishment, i.e. sowing and mechanical destruction were equally split between sugar beet, winter wheat and maize. Annual P and K fertilisation rates in sugar beet plots were 70 kg ha -1 P 2 O 5 , and 110 kg ha -1 K 2 O. These inputs, as well as pesticides and tillage operations (except for the introduction of the cover crop) did not vary between the two management scenarios. N-fertiliser rates and modelled yields are shown in Table 1.

Modelling of field emissions

To take into account local soil and climatic factors in the LCA, we modelled feedstock production with the agroecosystem model CERES-EGC [START_REF] Gabrielle | Process-based modeling of nitrous oxide emissions from wheat-cropped soils at the subregional scale[END_REF]). This process-based model simulates crop growth by considering the type of soil, climate conditions, plant variety, and management practices at the field scale. It also predicts substance losses outside the ecosystem such as nitrate leaching, ammonium volatilization [START_REF] Génermont | A mechanistic model for estimating ammonia volatilization from slurry applied to bare soil[END_REF], and nitrous oxide emissions through nitrification and denitrification which are predicted with the NOE sub-model [START_REF] Hénault | Predicting in situ soil N 2 O emission using NOE algorithm and soil database[END_REF]. In order to improve its accuracy, we implemented the NOE2 submodel (Bessou et al. 2010b) in CERES-EGC and proceeded to a Bayesian calibration of the 22 parameters of NOE2. This calibration makes it possible to reduce significantly the spread in parameter distribution and the subsequent uncertainty on N 2 O emissions by updating these distributions against a priori probability distributions of parameter values gathered from other sites [START_REF] Lehuger | Bayesian calibration of the nitrous oxide emission module of an agro-ecosystem model[END_REF]). This calibration reduced the Root-Mean Square Error on daily and annual fluxes by 15% and 63% respectively when compared to the uncalibrated simulations (Fig. 2), based on experimental data collected in our study site over sugar-beet (Bessou et al., 2010b). Calibrated parameters were then used for the simulations of sugar beet cropping system with CERES-EGC [START_REF] Leviel | Evaluation of risks and monitoring of nitrogen fluxes at the crop level on the Romanian and Bulgarian plain[END_REF][START_REF] Leviel | CERES-beet, a prediction model for sugar beet yield and environmental impact[END_REF]. Despite our efforts, CERES-EGC still underestimated emissions in 2008-2009 due to several combined factors (Bessou et al. 2010b). Other sources also showed a marginal error of roughly 20% with CERES-EGC [START_REF] Hénault | Predicting in situ soil N 2 O emission using NOE algorithm and soil database[END_REF][START_REF] Gabrielle | IMproved Assessment of the Greenhouse gas balance of bioeNErgy pathways (IMAGINE)[END_REF]). This error remains lower than the uncertainty associated with IPCC factors.

We used daily climate data from a weather station located on site, and input soil and management data for the 21-year simulation period . According to climate records over this period and annual rainfall, we identified 3 climate patterns: 1) median years (R50; there were 9 years in this class in the simulation period), 2) inferior quartile years, "drier" than median years (R25; 5 years), and 3) superior quartile years, "wetter" than median years (R75; 5 years) (Fig. 3). Average values (arithmetic means) of modelled yields and emissions were calculated for the 6 combinations of rotation management and climatic years, noted R25, R50, and R75 for the baseline crop rotation, and R25 optim, R50 optim, and R75 optim for the optimized crop rotation. The resulting data are given in Table 1, and were fed into the life cycle inventories. An overview of the study approach and tested parameters is given in Figure 4.

Field emissions not modelled with CERES-EGC

Changes in the spatial and temporal scales between direct and indirect field emissions make it particularly difficult to assess indirect emissions. Mechanisms are poorly characterized and indirect emissions are therefore not modelled by CERES-EGC. We thus used IPCC coefficients as an alternative to estimated indirect emissions, and also to estimate CO 2 emissions due to lime application.

Methane emissions are not considered by CERES-EGC, but were ignored since the soil was well-drained and unlikely to be a net emitter or consumer of CH 4 [START_REF] Biois | Élaboration d'un référentiel méthodologique pour la réalisation d'Analyses de Cycle de Vie appliqués aux biocarburants de première génération en France[END_REF]. Finally, we accounted for heavy metals brought to the soil by fertilisers following the corresponding inventory method of Ecoinvent. Due to the lack of reliable data on the heavy metals brought to the soil in pesticides or exported with the harvested biomass, we decided not to account for them. The modelling of direct and indirect emissions linked to agricultural productions in this study in summarized in Table 2, also showing the differences with their respective models in the Ecoinvent3 documentation [START_REF] Nemecek | Life Cycle Inventories of Agricultural Production Systems[END_REF].

Life cycle inventory of the industrial phase

Background data on primary energy sources, infrastructures, machines, industrial production and disposal were mainly taken from Ecoinvent v2.0 databases (Swiss Centre for LCI). We used the data provided on the average French mix for electricity from the grid, as well as European average data for crude oil supply, oil refinery and energy embedded in infrastructures and machines. Transports of inputs to the agricultural field encompassed that of co-products from the refinery to the field, as well as saved transports for the products they substituted, except for maize silage which was produced on farm. Transport distances corresponded to current practices at the study site: 65 km for the supply of agricultural inputs to the farm, 22 km for the transport of sugar-beet roots to the sugar refinery, and 200 km for the other inputs of the refinery. Conversion data was taken from the Arcis-sur-Aube sugar refinery-distillery, which is located in the Champagne-Ardennes region neighbouring Picardy. This refinery-distillery is representative of the state of the art of such production units in France (ADEME 2010).

Impact characterization

We used the CML 2000 Baseline v2 method [START_REF] Guinée | Handbook on LCA, Operational Guide to the ISO Standards[END_REF] for the impact characterization, similarly to the reference LCA study commissioned by the French Environment Agency (ADEME, 2010). CML 2000 encompasses the impact categories listed in Table 3. Impact indicators were not subsequently normalized or weighted since these steps are partly subjective and uncertain, and hamper the interpretation of the LCA results [START_REF] Guinée | Handbook on LCA, Operational Guide to the ISO Standards[END_REF]. Weighting in particular is not allowed by LCA-ISO standards when publicly comparing products, which is our objective here. LCA calculations were carried out with the SimaPro 7.1 software (PRé Consultants bv, NL).

Results and discussion

Biofuel versus fossil fuel

Figure 5 compares the environmental impacts of the production and the pseudo complete combustion of sugar beet ethanol and gasoline (low sulphur grade) on a MJ basis. Six scenarios of sugar beet ethanol productions were compared, corresponding to the six combinations of climate patterns (3) and crop rotations managements

(2). Overall, the impacts of sugar beet ethanol were lower than those of gasoline in four categories: abiotic depletion, global warming, ozone layer depletion, and photochemical oxidation. Conversely, gasoline outranked bio-ethanol for acidification, eutrophication, human toxicity, and fresh water or terrestrial ecotoxicity. Feedstock production contributed more than 75% of total impact indicators for acidification and eutrophication for ethanol, with emissions of reactive N from fertiliser inputs in the field being the top contributors. Despite substantial reduction in nitrate leaching with the optimized rotation (Table 1), field emissions dominated the eutrophication impact. Reactive N also contributed to a large extent to GHG emissions in the field, while agricultural production contributed 25% to 68% of the other impact categories. The industrial conversion processes contributed to a large extent (more than 55%) to abiotic depletion, ozone layer depletion, aquatic ecotoxicity and photochemical oxidation. Across impact categories, transport only contributed to 5 to 10% of total impact indicators.

Sugar beet ethanol produced in Picardy lead to savings of 28-42% greenhouse gases and 20-28% fossil resources compared to gasoline, on a MJ basis. The mean GHG emissions across scenarios amounted to 5.78 10-2 kg CO 2 eq per MJ, corresponding to a 35.7% of GHG saving compared to gasoline. These emissions are larger than the France-wide average than those reported for sugar beet ethanol by ADEME, at 3.04 10-2 kg CO 2 eq MJ-1

(ADEME 2010), but close to the European average value of 5.75 10-2 kg CO 2 eq MJ-1 published by JRC (2008), where sugar beet pulp was also used as cattle feed. Across our 6 feedstock scenarios, the global warming, eutrophication, and human toxicity indicators laid within -51% and +113% of the ADEME study (2010). Global warming impacts were all higher than ADEME (2010) (+80% to +113%), as well as human toxicity impacts (+24% to +52%), while eutrophication impacts were either lower (-51%) or higher (+23%)

depending on the feedstock scenario. However, both studies are not directly comparable due to differences in system boundaries and field emission models, and scope. The ADEME (2010) and JRC ( 2008) estimates apply to national to continental scales and are relevant to public policies at macro-economic level, while our results

were more local and targeted at stakeholders such as farmers or chain operators in the region. The sensitivity of LCA results to local factors highlights the relevance of this local LCA to define strategies at this level.

In our study, the conversion of one-hectare sugar beet provided between 2.60 and 3.97 t ethanol across the scenarios, since ethanol only made up 35% of the total outputs from the sugar refinery-distillery. Should this ratio rise to 100%, as assumed in the JRC study ( 2008), ethanol yields per ha would be nearly twice as high (at 5.78 t ha -1 -ADEME/DIREM, 2002). Because the data collected from the sugar refinery-distillery were aggregated across the ethanol and sugar end-products and both chains were tightly entangled, it was impossible to test such a scenario and subsequently apply an energy-based allocation between ethanol and its remaining coproducts, as recommended in the European Renewable Directive (RED) methodology (2009/28/EC, European Commission 2009). At any rate, this scenario would not be representative of the current situation, since industrial processes have been up to now optimized to reduce energy costs for the combined production of sugar and ethanol during both campaign and inter-campaign periods. Moreover, sugar has a higher added-value than ethanol, making the 100% ethanol unrealistic. To our understanding, this duality was not considered in the RED methodology. Despite its particular configuration, sugar beet ethanol in Picardy would comply with the RED requirement of 35% GHG savings. Further conversion of the current sugar co-product to ethanol would indeed lead to higher ethanol yields per hectare with identical field emissions, and consequently lower GHG emissions per MJ of ethanol. Nevertheless, our results pointed out though that considering local factors, when data is available, might be crucial and more relevant than default parameters from the RED guidelines.

Since assessing the life-cycle GHG emissions of biofuels is essential from a policy standpoint, we examined its sensitivity to the global warming potential (GWP) of GHGs. We found an inconsistency between the value used in the JRC ( 2008) report and that reported in the RED e methodology description (Annex V.C), both cited by the same Directive. This was also reported in the Biograce calculator [START_REF] Ie | Biograce, Harmonised Calculations of Biofuel Greenhouse Gas Emissions in Europe, by Intelligent Energy Europe[END_REF]. These sources used GWP values (for a 100-year horizon) of 23 kg CO 2 eq per kg CH 4 and 296 kg CO 2 eq per kg N 2 O (IPCC 2001) or 25 kg CO 2 eq per kg CH 4 and 298 kg CO 2 eq per kg N 2 O (IPCC 2007). In our calculations, there were actually no discernible differences on the final GHG balances between the 2 sets of GWP values. Using GWPs for a 20-year period (considering higher concerns for immediate consequences and action needs) had a more visible effect. For the R50 scenarios, for instance, the largest differences occurred between the 20-year ( 2007) and 100year ( 2001) perspectives, with GHG emissions of 6.20.10 -2 and 5.70.10 -2 kg CO 2 eq per MJ, respectively. This difference would correspond to either 32.6% or 36.8% greenhouse gas savings compared to gasoline, respectively. We completed this sensitivity analysis by halving the CO 2 emission factor of applied lime, as suggested in the IPCC Guidelines ( 2006), but it only had a marginal effect on GHG budgets. Sugar-beet development is sensitive to pH and to a risk of surface crust in the soil of Estrées-Mons, so that liming must be carefully managed. In our study site, the liming rates were minimal because of regular lime applications in the past. However, in the cases of soils with higher risks of surface crusting or insufficient liming record, rates could easily double and the consequences on global warming impact become more important. This factor should be accounted for while identifying the best locations and managements for sugar-beet farming.

Impact of local production factors

LCA results were sensitive to changes in climatic conditions during biomass production. As detailed in Table 1, local production factors influenced fresh matter yields, but also all N-emissions that contribute to several impact categories. Consequently, local factors also had an influence on the final impacts. Compared to the sugar yields recorded on site over the 1990-2008 period, modelled yields were higher but with a larger standard deviation across years, but within the same order of magnitude as the observed yields. The observed yields as averaged over the drier, median and wetter years amounted to 78, 78 and 81 tonnes per hectare (standard deviations: ± 11-13%), compared to modelled yields of 76, 95, and 96 tonnes per hectare, respectively (standard deviations: ± 15-44%) (Table 1). Climatic patterns affected impacts across categories and management scenarios with a maximum relative difference of about 60% in terms of GHG savings and an average difference per impact around 15% (Fig. 5). The largest difference occurred with eutrophication between the R25 and R50 climates.

Drier years (R25) were more radically distinct from the other climates, and had the largest standard deviations, indicating a higher uncertainty in dry years. On a hectare basis (Fig. 6), the impacts of sugar beet ethanol under the R25 climatic pattern were lower than for the other patterns, whatever the impact category. Drier years resulted in lower direct emissions of all N-compounds and subsequent indirect emissions, leading to reductions in the eutrophication, acidification, and global warming impacts. However, drier years (R25) were also characterized by lower biomass yields and ethanol ethanol production per hectare. Ethanol yields (kg) were 20% lower on average for the R25 scenario compared to R50 and R75, the latter showing similar ethanol yields per hectare (±2%). On a MJ basis (Fig. 5), R25 ethanol had therefore higher environmental impacts, except for eutrophication, which was the most sensitive to rainfall patterns. In the drier years (R25), nitrate leaching was on average eight times lower than in the other years. Between the R50 and R75 scenarios, differences also appeared for the acidification and eutrophication impacts, which emphasize their sensitivity to climatic conditions.

When comparing baseline and optimized cropping systems on a MJ basis, the impact reductions between ethanol and gasoline varied from 10% to 45% across impacts (Fig. 5). The largest difference occurred for eutrophication between R50 and R50 optim. The introduction of a cover crop reduced nitrate leaching more efficiently during median years (R50 optim) than during drier (R25 optim) or wetter years (R75 optim). Across impact categories and scenarios, the optimized rotations had higher impacts, except for acidification (in the drier years) and eutrophication (in the median to wet years). However, robust conclusions on the comparison of both rotations could not be drawn because of the trade-off between yield levels and field emissions, resulting in inconsistent rankings across impact categories. On average, yields were 16% lower with the optimized scenarios because of the reduced fertiliser inputs. The lower yields counter-balanced the lower field emissions occurring with the optimized system, which is a result of the strategic choices behind the optimization of the crop rotation. The latter implicitly considered land area as the main constraint for resource preservation: reducing fertiliser inputs per hectare aimed at abating N losses, while shortening the period under bare soil was expected to reduce nutrient losses. Yield optimization was therefore not a major factor in the management design although they certainly were in the LCA. This emphasizes the need to factor in ecological intensification targets when designing agricultural strategies, to avoid potential extensification and consequential increases in agricultural land area where land area is a limiting factor. This study, however, does not consider consequential impacts.

The lower yields with optimized systems may be also partly attributed to a modelling artefact. Indeed, the relative benefit from topsoil fertiliser incorporation at sowing could not be modelled since CERES-EGC considers that fertilizer N is always incorporated into the topsoil. It is thus likely that the baseline scenario without incorporation should have higher nitrogen losses, in particular through ammonia volatilization. On the contrary, the impact of introducing a cover crop was better modelled, since nitrate leaching was reduced by more than 50% in R50 and R75 compared to initial crop rotation (Table 1). Differences in LCA results between the baseline and optimized rotations were hence the largest for the eutrophication indicator (Fig. 5 &6).

Eutrophication and acidification were the only categories for which optimized rotations performed better than baseline ones on both hectare and MJ bases, i.e. the reduction of impacts compensated for reduced yields. Across the three optimized scenarios, R50 optim had the least global impacts when considering both hectare and MJ bases. Despite the above shortcomings in the modelling of management effects of the optimized rotation, standard deviations were overall smaller for optimized scenarios than for the baseline ones. Moreover, score differences per category were larger for the baseline rotation than for the optimized one. Hence, the optimized rotation might help reduce risk of high environmental impacts in case of variable climatic conditions.

Modelled field emissions were within the same order of magnitude as those calculated with the coefficients from IPCC Tier 1 or Ecoinvent, although generally slightly lower for N 2 O and NO 3 -, and larger for NH 3 and NO x emissions (Table 1). Compared to our modelled results, IPCC Tier 1 tended to over-estimate these emissions, whereas Ecoinvent modelling would lead to much lower figures. Using inventory data output by the CERES-EGC model made it possible to better assess the combined effects of local soil, climate and agricultural management factors than using default values per rotation scenario calculated with simpler methodologies.

Conclusions

The local LCA reported here provided detailed assessments of potential environmental impacts of ethanol from sugar beet at Estrées-Mons in the Picardy region in Northern France. Effects of local soil types, climatic conditions and management practices were visible for all impact categories and on both hectare and MJ bases.

They emphasized the need to take into consideration these local factors when evaluating biofuel chains to provide guidance in their implementation. The environmental performance of biofuels was highly variable according to management and climatic conditions, within a span that could include threshold values such as the 35% GHG binding savings of the RED directive for instance. The magnitude of these effects was particularly important for the eutrophication and acidification impacts, which are strongly dependent on field emissions and hence local conditions.

Greenhouse gas savings of sugar beet ethanol compared to gasoline ranged between 28% and 42% with a mean global warming indicator across scenarios of 0.0578 kg CO 2 eq per MJ, i.e. 35.7% of GHG savings. These 35.7% savings might be critical because they are closed to the limit of 35%, prerequisite of the European Directive (2009/28/EC), and lower than the 50% limit to be enforced in 2017. In the EU Directive, biofuel chain performances were calculated with energy allocation for co-product handling, which might allow for more savings in the sugar beet case. Moreover, this indicator could vary largely according to the time-scale and global warming potentials chosen.

The results on Ozone layer depletion left little scope for discussion here, since the method we used to characterize this impact (Table 3) does not account for any contribution of N 2 O to stratospheric ozone depletion, while it is recognized that N 2 O plays an important part in ozone chemistry [START_REF] Forster | Changes in Atmospheric Constituents and in Radiative Forcing[END_REF]). This should be further investigated in order to reflect better the impacts of the biofuel chains we tested here. We also remained cautious with the ecotoxicity impacts, since we could not account for the complete balance of heavy metals in our agro-ecosystems, or for a likely distribution of pesticides residues in the various environmental compartments. It stresses that despite the holistic nature of LCA, many environmental mechanisms are still not fully understood, nor clearly assessed with the current methodology [START_REF] Mamy | Compared environmental balances of weeding programmes for glyphosate -tolerant and non-tolerant crops[END_REF].

Analysis on both hectare and MJ bases showed important trade-offs between low impact scenarios and low ethanol yields, which made it more complex to define optimal choices in terms of agricultural management. The ranking of the baseline and optimized crop rotations was inconsistent across impacts as a result. It emphasizes the need to factor in ecological intensification targets when designing agricultural strategies, to avoid potential extensification and consequential increases in agricultural land area, especially in situations where land area is a limiting factor. LCAs may play a prominent role in designing such strategies. Climatic years with extreme rainfall patterns (R25 and R75 scenarios) presented the worst impacts, while drier years led to more severe impacts on a MJ basis due to poor yields per hectare. R75 tended to increase several impacts such as eutrophication due to increased nitrate leaching, or acidification and global warming. This effect might be due to nitrogen cycling processes and microbial activities that are generally enhanced in wet conditions.

Overall, the optimized scenarios had lower environmental impacts than the other scenarios, although lower yields counteracted this positive effect to some extent. For eutrophication in particular, optimized rotations would be very beneficial. If the risk of drought or heavy rainfalls were higher, optimized rotations would decrease the risks of high impacts, the indicators of these scenarios varying within a narrower range than those of baseline scenarios.

Examining the sensitivity of LCA results to local factors makes it possible to define the probability distribution of environmental impacts around average results. This approach should provide guidance to decision-makers by identifying climatic and soil configurations that may lead to high environmental impacts. Further model developments would be also needed to improve the process-based modelling of the local factors and notably agricultural practices. In the current version of CERES-EGC, nitrogen-fertilisers are distributed over the first 30 cm and nitrification and denitrification calculated over the first 20 cm with average temperature and water content for two sub-layers across these 20 cm. The discretization of ammonium distribution and soil water and temperature within fine soil layers could improve the accuracy of model estimation (Bessou et al. 2010b). The modelling of N dynamics in soil also deserves further improvements by differentiating between fertilizer incorporation depths and potentially improved sub-routine for N-release from cover crop residues.

In Picardy region, a new potential local factor is land use change. Indeed, experiments have been ongoing since 2006 on comparing the agricultural potential of diverse biofuel feedstock from perennial crops (REGIX project).

In the near future, some of these perennials, such as Miscanthus, may replace or displace sugar beet fields.

Figure 1 :Figure 2 :

 12 Figure 1: Well-to-Tank system boundaries of compared fuel chains

FigureFigure 4 :Figure 5 :

 45 Figure 3: Rainfall patterns

Table 1 :

 1 Key data on the sugar beet production modelled with CERES-EGC; 4 simulations of the crop rotations over 21 years to grow sugar beet every year; R25: mean of 6 years; R50: mean of 9 years; R75: mean of 6 years, with standard deviations into brackets. Emissions calculated with the coefficients from IPCC Tier 1 and Ecoinvent are given in italics for comparison; x is the weighted average of yields modelled with CERES-EGC.

			Baseline rotation				Optimized rotation
		R25	R50	R75	IPCC	Eco-	R25	R50	R75	IPCC	Eco-
					Tier1	invent				Tier 1	invent
	N-fertilization	140	140	140	140	140	125	125	125	125	125
	kg N ha -1
	Mean yields	76	94	96	x=84 x=84	64	79	80	x=70 x=70
	tFM (16% sugar)	(±41%)	(±18%)	(±16%)			(±44%)	(±15%)	(±17%)
	Mean direct N 2 O	1.08	1.34	1.23	1.4	1.72	0.97	1.12	1.16	1.25	1.53
	kg N-N 2 O ha -1 yr -1	(±43%)	(±20%)	(±13%)			(±42%)	(±11%)	(±12%)
	Mean NO 3 -	5.3	43.7	41.5	42	33.6	8.2	15.4	21.3	37.5	30
	kg N-NO 3 -ha -1 yr -1	(±149	(±81%)	(±65%)			(±66%)	(±43%)	(±57%)
		%)
	Mean NO x	0.85	0.80	0.81		0.36	0.71	0.65	0.66		0.32
	g N-NO x ha -1 yr -1 Mean NH 3	(±42%) 5.4	(±14%) 4.9	(±18%) 7.3	14	2.8	(±42%) 3.5	(±11%) 3.3	(±14%) 4.9	12.5	2.5
	kg N-NH 3 ha -1. yr -1	(±63%)	(±84%)	(±38%)			(±59%)	(±93%)	(±33%)

Table 2 :

 2 Modelling of field natural emissions in our case study compared to modelling field emissions in Ecoinvent.

Emissions /kg ha -1 yr -1 Modelled in our case study Modelled in Ecoinvent (Nemecek and Käki 2007) Direct Modelled with CERES-EGC model Modelled with several operational models

	N-N 2 O		Produced via denitrification and nitrification of	1.25% of N-input (less volatilized N) in kg ha -1
			ammonium nitrate as influenced by soil
			temperature, soil water content, soil
			compaction, substrate availability, and
			microbial potentials.
			Source: (Hénault et al. 2005; Bessou et al.	Source: (Schmid et al. 2000)
			2010)
			Modelled range: [0.8 -1% of N-input]	Single value
	N-NO x		0.5% of nitrified N	N-NO x = 21% of N-N 2 O
			Source: (Rolland et al. 2010)	Source: (Schmid et al. 2000)
			Modelled range: [0.5-0.6% of N-input]	Single value
	N-NH 3		Produced via volatilization as influenced by	2% of N-input in kg ha -1
			soil energy balance
			Source: (Gabrielle et al. 2006)	Source: (Asman 1992)
			Modelled range: [2.6-5.2% of N-input]	Single value
	N-NO 3	-	Through leaching as influenced by soil type	24% of N-input in kg ha -1 for sugar beet
			and depth, soil water content, plant uptake
			Source: (Gabrielle et al. 2006)	Source: (Richner et al. 2006)
			Modelled range: [3.7-31.2% of N-input]	Single value
	Direct		Not

modelled with CERES-EGC model but with several operational models Modelled with several operational models

  In kg P ha -1 yr -1 -through leaching in arable land (to groundwater): 0.07 -through run-off in open arable land (to surface water): 0.175*(1+0.2/80)*kg P 2 O 5 -through erosion to rivers (not considered in our case study due to some lack of data) Source:[START_REF] Prasuhn | Erfassung der PO4-Austräge für die Ökobilanzierung SALCA Phosphor[END_REF]

	C-CO 2	From lime application 12% of C-CaCO 3 yr -1	Not available
		with a large uncertainty (50%), 12% being the
		maximum possible fraction
		Source: (IPCC 2006)
	C-CH 4	Not considered	Not available
	P-PO 4 3-
	Indirect	Not modelled with CERES-EGC model but	Modelled with several operational models
		with several operational models
	N-N 2 O	0.75% of leached NO 3 -N + 1% of volatilized	2.5% of leached NO 3 --N + 1% of volatilized
		NO x -N and NH3-N	NH 3 -N
		Source: (IPCC 2006)	Source: (Schmid et al. 2000)

Table 3 :

 3 Baseline impact categories in CML 2000 v2.0[START_REF] Guinée | Handbook on LCA, Operational Guide to the ISO Standards[END_REF]

	Impact categories	Reference substances	Main contributing substances
	Depletion of abiotic resources	kg eq Sb	Iron ore, Crude oil
	Acidification	kg eq SO 2	SO 2 , NO x , NH 3
	Eutrophication	kg eq PO 4 3-	PO 4 3-, NO 3 -, most N-compounds
	Global warming (GWP20, GWP100) kg eq CO 2	CO 2 , N 2 O
	Stratospheric ozone layer depletion	kg eq CFC-11	CFC
	Human toxicity	kg eq 1,4-DB	N 2 O, NO x , NH 3 , Particules, SO 2 , Acrylonitrile, Cadmium
	Ecotoxicity: freshwater, marine, and terrestrial	kg eq 1,4-DB	Acrylonitrile, Cadmium, Particles, N 2 O, NH 3 , SO 2
	Photo-oxidant formation	kg eq C 2 H 4	CO, Toluene, NO x

The ecoinvent Centre -a Swiss Competence Centre of ETHZ, EPFL, PSI, Empa and ART -is the world's leading supplier of consistent and transparent life cycle inventory (LCI) data of known quality with the database ecoinvent data v2.2. See http://www.ecoinvent.ch/

Acknowledgements

This work was supported by ADEME and the Picardy Region. The authors, members of the ELSA group (Environmental Life-cycle and Sustainability Assessment www.elsa-lca.org), thank the French Region Languedoc-Roussillon for its support to ELSA. We are very grateful to Mrs Damay for her invaluable expertise.

We also express warm thanks to all the staff of the AgroImpact research unit in Laon and Estrées-Mons for their remarkable involvement. Finally, we would like to thank the anonymous reviewers for their highly valuable comments.