Raphaël Carpine

Silvia Ientile

Pierre Argoul

Investigating the error on autocorrelation for operational modal analysis

Keywords: Autocorrelation, Linear time-invariant systems, Operational modal analysis, Ambient excitation, Damping, Wavelet analysis, Prestressed concrete bridge

Autocorrelation is commonly used in signal processing for analyzing time signals, however the shape and magnitude of its error is rarely addressed. Previous research showed that in the general case, the error on the autocorrelation estimator of an arbitrary signal is inversely proportional to the square root of the signal length. For operational modal analysis of linear systems under unknown ambient excitation, this error seems to present a peculiar shape influencing the estimation of damping ratios. In this paper the error on autocorrelation for a linear, time-invariant system subjected to white Gaussian noise is analytically and numerically studied. It is found to be very similar to the system's response to an ambient noise, thus with a frequency content close to that of the expected autocorrelation itself.

An upper bound of error magnitude is found for each mode of the system. Then, the resulting error on damping computations is investigated through numerical simulations applied to a two degrees of freedom mechanical system. Numerical outcomes show good agreement with the theoretical part and are then supported by experimental data of a prestressed concrete bridge under ambient traffic. This study allows for a better understanding and quantification of the inaccuracy on damping ratios computation through techniques using autocorrelation in time domain, notably the logarithmic decrement or time-frequency domain decomposition based on wavelet analysis.

Introduction

Techniques estimating modal structural parameters only based on the output dynamic responses became more and more popular as Operational Modal Analysis (OMA) or output-only modal analysis, particularly in the civil engineering community because they allow for the identification of the modal characteristics of a given structure under operating conditions. In ambient vibration tests, the structure under study may be subjected to several sources of excitation caused by urban traffic, seismic activity, wind, etc, which are not measured but assumed to be "broadband random" (and often modeled as a white noise), and only responses of the structure are measured. All aspects of operational modal analysis for civil engineering are covered in [START_REF] Rainieri | Operational modal analysis of civil engineering structures: an introduction and guide for applications[END_REF] from theoretical background to applications. OMA has become the primary modal testing method in civil engineering applications and the number of reported case studies is abundant [START_REF] Mohanty | Operational modal analysis in the presence of harmonic excitation[END_REF][START_REF] Vu | Towards an automatic spectral and modal identification from operational modal analysis[END_REF][START_REF] Zhang | Automated eigensystem realisation algorithm for operational modal analysis[END_REF].

A broad classification can be made for OMA methods according to two criteria: frequency domain or time domain, and Bayesian or non-Bayesian [START_REF] Au | Operational Modal Analysis[END_REF]. Bayesian methods were developed in time domain and frequency domain after Non-Bayesian ones. In Bayesian techniques, modal parameters are modeled as random variables with a probability distribution depending on the available information. The direct problem is first addressed: given the modal parameters, what is the distribution of data? Bayes' theorem determines the probability that an event occurs from another event already occurred, provided that these two events are interdependent. The theorem allows here to swap the roles of modal parameters and available data, so that the inverse problem: given the data, what is the distribution of the modal parameters? can also be addressed in full details. Probability is used as a measure of the relative possibility of outcomes, given a model of the system and measured data. Recently, some Bayesian methods estimating modal parameters through maximum likelihood computations were developed, allowing an estimation of their error [START_REF] Yuen | Bayesian Methods for Updating Dynamic Models[END_REF][START_REF] Goller | Investigation of model uncertainties in Bayesian structural model updating[END_REF]. In this paper, the study is restricted to non-Bayesian methods.

As OMA is based on the assumption of a random input, non-Bayesian methods generally use certain statistical estimators with known theoretical expectations such as the correlation function or the spectral density of the mea-sured vibrations. Common non-Bayesian methods include stochastic subspace identification (time domain) [START_REF] Reynders | Uncertainty bounds on modal parameters obtained from stochastic subspace identification[END_REF] and frequency domain decomposition (frequency domain), using the singular value decomposition of the power spectral density matrix [START_REF] Brincker | Modal identification of output-only systems using frequency domain decomposition[END_REF]. In [START_REF] Ceravolo | Use of instantaneous estimators for the evaluation of structural damping[END_REF][START_REF] Nguyen | Wavelet analysis of the structural response under ambient excitation for modal identification[END_REF], time-frequency instantaneous estimators are proposed for the identification of damping from signals measured in ambient vibration conditions. In [START_REF] Ceravolo | Use of instantaneous estimators for the evaluation of structural damping[END_REF], from each signal, a time function of modal damping and amplitude is extracted, providing punctual information on the stability and consistency of structural damping estimate. In [START_REF] Nguyen | Wavelet analysis of the structural response under ambient excitation for modal identification[END_REF], the wavelet spectral and instantaneous wavelet spectral functions defined from the continuous wavelet transform of response signals, give an estimation of modal viscous damping ratio for stationary processes and locally stationary processes. A "smoothed" estimate has been then produced, strongly depending on the choice of the timefrequency resolution of the wavelet transform. Based on energetic properties, an optimal value of this quality factor controlling the wavelet time-frequency resolution is proposed. Numerous techniques for OMA purposes are based on autocorrelation and cross-correlation functions, especially in frequency domain using power spectrum density [START_REF] Heylen | Modal analysis theory and testing[END_REF]. In this paper, only OMA methods based on the analysis of autocorrelation functions in time domain are considered, notably those that rely on the wavelet transform [START_REF] Le | Modal identification based on continuous wavelet transform and ambient excitation tests[END_REF][START_REF] Le | Modal identification based on the time-frequency domain decomposition of unknown-input dynamic tests[END_REF] and the logarithmic decrement [START_REF] Magalhães | Damping estimation using free decays and ambient vibration tests[END_REF]. Estimating autocorrelation from a finite size signal inevitably introduces an error (defined as the difference with its expectation for a non-biased estimator), yet the matter of the results precision is rarely addressed, especially for the damping computations which often yield significant inaccuracies, in some cases more than 100 % [START_REF] Nguyen | Wavelet analysis of the structural response under ambient excitation for modal identification[END_REF][START_REF] Ceravolo | Time domain identification of structures: Comparative analysis of output-only methods[END_REF]. Bendat and Piersol [START_REF] Bendat | Random data: analysis and measurement procedures, 4th Edition[END_REF] studied the variance of the autocorrelation estimator in the general case, and found that it is inversely proportional to the length of the acquired signal. Similarly, Vandiver [START_REF] Vandiver | A Mathematical Basis for the Random Decrement Vibration Signature Analysis Technique[END_REF] studied the variance of the random decrement signature, which can be directly linked to the autocorrelation function [START_REF] Asmussen | Modal analysis based on the random decrement technique: application to civil engineering structures[END_REF], and came to the same conclusion. However, to our knowledge, the special case of linear systems under white noise, and specifically the shape of the error on the associated autocorrelation, has never been investigated. The aim of this paper is to characterize the shape and magnitude of the error on the autocorrelation function estimator in time domain for responses of linear systems to unknown white Gaussian noise. The outcomes of the study allow for a better understanding and quantification of the resulting errors on modal parameters, especially damping ratios. This paper is structured as follows: the expectation of the autocorrelation of a linear system under white Gaussian noise is reminded in section 2 and the shape and magnitude of its error is investigated in section 3. Finally, the resulting error on damping computations is derived, and numerical simulations and experimental results of a monitored bridge are presented.

Definitions and expected autocorrelation

For simplicity and similarity with numerical computations, we will use discrete sampled signals instead of continuous ones. In addition, the considered linear systems will have only one input and output, although they can model multiple degrees of freedom, acting as linear filters.

Reminders and notations

For discrete signals u, v ∈ C Z , we define here the convolution product as:

u * v [n] = ∆t +∞ k=-∞ u[n -k] v[k], (1)
where n ∈ Z, and ∆t > 0 is the time increment. Then autocorrelation of a finite energy signal u is defined as:

R u [n] = ∆t +∞ k=-∞ u[k] u * [k -n], (2)
where the exponent * refers to the complex conjugate. This implies notably that R

u [-n] = R * u [n].
Alternative definitions for autocorrelation are often used, with normalization coefficients that can lead to biased or unbiased estimators [START_REF] Bendat | Random data: analysis and measurement procedures, 4th Edition[END_REF]. We decide to use a simple definition, because it can always be normalized afterwards.

Realistically, physical signals are measured only on finite time intervals. Thus, for any discrete signal u ∈ C Z , we introduce its windowed counterpart ũ:

ũ[n] = u[n] if n ∈ {0, . . . , N -1} 0 else, (3)
where N ∈ N * is the number of sampled points.

Expected autocorrelation for a linear system

Let w be a discrete, white Gaussian noise, defined by:

w[n] ∼ N(0, σ 2 ), (4)
where the w[n] are mutually independent. Then we define the discrete response x of a linear system to w as:

x[n] = h * w [n], ( 5
)
where h is the discrete impulse function of the system. If λ 1 , . . . , λ P denote the poles of the system's transfer function, its impulse function can be written as [START_REF] Géradin | Mechanical vibrations: theory and application to structural dynamics[END_REF]:

h[n] = Θ[n] P p=1 A p e λ p n∆t ∈ R, (6)
where A 1 , . . . , A P are complex coefficients, and Θ is the discrete Heaviside function. Assuming the system is damped on each one of its modes, i.e. Re(λ p ) < 0 for all p, its autocorrelation becomes:

∀ n ∈ N, R h [n] = R h [-n] = P p=1
B p e λ p n∆t ∈ R with B p = ∆t

P q=1 A p A * q 1 -e (λ p +λ * q )∆t . (7)
At last, let x be the windowed signal on interval {0, . . . , N -1}, and R x its autocorrelation. It can be shown from Eq. ( 5) that:

∀ n ∈ N, E [R x[n]] = (N -n)∆t 2 σ 2 R h [n]. (8)
Therefore the windowed signal's autocorrelation constitutes an indirect estimator of R h . Then, using various signal processing methods [START_REF] Heylen | Modal analysis theory and testing[END_REF][START_REF] Le | Modal identification based on continuous wavelet transform and ambient excitation tests[END_REF][START_REF] Le | Modal identification based on the time-frequency domain decomposition of unknown-input dynamic tests[END_REF], its poles λ 1 , . . . , λ P can be computed through Eq. ( 7). Finally, these poles give the natural frequencies and damping ratios of the system's modes [START_REF] Géradin | Mechanical vibrations: theory and application to structural dynamics[END_REF]. However, an error as a significant difference between autocorrelation computation and its expectation can be observed in experimental applications. This error is similar to the system's response to a random noise, i.e. oscillations at around its natural frequencies with varying amplitudes, as demonstrated in the next section.

Shape and magnitude of the error on autocorrelation

3.1. Autocorrelation of a windowed white Gaussian noise To give a simple example of error on the autocorrelation of a windowed signal, and to obtain necessary preliminary results, in this part we study a windowed white Gaussian noise. Let w be the white Gaussian noise defined by Eq. ( 4), and w its windowed counterpart (see Eq. ( 3)). As windowed noise w is real valued, its autocorrelation R w is even, and for |n| N, R w[n] is equal to 0. Then, using Eq. (2) and w[k] independence, we get:

E [R w[n]] = N∆t σ 2 for n = 0 0 for |n| ∈ {1, . . . , N -1}, (9)
and:

Var (R w[n]) = 2N∆t 2 σ 4 for n = 0 (N -|n|) ∆t 2 σ 4 for |n| ∈ {1, . . . , N -1}. ( 10
)
Autocorrelation R w can therefore be divided into a deterministic 'spike' at n = 0, and a random, zero-expectation signal W: R w

[n] = N∆t 2 σ 2 δ[n] + W[n], (11)
where δ[n] equals 1/∆t for n = 0, and 0 everywhere else. Variance for W is determined by Eq. [START_REF] Ceravolo | Use of instantaneous estimators for the evaluation of structural damping[END_REF], and as for R w, it is even. In addition, for any i, j such as 0 i < j, W[i] and W[ j] are uncorrelated. Simulations of w and R w are shown in Fig. 1.

It should be noted that the 'spike' impulsion amplitude at n = 0, defined by Eq. ( 9), is proportional to N, while the standard deviation of W[n], defined by Eq. [START_REF] Ceravolo | Use of instantaneous estimators for the evaluation of structural damping[END_REF], is proportional to N 1/2 . Thus, when the number of points N increases, R w becomes closer to its expectation such as a pure 'spike'.

Autocorrelation of a windowed response of a linear system to white Gaussian noise

We now study the error on autocorrelation of a windowed response of a linear system to white Gaussian noise R x, i.e. the difference with its expectation. First, it is proven in Appendix A that:

R x[n] ≈ N n R h * w[n], (12)
with a relative error of order 1/N. As can be seen in Fig. 2, x and h * w only differ around n = 0 and n = N -1, where their difference is a free response of the system, hence the approximation. Then, using a classical formula on Figure 2: Numerical simulation of a one degree of freedom system under white Gaussian noise w, with its windowed response to w, x = h * w (a), its response h * w to windowed noise w (b), and their difference h * wx (c). The system's response is computed using a convolution product (see Eqs. ( 5) and ( 6)), using parameters

λ 1 = -0.1 + 2iπ, λ 2 = λ * 1 , A 1 = -i, A 2 = A * 1 , σ = 1, ∆t = 0.05 and N = 2000.
autocorrelation of a convolution product [START_REF] Bendat | Random data: analysis and measurement procedures, 4th Edition[END_REF], we get R h * w = R h * R w, which, combined with Eq. ( 11), leads to:

R h * w[n] = N∆t 2 σ 2 R h [n] + R h * W [n]. ( 13
)
Autocorrelation R h * w constitutes therefore an estimation of R h if the right-hand term R h * W remains small enough.

Then it can be used to compute the system's natural frequencies and damping ratios, as stated before. This right-hand term R h * W, given the shapes of R h and W, is similar to the system's response to a random noise. Hence, as these autocorrelation signals are generally processed and filtered to isolate and analyze each mode individually, we split them into P sub-signals corresponding to each pole λ p , by introducing

R (p) h [n] = R (p) h [-n] = B p e λ p n∆t for all n ∈ N, and R (p) h * w = R (p) h * R w .
This way, we get:

E R (p) h * w[n] = N∆t 2 σ 2 R (p) h [n], (14)
and, as proven in Appendix B:

Var

R (p) h * W [n] N∆t 4 σ 4 B p 2        8 1 -e (λ p +λ * p )∆t + 4 1 -e (λ p -λ * p )∆t        (15)
≈ |λ p ∆t| 1 N∆t 3 σ 4 B p 2           4 -Re λ p + 2 Im λ p           . (16)
Finally, considering pole p as λ p = -µ p ± iω d,p with µ p as the damping constant and ω d,p as the damped angular frequency, total response signal time N∆t as T , and introducing the ratio between the characteristic amplitude of the error on pole p, R (p) h * W, and its expected initial amplitude R (p) h * w[0], we get an upper bound α p which satisfied:

Var R (p) h * W [n] N∆t 2 σ 2 R (p) h [0] α p , (17)
where:

α p = 4 µ p T + 2 ω d,p T . ( 18
)
This way, an upper bound for the magnitude of the error on autocorrelation can be computed for each mode. This upper bound depends on pole λ p of the associated mode p, predominantly its real part -µ p for lightly damped systems (i.e. µ p ω d,p ). It should be noted that α p is of order 1/N 1/2 , while the relative difference between R x and R h * w is of order 1/N, thus the use of Eq. ( 12) is justified. The error on autocorrelation for a one degree of freedom system and its upper bound derived from Eq. ( 17) are presented in Fig. 3. Mode amplitude is estimated using the Continuous Wavelet Transform skeleton as described in [START_REF] Le | Modal identification based on continuous wavelet transform and ambient excitation tests[END_REF], in order to better illustrate and understand the effect of the error. Furthermore, the use of an averaging method [START_REF] Heylen | Modal analysis theory and testing[END_REF], for instance dividing the signal into M sub-signals of length N/M, calculating their autocorrelation and taking the mean result, does not change the magnitude of the final error. As a matter of fact, according to the central limit theorem, and assuming the sub-signals are long enough to be considered independent, averaging the errors will reduce their magnitude by a M 1/2 coefficient, while their magnitude is inversely proportional to the square root of their size, (N/M) 1/2 (see Eq. ( 18)). Consequently, the square root of M will cancel out, and the resulting error will be the same as without the averaging step, making the signal total acquisition length N the only relevant parameter. This has been verified numerically, giving almost identical error profiles with and without the averaging process.

Applications on damping estimation

Subsequent error on damping

This error on autocorrelation eventually induces an error on the damping estimated from its exponentially decaying amplitude. To asses this error, we will consider a linear regression on the log of the amplitude of R(p) h , the estimator of R (p) h obtained through Eq. ( 8) after normalization and a filtering process (for instance, using the wavelet transform [START_REF] Le | Modal identification based on continuous wavelet transform and ambient excitation tests[END_REF], singular value decomposition [START_REF] Magalhães | Damping estimation using free decays and ambient vibration tests[END_REF], or both [START_REF] Le | Modal identification based on the time-frequency domain decomposition of unknown-input dynamic tests[END_REF]). For this purpose, we must first assume that the error to signal ratio (which is computed from 7) and ( 17)) remains low in the autocorrelation, i.e.: α p e µ p n∆t 1.

R (p) h module, |R (p) h [n]| = |B p e λ p n∆t | = |B p | e -µ p n∆t , see Eqs. (
Then, using Eq. ( 17), and assuming the phase shift between R(p) h [n] expectation and its error is uniformly distributed, we get:

E ln R(p) h [n] ≈ ln |B p | -µ p n∆t, (20)
and: Amplitude (CWT skeleton) (f) Figure 3: Numerical simulation of a one degree of freedom system under white Gaussian noise, with autocorrelation R x (a), its expectation (N -|n|)∆t 2 σ 2 R h (b), and their difference, the error (c). The amplitude of R x (d), (N -|n|)∆t 2 σ 2 R h (e), and their difference (f), are computed using the continuous wavelet transform skeleton [START_REF] Le | Modal identification based on continuous wavelet transform and ambient excitation tests[END_REF] (log scale). Red dotted lines correspond to plus and minus the upper bound on error magnitude, derived from Eq. [START_REF] Bendat | Random data: analysis and measurement procedures, 4th Edition[END_REF]. The system's response is computed using a convolution product (see Eqs. ( 5) and ( 6)), using parameters Although the approximation from Eq. ( 20) holds up to at least the 8th order in α p e µ p n∆t , the assumption from Eq. [START_REF] Asmussen | Modal analysis based on the random decrement technique: application to civil engineering structures[END_REF] 155 still needs to be verified. Otherwise, it would induce a bias in Eq. ( 20), and therefore on the estimated damping ratio. This is especially true for the end of the regression, where e µ p n∆t is at its highest. Then, through a linear regression on ln | R(p) h | from n = n ri to n = n r f , with a total number of points N r = n r f -n ri +1, the estimated damping constant μp can be expressed as:

Var ln R(p) h [n] √ 2 α p e µ p n∆t . (21)
λ 1 = -0.1 + 2iπ, λ 2 = λ * 1 , A 1 = -i, A 2 = A * 1 , σ = 1, ∆t = 0.
μp = -D T Y where D = 6 N r (N r -1)(N r + 1)∆t                  -N r + 1 -N r + 3 . . . N r -1                  and Y =                 ln R(p) h [n ri ] . . . ln R(p) h [n r f ]                 , (22)
which implies, from Eq. ( 20),

160

E[ μp ] = -D T E[Y] ≈ µ p , (23)
and:

Var( μp ) = D T Cov(Y) D N r n=1 |D n | Var(Y n ). ( 24
)
We now introduce the regression initial time t ri = n ri ∆t, final time t r f = n r f ∆t and total time T r = N r ∆t. Because t r f is the last moment of the regression, thus with the largest time, condition from Eq. ( 19) becomes α p e µ p t r f 1. Then, assuming ∆t is sufficiently small (µ p ∆t 1), we get from Eqs. ( 21) and [START_REF] Lorenzo | Nonstationary and stationary noise[END_REF]:

Var( μp ) E[ μp ] 6 √ 2 α p e µ p t ri e µ p T r (µ p T r -2) + 2e µ p T r /2 µ p T r + (2e -µ p T r /2 -1)(µ p T r + 2) (µ p T r ) 3 . ( 25
)
Finally, this upper bound can be minimized to give the optimal value of regression time T opt , which is found numerically to be equal to:

T opt = argmin T r 6 √ 2 e µ p T r (µ p T r -2) + 2e µ p T r /2 µ p T r + (2e -µ p T r /2 -1)(µ p T r + 2) (µ p T r ) 3 1.4326 µ p , (26)
with:

M opt = min T r 6 √ 2 e µ p T r (µ p T r -2) + 2e µ p T r /2 µ p T r + (2e -µ p T r /2 -1)(µ p T r + 2) (µ p T r ) 3 9.8380. ( 27
)
This way, we now have an optimal value of regression time T opt , for which the error bound on μp is minimized. Therefore, from now on, the regressions are supposed to be carried out using a total time T r = T opt . Considering Eq. ( 18), Eq. ( 25) becomes:

Var( μp ) E[ μp ] M opt e µ p t ri 4 µ p T + 2 ω d,p T . ( 28
)
This upper bound depends only on the mode's pole real and imaginary parts, -µ p and ±ω d,p , on the response signal total length T = N∆t, and on the regression start time t ri . However, because the upper bounds found in Eqs. ( 15) and ( 24) both yield a significant margin, this upper bound may be much larger than the relative standard deviation of μp .

To that extent, we will study numerically and experimentally the "effective" factor M ef f , which replaces M opt in Eq. ( 28) in the case of an equality, and therefore satisfies by definition the following equation:

M ef f = Var( μp ) E[ μp ] e -µ p t ri 4 µ p T + 2 ω d,p T -1/2 . ( 29
)
Although M ef f may depend on the system parameters and regression initial and total times, we will see in the numerical and experimental applications that it seems to be a constant.

Numerical simulations

To illustrate the error on damping found in OMA, and find the effective factor M ef f from Eq. ( 29), we carry out several numerical simulations of a two degrees of freedom system pictured in Fig. 4, whose modal parameters are given in Table 1. A white Gaussian noise is applied to the mass located on the left, where the response of the system x is measured. This response is computed through a convolution product with the the system's impulse response function (see Eq. ( 5)). The time increment taken for the simulations is ∆t = 0.05 s. For several response time lengths T , 100 simulations are performed. Autocorrelation of the response signals is then computed, and Rh is obtained through Eq. ( 8). The damping constant estimate μp is computed for both modes using a linear regression on the log of the amplitude associated with each mode, which is retrieved using the wavelet transform, as described in [START_REF] Le | Modal identification based on continuous wavelet transform and ambient excitation tests[END_REF]. The regression initial time t ri is set by the wavelet transform edge effect zone, and its total time T r is set to T opt to obtain minimal variance in the result, as explained earlier. System modal parameter estimates fp and ζp are then computed from the pole formulaμp + i ωd,p = 2π fp (-ζp + i(1 -ζ2 p ) 1/2 ) for the 100 simulations, for each response time length T and each mode, and their means and standard deviations are presented in Table 2, along with M ef f computed from Eq. ( 29). To assess the error to signal ratio in autocorrelation at the end of the regression, that is at its maximum, α p e µ p t r f is given for each mode (see Eq. ( 19)). In some cases, the relative error at the end of the regression is high, i.e. α p e µ p t r f > 1, thus the assumption from Eq. ( 19) is not met (both modes for T = 100 s, and mode 1 for T = 1000 s). For those cases, the mean value obtained for the damping ratio seems to be lower than expected. This indicates a bias not accounted for in Eq. ( 20), especially for the first mode for T = 100 s, where the difference with the expected value can hardly be explained by statistical chance. They also seem to give lower values for M ef f , which should therefore be discarded. However, in the other cases, the results for M ef f seem to be fairly steady across the different signal lengths (which vary by 3 orders of magnitude) and modes, with a mean value around 1. It is therefore reasonable to assume the following approximation:

Response

M ef f 1, (30)
which finally gives an estimate of the error on the damping computation through Eq. ( 29). This value, combined with Eq. ( 29), is a significant improvement from Eq. ( 28), given that M ef f is about ten times lesser than M opt , thus providing tighter margins on the damping error estimate. To test the dependency of M ef f on the damping ratios, three other series of simulation were carried out using the same system with a damping factor ten times greater, ten times lesser and one hundred times lesser than first simulation's one, which all gave similar results.

These numerical results also highlight the significant inaccuracies on damping that arise from the statistical nature of OMA. For instance, estimating damping of mode 1 from a signal about 17 minutes long (corresponding to mode 1 with T = 1000 s in Table 2) would result in a standard deviation of more than a fifth of its value. This corresponds to a typical situation in civil engineering, where modal parameters need to be estimated regularly at relatively short intervals, because of the temperature influence that must be evaluated afterwards.

A number of assumptions made in this study can be questioned, especially regarding the nature of excitation, namely that it is a nonstationary white Gaussian noise and that the system is linear and nonstationary as well. First, it is not in the general case a one channel signal, but rather a multi-channel signal or field, modeling the various loads on each part of the structure. Second, although the assumption of a white noise excitation is generally made in OMA [START_REF] Heylen | Modal analysis theory and testing[END_REF], and can be justified under certain conditions [START_REF] Ditlevsen | Traffic loads on large bridges modeled as white-noise fields[END_REF], real excitation signals often present more complex profiles in frequency domain. For instance, they can be seen as white noise convoluted with a linear filter, whose poles can be extracted with those of the system and eventually discarded [START_REF] Ibrahim | Modal Parameter Identification from Responses of General Unknown Random Inputs[END_REF], or more generally as colored noise, whose parameters can be retrieved and taken into account in the modal analysis of the system [START_REF] Cooper | Model parameter identification using an unknown coloured random input[END_REF]. Excitation can also be nonstationary [START_REF] Lorenzo | Nonstationary and stationary noise[END_REF], which is handled by some OMA techniques [START_REF] Zhang | An overview of operational modal analysis: Major development and issues[END_REF]. The dynamical behavior of the system itself poses other issues, as it is generally nonstationary as well, for example due to the stiffness and damping dependence of concrete on temperature for civil engineering applications, and of steel for aerospace engineering applications [START_REF] Xia | Long term vibration monitoring of an RC slab: Temperature and humidity effect[END_REF], and can present nonlinearities for example [START_REF] Vacca | Characterization of dissipative behaviour of a reinforced concrete mock-up after soft impact tests through wavelet analysis[END_REF] in the case of a soft impact response behavior of a reinforced concrete mock-up. For all these reasons, an application to an experimental study is presented in the next section.

Experimental testing

An experimental campaign on a bridge under ambient traffic was carried out, to support our study. The structure under study is a 74 m long bridge, supported by 6 parallel prestressed concrete beams. It is part of a series of five identical bridges build across the Marne River in France in the 1940s and 1950s under the advice of the expert engineer Eugène Freyssinet of the Campenon Bernard companies [START_REF] Chaudesaigues | La reconstruction en béton précontraint des ponts sur la Marne à Annet, Trilbardou, Esbly, Ussy et Changis-Saint-Jean[END_REF], as a demonstration of the capabilities of prestressed concrete for slender, long-span bridges. A total of 14 triaxial wireless accelerometers (G-Link-200) were installed on the bridge, as shown in To obtain the modal parameters from the accelerometric data of the bridge, the CWT-based method, described in [START_REF] Le | Modal identification based on the time-frequency domain decomposition of unknown-input dynamic tests[END_REF], was used. This method combines cross-correlation including autocorrelation, CWT and singular value decomposition, and leads to instantaneous amplitudes, frequencies and mode shapes as functions of the cross-correlation lag. The autocorrelation function of sensor 29278 signal is showed as an example in Fig. 6a, only for positive time lags as it is even. It features an interference beat pattern, originating from the first four modes close frequencies. Fig. 6b displays the first singular value of the CWT of the cross-correlation matrix [START_REF] Le | Modal identification based on the time-frequency domain decomposition of unknown-input dynamic tests[END_REF] between 2 Hz and 2.3 Hz, with ridges associated with the first two modes. The modal parameters are then retrieved using averages, and a linear regression on the log of the amplitude for damping. The method is slightly modified, by using T opt as the total regression time, providing theoretically a minimal error on damping as explained earlier, instead of the frequency and mode shape stability stopping conditions proposed in the original paper. At first, the method is implemented on the whole signal, which provides reference parameters that will be considered the true modal parameters of the bridge for the rest of the study (hence the lack of "∼" exponent for these parameters). The results obtained for the natural frequencies f p and damping ratios ζ p of the 10 identified modes are presented in Table 3, along with the relative error on autocorrelation at its maximum α p e µ p t r f , and the expected standard deviation on the ζ p computed from Eqs. ( 29) and (30), which gives an estimation of their error. The corresponding mode shapes are shown in Fig. 7, where their longitudinal edges curves are smoothed using quadratic interpolation.

Observing Fig. 7's mode shapes, some modes appear to be missing, as for example the third and fourth torsional modes. This is likely due to insufficient excitation and/or excessive additive noise in their frequency range. It is not a 3: Experimental data: natural frequencies f p and damping ratios ζ p estimated from the method described in [START_REF] Le | Modal identification based on the time-frequency domain decomposition of unknown-input dynamic tests[END_REF] using the whole signal, with expected coefficient of variation (C.V.) computed from Eqs. ( 29) and (30).

problem for our study however, which is not intended to be a complete modal analysis of the bridge. All the modes are pure bending or torsional modes, except for the fourth one which is a combination of torsional and lateral movement.

There also seems to be spatial aliasing in the tenth mode due to a lack of sensors, which presumably corresponds to the ninth bending mode, which is why it is not displayed. Moreover, the expected standard deviation of the damping ratios and related error, is quite high as shown in Table 3. Condition from Eq. ( 19) is not met either for the first four modes. Therefore, although these values are taken as reference, we must keep in mind that they are potentially subject to errors. Next, the accelerometric signals are divided into 20 sub-signals of about 415 s long in order to support the theoretical and analytical results, especially regarding M ef f . For each one, the same procedure from [START_REF] Le | Modal identification based on the time-frequency domain decomposition of unknown-input dynamic tests[END_REF] is applied. The number of sub-signals is chosen from the compromise between statistical representativeness and respect of Eq. [START_REF] Asmussen | Modal analysis based on the random decrement technique: application to civil engineering structures[END_REF].

Results are presented in Table 4. In this case, the assumption of Eq. ( 19) is not met for any mode. There are however a few modes (5, 8, 9 and 10) whose autocorrelation relative error α p e µ p t r f is lower or close to 1. For these modes, the results for M ef f are around 1 (with a large error margin though, considering the small sample size), which supports 7: Experimental data: modes shapes estimated from the method described in [START_REF] Le | Modal identification based on the time-frequency domain decomposition of unknown-input dynamic tests[END_REF] using the whole signal. The tenth mode shape could not be portrayed correctly because of a lack of sensors. the numerical results of Eq. (30). Additionally, the mean values found for damping are significantly smaller than the reference values of Table 3, especially for modes with high autocorrelation relative error α p e µ p t r f , indicating a bias. This bias is due to the non-fulfillment of the condition from Eq. ( 19), as demonstrated and discussed in the numerical part. These experimental data highlight the importance of the condition from Eq. ( 19), to get unbiased estimators of damping. Its non-fulfillment leads to a bias that tends to underestimate the damping ratios. This implies that one single value of damping computed from the whole length of a signal is closer to the real damping of the system than the average of several damping values computed from different parts of this signal. In addition, they show once again the large statistical errors (variance and bias) that can emerge in OMA for damping estimation, which can however be estimated using Eqs. ( 19), ( 29) and (30).

Conclusions

The error on autocorrelation for a discrete, finite size response of a linear system to white noise, has been shown to be very similar to its response to a random noise with varying standard deviation. This error can be divided as a sum of terms centered in the Fourier domain around the natural frequencies of the system, interfering with the meaningful signal parts of the corresponding modes which are exponentially decaying sinusoids. Thus, these error terms eventually become predominant for large enough lag values of the autocorrelation. For each mode p, the magnitude of the associated error term can be bounded by using coefficient α p .

In this paper, the error on the derived damping ratios, resulting from the error on autocorrelation, has been investigated. An upper bound on its standard deviation, and an associated optimal regression time, have been found analytically. It indicates a relation of inverse proportionality with the square root of the response signal total length. Numerical simulations of a two degrees of freedom system corroborate the analytical results, highlighting a bias which appears when a condition on the signal length is not met. Then, a refinement of this upper bound is carried out through the numerical simulations in order to better estimate the damping computations inaccuracies. Experimental accelerometric data of a prestressed concrete single-span bridge allow for validation of the theoretical and numerical results. Indeed, the analysis on the experimental data underline the importance of the established condition on autocorrelation relative error associated with the signal length. This study shows the inaccuracies deriving from the statistical nature of the signals in operational modal analysis, which remain quite large for typical civil engineering case studies, highlighting the relevance of our work in quantifying them.

under their supervision, and to the Centre for Studies on Risks, the Environment, Mobility and Urban Planning, especially Anil Abdoulhoussen, Thomas Massaro and Pierre Marchand, for their fruitful help during the experimental campaign.

Appendix A. Proof of Eq. [START_REF] Heylen | Modal analysis theory and testing[END_REF] Let n be a natural integer, n ∈ N. In this appendix, we will prove Eq. ( 12) by finding upper bounds for the expectation and variance of the difference between both terms, independent from N. This way, as the expectation of R h * w[n] is proportional to N (see Eq. ( 14)), the relative error is of order 1/N. For readability, some brackets will be noted as indices from now on, for instance w n = w[n].

First, to obtain the upper bound on the expectation, Eqs. ( 8) and ( 14) are combined to find:

E [R h * w[n] -R x[n]] = n∆t 2 σ 2 R h [n].
Then, for the variance upper bound:

x

[k] = h * w [k] = ∆t +∞ i=-∞ w i h k-i for k ∈ {0, . . . , N -1} 0 else h * w [k] = ∆t N-1 i=0 w i h k-i ,
with, for all i < 0, h i = 0. Next:

R x[n] = ∆t 3 N-1 k=n +∞ i=-∞ w i h k-i +∞ j=-∞ w j h k-n-j = ∆t 3 N-1 k=n N-1 i=-∞ N-1 j=-∞ h k-i h k-n-j w i w j R h * w[n] = ∆t 3 +∞ k=-∞ N-1 i=0 w i h k-i N-1 j=0 w j h k-n-j = ∆t 3 +∞ k=n N-1 i=0 N-1 j=0 h k-i h k-n-j w i w j .
As can be seen from Eq. ( 6), there exist C 0 , β ∈ R * + such as:

|h k | Θ[k] C 0 e -βk ,
and for all i, j, i , j ∈ Z,

Cov w i w j , w i w j =          2σ 4 if i = j = i = j σ 4 if i = i j = j or i = j j = i 0 else.
Thus:

1 ∆t 6 Var (R h * w[n] -R x[n]) = N-1 k=n N-1 k =n N-1 i=-∞ N-1 i =-∞ N-1 j=-∞ N-1 j =-∞ h k-i h k -i h k-n-j h k -n-j Cov w i w j , w i w j -2 N-1 k=n +∞ k =n N-1 i=-∞ N-1 i =0 N-1 j=-∞ N-1 j =0
h k-i h k -i h k-n-j h k -n-j Cov w i w j , w i w j e -2β(k+k -i-j)

       
where H k,k ,i, j = h k-i h k -i h k-n-j h k -n-j + h k-i h k -j h k-n-j h k -n-i . At last: e -2β(k+k -i-j) e -4β

1e -2β 4 .

Appendix B. Proof of Eq. ( 16)

First, we write R (p) h * W as:

R (p) h * W [n] = ∆t N-1 k=-N+1 R (p) h [n -k] W k = ∆t R (p) h [n] W 0 + ∆t N-1 k=1 R (p) h [n -k] + R (p) h [n + k] W k .
Then, knowing that for any i, j such as 0 i < j, W i and W j are uncorrelated, we get:

Var R (p) h * W [n] = ∆t 2 R (p) h [n] 2 Var (W 0 ) + ∆t 2 N-1 k=1 R (p) h [n -k] + R (p) h [n + k] 2 Var (W k ) = ∆t 4 σ 4         -2N R (p) h [n] 2 + N-1 k=0 R (p) h [n -k] + R (p) h [n + k] 2 (N -k)         N∆t 4 σ 4 +∞ k=0 R (p) h [n -k] + R (p) h [n + k] 2 N∆t 4 σ 4        n k=0 R (p) h [k] + R (p) h [2n -k] 2 + +∞ k=0 R (p) h [k] + R (p) h [2n + k]

Figure 1 :

 1 Figure 1: Numerical simulation of the autocorrelation R w of a windowed white Gaussian noise w (a), its expectation N∆t 2 σ 2 δ[n] (b), and their difference W (c). The parameters taken are σ = 1, ∆t = 0.05 and N = 10000.

  Figure3: Numerical simulation of a one degree of freedom system under white Gaussian noise, with autocorrelation R x (a), its expectation (N -|n|)∆t 2 σ 2 R h (b), and their difference, the error (c). The amplitude of R x (d), (N -|n|)∆t 2 σ 2 R h (e), and their difference (f), are computed using the continuous wavelet transform skeleton[START_REF] Le | Modal identification based on continuous wavelet transform and ambient excitation tests[END_REF] (log scale). Red dotted lines correspond to plus and minus the upper bound on error magnitude, derived from Eq. (17). The system's response is computed using a convolution product (see Eqs. (5) and (6)), using parametersλ 1 = -0.1 + 2iπ, λ 2 = λ * 1 , A 1 = -i, A 2 = A * 1 , σ = 1, ∆t = 0.05 and N = 100000 (although graphs are plotted for |n| 3000 only).

Figure 4 :

 4 Figure 4: Numerical simulations: system modeled.

Fig. 5 .Figure 5 :

 55 Figure 5: Experimental data: overview of the bridge accelerometric instrumentation.

Figure 6 :

 6 Figure 6: Experimental data: (a) autocorrelation of sensor 29278 acceleration channel; (b) first singular value (module) of the CWT of the crosscorrelation matrix[START_REF] Le | Modal identification based on the time-frequency domain decomposition of unknown-input dynamic tests[END_REF] (log scale), using the Cauchy mother wavelet with quality factor Q = 52 whose choice of value is detailed in[START_REF] Le | Continuous wavelet transform for modal identification using free decay response[END_REF], with ridges of the first two modes. The shaded area correspond to the edge effect zone.

Figure

  Figure7: Experimental data: modes shapes estimated from the method described in[START_REF] Le | Modal identification based on the time-frequency domain decomposition of unknown-input dynamic tests[END_REF] using the whole signal. The tenth mode shape could not be portrayed correctly because of a lack of sensors.

  i h k -i h k-n-j h k -n-j Cov w i w j , w i w j

e 4 ,

 4 -2β(k+k -i-j) e -2β(n+1) 1e -2β 2 +∞ k=0 (k + 1)e -2βk + e -2β(n+2) 1e -2β 4 e -2β(n+1) 1 + e -2β1e -2β

ee 4 1

 4 λ p k∆t + e λ p (2n-k)∆t 2 + +∞ k=0 e λ p k∆t + e λ p (2n+k)∆t 2 λ p k∆t + e λ p (2n+k)∆t 2 = 1 + e 2λ p n∆t 2 1e (λ p +λ * p )∆t[START_REF] Zhang | Automated eigensystem realisation algorithm for operational modal analysis[END_REF] 1e (λ p +λ * p )∆t , and finally:n k=0 e λ p k∆t + e λ p (2n-k)∆t 2 = 1e (λ p +λ * p )(n+1)∆t 1e (λ p +λ * p )∆t + 1e -(λ p +λ * p )(n+1)∆t 1e -(λ p +λ * p )∆t e 2(λ p +λ * p )n∆t + 1e (-λ p +λ * p )(n+1)∆t1e (-λ p +λ * p )∆t e 2λ p n∆t +1e (λ p -λ * p )(n+1)∆t1e (λ p -λ * p )∆t e 2λ * p n∆t 4 1e (λ p +λ * p )∆t + e (λ p -λ * p )∆t .

Table 1 :

 1 Numerical system modal parameters.

	Mode p f p [Hz] ζ p [%] ω d,p [rad.s -1 ] µ p [s -1 ] 1/µ p [s]
	1	0.984	1.118	6.181	0.0691	14.5
	2	2.575	1.118	16.178	0.1809	5.5

Table 2 :

 2 Numerical simulations: mean and standard deviation (S.D.) of damping computations from 100 simulations, for several signal lengths, with effective bound coefficient M ef f .

				Mode 1					Mode 2
	length T	Mean f1 Mean ζ1 S.D. ζ1 α 1 e µ 1 t r f M ef f Mean f2 Mean ζ2 S.D. ζ2 α 2 e µ 2 t r f M ef f
	[s]	[Hz]	[%]	[%]			[Hz]	[%]	[%]
	100	0.984	0.906	0.518	3.53	0.55	2.574	1.057	0.471	2.37	0.74
	1000	0.984	1.065	0.223	1.12	0.79	2.576	1.127	0.157	0.75	0.88
	10000	0.984	1.123	0.083	0.35	0.92	2.576	1.119	0.054	0.24	0.96
	100000	0.984	1.116	0.028	0.11	1.00	2.575	1.117	0.017	0.08	0.92
	1000000	0.984	1.116	0.010	0.04	1.01	2.575	1.116	0.006	0.04	0.93

Table

Table 4 :

 4 Mode p Mean fp Mean ζp S.D. ζp α p e µ p t r f M ef f Experimental data: mean natural frequencies fp , and mean and standard deviation (S.D.) of damping ratios ζp estimated from the method described in[START_REF] Le | Modal identification based on the time-frequency domain decomposition of unknown-input dynamic tests[END_REF] using 20 sub-signals, with corresponding M ef f .

		[Hz]	[%]	[%]
	1	2.07	0.56	0.25	4.90	0.24
	2	2.18	0.62	0.55	5.12	0.50
	3	2.84	0.54	0.43	6.00	0.37
	4	2.95	0.50	0.34	8.70	0.16
	5	5.45	1.43	0.62	1.06	1.37
	6	6.45	2.38	0.93	1.89	0.56
	7	7.99	2.76	0.67	2.60	0.21
	8	15.07	1.71	0.49	1.35	0.63
	9	16.76	0.86	0.25	0.84	1.25
	10	21.14	0.95	0.27	0.86	1.34

Acknowledgements

We would like to express our gratitude to the Département de Seine-et-Marne for giving us access to the bridges


OF THREATENED SPECIES™ Taxonomy Kingdom Phylum Class Order Family

Keywords: Animalia Chordata Actinopterygii Pleuronectiformes Scophthalmidae Native, Extant (resident): Albania, Belgium, Bosnia and Herzegovina, Croatia

This widely distributed, demersal species is common in parts of its range and has an estimated generation length of 7 years. It is taken in commercial fisheries in much of its range. Stock assessment estimates across most of its range in the Atlantic Ocean indicate biomass has been increasing over the past 8 to 18 years in multiple stocks. Abundance data are limited for the subpopulation in the Mediterranean. Given the recent general increases in biomass in several areas along with the reduction of fishing effort in other areas, no evidence indicates that fishing activity at this time is driving globalscale declines approaching a threatened or Near Threatened level for this species, nor is it expected that fishing activities will result in significant declines in the near future. This species is listed therefore as Least Concern. It is recommended that improved monitoring of individual catch data for this species be conducted to improve future assessments.

Geographic Range Range Description:

This species is distributed in the northeast Atlantic Ocean from the Norwegian Sea as far north as 69°27.1'N, 16°10'E, and including southern Iceland, the British Isles and the Faroe Islands (63°N) southwards to Cape Bojador (26°N), Western Sahara. It occurs in the Mediterranean Sea in the Gulf of Lion, Ligurian Sea, Tyrrhenian Sea, Ionian Sea, the Mediterranean coasts of Turkey, Aegean Sea, Cretan

Population

According to genetics studies, connectivity between the Atlantic and Mediterranean subpopulations is low [START_REF] Danancher | Population differentiation in megrim (Lepidorhombus whiffiagonis) and four spotted megrim (Lepidorhombus boscii) across Atlantic and Mediterranean waters and implications for wild stock management[END_REF], but further work is needed to determine connectivity between the Celtic Sea and Bay of Biscay (ICES 2015).

Atlantic: This species is common and abundant off western Ireland [START_REF] Robson | Age and growth of a sample of Four-Spot Megrim, Lepidorhombus boscii, from off the west coast of Ireland[END_REF], in continental waters off Portugal, in the Bay of Biscay and on the Northern Spanish Shelf [START_REF] Castilho | Age and growth of megrim i> Lepidorhombus boscii, Risso of the Portuguese continental coast[END_REF][START_REF] Fernández-Zapico | Environmental drivers of the distribution of the order Pleuronectiformes in the Northern Spanish Shelf[END_REF]. Its occurrence and abundance have been increasing in the northern part of its range off Iceland [START_REF] Valdimarsson | Hydrographic variablility in Icelandic waters during recent decades and related changes in distribution of some fish species[END_REF] and in Norwegian waters since about 2011, but it is not commercially important in Norway [START_REF] Wienerroither | Teleostei, Scophthalmidae: four-spot megrim spotted in Norwegian waters[END_REF]. Catch data generally comprises landings for both L. boscii and L. whiffiagonis. Lepidorhombus whiffiagonis is more abundant in shallower depths (100-200 m), while L. boscii is more abundant in deeper depths (100-350 m). In addition, L. boscii appears to tolerate saltier bottom waters than does L. whiffiagonis [START_REF] Abad | Integrating spatial management measures into fisheries: The Lepidorhombus spp. case study[END_REF]. Lepidorhombus whiffiagonis is more common than L. boscii in the northern part of their ranges [START_REF] Rodríguez-Gutierrez | Spanish onshore sampling of Lepidorhombus spp[END_REF]. It is taken in commercial quantities in the following ICES divisions: 4a and 6a (northern North Sea and West of Scotland); 6b (Rockall Trough); 7b-k, 8a, 8b and 8d (west and southwest of Ireland, Bay of Biscay including Porcupine Bank); 8c and 9a (Cantabrian Sea and Atlantic Iberian waters).

In the stock in the northern North Sea and west of Scotland (Divs. 4a and 6a), biomass of both species has been estimated for the years 1985-2019. Biomass has been increasing since the mid-2000s, during the past 15 years. Fishing effort has declined since the mid-1990s. Lepidorhombus boscii constitutes a negligible proportion of the commercial catch as compared to that of L. whiffiagonis (ICES 2019).

In the stock in the Rockall Trough (Div. 6b), biomass of both species has been estimated for the years 2005-2019. Biomass has been generally increasing or remaining stable since 2012, or over the past 8 years. There is, however, high uncertainty associated with the biomass index. Fishing mortality estimates are also uncertain due to the poor estimates of the discard rate, but mortality estimates have been below the recommended limit since about 2007 (ICES 2019).

In the stock west and southwest of Ireland and in the Bay of Biscay (ICES Divisions 7b-k, 8a, 8b and 8d), spawning stock biomass (SSB) has been estimated for the years 1984-2019. SSB has generally increased over 14 years since the time series low in 2006, and has sharply increased since 2015 to levels exceeding those in the beginning of the time series. Recruitment has been relatively stable over time and above average in the most recent years. Fishing mortality has been mostly declining since the mid-2000s (ICES 2019; 2020). The abundance of L. boscii is low in the area from the Celtic Sea (Subarea 7) to the Bay of Biscay (Divisions 8abd) compared to that of L. whiffiagonis [START_REF] Rodríguez-Gutierrez | Spanish onshore sampling of Lepidorhombus spp[END_REF]. According to the fishery independent survey conducted annually by Spain on the Porcupine Bank (Divs. 7c and 7k) since 2001, biomass and abundance of this species have increased over the past 19 years. Both biomass and abundance of this species increased sharply in 2019 [START_REF] Ruiz-Pico | budegassa (black anglerfish) and Lophius piscatorius (white anglerfish), Lepidorhombus boscii (four-spot megrim) and Lepidorhombus whiffiagonis (megrim) from the Spanish Ground Fish Survey on the Porcupine bank (NE Atlantic). Working Document to be presented to the Working Group for the Bay of Biscay and the Iberian Waters Ecoregion[END_REF]. Improvements in available data and stock assessment modelling have occurred recently, but the survey area does not sufficiently cover the stock area, so a level of uncertainty remains (ICES 2020; E. Kelly pers. comm. 2020).

Both L. boscii and L. whiffiagonis are taken from the fishing areas in the Cantabrian Sea and Atlantic Iberian waters (ICES Divisions 8c and 9a). Lepidorhombus boscii is taken in mixed-species demersal fisheries off Portugal and Spain and 'megrim' represents about 5% of the total landings with L. boscii constituting the large majority of those landings. Discarding undersized individuals is frequent and historically not well quantified, which introduces uncertainty to the management of this species [START_REF] Abad | Integrating spatial management measures into fisheries: The Lepidorhombus spp. case study[END_REF]. Spawning stock biomass (SSB) has been estimated for the years 1986-2019. SSB has generally increased over the past 18 years since the time series low in 2001. Recruitment has been variable over time. Fishing mortality has been variable with a generally declining trend since the early 1990s and with further decline since 2015 (ICES 2020).

Mediterranean Sea: This species is relatively common in the Ionian Sea [START_REF] Politou | Fisheries resources in the deep waters of the eastern Mediterranean (Greek Ionian Sea)[END_REF][START_REF] D'onghia | Biodiversity of the upper slope demersal community in the Eastern Mediterranean: preliminary comparison between two areas with and without trawl fishing[END_REF][START_REF] Madurell | Trophodynamics of a deep-sea demersal fish assemblage from the bathyal eastern Ionian Sea (Mediterranean Sea)[END_REF][START_REF] Mytilineou | Deepwater fish fauna in the Eastern Ionian Sea[END_REF], the central Tyrrhenian Sea [START_REF] Carpentieri | Day-night variations in the demersal nekton assemblage on the Mediterranean shelf break[END_REF]) and the north Aegean Sea [START_REF] Vassilopoulou | Abundance and distribution of four-spotted megrim Lepidorhombus boscii) in the Aegean Sea[END_REF][START_REF] Sartor | Distribution and abundance of Citharus linguatula, Lepidorhombus boscii, and Solea vulgaris (Osteichthyes : Pleuronectiformes) in the Mediterranean sea[END_REF][START_REF] Labropoulou | Community structure and diversity of demersal fish assemblages: the role of fishery[END_REF]. It is also common and abundant around the Balearic Islands (Mallorca and Menorca) in the western Mediterranean [START_REF] Johnson | Effect of prey abundance and size on the distribution of demersal fishes[END_REF]. It is commercially valued in Turkish waters of the Aegean and Mediterranean, but data on stock trends are not available [START_REF] Cengiz | Age and growth of the four-spotted megrim (Lepidorhombus boscii Risso, 1810) from Saros Bay (Northern Aegean Sea, Turkey)[END_REF], C. Turan pers. comm. 2020). The prohibition of trawling in part of this area has caused fishing effort to decline over time [START_REF] Cengiz | Distribution and abundance of Four-spotted megrim (Lepidorhombus boscii Risso, 1810) from Saros Bay (Northern Aegean Sea, Turkey)[END_REF][START_REF] Cengiz | Some reproductive characteristics of Four-spotted megrim (Lepidorhombus boscii Risso, 1810) from Saros Bay (Northern Aegean Sea, Turkey)[END_REF]. It is also commercially important in the northeastern Mediterranean (Vassilopoulou 2006). Data are not available to quantify subpopulation trends in this region (M. Cardinale and P. Martinez pers. comm. 2020).

Current Population Trend: Increasing

Habitat and Ecology (see Appendix for additional information)

This demersal species occurs on soft bottoms on the continental shelf and slope (Nielsen 1990, Chanet and[START_REF] Chanet | Expliquer la biologie des espèces par leurs relations de parenté. Exemple des Scophthalmidae [Teleostéens : Pleuronectiformes[END_REF]. It prefers fine sand sediments on the middle-outer shelf at depths between about 150-250 m [START_REF] Fernández-Zapico | Environmental drivers of the distribution of the order Pleuronectiformes in the Northern Spanish Shelf[END_REF]. The maximum total length is 49 cm [START_REF] Wienerroither | Teleostei, Scophthalmidae: four-spot megrim spotted in Norwegian waters[END_REF]. The length-weight relationship is reported in [START_REF] Silva | Length-weight relationships of marine fish collected from around the British Isles[END_REF]. It has been aged to a maximum of 15 years [START_REF] Fuertes | Edad y crecimiento del gallo (Lepidorhombus boscii, RISSO) en el litoral gallego [Espana] . Investigacion Pesquera[END_REF]). Age at first maturity is about 2 years [START_REF] Vassilopoulou | Abundance and distribution of four-spotted megrim Lepidorhombus boscii) in the Aegean Sea[END_REF]Ondrias 1999, Cengiz et al. 2013;2015) and natural mortality is estimated at 0.24 [START_REF] Cengiz | Distribution and abundance of Four-spotted megrim (Lepidorhombus boscii Risso, 1810) from Saros Bay (Northern Aegean Sea, Turkey)[END_REF]. Natural mortality in the Bay of Biscay and Iberian Waters Ecoregion is estimated at 0.2 (ICES 2020). When applying the following equation recommended by the IUCN Red List methods: 1/adult mortality + age of first reproduction, the generation length is calculated to be about 7 years.

Systems: Marine

Use and Trade

This species is almost exclusively caught in mixed bottom-trawl fisheries targeting demersal fishes, including L. whiffiagonis, hake, anglerfish and species of lobsters (Nephrops species). It is one of the most important species in terms of commercial demersal fisheries on the Galician shelf [START_REF] Fuertes | Edad y crecimiento del gallo (Lepidorhombus boscii, RISSO) en el litoral gallego [Espana] . Investigacion Pesquera[END_REF] and the main market for this species is located in Spain [START_REF] Crego-Prieto | Inaccurate labelling detected at landings and markets: The case of European megrims[END_REF]. It is also commercially important in the Mediterranean Sea (Vassilopoulou 2006[START_REF] Cengiz | Some reproductive characteristics of Four-spotted megrim (Lepidorhombus boscii Risso, 1810) from Saros Bay (Northern Aegean Sea, Turkey)[END_REF]. Smaller individuals are frequently discarded as bycatch (ICES 2020).

Threats

Fishing activity is not expected to be driving global-scale declines approaching a threatened or Near Threatened level at this time.

Conservation Actions (see Appendix for additional information)

The International Council for the Exploration of the Sea provides advice for setting combined total allowable catch limits in the Atlantic Ocean for both this species and L. whiffiagonis. It has been recommended to amend this management strategy by separating the catch limits by individual species to avoid overexploitation of either species. Improvements are needed in data collection on discards [START_REF] Ices | Four-spot megrim (Lepidorhombus boscii) in divisions 7.b-k, 8.a-b, and 8[END_REF]2020). Regulations set by the European Union include total allowable catch limits, bycatch monitoring and minimum size limits and the Landing Obligation that prohibits the discarding of species which are subject to catch limits and those which are subject to minimum landing sizes (MLS) in the Mediterranean. It has been suggested to consider using spatial closures and an increase in gear selectivity to reduce the capture of immature individuals in Iberian waters [START_REF] Abad | Integrating spatial management measures into fisheries: The Lepidorhombus spp. case study[END_REF].

It is recommended to designate minimum size limits on catches and a seasonal fishing restriction during spawning season to encourage the sustainability of this resource in Turkish waters [START_REF] Cengiz | Some reproductive characteristics of Four-spotted megrim (Lepidorhombus boscii Risso, 1810) from Saros Bay (Northern Aegean Sea, Turkey)[END_REF].

This species was assessed as Least Concern in the European regional assessment conducted in 2014.

Credits Assessor(s):

Abad, E., Cardinale, M., Chanet, B., Kelly, E., Martínez Portela, P., Munroe, T.A. & Turan, C.

Reviewer(s):

Linardich, C.

Facilitator(s) and Compiler(s):

Linardich, C.

© The IUCN Red List of Threatened Species: Lepidorhombus boscii -published in 2021. https://dx.doi.org/10.2305/IUCN.UK.2021-2.RLTS.T198729A144940278.en

Disclaimer

To make use of this information, please check the Terms of Use.

External Resources

For Supplementary Material, and for Images and External Links to Additional Information, please see the Red List website.

Appendix

Habitats

Additional Data Fields Distribution

Lower depth limit (m): 800

Upper depth limit (m): 7

Habitats and Ecology

Generation Length (years): 7

The IUCN Red List Partnership

The IUCN Red List of Threatened Species™ is produced and managed by the IUCN Global Species Programme, the IUCN Species Survival Commission (SSC) and The IUCN Red List Partnership.

The IUCN Red List Partners are: ABQ BioPark; Arizona State University; BirdLife International; Botanic Gardens Conservation International; Conservation International; Missouri Botanical Garden; NatureServe; Re:wild; Royal Botanic Gardens, Kew; Sapienza University of Rome; Texas A&M University; and Zoological Society of London.


Lepidorhombus Whiffiagonis

Whiff Megrim

Cardinale, M E Abad

Martínez Portela

T A & Turan

Harvest level trends

Keywords: Animalia Chordata Actinopterygii Pleuronectiformes Scophthalmidae Whiff Megrim, European Common Megrim, Whiff Native, Extant (resident): Albania, Algeria, Belgium, Bosnia and Herzegovina, Croatia

This widely distributed, demersal species is common in parts of its range and has an estimated generation length of 8 years. It is taken in commercial fisheries and also constitutes a proportion of the bycatch of demersal trawl fisheries in much of its range. Stock assessment estimates across most of its range in the Atlantic indicate biomass has been increasing over the past 8 to 19 years depending on the stock area. The exception to this trend is that spawning stock biomass of this species in Icelandic waters has declined by 82% over about the past two generations. The cause of this decline is not understood and requires further study. Abundance data are limited for the subpopulation in the Mediterranean Sea and should be examined further to gain knowledge about abundance trends for this species in this region. For the population, fishing activity is not driving global-scale declines approaching a threatened or Near Threatened level at this time, nor is it expected to do so in the near future. Therefore, this species is listed as Least Concern. It is recommended that improved monitoring of individual catch data for this species be conducted to improve future assessments.

Population

This species is fairly common across its range [START_REF] Went | List of Irish Fishes[END_REF][START_REF] D'onghia | Biodiversity of the upper slope demersal community in the Eastern Mediterranean: preliminary comparison between two areas with and without trawl fishing[END_REF], Politou et al. 2003[START_REF] Mytilineou | Deepwater fish fauna in the Eastern Ionian Sea[END_REF][START_REF] Gerritsen | Differences in habitat selection of male and female megrim ( i> Lepidorhombus whiffiagonis, Walbaum) to the west of Ireland. A result of differences in life-history strategies between the sexes?[END_REF]. Catch data generally comprises landings for both L. boscii and L. whiffiagonis. Lepidorhombus whiffiagonis occurs more abundantly in shallower depths (100-200 m), while L. boscii is more abundant in deeper depths (100-350 m). In addition, L. boscii appears to tolerate saltier bottom waters than does L. whiffiagonis [START_REF] Abad | Integrating spatial management measures into fisheries: The Lepidorhombus spp. case study[END_REF]. Lepidorhombus whiffiagonis is more common than L. boscii in the northern parts of their range [START_REF] Rodríguez-Gutierrez | Spanish onshore sampling of Lepidorhombus spp[END_REF]. According to genetic studies, connectivity between Atlantic and Mediterranean subpopulations is low [START_REF] Danancher | Population differentiation in megrim (Lepidorhombus whiffiagonis) and four spotted megrim (Lepidorhombus boscii) across Atlantic and Mediterranean waters and implications for wild stock management[END_REF], but further work is needed to determine connectivity between subpopulations in the Celtic Sea and Bay of Biscay (ICES 2015). In the Atlantic Ocean, it is caught in the following ICES divisions: 4a and 6a (northern North Sea and West of Scotland); 6b (Rockall Trough); 7b-k, 8a, 8b and 8d (west and southwest of Ireland, Bay of Biscay including Porcupine Bank); 8c and 9a (Cantabrian Sea and Atlantic Iberian waters).

Atlantic:

In the stock in the northern North Sea and west of Scotland (Divs. 4a and 6a), biomass of both species has been estimated for the years 1985-2019. Biomass has been increasing in these areas for the past 15 years since the mid-2000s. Fishing effort has declined since the mid-1990s. Lepidorhombus whiffiagonis constitutes the majority of the commercial catches compared to the smaller contribution of L. boscii (ICES 2019). The value of this fishery in the North Sea has increased in the recent decade and the distribution and abundance of both species has extended northward [START_REF] Macdonald | Fishers' knowledge as an indicator of spatial and temporal trends in abundance of commercial fish species: megrim (Lepidorhombus whiffiagonis) in the northern North Sea[END_REF].

Off Iceland, this species is taken as bycatch in relatively small quantities and is not directly targeted. Spawning stock biomass (SSB) off Iceland has been estimated for this species for the years 1985-2020. SSB declined from the late-1980s to 2000, then recovered by 2006, and gradually declined to 2018 after which it declined somewhat steeply in 2019 and 2020. Over the past 14 years since 2006, SSB has declined by 82%. The juvenile abundance index has been low since about 2012. The cause of this decline is not understood. Three generations ago, in about 1996, SSB was at a similar level as it was in 2020. Catch data are highly uncertain prior to 2009 as this species was not well reported in logbooks in the past. The occurrence and abundance, as well as annual total catches of L. boscii have been increasing off Iceland in the recent decade [START_REF] Valdimarsson | Hydrographic variablility in Icelandic waters during recent decades and related changes in distribution of some fish species[END_REF], MFRI 2020).

In the stock in the Rockall Trough (Div. 6b), biomass of both species has been estimated for the years 2005-2019. Biomass has been generally increasing or stable over the past 8 years since 2012. There is, however, high uncertainty associated with the biomass index. Fishing mortality estimates also uncertain due to poor estimates of discard rates have been below the recommended limit since about 2007 (ICES 2019).

In the stock west and southwest of Ireland and in the Bay of Biscay (ICES Divisions 7b-k, 8a, 8b and 8d), spawning stock biomass (SSB) has been estimated for the years 1984-2019. SSB has generally increased over the past 14 years since the time series low in 2006, and has sharply increased since 2015 to levels exceeding those in the beginning of the time series. Recruitment has been relatively stable over time and has been above average in the most recent years. Fishing mortality has been mostly declining since the mid-2000s (ICES 2019;[START_REF] Ices | Working Group for the Bay of Biscay and the Iberian Waters Ecoregion[END_REF]. The abundance of L. boscii is low in the area from the Celtic Sea (Subarea 7) to Bay of Biscay (Divisions 8abd) compared to that of L. whiffiagonis [START_REF] Rodríguez-Gutierrez | Spanish onshore sampling of Lepidorhombus spp[END_REF]. According to the fishery independent survey conducted annually by Spain since 2001 on the Porcupine Bank (Divs. 7c and 7k), biomass and abundance of this species has increased over the past 19 years [START_REF] Ruiz-Pico | budegassa (black anglerfish) and Lophius piscatorius (white anglerfish), Lepidorhombus boscii (four-spot megrim) and Lepidorhombus whiffiagonis (megrim) from the Spanish Ground Fish Survey on the Porcupine bank (NE Atlantic). Working Document to be presented to the Working Group for the Bay of Biscay and the Iberian Waters Ecoregion[END_REF]).

Both L. boscii and L. whiffiagonis in the stock from the Cantabrian Sea and Atlantic Iberian waters (ICES Divisions 8c and 9a) are caught in the same fishery. Lepidorhombus whiffiagonis is caught in mixedspecies demersal fisheries off Portugal and Spain with 'megrim' representing about 6-27% (between 1986 and 2017) of the annual total landings, and L. boscii constituting the large majority of those landings. Discarding of undersized individuals is frequent and historically not well quantified, and this introduces uncertainty to the management of this species [START_REF] Abad | Integrating spatial management measures into fisheries: The Lepidorhombus spp. case study[END_REF]. Spawning stock biomass (SSB) has been estimated for the years 1986-2020. SSB has generally increased over the past 12 years since the time series low in 2008, and has sharply increased since 2015. Recruitment was particularly high from 2015 to 2019. Fishing mortality has been variable with a generally declining trend since the early 1990s and a sharp decline since 2015 (ICES 2020).

Mediterranean Sea: This species is common and abundant in the central and southern Adriatic Sea and is a main target species of commercial trawl fisheries operating in that area [START_REF] Danancher | Population differentiation in megrim (Lepidorhombus whiffiagonis) and four spotted megrim (Lepidorhombus boscii) across Atlantic and Mediterranean waters and implications for wild stock management[END_REF]Garcia-Vazquez 2009, Šantić et al. 2017). It is also trawled off the Aegean and northeastern Mediterranean coasts of Turkey [START_REF] Keskin | Distribution of the Demersal Fishes on the Continental Shelves of the Levantine and North Aegean Seas (Eastern Mediterranean)[END_REF]. Data are not available to quantify subpopulation trends in this region (M. Cardinale and P. Martinez pers. comm. 2020).

Current Population Trend: Increasing

Habitat and Ecology (see Appendix for additional information)

This demersal species occurs on soft mud or muddy sand bottoms [START_REF] Muus | Havfisk og Fiskeri i Nordvesteuropa[END_REF]Dahlstrøm 1989, Chanet and[START_REF] Chanet | Expliquer la biologie des espèces par leurs relations de parenté. Exemple des Scophthalmidae [Teleostéens : Pleuronectiformes[END_REF]. It prefers fine-medium sand sediments on the middle-outer shelf at depths between 150-250 m [START_REF] Fernández-Zapico | Environmental drivers of the distribution of the order Pleuronectiformes in the Northern Spanish Shelf[END_REF]. Growth in larvae and juveniles are influenced by cyclical interannual environmental and feeding conditions [START_REF] Landa | Megrim (Lepidorhombus whiffiagonis) in northern Iberian waters: Age determination corroboration, growth, abundance and mortality of the year-classes[END_REF]. The maximum total length is 70 cm (MFRI 2020). The length-weight relationship is reported in [START_REF] Silva | Length-weight relationships of marine fish collected from around the British Isles[END_REF].

Maturity occurs at 2-4 years [START_REF] Macdonald | Spatial variation in life history characteristics of common megrim (Lepidorhombus whiffiagonis) on the Northern Shelf[END_REF][START_REF] Fernández-Zapico | Environmental drivers of the distribution of the order Pleuronectiformes in the Northern Spanish Shelf[END_REF]. Longevity is 14 years (Landa andPiñeiro 2000, Abad 2015). Natural mortality in the Bay of Biscay and Iberian Waters Ecoregion is estimated to be 0.2 (ICES 2020). When applying the following equation recommended by the IUCN Red List methods: 1/adult mortality + age of first reproduction, the generation length is calculated to be about 8 years.

Systems: Marine

Use and Trade

This species is almost exclusively caught in mixed bottom-trawl fisheries targeting demersal fishes, including L. boscii, hake, anglerfish and species of lobsters (Nephrops species). Lepidorhombus boscii is one of the most important species in terms of commercial demersal fisheries on the Galician shelf (Fuertes 1978), and the main markets for this species are located in Spain (Crego-Prieto et al. 2012). It is also commercially important in the Mediterranean (Vassilopoulou 2006(Vassilopoulou , Šantić et al. 2017)). Smaller individuals are frequently discarded at sea as unwanted bycatch [START_REF] Ices | Working Group for the Bay of Biscay and the Iberian Waters Ecoregion[END_REF].

Threats

This species is targeted by commercial fishing interests and also constitutes a portion of the bycatch of demersal trawl fisheries. Thus far, these fishing activities are not driving global-scale declines approaching a threatened or Near Threatened level for this species at this time, nor is it expected that fishing activities will result in a threatened or Near Threatened assessment in the near future.

Conservation Actions (see Appendix for additional information)

The International Council for the Exploration of the Sea (ICES) provides management advice for setting combined total allowable catch limits for this species and L. boscii in the northeast Atlantic waters. It has been recommended to amend this management strategy to separate catch limits by individual species to avoid overexploitation of either species. Improvements are needed in data collection on estimating discards (ICES 2019). Regulations set by the European Union include total allowable catch limits, bycatch monitoring and minimum size limits for fishes landed by commercial fisheries and the Landing Obligation that prohibits the discarding of species which are subject to catch limits and those which are subject to minimum landing sizes (MLS) in the Mediterranean. Also under consideration in Iberian waters is the use of spatial closures and an increase in gear selectivity to reduce capture of immature individuals [START_REF] Abad | Integrating spatial management measures into fisheries: The Lepidorhombus spp. case study[END_REF].

This species was assessed as Least Concern in the European regional assessment conducted in 2014.

Credits Assessor(s):

Abad, E., Cardinale, M., Chanet, B., Iriondo, A., Martínez Portela, P., Munroe, T.A. & Turan, C.

Reviewer(s):

Linardich, C.

Facilitator(s) and Compiler(s):

Linardich, C.

© The IUCN Red List of Threatened Species: Lepidorhombus whiffiagonis -published in 2021. https://dx.doi.org/10.2305/IUCN.UK.2021-2.RLTS.T198730A144939913.en

Disclaimer

To make use of this information, please check the Terms of Use.

External Resources

For Supplementary Material, and for Images and External Links to Additional Information, please see the Red List website.

Appendix

Habitats

Distribution

Lower depth limit (m): 850

Upper depth limit (m): 20

Habitats and Ecology

Generation Length (years): 8

The IUCN Red List Partnership

The IUCN Red List of Threatened Species™ is produced and managed by the IUCN Global Species Programme, the IUCN Species Survival Commission (SSC) and The IUCN Red List Partnership.

The IUCN Red List Partners are: ABQ BioPark; Arizona State University; BirdLife International; Botanic Gardens Conservation International; Conservation International; Missouri Botanical Garden; NatureServe; Re:wild; Royal Botanic Gardens, Kew; Sapienza University of Rome; Texas A&M University; and Zoological Society of London.


Siskey, M S Cadrin

T A & Munroe

B Bruno Chanet

Chanet

Keywords:

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

Population

Canada: No directed fishery for this species occurs in Canadian waters and it is uncommon there compared to its abundance further south in U.S. waters [START_REF] Stokesbury | Windowpane seasonal distribution and survey availability on the southern portion of Georges Bank, USA[END_REF]. It is common in the southern Gulf of St. Lawrence in shallow, warmer waters, but is not fished there. Abundance in the Northumberland Strait has not declined since surveys began in 2001 but juveniles less than 10 cm in length were absent from the survey catch, indicating this area may not be utilized for nursery grounds [START_REF] Benoit | Impacts of environmental change and direct and indirect harvesting effects on the dynamics of a marine fish community[END_REF][START_REF] Bosman | Fish assemblages in a north Atlantic coastal ecosystem: Spatial patterns and environmental correlates[END_REF][START_REF] Hanson | Abundance, distribution, and diet of a small-bodied ecotype of windowpane[END_REF].

United States: This species is most abundant from the Gulf of Maine to the Chesapeake Bay in southern Virginia [START_REF] Hendrickson | Status of fishery resources off the northeastern U.S.: Windowpane flounder (Scophthalmus aquosus)[END_REF][START_REF] Stokesbury | Windowpane seasonal distribution and survey availability on the southern portion of Georges Bank, USA[END_REF]. Two fishery stocks are commercially exploited in U.S. waters: the Gulf of Maine/Georges Bank stock and the southern New England/Mid-Atlantic stock. Fishery independent scientific surveys are conducted annually in U.S. waters. Currently, the total stock biomasses (based on swept-area calculations using estimated gear efficiencies) are similar, but the biomass of the southern stock was estimated to be slightly smaller than that of the northern stock in terms of total tons in 2019 (NEFSC 2020).

The Gulf of Maine/Georges Bank stock has been overfished since 2007, but overfishing is not occurring. Biomass estimates are available for the years 1977-2019 (NEFSC 2020). A period of higher survey catch per unit effort (kg/tow) occurred in the 1970s and 1980s compared to a period of lower CPUE in the 1990s and 2000s. Annual abundance indices based on fishery independent scientific surveys have declined since 2000 despite decreasing fishing mortality and while being under a rebuilding plan. Based on length frequencies of the fish caught in the survey, no evidence indicates a lack of annual recruitment. Since about 2006, survey biomass has been relatively stable. Further research is needed on sources of mortality that may have increased as well as exploring a change in stock assessment models (NEFSC 2017, NOAA Fisheries 2020, T. Chute pers. comm. 2020). Regional shifts in water temperature may explain some of this population trend as the changes in abundance of this species are known to occur depending on changes in water temperature [START_REF] Stokesbury | Windowpane seasonal distribution and survey availability on the southern portion of Georges Bank, USA[END_REF].

The southern New England/Mid-Atlantic stock is not overfished, and overfishing is not occurring. Biomass estimates are available for the years 1977-2019. A period of steady decline in survey catch per unit effort (kg/tow) occurred until the 1990s, but CPUE has remained relatively stable or has increased slightly since then. Since about 2006, biomass in this stock has increased overall. Biomass still remains well below levels recorded during the early 1980s but it is above the recommended biomass sustainability limit. Fishing mortality is low. Survey biomass indices have been generally increasing since 2000 though the stock was considered overfished in 2005 and considered recovered by 2008. The adult condition index appears to be stable (NEFSC 2017, NOAA Fisheries 2020). Abundance in the New York/New Jersey Harbor estuary was low during a multi-year period of cold winter temperatures [START_REF] Wilber | Windowpane flounder (Scophthalmus aquosus) and winter flounder (Pseudopleuronectes americanus) responses to cold temperature extremes in a Northwest Atlantic estuary[END_REF]. The cause of biomass decline is unknown. Both stocks have experienced past periods of lower biomass, including in the late 1980s and early 1990s (NEFSC 2020). Comparison of surveys conducted by the federal government with those conducted by state agencies, which cover different depth strata in certain years within the time series, may help clarify stock trends (NEFSC 2008).

Current Population Trend: Stable

Habitat and Ecology (see Appendix for additional information)

This species generally inhabits sand to sand/silt and less frequently, mud bottoms on the inner continental shelf and in high salinity regions (generally) of bays and estuaries [START_REF] Dahlberg | An ecological study of Georgia coastal fishes[END_REF][START_REF] Weinstein | Shallow marsh habitats as primary nurseries for fishes and shellfish, Cape Fear River, North Carolina[END_REF], Wenner et al. 1982[START_REF] Murdy | Assessment of 19 Northeast Groundfish Stocks through 2007: Report of the 3rd Groundfish Assessment Review Meeting (GARM III)[END_REF][START_REF] Able | Ecology of Estuarine Fishes: Temperate Waters of the Western North Atlantic[END_REF]. This species avoids hypoxic conditions. Both adults and juveniles are found on the inner and mid-continental shelf year-round. Seasonal shifts in the location of high abundance of adults coincides with changes in water temperature throughout the year [START_REF] Stokesbury | Windowpane seasonal distribution and survey availability on the southern portion of Georges Bank, USA[END_REF]. Juveniles are present year-round within some estuaries. Juveniles move from shallow, inshore waters to deeper offshore waters as they grow [START_REF] Chang | Essential fish habitat source document: Windowpane, Scophthalmus aquosus, life history and habitat characteristics[END_REF].

Spawning season and location were discussed in detail by [START_REF] Able | Ecology of Estuarine Fishes: Temperate Waters of the Western North Atlantic[END_REF] who noted that spawning occurs over a protracted season from February to November. Spawning occurs on the inner continental shelf, Georges Bank and also in high salinity portions of estuaries. Spawning begins in spring in the southern Middle Atlantic Bight and coastal habitats of North and South Carolina (Morse and Able 1995, Able and Fahay 2010), reaches a peak in summer on Georges Bank, and then resumes in fall as a second part of a split season in the southern Middle Atlantic Bight (Able and[START_REF] Morse | Distribution and life history of windowpane, Scophthalmus aquosus, off the northeastern United States[END_REF][START_REF] Able | Ecology of Estuarine Fishes: Temperate Waters of the Western North Atlantic[END_REF]. This split spawning season produces two cohorts. Eggs and larvae are pelagic. Juveniles (10-20 mm standard length) settle from the pelagic in estuaries and on the continental shelf for the spring cohort, and primarily on the shelf for the fall cohort [START_REF] Morse | Distribution and life history of windowpane, Scophthalmus aquosus, off the northeastern United States[END_REF]. Growth rates observed for individuals from spring and fall cohorts were different, with growth rates of the spring cohort faster than those of the fall-spawned individuals (Able and Fahay 2010). These growth differences may produce differential survival rates for the two cohorts (Able and Fahay 2010) as sizeselected survival due to low winter temperatures was observed by [START_REF] Neuman | Overwinter growth and mortality of young-of-the-year windowpanes: Cohort-specific responses[END_REF] for youngof-the-year individuals. Smaller fish of both cohorts suffered higher mortalities than larger individuals, suggesting that spring-spawned individuals, which were larger at wintertime than were fall-spawned individuals, would have higher odds of over-wintering survival. This species feeds primarily on mysid shrimps, small fishes, and decapod shrimps [START_REF] Bowman | Food of northwest Atlantic fishes and two common species of squid[END_REF]. It also occasionally consumes a variety of other prey including chaetognaths, amphipods, isopods, euphausiids, other crustaceans, squids, mollusks, polychaetes, salps, and ascidians [START_REF] Hildebrand | Fishes of Chesapeake Bay[END_REF][START_REF] Bowman | Food of northwest Atlantic fishes and two common species of squid[END_REF][START_REF] Able | Ecology of Estuarine Fishes: Temperate Waters of the Western North Atlantic[END_REF].

The maximum total length is 51 cm [START_REF] Hendrickson | Status of fishery resources off the northeastern U.S.: Windowpane flounder (Scophthalmus aquosus)[END_REF]). Length at 50% maturity (L50) occurs at sizes slightly greater than 20 cm and 1.5 years of age (T. Chute pers. comm. 2020). Longevity is estimated to be 8 years [START_REF] Moore | Studies on the marine resources of Southern New England, VI: The sand flounder, Lophopsetta aquosa (Mitchill); a general study of the species with special emphasis on age determination by means of scales and otoliths[END_REF]. As an estimate of natural mortality is not available, the recommended IUCN Red List equation where generation length = (1/adult mortality) + age of first reproduction, was not applied here. When applying an age at first reproduction of 1.5 years and longevity of 8 years, generation length for this species is estimated at 5 years based on the following alternative equation recommended by the IUCN Red List methods: Age at first reproduction + (Age at last reproduction -age at first reproduction)/2. By comparison, Scophthalmus rhombus, an eastern Atlantic species that reaches a slightly larger size than S. aquosus, has an estimated generation length of 7 years based on an age at first maturity of 2 years.

Systems: Marine

Use and Trade

Because of its relatively small size and thin body, this species is not directly targeted by recreational or commercial fisheries. It is taken as bycatch in commercial bottom trawl and dredge fisheries [START_REF] Grothues | Reducing discards of flatfish in the sea scallop dredge fishery by dredge pause[END_REF][START_REF] Stokesbury | Windowpane seasonal distribution and survey availability on the southern portion of Georges Bank, USA[END_REF], and sometimes retained in the trawl fisheries. Recreational catches occur but are negligible [START_REF] Hendrickson | Status of fishery resources off the northeastern U.S.: Windowpane flounder (Scophthalmus aquosus)[END_REF].

Threats (see Appendix for additional information)

The cause of declines in subpopulations (stocks) of this species is not well understood. Fishing pressure has been low, but mortality estimates for individuals in the discarded bycatch, which are considered to be 100% regardless of fishing gear type (T. Chute pers. comm. 2020), may contribute to these declines [START_REF] Hendrickson | Status of fishery resources off the northeastern U.S.: Windowpane flounder (Scophthalmus aquosus)[END_REF]. Also, as this species is sensitive to shifts in water temperature, stock size and location may be impacted by climate change [START_REF] Wilber | Windowpane flounder (Scophthalmus aquosus) and winter flounder (Pseudopleuronectes americanus) responses to cold temperature extremes in a Northwest Atlantic estuary[END_REF][START_REF] Stokesbury | Windowpane seasonal distribution and survey availability on the southern portion of Georges Bank, USA[END_REF].

Estuarine fish habitats in Downeast Maine are generally characterized by low to very low composite stressor index scores, while those in southern Maine and New Hampshire have higher stressor scores (Greene et al. 2015). If environmental conditions decline in these estuaries, negative impacts can be expected on populations of species residing in these habitats, including that of this species.

Conservation Actions (see Appendix for additional information)

The U.S. stocks are managed by NOAA Fisheries and the New England Fishery Management Council under the Northeast Multispecies Fishery Management Plan. The Gulf of Maine/Georges Bank stock is under a rebuilding plan. Fishing regulations include vessel permitting, recreational restrictions, seasonal area fishing closures, minimum fish size and annual catch limits. Since 2010, this species has not been permitted to be possessed in U.S. federal waters. Research is needed on causes of past decline.

Credits

Reviewer(s):

Linardich, C.

Contributor(s):

Chute, T.

Facilitator(s) and Compiler(s):

Linardich, C.

  Siskey, M., Munroe, T.A. & Chanet, B.

© The IUCN Red List of Threatened Species: Scophthalmus aquosus -published in 2021. https://dx.doi.org/10.2305/IUCN.UK.2021-2.RLTS.T190417A16510832.en

External Resources

For Supplementary Material, and for Images and External Links to Additional Information, please see the Red List website.

Appendix

Habitats and Ecology

Generation Length (years): 5

The IUCN Red List Partnership

The IUCN Red List of Threatened Species™ is produced and managed by the IUCN Global Species Programme, the IUCN Species Survival Commission (SSC) and The IUCN Red List Partnership.

The IUCN Red List Partners are: ABQ BioPark; Arizona State University; BirdLife International; Botanic Gardens Conservation International; Conservation International; Missouri Botanical Garden; NatureServe; Re:wild; Royal Botanic Gardens, Kew; Sapienza University of Rome; Texas A&M University; and Zoological Society of London.