Keywords: Chronoamperometry, Calcium carbonate, Modeling, Nucleation-growth process, Simulation

Nucleation-growth process of calcium carbonate on rotating disk electrode in mineral potable water

Introduction

Calcium carbonate deposition leads to the formation of compact layers which show by themselves efficient protection properties with respect to dioxygen diffusion. Its precipitation remains a problem for industrial and domestic installations [START_REF] Roques | Fondements théoriques du traitement chimique des eaux[END_REF]. Several investigations were performed in order to get a better understanding about the CaCO 3 crystallization process [START_REF] Teghidet | Calcite epitaxy on Au and Ag (1 1 1)[END_REF][START_REF] Rinat | Electrocrystallization of calcium carbonate on carbon-based electrodes[END_REF][START_REF] Beaunier | Investigation of electrochemical calcareous scaling Nuclei counting and morphology[END_REF]. Gabrielli et al. [START_REF] Gabrielli | Characterization of the efficiency of antiscale treatments of water -Part I: Chemical processes[END_REF][START_REF] Gabrielli | Nucleation and growth of calcium carbonate by an electrochemical scaling process[END_REF] have proposed a theoretical approach to interpret the measurement obtained at the first step of precipitation. It was demonstrated that whether the mass measurement was proportional to t 2 , the nucleation was instantaneous whereas a t 3 proportionality corresponded to a progressive nucleation. Devos et al. [START_REF] Devos | Nucleation-growth processes of scale crystallization under electrochemical reaction investigated by in situ microscopy[END_REF][START_REF] Devos | Nucleation-growth process of scale electrodeposition: influence of the supersaturation[END_REF] have developed an original set-up for following calcite deposition by coupling electrogravimetry and optical measurements in an impinging jet cell. In this way, three kinds of information were accessible simultaneously: the mass of CaCO 3 on the surface, the faradic current of dioxygen reduction, and the direct observation of the growth process under an optical microscope. It was clearly established that the growth rate of the vaterite was faster than the one measured for the calcite on the same electrode surface.

In order to quantify the scaling's power of water; electrochemical technique such as chronoamperometry (CA) was used for monitoring kinetic rate of CaCO 3 precipitation on materials [START_REF] Hui | Evaluation methods for the scaling power of water[END_REF][START_REF] Devos | Simultaneous EIS and in situ microscope observation on a partially blocked electrode application to scale electrodeposition[END_REF][START_REF] Ras | Determination of anti-scale effect of hard water by test of electrodeposition[END_REF]. In brief, a metallic electrode was polarized at cathodic potential (-1 V vs SCE) to promote the O 2 reduction according to the equation 1

     OH e O H O 4 4 2 2 2 (1)
The formation of hydroxide ions at the electrode, from O 2 reduction as displayed in equation 1, increases the local pH [START_REF] Gabrielli | Characterization of the efficiency of antiscale treatments of water -Part I: Chemical processes[END_REF] and makes easier the calcium carbonate precipitation into a solid crystalline phase according to the following chemicals reactions

O H CO OH HCO 2 2 3 3       (in bulk) (2) 4 3 2 3 2 CaCO CO Ca     (at the interface) (3)
The data analysis of the chronoamperometric curve is commonly used for investigating nucleation and growth kinetics of CaCO 3 on metallic electrodes [START_REF] Gabrielli | Investigation of electrochemical calcareous scaling Potentiostatic current -and mass -time transients[END_REF][START_REF] Devos | Nucleation-growth process of scale electrodeposition-Influence of the mass transport[END_REF]. Until now, CA was used to classical determination of scaling time of calcite precipitation that is easy to use as a test. Indeed, the CA has permitted obtention of only partial information on the screening effect of the insulating scale deposit on the electrode surface and in particular, it has not allowed differentiation between 2-D and 3-D blocking. To a better data exploitation and understanding of nucleation-growth process, it appeared interesting to investigate experimentally and theoretically kinetics and mass transfer phenomena at mineral potable water solution/ carbon steel interface.

Experimental

Electrochemical measurements

Experiments were performed in mineral potable water containing the main species displayed in table 1. The electrochemical measurement was conducted in a three electrode cell configuration. The working electrode was a carbon steel disk mounted on rotating disk electrode. Its surface was prepared by mechanical polishing with silicon carbide paper (grade 4000), rinsed thoroughly with bidistilled water before introduction in the cell. The area in contact with the mineral potable water was equal to 0.196 cm². A platinum grid was used as a counter electrode. The potential was measured versus a saturated calomel electrode (SCE).

Electrochemical experiments were driven under potentiostatic conditions using Biologic ® interface. For all studies, the temperature of the cell was set at 20 °C. The current/ potential curves (I/E curves) were plotted at a scan rate of 1 mVs -1 by a forward scan from an anodic potential (-0.39 V vs SCE) to a cathodic potential (-1.9 V vs SCE) at various rotation speeds (100-1000 rpm). In order to generate the CaCO 3 deposition, cathodic potential was applied at -1V vs SCE for a period of 140 min at 500 rpm. Electrochemical impedance spectroscopy (EIS) measurements were performed in situ as calcareous deposits were forming on electrodes polarized at -/1 V vs SCE with a rotation speed of 500 rpm. The impedances were measured in a relatively high frequency (HF) domain in order to reduce the EIS measurement time (25 kHz-0.1 Hz)

Characterizations

Ex situ characterization of the deposit obtained after 140 minutes of deposition was performed by SEM and X-ray diffraction (XRD). SEM pictures were obtained on a FEG-SEM Zeiss Ultra55 microscope operated at 10 kV. The crystal structures of the calcareous deposits were investigated by X-ray diffraction (XRD) on a Diffractometer Panalytical with Prefix configuration using the Cu-/K α radiation (1.54 Å). XRD analysis was carried out at room temperature (20°C).

Numerical simulation

The mass transfer equations are solved using COMSOL Multiphysics 3.5, a commercial Finite Element Method (FEM) based software package. The computations were performed on a Windows7-64 bits with Pentium (R) Dual-Cor CPU 2.30 GHz with 4 GB memory.

Results and discussion

Formation of calcareous deposits on steel

The voltammetry curves displayed in Fig. 1 were obtained just after immersion at various rotation speeds (100 -1000 rpm) at fixed scan rate of 1 mV.s -1 and for a potential window from -0.4 to -1.9 V vs SCE in mineral potable water. The modulus of the cathodic current increases for each curve until reaching a plateau. This latter corresponds to the current limit of dioxygen reduction (see equation 1). Then, it follows a quick increase for more negative potential corresponding to water reduction into dihydrogen. In Fig. 2, the limiting current corresponding to the reduction plateau could be plotted against the square root of the rotation speed as in the Levich's model [START_REF] Levich | Physiochemical hydrodynamics[END_REF].

The observation of the electrode surface after the CA experiment by applying -1 V vs SCE at 500 rpm during 140 minutes of electrodeposition highlighted cubic-shaped crystals which has been obtained by SEM (Fig. 3a) and corresponds to calcite form [START_REF] Devos | Simultaneous EIS and in situ microscope observation on a partially blocked electrode application to scale electrodeposition[END_REF][START_REF] Benamor | Nucleation-growth process of calcium carbonate electrodeposition in artificial water-Influence of the sulfate ions[END_REF]. It has been verified by XRD analysis performed on the deposits. The recorded spectrum displayed in Fig. 3b confirmed that the CaCO 3 sample constituted mainly by the calcite form.

CA modeling of nucleation-growth process of calcium carbonate

In the present work, the rotating disk electrode (RDE) was used to obtain controlled conditions of convective diffusion of O 2 reduction at the bare electrode surface and then at the calcite/ electrode interface. The model assumptions were: i) the steady-state conditions; ii) no convection effects caused by the walls of the cell where the experiment is carried out, nor effects resulting from the finite dimensions of the electrode i.e. no edge effects [START_REF] Brett | Electrochemistry. Principles, Methods, and Applications[END_REF]; iii) the migration has not been taken into account according to the presence of the supporting electrolyte. The mass transport problem related to reaction (1) is described by convectivediffusion equation ( 4)

0 2       C V C D (4)
The fluid dynamics problem of a RDE for a constant rotation speed and for a fluid with constant physical properties was solved by Von Karman [START_REF] Karman | Uber Laminare und Turbulente Reibung[END_REF] and Cochran [START_REF] Cochran | The Flow due to a Rotating Disc[END_REF] and used by Barcia et al for anodic dissolution of metals under mass transport control [START_REF] Barcia | Anodic dissolution of metals under mass transport control[END_REF]. Levich applied these equations to solve the convective-diffusion equations in the case of the rotating disk electrode [START_REF] Levich | Physiochemical hydrodynamics[END_REF]. The equations of the fluid velocity components near to the rotating disk can be expressed as follow

2 2 1 2 3 51 . 0 y V y      (5) ry V r 2 1 2 3 51 . 0     (6)
where y V (cm.s -1 ) and r V (cm.s -1 ) are axial velocity component and radial velocity component, respectively,  is the rotation speed in rad.s -1 ,  is the kinematic viscosity of the electrolyte (cm 2 .s -1 ), y and r are axial distance from disk (cm) and radial coordinate (cm), respectively.

The current reflects the change in the concentration gradient at the vicinity of the electrode surface. It can be easily computed by the classical integral equation:

dS y C nFD I L 0     (7)
where C is the concentration of electroactive species, n is the number of electrons involved in the electronic transfer reaction, F is Faraday's constant, S is the electrode surface area, D is the diffusion coefficient of electroactive species in the electrolyte.

The numerical values of the all parameters mentioned above for numerical resolution are listed in table 2 for dioxygen.

Numerical resolution of the mass-transfer equations described below was performed by using finite elements. The domain area was divided into subdomains which were delimited by nodes where the unknown (C) were discretizated. The domain has been meshed using Lagrange triangular quadratic elements. Triangular elements were selected to allow local mesh refinement. It is well adapted to the problem of concentration profiles for convergence and ensured that the solution is accurate and independent of the fineness of the mesh. The distance of the simulation area, y ∞ , was taken as 10-fold higher than the diffusion layer thickness, δ O2 , of the RDE in order to avoid meshing effects.

Dioxygen reduction on a bare electrode surface

To simplify the resolution from a 3-D to a 2-D, an axial symmetry was found to decrease computation time as described through the domain area description given in Fig. 4.

The concentration profile in the diffusion layer is governed by the one dimensional steady

equation of convective diffusion 0 2 2 2 2 2       y C V y C D O y O O (8)
The boundary conditions for the case of the bare electrode are

    2 2 ) ( O O C y C (bulk solution) (9) 0 ) 0 ( 2   y C O (limiting current) (10)
The convective-diffusion equation [START_REF] Devos | Nucleation-growth process of scale electrodeposition: influence of the supersaturation[END_REF] was solved in order to calculate the concentration gradient and then equation [START_REF] Devos | Nucleation-growth processes of scale crystallization under electrochemical reaction investigated by in situ microscopy[END_REF] was used to calculate the limiting current diffusion at various rotation speeds. Fig. 5 compared the results of the numerical simulation, Levich curve and experimental points for the reduction current on the diffusion plateau at -1V/SCE. It shows a good agreement between the obtained results from numerical simulation at various rotation speeds with the expected theoretical limiting current. Indeed, the theoretical limiting current was described by the well-known Levich equation

2 2 2 4 O O O L S C FD I    (11) 2 / 1 6 / 1 3 / 1 2 2 61 . 1     v D O O (12)
Where  O2 is estimated at 28 µm for a rotation speed equals to 500 rpm.

The results displayed in Fig. 5 confirm that the dioxygen reduction at the interface electrodesolution is governed by linear diffusion verifying the Levich conditions.

Dioxygen reduction on a blocked surface

The dissolved dioxygen reduction was supposed to diffuse through the heterogeneous porous layer (in the y-direction) constituted by calcite blocks on carbon steel. In agreement with previous models derived for calcium carbonate electrocrystallization [START_REF] Beaunier | Investigation of electrochemical calcareous scaling Nuclei counting and morphology[END_REF], it was assumed that the unit area of the substrate had a finite and constant number of nucleation active sites, N 0 (µm -2 ), and that all sites were assumed to be converted into nuclei.

By considering, the hypothesis that the growth of the nucleus, S nucl , was considered as linear with time, the nucleus surface could be supposed to obey to the following equation

2 ) ( d t k t S L nucl    (13)
where k L (µm 2 min -1 ) and d (µm) were defined as the lateral growth rate and CaCO 3 crystal length, respectively.

The covered surface by the scale deposit without effect of overlapping could be expressed as

0 ) ( ) ( N t S t nucl    (14)
From equation 13 and 14, the lateral growth rate is equal to

t N t k L   0 ) (  (15)
The only measurement of the stationary current does not allow the surface coverage determination. For modeling the nucleation-growth process of calcium carbonate, the surface coverage (t) must be accurately known. According previous work in our laboratory [START_REF] Devos | Simultaneous EIS and in situ microscope observation on a partially blocked electrode application to scale electrodeposition[END_REF], the blocked area ratio of the electrode can be determined from the EIS measurement through calculation of the double layer capacitance C d values. To this goal, EIS spectra in the high frequency domain at various times during the experiment were carried out from a bare electrode until a completely blocked surface (see Appendix A). Indeed, the variation of C d value measured by EIS versus time was directly correlated to the active surface and C d constitutes a characteristic parameter for the surface coverage. As a consequence, C d0 is the capacitance value at t=/0 for a bare electrode and (1-C d /C d0 ) ratio represents the fraction of the covered electrode area (θ) calculated using in situ EIS measurements. This procedure was checked successfully in previous works [START_REF] Devos | Simultaneous EIS and in situ microscope observation on a partially blocked electrode application to scale electrodeposition[END_REF][START_REF] Ch | Characterization of calcareous deposits in artificial seawater by impedance techniques 3-/Deposit of CaCO 3 in the presence of Mg(II)[END_REF]. In the present paper, the obtained data are presented in Fig. 6 and show the fractional area covered by CaCO 3 deposition which was increasing with time and follows the empirical law in equation ( 16) according to equation [START_REF] Benamor | Nucleation-growth process of calcium carbonate electrodeposition in artificial water-Influence of the sulfate ions[END_REF] where the lateral growth is not linear with time.

    2 4 3 . 4 5 . 78 10 exp 1 ) ( t t t          (16)
θ The geometry of the active site was assuming rectangular with its length, perpendicular to the streamline of the flow (see Fig. 7), and by disregarding the diffusion in the z-direction, the problem was reduced in two dimensions (x and y). As a consequence, the complete mass balance equation was simplified as

                   2 2 2 2 2 2 2 2 2 y C x C D y C V x C V O O O O y O x (17)
The series expansions of velocity components V x , and V y were limited to the first term as described previously in reference [START_REF] Deslouis | Non stationary mass transfer in the flow due to a disk rotating in an Ostwald Fluid. Application to the measurement of the molecular diffusion coefficient in a polymer solution[END_REF].

              2 2 1 2 3 2 1 2 3 2 2 51 . 0 80 . 0 y V y r V V V y r x      (18)
For modeling CA curves during CaCO 3 deposition scaling, a 2-D and 3-D growth models were considered. It is assumed that the lateral growth of the crystal is on the surface of the substrate itself and the crystal blocked totally the corresponding surface. This assumption is different to the one of Gabrielli et al [START_REF] Gabrielli | Study of calcium carbonate scales by electrochemical impedance spectroscopy[END_REF] who considers that the face of the calcite crystal can do a small angle with the substrate. Due to the fact that a residual small current exists even at the long immersion time under consideration, a free active surface must exist and no overlapping is considered in this work. Firstly, lateral growth was considered in the 2-D model, i.e. growth in the parallel direction from the electrode surface (Fig. 8a). In this model it was assumed that thickness of crystal on the electrode was neglected (Fig. 8b). The current intensity was normalized with I 0 , the maximum current intensity obtained for each curve. It is also also the Levich current measured on a bare electrode. This latter operation makes easier comparison between different experiments. The modeled curves obtained at a fixed rotation speed (500 rpm) were plotted with time for various values of site density N 0 , and were superimposed on the experimental curve as displayed in Fig. 9. The results highlight the effect of site density on the O 2 reduction current intensity. In the first minutes of the experiment, the count of the nuclei indicated no effect on the current intensity. The influence of lateral growth rate of CaCO 3 crystals seems to be predominant at the scaling start. The value of N 0 = 2× 10 -4 µm -2 was found in a good agreement with the experimental curve for time shorter than 40 minutes as observed in Fig. 9. At a constant surface coverage, the surface of each nuclei decreases with the number of nuclei N 0 and as a consequence the current, which is mass transport limited, increases.

Secondly, for time longer than 40 minutes, vertical growth was considered in the 3-D model i.e. growth in the vertical direction from the electrode surface (fig. 10a). As indicate in Fig. 10b, in a first approximation, the vertical growth rate, k V , was assumed to be linearly dependent with the lateral growth rate, k L , and by assuming that cube-like centers were formed (calcite).

L V k k    (19)
d h t k S V V     (20)
From equations 13, 19 and 20, α is equal to

d h   (21)
where  is a constant, S v (µm 2 ) and h (µm) were the vertical nucleus surface and CaCO 3 thickness, respectively. From experimental observations it was noticed that h is inferior to δ O2 , the diffusion layer thickness of oxygen.

The previous N 0 found value of 2×10 -4 µm -2 was taken as the optimum value of the site density and was inputted in the current intensity calculation with k V values for CaCO 3 growth.

The normalized current obtained at various values of k V , calculated from equations ( 15) and [START_REF] Barcia | Anodic dissolution of metals under mass transport control[END_REF], were displayed in Fig. 11a and superimposed with the same experimental curve as seen previously in Fig. 9. As mentioned above, it was observed that the influence of vertical rate growth of the crystals is more important for time larger than 40 minutes because the obtained curves split by far than those obtained in Fig. 9. For  values between 0 and 0.5 no correspondence were found with the experimental curve. This indicates that the linearity approximation used in equation 19 was not valid. To solve this problem, calculations were performed point by point taken into account that  varied with time. The procedure was consisted to determine the ratio k V /k L at each time on the experimental curve of Fig. 9. As seen in Fig. 11a at time shorter than 40 minutes the ratio k V /k L is close to zero confirming no influence of k V on the growth rate. However, at time longer than 100 minutes the ratio k V /k L is close to 0.5 indicating that k V could reach by half of the k L value. To verify  dependence with time, the current intensities were calculated in order to fit the experimental curve all the 10 minutes from start (t=0) to end (t=140) minutes. Data obtained are presented in Fig. 11b and show a good agreement between the experimental curve and the fitted curve. In figure 12 the observed dependence of  was plotted with time and highlights the relationship between k V /k L . The evolution of k V /k L ratio with time varies according to following relation

t k k L V      054 . 0 08 . 6
ln ln [START_REF] Deslouis | Interfacial pH measurement during the reduction of dissolved oxygen in a submerged impinging jet cell[END_REF] This result shows that 3-D model is adequate for the modeling CaCO 3 nucleation-growth process at electrode material. The parameter α was increased with the time up to a value of 0.5. For higher values of time, a plateau was observed. The measurements of the stationary current I(t) and of the surface coverage θ(t) allowed lateral and vertical growth rate determination.

 For t ≤ t critical t t k L    4 10 2 ) (  (21) L V k t k      ) 054 . 0 08 . 6 exp( (22)
 For t > t critical t k L    4 10 2 1 (23) L V k k   5 . 0 (24)
In agreement with observations and results described above, the variations of d and h dimensions of CaCO 3 crystal with time have been calculated using equations [START_REF] Devos | Nucleation-growth process of scale electrodeposition-Influence of the mass transport[END_REF][START_REF] Levich | Physiochemical hydrodynamics[END_REF] and [START_REF] Ch | Characterization of calcareous deposits in artificial seawater by impedance techniques 3-/Deposit of CaCO 3 in the presence of Mg(II)[END_REF], respectively. Fig. 13 shows that CaCO 3 crystals mainly grow laterally for time lower than 40 minutes. That is observed through the linear variation of d whereas h is close to zero.

Indeed, the vertical growth has no influence on the beginning of the nucleation-growth process. For time comprises between 40 and 100 minutes, d increases again until reaching a plateau value of 50 µm. At the same time, h increases until a maximum value of 25 µm. This latter value is close to  O2 (28 µm), which had been estimated with equation [START_REF] Gabrielli | Investigation of electrochemical calcareous scaling Potentiostatic current -and mass -time transients[END_REF], and reinforces the assumption that h cannot exceed the diffusion layer width (h <  O2 ). For time higher than 100 minutes, d and h are remain stables, that is again in agreement with the fact that the vertical and lateral growths tend towards zero. Theses obtained plateau values for h= 25 µm, d = 50 µm and for the site density number N 0 = 2×10 -4 µm 2 allow to derive the corresponding value,which is found to be equal to 50 percent of the electrode surface using equations ( 13) and [START_REF] Levich | Physiochemical hydrodynamics[END_REF]. A half-surface coverage could be explained by the overlapping of crystals on electrode surface as observed in Fig. 3 which has no taking into consideration in the model. However, these results confirm that the model works well and it is valid for investigation of nucleation-growth process..

Conclusions

In this paper, it was shown that the equation governing convective diffusion in complex electrochemical systems can be solved by finite element method. The data analysis of the chronoamperometric curves were used for investigating nucleation and growth kinetics of

Tables Caption

Table 1: Chemical composition and characteristics of the mineral water used in this study.

Table 2: Physical parameters used for numerical simulations for dioxygen [START_REF] Deslouis | Interfacial pH measurement during the reduction of dissolved oxygen in a submerged impinging jet cell[END_REF].

Figure captions

1

  Nucleation-growth process of calcium carbonate on rotating disk electrode in mineral potable water Zineb Belarbi a,b,c , Jean Gamby a, b,*,1 , Laid Makhloufi c , Bernard Tribollet a,b a CNRS, Laboratoire Interfaces et Systèmes Electrochimiques, UPR 15, F-75252 Paris, France b UPMC, LISE UPR 15 CNRS ; 4 Place Jussieu, case postale 133, F-75252 Paris, France c Laboratoire d'Electrochimie, Corrosion et de Valorisation Energétique (LECVE) Faculté de Technologie, Université A. MIRA -Béjaia 06000, Algeria

CaCO 3

 3 on electrode. CA has permitted obtention of information on the screening effect of the insulating scale deposit on electrode surface and in particular, it has allowed discrimination between 2-D and 3-D blocking by modeling the mass transfer phenomena at mineral water solution/ carbon steel interface. The model elaborated in this work predicts within a good accuracy the relative contributions of 3-D growth to the nucleation-growth process of calcium carbonate at disk electrode. It was found that the effect of vertical growth of the crystals is negligible at the beginning of the scaling phenomenon.

Fig. 1 :Fig. 2 :

 12 Fig. 1: Current-potential curves for dioxygen reduction in mineral water on steel electrode. Scan rate: 1 mV.s -1 .

Fig. 3 :

 3 Fig. 3: a. SEM micrographs of CaCO 3 formed in the mineral water after 140 min of immersion. ω = 500 rpm, E = -1V/SCE. b. X-Ray diffraction pattern of the crystals CaCO 3.

Fig. 4 :

 4 Fig. 4: FEM boundary conditions at rotating disk electrode.

Fig. 5 :Fig. 6 :

 56 Fig. 5: Limiting current as function of ω 1/2 for a carbon steel electrode in mineral water, E=-1V vs SCE. The straight line corresponds to Levich equation:

Fig. 7 :

 7 Fig.7: Geometry of the problem used for the numerical integration adapted from reference[START_REF] Caprani | Transient mass transfer at partially blocked electrodes: a way to characterize topography[END_REF].

Fig. 8 .

 8 Fig. 8. Scheme of the considered 2D crystal growth of CaCO 3 on a substrate, d: CaCO 3 crystal length, l: distance between CaCO 3 crystals. b. FEM boundary conditions at rotating disk electrode. 2-D model with lateral growth of CaCO 3 .

Fig. 9 :

 9 Fig. 9: Current time-transients plotted with respect to time for various values of the site density N 0 , ω = 500 rpm. I 0 = I Levich has been used for normalization.

Fig. 10 :

 10 Fig. 10: a. Scheme of the considered 3-D crystal growth of CaCO 3 on a substrate, d: CaCO 3 crystal length, l: distance between CaCO 3 crystals and h: CaCO 3 thickness. b. FEM boundary conditions at rotating disk electrode. 3-D model with vertical growth of CaCO 3 .

Fig. 11 :

 11 Fig. 11: Current time-transients plotted with time for various values of k V , ω = 500 rpm. I 0 = I Levich has been used for normalization.

Fig. 12 :Fig. 13 .

 1213 Fig. 12: Calculated values of α with time. (1): t     054 . 0 08 . 6 ln ,

Fig. 1 :Fig. 2 :Fig. 3 :Fig. 4 :Fig. 5 :Fig. 6 :Fig 11 Fig. 13

 1234561113 Fig. 1:

Acknowledgments

We thank Stephan Borensztajn and Françoise Pillier at "Laboratoire Interfaces et Systèmes Electrochimiques -Université Pierre & Marie Curie, UPMC Paris 6" for technical assistance on SEM micrographs acquisition, Cyril Bazin for X-Ray diffraction experiment. This research was supported by the French research organism "Institut de Recherche pour le développement" (IRD).

List of table


T Mediero

E Albuquerque

T R Kjeldsen

N Macdonald

M Lang

L Mediero

T Albuquerque

E Bogdanowicz

R Braźdil

A Castellarin

V David

A Fleig

G O Gül

J Kriauciuniene

S Kohnova

B Merz

O Nicholson

L A Roald

J L Salinas

D Sarauskiene

M Sraj

W Strupczewski

J Szolgay

A Toumazis

W Vanneuville

N Veijalainen

D Wilson

Documentary evidence of

Keywords: flood frequency estimation, historical events, Europe

Introduction

The reliable estimation of extreme flood events is challenging, but necessary for the design and operation of vital infrastructure such as flood defences, bridges, culverts and dams, and for more general flood risk management and 2 planning, e.g. emergency planning, flood risk mapping, and for defining flood insurance premiums. In practice, this information is obtained using flood frequency estimation techniques. Through statistical analysis of observed events, a probabilistic behaviour of flood events is inferred which is then extrapolated to provide estimates of the likely magnitude of future extreme events (e.g. the magnitude of the flood expected to be exceeded on average once every 100-year is estimated from a 40-year record). By nature, extreme flood events are rare and seldom observed locally and as a result hydrologists have little chance of gathering an adequate sample of recorded events to make confident predictions. This naturally raises the question of how best to extrapolate to extreme events, when no or only short series of recent events are available. As floods occur in almost all regions of the world, reliable flood estimation is a generic and shared problem. In Europe, the last couple of decades have witnessed a number of high-magnitude lowfrequency flood events [START_REF] Kundzewicz | Large floods in Europe, 1985-2009[END_REF], causing widespread damage and destruction. But flooding in Europe is not a recent phenomenon, and there are multiple accounts of damaging flood events across the continent going back centuries (e.g., [START_REF] Glaser | Floods in Central Europe since AD 1300 and their regional context[END_REF][START_REF] Glaser | The variability of European floods since AD 1500[END_REF][START_REF] Baptista | Potential inundation of Lisbon downtown by a 1755-like tsunami[END_REF].

While the occurrence of extreme floods is a shared problem across Europe (and beyond), the lack of cross-boundary cooperation (national and regional) has lead to individual countries investing in research programmes to develop national procedures for flood frequency estimation. As a result, no standardised European approach or guidelines to flood frequency estimation exist.

Where methods do exist they are often relatively simple and their ability to accurately predict the effect of environmental change (e.g. urbanisation, land-use change, river training and climate change) is unknown [START_REF] Castellarin | Review of applied-statistical methods for flood-frequency analysis in Europe. WG2 Milestone Report, COST Action ES[END_REF][START_REF] Madsen | A review of applied methods in Europe for flood-frequency analysis in a changing environment[END_REF]. Also, the problem of consistent estimates of extreme floods for trans-boundary rivers is rarely considered [START_REF] Pappenberger | Deriving global flood hazard maps of fluvial floods through a physical model cascade[END_REF]. The COST Action ES0901 European procedures for flood frequency estimation represents a novel opportunity to develop closer understanding of the methods of flood frequency employed across Europe.

The Action is undertaking a pan-European comparison and evaluation of different methods available for flood frequency estimation under the various climatologic and geographic conditions found across Europe, and different levels of data availability. The availability of such procedures is crucial for the formulation of robust flood risk management strategies as required by the Directive of the European Parliament and of the Council on the Assessment and Management of Flood Risks (2007/60/EC).

Currently, flood frequency is most commonly based on systematic instrumental data, collected from established networks of gauging stations operated and maintained by a variety of station authorities/bodies across Europe.

These gauging stations are of various forms and complexity depending on the level of data accuracy required. A more detailed discussion of availability, length and types of flood data records as well as procedures for flood frequency estimation procedures used across Europe is provided by [START_REF] Castellarin | Review of applied-statistical methods for flood-frequency analysis in Europe. WG2 Milestone Report, COST Action ES[END_REF].

A well-known consequence of the extrapolation from short series is the high level of uncertainty associated with estimates of design floods with large return periods. For example, estimating the 100-year design flood peak from a 24-year record [START_REF] Stedinger | Getting from here to where? Flood frequency analysis and climate[END_REF] reported a factor of 4-to-1 be-4 tween the upper and lower bounds of the 90% confidence interval. Given that the average record length is typically in the range 20-40 years, hydrologists have attempted to reduce the uncertainty levels by either: i) bringing additional gauged data from nearby and comparable catchments into the analysis (e.g., [START_REF] Hosking | Regional Frequency Analysis: An approach based on L-moments[END_REF], or ii) extending the available records by bringing flood data from before the beginning of systematic flow recording into the analysis in the form of historical and palaeoflood data [START_REF] Guo | Evaluation of the usefulness of historical and palaeological floods in quantile estimation[END_REF], or iii) using rainfall stochastic generators and rainfall-runoff models to constrain extreme flood assessment by rainfall information (e.g., [START_REF] Paquet | The SCHADEX method: a semi-continuous rainfall-runoff simulation for extreme flood estimation[END_REF]. The three methods all have merit, but only the second is the focus of this review.

Realising the importance and utility of long-term datasets, flood hydrologists have increasingly turned their attention to historical flood information [START_REF] Brázdil | Flood events of selected European rivers in the sixteenth century[END_REF][START_REF] Brázdil | Historical hydrology for studying flood risk in Europe[END_REF][START_REF] Glaser | Floods in Central Europe since AD 1300 and their regional context[END_REF][START_REF] Böhm | Flood history of the danube tributaries lech and islar in the alpine foreland of germany[END_REF]Macdonald, 2006;[START_REF] Mcewen | The Muckle Spate of 1829: the physical and societal impact of a catastrophic flood on the River Findhorn, Scottish Highlands[END_REF][START_REF] Glaser | The variability of European floods since AD 1500[END_REF][START_REF] Herget | Reconstructing peak discharges for historic flood levels in the city of Cologne, Germany[END_REF][START_REF] Kobold | Comparison of floods in September 2010 with registered historic flood events[END_REF][START_REF] Santos | Comparing historicalhydrogeomorphological reconstitution and hydrological-hydraulic modelling in the estimation of flood-prone areas-a case study in Central Portugal[END_REF][START_REF] Brázdil | Historical floods in Europe in the past millennium[END_REF], and how best to incorporate documentary evidence of such historical floods into flood frequency estimation (e.g., [START_REF] Stedinger | Flood frequency analysis with historical and paleoflood information[END_REF][START_REF] Williams | The use of historical flood information in the English Midlands to improve risk assessment[END_REF][START_REF] Benito | Use of systematic, palaeoflood and historical data for the improvement of flood risk estimation. Review of scientific methods[END_REF][START_REF] Gaume | Bayesian MCMC approach to regional flood frequency analyses involving extraordinary flood events at ungauged sites[END_REF]Macdonald and Black, 2010;[START_REF] Gaál | Inclusion of historical information in flood frequency analysis using a Bayesian MCMC technique: a case study for the power dam Orlík, Czech Republic[END_REF]. However, the application of non-instrumental data into flood risk analysis is not new, as is evident from already existing guidance documents such as the Flood Studies Report (FSR) (NERC, 1975) in the UK, a French handbook for flood risk assessment with historical data [START_REF] Miquel | Guide pratique d'estimation des probabilités de crues[END_REF], the guidelines for flood frequency estimation in Germany (DVWK, 1999), and the methodological guide to implement the Floods Di-rective in Spain [START_REF] Marm | Gua metodológica para el desarrollo del Sistema Nacional de Cartografa de Zonas Inundables[END_REF]. For the purpose of this study we propose three definitions are adopted for the broad classification of different types of hydrological data.

• Instrumental: long records, where records have been kept using available technologies, e.g. gauging stations or stage-boards (c. 1850present)

• Documentary: data derived from sources which are intermittent e.g. documentary descriptions or flood levels marked on bridges (c. AD 1000-present). Documentary evidence most often refers to historical events that occurred decades, centuries or even millennia ago, but it can also relate to more recent events in locations where no instrumental data are available.

• Palaeoflood: flood signatures recorded within depositional sequences, often sedimentary (channel cut-offs and lakes), though recent work has also witnessed flood signatures retrieved through dendrochronological approaches (Pleistocene present). As with documentary evidence, geomorphological evidence can also refer to recent flood events.

Regarding the historical and palaeoflood data we can add the following definitions:

• Perception threshold: level or discharge above which contemporary society considered the event sufficiently severe to record information about it, e.g. epigraphic markings (Macdonald, 2006) or a written account in news media or a specialist publication.

6

• Censored data: unmeasured floods known to have occurred above or below the perception threshold, despite not knowing their exact magnitude. Several researchers have shown that just knowing that a flood exceeded a perception threshold can add significant value to the flood frequency analysis (e.g., [START_REF] Stedinger | Flood frequency analysis with historical and paleoflood information[END_REF][START_REF] Cohn | Use of historical information in a maximum-likelihood framework[END_REF][START_REF] Payrastre | Usefulness of historical information for flood frequency analyses: Developments based on a case study[END_REF] An important complication when considering documentary and palaeoflood data is the impact of a changing environment (i.e. changes in climate and land-use, or river engineering works) on the characteristics of the flood series, and how to include this impact in future predictions.

The importance of data for assessing both the hydrology and impact of past events has been recognised as an integral part of flood risk management by the EU Flood Directive. The information collected in the Preliminary Flood Risk Assessment (PFRA) documents developed by the individual EU Member States starts with readily available or easily derivable information, such as records and studies on long term developments. Member States describe flood events that occurred in the past, which had significant adverse impacts, and for which the likelihood of similar future events is still relevant, reporting the frequency or recurrence of these events. The likely impact of climate change on the occurrence and impact of floods shall be taken into account in the review of the PFRA. For this, information beyond the instrumental records is acknowledged as being able to reduce the uncertainty of the assessment.

A key part of the COST Action ES0901 is to improve understanding of the barriers to new approaches to flood estimation. The results and discussions presented in this paper are mainly based on responses from a questionnaire circulated among COST Action participants on the use of historical floods and documentary evidence in flood frequency estimation. Specifically, this paper will undertake, first, a review of the general challenges for the incorporation of documentary evidence within flood frequency estimation. The focus of this paper is not to address the issues of data sources and information, which have previously be examined in detail by others, such as [START_REF] Brázdil | Historical hydrology for studying flood risk in Europe[END_REF][START_REF] Brázdil | Historical floods in Europe in the past millennium[END_REF], but to examine the use and application of historical records and information in flood frequency analysis; specifically. Second, challenges with the application of historical information within a changing environment will be assessed. Then, a review of the use of historical information in flood frequency estimation across Europe is undertaken by examining the detailed questionnaire responses which represent the position and statements of the individual countries. Finally, the paper will conclude by considering the current barriers to further application and potential developments.

Challenges for broader application of historical information

As documentary evidence most often predates the installation of gauging stations, and is not directly supported by other instrumental sources (using a limnimetric scale e.g. stageboards), it generally provides indirect information on peak flood discharge, often in the form of a water level marker (Figure 1), or information that a specific location had been flooded, damaged or destroyed, or that the water level had reached a level relative to a structure (e.g. it had reached the top of the doorframe).

Different quantitative methods have attempted to extract the information 8 contained in historical data using a variety of approaches. The most common approach is to consider a perception threshold for a historical period or sub-period, with the assumption that each flood exceeding this threshold has been recorded (e.g. NERC, 1975). As the consequences are important, this can sometimes be aided by thresholds within the environment of known exceedance. An example is the flooding of the Lincolnshire Plains by the River Trent in Central England when a low lying moraine (Spalford Bank) is overtopped, which is known to occur at flows in excess of 1000 m 3 s -1 (Macdonald, 2013). Having established the threshold, the number of exceedance events during a period can then be retrieved from historical records. A more detailed approach involves the use of hydraulic formulae (e.g. Manning equation) or one or two dimensional hydraulic models (St Venant equations) to convert historical flood levels into historical discharges (Lang et al., 2004a).

As shown by [START_REF] Neppel | Flood frequency analysis using historical data: accounting for random and systematic errors[END_REF] it is important to ensure that the hydraulic model calibrates with flood marks and rating curves (when available) and reassess the hydrological homogeneity of discharge estimates at several places. Hydraulic studies should provide a discharge estimate, but also a range of possible values within an interval, based on a sensitive analysis or an uncertainty analysis.

Several statistical approaches were developed in the past to improve the flood frequency curve estimation by extracting the information contained in the different types of historical records discussed above. In the USA, Bulletin 17 B (USWRC, 1982) proposed the weighted moments (WM) technique for incorporating historical information in a flood frequency analysis. The WM technique is a straightforward method that is noticeable for ease of im-9 plementation. [START_REF] Stedinger | Flood frequency analysis with historical and paleoflood information[END_REF] developed a maximum likelihood estimator (MLE), which was more flexible, efficient and robust than the WM technique. Moreover, it allowed the introduction of binomial censored data into the likelihood function; however, MLEs present numerical problems in some occasions. To avoid this drawback, while maintaining the efficiency of MLE technique, the expected moments algorithm (EMA) was developed [START_REF] Cohn | An algorithm for computing momentsbased flood quantile estimates when historical flood information is available[END_REF]. [START_REF] Reis | Bayesian MCMC flood frequency analysis with historical information[END_REF] proposed a Bayesian technique based on Markov Chain Monte Carlo methods (BMCMC) that improves previous techniques by providing the full posterior distributions of flood quantiles. Likewise, the BMCMC technique allows for the introduction of uncertainty into historical peak discharge estimates. The WM technique was adapted to the case of probability weighted moments (PWM), to produce the partial probability weighted moments (PPWM) approach [START_REF] Wang | Unbiased estimation of probability weighted moments and partial probability weighted moments from systematic and historical flood information and their application to estimating the GEV distribution[END_REF]. The EMA technique was also adapted to the PWM case, providing the expected probability weighted moment (EPWM) estimator, which improves the estimation of the shape parameter, but has also shown some bias [START_REF] Jeon | Expected probability weighted moment estimator for censored flood data[END_REF].

An example of how the inclusion of historical events can help flood frequency estimation to better represent the probabilistic behaviour of flood events can be seen in Figure 2. It shows the results at the Tortosa gauging station located on the River Ebro in Spain, a comparison between two Generalised Extreme Value (GEV) distributions fitted to i) a sample of 31 annual maximum flood peaks recorded at the gauging station (instrumental) by the method of L-moments, and ii) the same sample of instrumental events, but enhanced with seven historical flood events by the method of PPWM. From the frequency plot in Figure 2 it is clear that the GEV distribution fitted to the instrumental record only, would result in severe under-estimation of the real flood risk at the site of interest. However, the inclusion of the historical records estimated from a set of flood marks recorded at a house close to the reach improved the estimation of extreme return period floods, as their magnitude was unknown from the short instrumental record.

Most of these analytical developments have been undertaken within the academic field. However, extending these improvements to routine practical use is not trivial, principally because of the mathematical complexity of most techniques. For instance, classical MLEs are efficient for sufficiently long records, but may produce numerical problems in application to case studies when sample size is small (El Adlouni et al., 2007); a significant drawback for recommending this technique for practical application. Bayesian techniques also present critical steps, such as the estimation of prior distributions and the computation of posterior distributions which are not always straightforward. The elegant statistical models based on censored data sources and solved using likelihood functions, sometimes combined with Bayesian statistics [START_REF] Reis | Bayesian MCMC flood frequency analysis with historical information[END_REF], can provide very good results. Nevertheless, this review suggests that whilst these models exist, there is limited evidence that they have migrated from the academic field into operational guidelines.

Potential barriers to the broader application of these approaches may reflect the complex computational requirements and site specific characteristics that may be best combined with specific methods, though the survey undertaken in this study did not contain information on why certain approaches are not applied. These problems lead to the use of the more simplistic, but robust, 11 methods in practice, as recommended by operational guidelines, such us the WM technique in the United States and the PPWM in Spain.

In addition to providing formal input into quantitative flood frequency estimation, documentary evidence of past events can be helpful in communicating flood risk to non-specialist stakeholders [START_REF] Mcewen | Archiving memories of changing flood risk: Interdisciplinary explorations around knowledge for resilience[END_REF] and for better understanding variations in flood seasonality (Macdonald, 2012).

The transformation of information from descriptive accounts of past events into more easily understood groups of flood magnitude has seen the use of indices, often using a scale dividing the events into a set of qualitative classes [START_REF] Sturm | Hochwasser in Mitteleuropa seit 1500 und ihre Beziehung zur atmosphäerischen Zirkulation[END_REF]Llasat et al., 2005) for flood severity, see [START_REF] Brázdil | Historical hydrology for studying flood risk in Europe[END_REF][START_REF] Brázdil | Historical floods in Europe in the past millennium[END_REF]; for example class 1 (low to intermediate events: damage and flooding are limited to restricted areas), class 2 (high events: flooded area and debris flow are important, structures such as dikes and roads have been destroyed for several hundred of meters), class 3 (extreme events: damage or destruction of important structures and flooding on the whole plain). Although a useful tool for categorising and visualising flood magnitude, this approach has yet to be useful in the estimation of flood frequency, and is unlikely to present any advances as the approach removes individual event information and groups the events, thereby reducing the potential value of the data.

Assessment of environmental change

There is some discussion provided as to means of accounting for the impact of environmental change on flood occurrence, with several countries undertaking comparison to nearby stations, for non-homogeneity and trend 12 studies. However, in a review of existing guidance in European countries on how to include considerations of environmental change in flood frequency estimation, [START_REF] Madsen | A review of applied methods in Europe for flood-frequency analysis in a changing environment[END_REF] found that generally little or no guidance is provided for how to deal with trend or non-homogeneity when identified, and how this knowledge should be incorporated into flood estimation. This is clearly an area where much more effort is required to translate scientific research into operational guidelines.

Different types of non-stationarity can be considered within historical records, as the frequency distribution could change during the period for which historical and palaeoflood data are recorded: i) the changes related to non-homogeneity problems (historical data availability, transformation of indirect information to discharge estimate); ii) climatic variability over long time scales could limit the utility of historical data under a stationarity framework to some hundreds of years in the past [START_REF] Hosking | Regional Frequency Analysis: An approach based on L-moments[END_REF]. This topic remains an open field of research, with present interest amplified by the perspective of climate change for the 20th and 21st centuries; iii) channel changes (natural and anthropogenic) over long timeframes (e.g., Brázdil et al., 2011a). As a means of minimising the potential impact of these climatic non-homogeneities, historical records used for flood frequency analysis are not extended back beyond around 400 years in Spain. This practice limits the influence of past climatic changes; as a greater frequency of extreme flood events are found in the period 1540-1640 [START_REF] Benito | Magnitude and frequency of flooding in the Tagus basin (Central Spain) over the last millennium[END_REF]. Similar timeframes are recommended in a number of academic papers (e.g. [START_REF] Parent | Bayesian POT modeling for historical data[END_REF][START_REF] Mcewen | Archiving memories of changing flood risk: Interdisciplinary explorations around knowledge for resilience[END_REF], but this often focuses on concerns relating to data quality and quantity prior to this (as discussed above) rather 13 than climatic variability, with several studies commenting on the longer timeframe providing greater climatic variability, and therefore a more uncertain climate range (e.g. [START_REF] Macdonald | Historical and pooled flood frequency analysis for the River Tay at Perth, Scotland[END_REF]. These issues become even more important when attempting to merge gauged flow data with palaeoflood data stretching back millennia, though it could be argued that climatic variability over millennial timescales incorporates sufficient variability that climate phases become less significant. While some researcher have embraced the use of palaeoflood data [START_REF] Baker | The scientific and societal value of paleoflood hydrology[END_REF], others remain more sceptical of their practical utility, especially when regional flood frequency methods are available (e.g. [START_REF] Hosking | Paleoflood hydrology and flood frequency analysis[END_REF]. Notably, [START_REF] Neppel | Flood frequency analysis using historical data: accounting for random and systematic errors[END_REF] identified large error associated with historical flood magnitude estimation could lead to a reduction in the precision of design flood estimates when compared to estimates using gauged data only, supporting the view that palaeoflood data should be handled carefully when included into a flood frequency analysis. Lang et al. (2004b) proposed a statistical test based on the Poisson process for the detection of changes in peak-over-threshold series. It has been applied to several historical series in France and Spain [START_REF] Barriendos | Stationarity analysis of historical flood series in France and Spain (14th-20th centuries)[END_REF] and in central Europe [START_REF] Glaser | Floods in Central Europe since AD 1300 and their regional context[END_REF]. The power of the test is limited when the number of historical floods is low. On the contrary, including low to intermediate historical floods increases the risk of non-homogeneity, as such floods can be strongly influenced by anthropogenic changes. It is therefore recommended to check the validity of the rating curves used for historical floods.

The development of slackwater deposits as a tool in the reconstruction of palaeoflood series has expanded extensively over the last couple of decades 14

Author-produced version of the article published in Journal of Hydrology (2014), vol. 517, p. 963-973 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.jhydrol.2014.06.038 [START_REF] Werritty | Use of multi-proxy flood records to improve estimates of flood risk: Lower River Tay, Scotland[END_REF]; [START_REF] Jones | Geomorphological and sedimentological evidence for variations in holocene flooding in welsh river catchments[END_REF]; [START_REF] Huang | Holocene palaeoflood events recorded by slackwater deposits along the lower jinghe river valley, middle yellow river basin, china[END_REF]; Dezileau et al.

(2014), with a number of review papers (e.g. [START_REF] Benito | Palaeoflood hydrology: insight into rare events and extreme flood discharges[END_REF] and books [START_REF] Gregory | Palaeohydrology: understanding global change[END_REF] addressing the topic in detail.

Lakes can act as efficient repositories for sediments eroded from within the catchment and that are transported through the fluvial system [START_REF] Mackereth | Some chemical observations on post-glacial lake sediments[END_REF]. The sediments reaching a lake are dependent on a number of variables which may vary through time and space; see [START_REF] Schillereff | Flood stratigraphies in lake sediments: a review[END_REF] for a full review. The sediments that reach the lake may be laid down providing a sedimentary record of high-magnitude flows which appear as distinct laminations of coarse material. An increasing number of studies have examined lake sediment sequences with the intention of determining flood histories [START_REF] Noren | Millennial-scale storminess variability in the northeastern United States during the Holocene epoch[END_REF][START_REF] Gilli | Lake sediments as archives of recurrence rates and intensities of past flood events[END_REF][START_REF] Wilhelm | Palaeoflood activity and climate change over the last 1400 years recorded by lake sediments in the north-west European Alps[END_REF]. The sediments preserved within the lake can contribute valuable information on flood frequency and potential magnitude of single events over timeframes reaching several millennia [START_REF] Noren | Millennial-scale storminess variability in the northeastern United States during the Holocene epoch[END_REF]. For example, [START_REF] Swierczynski | Mid-to late Holocene flood frequency changes in the northeastern Alps as recorded in varved sediments of Lake Mondsee (Upper Austria)[END_REF] or passed onto colleagues better placed to do so. The questionnaire applied the definitions detailed above so as to distinguish between historical and instrumental data series. A summary version of the questionnaire responses is provided in Table 1.

TABLE 1

The following three sub-sections summarise the information collected from the questionnaires. In particular: i) the length of existing historical data series, ii) the accessibility to historical flood data, and iii) summaries of specific guidelines developed in European countries.

Data availability

Each country was asked to provide details of the sites and locations where the most complete historical series are available. This information is used to provide an indication of the types and use of historical records as a series of national summaries, but cannot be considered as an exhaustive inventory.

For each reported case-study the ratio between the length of the instru-16

Author-produced version of the article published in Journal of Hydrology (2014), vol. 517, p. 963-973 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.jhydrol.2014.06.038 mental record and the total time from the end of the instrumental record until the first recorded historical flood event was calculated. The average of the ratios calculated from the case studies within each country are reported (Table 2) together with the number of case-studies and the oldest recorded flood event. Note that the oldest flood refers to the oldest flood event associated with an estimate of peak flow; in some countries, older events were recorded but could not be assigned an estimate of the discharge.

TABLE 2

The average ratios are all below 0.50 suggesting that additional information of extreme floods can be found as far back in time as twice the period covered by the instrumental record. The countries listed in Table 2 are representative of North, South, East and West Europe, indicating that historically augmented flood estimation could be useful across the continent.

While no quantitative assessment of the benefit of the extended data series were conducted as part of this review, several previous studies have highlighted the utility of such series. For example, [START_REF] Mcewen | Archiving memories of changing flood risk: Interdisciplinary explorations around knowledge for resilience[END_REF] found that extending a 40-year instrumental record with documentary evidence of flooding dating back to 1772 resulted in an almost 50% reduction on the uncertainty of the estimated design flood with a return period of 100 years. [START_REF] Payrastre | Usefulness of historical information for flood frequency analyses: Developments based on a case study[END_REF]. Thus, the data series listed in Table 2 represent an important resource for providing more reliable estimates of flood risk across Europe.

Similar conclusions have been reached by other researchers such as

Central depository of historical data

No centralised database exists as a depository for flood information at a European scale. But a variety of laudable national/regional/local and individual databases exists. However, there is no common agreed format, and the databases often include either/or both qualitative and quantitative information with limited quality control on the information uploaded.

The purpose of existing data varies, which often reflects the structure and types of information collected, the result is that some disciplines may feel insufficient or 'the wrong' type of data may be present, reflecting the varied uses of historical information, from those examining social impacts of past floods to those interested in using the information in flood frequency estimates, as such some disciplines may consider important information to be absent. These databases tend to be funded through a variety of different mechanisms, with few receiving continuous central support; as such they are funded initially, but then become reliant on individuals or professional societies for continuation, good examples being the British Hydrological Society Chronology for British Hydrology Events (BHS CBHE), as described by [START_REF] Black | Development and utilization of a national web-based chronology of hydrological events[END_REF], or the French national Historical Database BDHI currently in development in the framework of the EU Flood Directive [START_REF] Lang | Preliminary flood risk assessment for the European Directive: Inventory of French past floods[END_REF]. Whilst a valuable resource the full potential of these databases cannot be realised in pan-European flood frequency estimation at present, due to the absence of a standardised method for construction and minimum data requirements. The National Disaster Archive compiled by the Disaster & Emergency Management Presidency (AFAD) in Turkey, for example, provides tabular and spatial information (date, location) about the entire spectrum of historic disaster events (e.g., floods, droughts, earthquakes, landslides, forest fires, nuclear accidents, etc.) associated with figures of deaths, injuries, affected populations, etc. However, this is not immediately utilizable 18

Author-produced version of the article published in Journal of Hydrology (2014), vol. 517, p. 963-973 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.jhydrol.2014.06.038 in flood frequency analyses due to the lack of data describing the physical characteristics of the events, such as flood levels and discharges.

Recent efforts by a group of researchers from the Slovak Academy of Sciences started with mapping of all historical flood marks and collecting historical reports of floods in Slovakia. Their results are continuously published, e.g. recent studies by [START_REF] Pekárová | Important floods of the past on the territory of Slovakia[END_REF][START_REF] Pekárová | Historical floods and flood frequency analysis of the Danube River at Bratislava, Slovakia[END_REF] give the overview of the history of floods and extreme events in Slovakia and in the upper Danube River Basin at Bratislava. These databases provide pockets of knowledge, but large areas of Europe remain ungauged. The use of geospatial databases for the visualisation of information and capability to embed images within such databases presents an important development, permitting flood levels and additional information beyond a basic descriptive account to be housed within each flood account, empowering the researcher to more rapidly and easily access required information. One of the principal constraints to the wider application of historical information in flood frequency analysis has been the time requirements for collecting the necessary data; well developed and constructed geospatial databases present a valuable step towards removing these constraints.

Practical guidelines for inclusion of historical data

A number of countries were identified as possessing practical guidelines for inclusion of historical flood information into flood frequency estimation, including: Austria, France, Germany, Ireland, Italy, Slovakia, Spain and the United Kingdom.

Austria 19

In Austria historical information, where available, was included in the development of national maps of flood discharge (Merz et al., 2008). The historical information was included in flood frequency estimation procedure based on the use of likelihood functions of censored information and Bayesian modelling techniques as described by Merz and Blöschl (2008) and [START_REF] Viglione | Flood frequency hydrology: 3. A Bayesian analysis[END_REF].

France [START_REF] Miquel | Guide pratique d'estimation des probabilités de crues[END_REF] presented a methodological guide for the inclusion of historical data in flood frequency analysis. It was based on a Bayesian approach to peak-over-threshold (POT) values with an a posteriori estimate of the flood distribution, by combining with the Bayes theorem and a priori distribution based on instrumental data and historical POT values. [START_REF] Parent | Bayesian POT modeling for historical data[END_REF] presented an application of this model, using a MCMC algorithm for computation. [START_REF] Naulet | Flood frequency analysis on the Ardeche River using French documentary sources from the last two centuries[END_REF] used a maximum likelihood approach on annual maximum values, with different sub-periods (each one being related to a threshold of perception according to documentary sources availability) and different types of data (censored, censored with uncertainties, binomial censored). [START_REF] Lang | Extrapolation of rating curves by hydraulic modelling, with application to flood frequency analysis[END_REF] and [START_REF] Neppel | Flood frequency analysis using historical data: accounting for random and systematic errors[END_REF] applied an error model on discharge estimate, accounting for random errors (sampling uncertainties) and systematic errors (water level and rating curve errors). They showed that ignoring the rating curve errors may lead to an unduly optimistic reduction in the final uncertainty in estimation of flood discharge distribution. [START_REF] Gaume | Bayesian MCMC approach to regional flood frequency analyses involving extraordinary flood events at ungauged sites[END_REF] and [START_REF] Payrastre | Usefulness of historical information for flood frequency analyses: Developments based on a case study[END_REF] presented a Bayesian framework allowing the use of regional information of historical floods at un-20 gauged sites. They also provided results on the usefulness of historical data in flood frequency analysis regarding the type of data (censored, censored with uncertainties, binomial censored).

Germany

The German Association for Water, Wastewater and Waste (DWA) and its predecessor DVWK have published guidelines which give recommendations for the use of historical sources and data: DWA ( 2008): Guidelines on how to exploit and interpret historical sources for determining extreme flood discharges. DVWK (1999): Guidelines for integrating large historical flood magnitudes in flood frequency analysis are based on the methods presented in Bulletin 17B [START_REF] Uswrc | Guidelines for determining flood flow frequency[END_REF]. This publication was superseded by the more recent guidelines on flood estimation which devotes a separate chapter to the integration of large historical flood magnitudes in flood frequency analysis (DWA, 2012). Three alternative approaches are offered to consider historical data in the parameter estimation of the frequency distribution.

One of them is based on the definition of a set of likelihood functions representing the actual nature of the available flood information, i.e.: i) discharge of historical information known, ii) discharge is known to fall within an interval (upper and lower bound specified), or iii) event is known to have exceed a perception threshold, but the actual discharge value is unknown.

Ireland

In Ireland, the generally accepted approach to incorporating historical flood data follows that put forward by [START_REF] Bayliss | The use of historical data in flood frequency estimation[END_REF] in a similar man-ner to that described for the UK. With the imminent release of the Flood Studies Update (FSU) methodologies in 2014, growth curve analysis will use L-moment methods to derive growth curves, with the EV1 and LN2 distributions being the preferred distributions for use at gauged locations. It is envisaged that methods of incorporating historical information will move towards the use of L-moment based methods in the future. The central source of information on historical floods will remain the Irish flood hazard mapping website, floodmaps.ie.

Italy

The gauging network for systematic river-stage monitoring in Italy was largely installed in the twentieth century, therefore Italian streamflow records are usually much shorter than 100 years [START_REF] Calenda | Selection of the probabilistic model of extreme floods: The case of the River Tiber in Rome[END_REF]. In this context, historical and non-systematic information on flood events is a valuable resource. Historical evidence of flooding in Italy has been recorded (e.g., [START_REF] Aldrete | Floods of the Tiber in ancient Rome[END_REF], and national databases of historical disasters (mainly landslides and floods) have been established [START_REF] Guzzetti | Map of sites historically affected by landslides and floods[END_REF][START_REF] Guzzetti | Information system on hydrological and geomorphological catastrophes in Italy (SICI): a tool for managing landslide and flood hazards[END_REF]. Nevertheless, these databases contain predominantly descriptive information such as: triggering mechanisms, economic losses and casualties, but little information related to peak discharge. Consequently, although basin authorities routinely use information on historical floods for geographically delineating the most vulnerable areas and acknowledge the value of this information for improving flood frequency estimation (see e.g., AdB-Po, 1999), no evidence of practical use of historical floods in flood frequency estimation was identified in Italy at a national level, though examples were found at regional and local scales.

22

For example an application to the Piedmont region reported by [START_REF] Claps | ARPIEM -Analisi Regionale delle PIEne nei bacini Montani (con applicazione alla valutazione delle piene in Piemonte) (ARPIEM -Regional flood frequency analysis in mountainous basins (with application flood estimation in in Piedmont, Italy)[END_REF] and [START_REF] Laio | Spatially smooth regional estimation of the flood frequency curve (with uncertainty)[END_REF], and local application by [START_REF] Calenda | Selection of the probabilistic model of extreme floods: The case of the River Tiber in Rome[END_REF] on the River Tiber.

Czech and Slovak Republics

There are several methods for inclusion of historical flood data in flood frequency estimation in the Czech and Slovak Republics, which were published in reports e.g. Dub and Nemec (1969), [START_REF] Kaspárek | O povodních z let 1872 a 1981 na Litavce a jejich význam pro odhad N-letých prutoku[END_REF] and [START_REF] Novický | Hydrologická data pro návrhové účely (Hydrologic data for design purposes)[END_REF]. These methods are based on corrections of systematic errors by estimation of statistical parameters (coefficient of variability, skewness) of applied distribution functions. The German guidelines for using historical floods, published in DVWK (1999), was applied by [START_REF] Szolgay | Posúdenie hydrologických návrhových velicín vodného diela Orlík[END_REF].

Recent studies in Slovakia used a Bayesian framework to include both local and regional information about historical floods at ungauged sites, and to provide results on the usefulness of different types of historical data in flood frequency analysis [START_REF] Gaál | Inclusion of historical information in flood frequency analysis using a Bayesian MCMC technique: a case study for the power dam Orlík, Czech Republic[END_REF][START_REF] Gaál | Assessing t-year flood quantiles by means of Bayesian MCMC simulations: A case study at the Myjava River, Slovakia[END_REF].

Flood frequency analysis in the Czech Republic is based on combination of floods derived from documentary evidence and systematic hydrologic measurements, which permits the creation of 500-year series: examples include the Vltava (Prague), Ohře (Louny) and Elbe (Děčín) series in Bohemia [START_REF] Brázdil | Historical and Recent Floods in the Czech Republic[END_REF]. In Moravia (eastern Czech Republic), similar compiled series are available for the River Morava, starting as early as 1691 (Brázdil et al., 2011b). More recently, knowledge of historical floods coupled with flood plain information in Prague was used for the estimation of hydraulic parameters, permitting the calculation of peak discharges of past disastrous floods during the pre-instrumental period [START_REF] Elleder | Historic floods in the city of Prague -a reconstruction of peak discharges for 1481-1825 based on documentary sources[END_REF].

Spain

In Spain, the use of historical records is generally recommended when possible, by fitting a GEV distribution by the PPWM method. In addition, historical records were used in some Mediterranean basins (3) to improve: i) the results of the regional flood frequency analysis, and ii) estimates of high return period quantiles along the Mediterranean East coast of Spain [START_REF] Jiménez-Álvarez | Map of maximum flows of intercommunity basins in Spain[END_REF].

The 92nd Region is located in the northeast of Spain, including the rivers of the left bank of the River Ebro with heads in the central Pyrenees (Figure 3). In this region the regional coefficient of skewness (L-CS) estimated from instrumental records was improved by the use of historical information. It was seen that two high flood events that occurred in the 20th century affected most of this region (1907 and 1982). However, they were not recorded, as the former occurred before the existence of a gauging station network in Spain, while the latter exceeded the maximum capacity of the gauging stations.

Values of at-site L-CS were improved by the use of a GEV distribution fitted with historical information by the PPWM method. The regional L-CS value was updated by a weighted mean of at-site L-CS with weighting factors dependent on the uncertainty of at-site estimations.

The 72nd and 82nd regions are located in the eastern part of Spain, including the lower parts of the Júcar and Segura catchments that are affected by rare and heavy rainfall events coming from the Mediterranean Sea (Figure 3). These events are caused by cut-off lows occurring in spring and autumn, when cold air in the upper part of the troposphere moves from northern latitudes to the south over the warm Mediterranean Sea, generating heavy convective rainfall events and, consequently, intense flood events. However, there is a lack of information recorded about these flood events; either they occurred in the past before a gauging station was installed, or they were not recorded, as they exceeded gauging station capacity. This lack of information can result in potentially severe underestimation of higher return period quantiles. Estimates with only instrumental records can lead to magnitudes around 5 to 10 times smaller for the 500-year return period. As floods come from two types of rainfall events, a Two-Component Extreme Value (TCEV) distribution [START_REF] Rossi | Two-component extreme value distribution for flood frequency analysis[END_REF] fitted by MLE is recommended. In these regions, the use of historical information in flood frequency is crucial to achieve reliable estimation of higher return period quantiles. In Spain, the use of historical information to improve flood frequency analyses is recommended [START_REF] Marm | Gua metodológica para el desarrollo del Sistema Nacional de Cartografa de Zonas Inundables[END_REF]. A large catalogue of historical floods is supplied by the Spanish civil defence organization.

United Kingdom

The use of historical record has been called for since the mid-1970s, initially through the early work of the Flood Studies Report (NERC, 1975) and [START_REF] Potter | The use of historical records for the augmentation of hydrological data[END_REF]. More recently, [START_REF] Bayliss | The use of historical data in flood frequency estimation[END_REF] provided the first approach designed specifically for practitioners on how to augment instrumental datasets with documental evidence of historical records. However, the uptake of this approach has been piecemeal and slow, in part as practitioners still require a user-friendly tool for incorporating historical data into 25

Author-produced version of the article published in Journal of Hydrology (2014), vol. 517, p. 963-973 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.jhydrol.2014.06.038 flood frequency analysis. Current methods widely employed for incorporating historical flood information into flood assessments often consist of a conventional flood frequency plot, with the historical levels/discharges marked on, but importantly not included within the statistical analysis. The use of an informal graphical plotting approach was advocated by [START_REF] Reed | Statistical procedures for flood freequency estimation[END_REF] to permit greater confidence among practitioners in the application of historical data. By contrast, [START_REF] Macdonald | Historical and pooled flood frequency analysis for the River Tay at Perth, Scotland[END_REF] and Macdonald and Black (2010) have advocated the use of L-Moments, as they permit greater flexibility and retained an approach practitioners were already familiar with in dealing with pooled data, compared to more mathematically involved Maximum-Likelihood approaches [START_REF] Mcewen | Archiving memories of changing flood risk: Interdisciplinary explorations around knowledge for resilience[END_REF]. Each of the approaches considered a preference for a Generalised Logistic distribution model to represent the flood growth curve. An interesting use of historical information was reported by [START_REF] Williams | The use of historical flood information in the English Midlands to improve risk assessment[END_REF] who used historical flood data to assess the return period of a recent large event.

Discussion

Despite general agreement in the scientific literature on the utility of historical flood information in flood frequency estimation, the survey undertaken has shown that there is only a limited transfer of methods from academia into practical guidance. A few good examples of guidelines and depositories for historical flood data were identified, but no single unified approach or database is evident. Depositories were identified both as part of larger government hydrometric databases, but also existing independently from official government databases, and operated mainly by volunteers and populated by citizen science efforts (e.g. UK BHS CBHE). The lack of practical guidelines and fragmented access to historical information are practical barriers towards more operational use of these data sources to support current risk mapping efforts and decision-making problems. In addition, it is also clear that the inclusion of historical information is not always straightforward, requiring a greater degree of scrutiny before application than typically required for instrumental data. In particular, it should be recognised that historical information is fundamentally different from quality controlled streamflow measurements obtained from gauging stations. For example, the degree of certainty associated with discharge estimates from historical information requires special consideration. Research has shown that simply ignoring uncertainties on discharge estimates will favour the use of historical information, as sampling uncertainty is reduced by increasing the length of the flood period. Nevertheless, it is important to correctly describe the uncertainties on peak discharge for the instrumental, historical and palaeoflood data, including errors on water level H, on the rating curve Q(H), on the threshold of perception and on the starting date of the historical period. The latter should not be systematically the date of the oldest flood in the historical data set [START_REF] Strupczewski | Flood frequency analysis supported by the largest historical flood[END_REF], but should include a period prior to this. The Bayesian framework appears to be a suitable statistical tool, enabling inclusion of several kinds of data (e.g. single values, intervals, number of exceedances) and able to include errors/uncertainties on discharge estimates (i.e., systematic error on water levels and on the rating curve transformation) into flood frequency analysis.

While this review has found that there is largely consensus in the sci-27 entific literature as to the usefulness of historical data in flood frequency estimation, the methods have overwhelmingly focussed on extending at-site estimates. Few studies have reported on the use of historical information in a regional context. A notable exception is the procedure for certain geographical regions of Spain, where the occurrence of very extreme events in the past has resulted in a set of regional flood frequency curves adjusted upwards to represent the worst case, even if no actual events has been observed at a particular site. This is potentially a very interesting methodological development, recognising the limitations of fitting current statistical models to datasets that are known not to include potentially very extreme events, similar to events that have occurred in other locations within the region.

By contrast, [START_REF] Hosking | Regional Frequency Analysis: An approach based on L-moments[END_REF] argue that historical information is of limited use in regional flood frequency estimation; their reservations are based on i) concerns about the accuracy and completeness of the historical information (historical data are most often found in old and large human settlements and not at a representative sample across all possible catchments), ii) representativeness of catchment within a region where historical data are available, and iii) using data so far in the past that the underlying frequency distribution might have changed too much (non-stationarity). A regional model combining both regional and historical data was presented by [START_REF] Jin | Flood frequency analysis with regional and historical information[END_REF] combining the index flood method with a GEV distribution where the model parameters are estimated using a combination of probability weighted moments and a maximum likelihood procedure. [START_REF] Gaume | Bayesian MCMC approach to regional flood frequency analyses involving extraordinary flood events at ungauged sites[END_REF] also presented a maximum-likelihood approach to combining regional and historical data within the framework of the index flood method. Sur-prisingly, no or only little further development of these procedures appears to have been reported in the literature, but this is an area where further research is still required to develop a new generation of risk tools to effectively allow regional models to use historical information, and to define procedures to enable the transfer of historical data between catchments.

The potential of historical information in public awareness of flood risk is considerable, historical events are tangible, with epigraphic markings providing an example of how communities have preserved evidence from past events to educate future generations of flood risk, which may not be witnessed within any single lifetime. Increasingly recognition of the non-quantitative information contained within historical flood accounts is being recognised, providing detailed descriptions of the social and cultural responses to extreme events, responses that inherently shape current flood risk management approaches through learned knowledge within communities. This informal knowledge is increasingly being sought and embedded within local flood risk management plans, as recognition of the value of local lay knowledge has developed [START_REF] Mcewen | Archiving memories of changing flood risk: Interdisciplinary explorations around knowledge for resilience[END_REF].

The development of national approaches in individual countries has resulted in no-single approach being applied at a European level, constraining the potential for cross border information transfer, and at worst leading to misunderstanding and poor communication to the public (e.g. flood maps with different flood extents at the boundary). Future research must address several key themes:

• construction of a single database framework within which data can be stored and managed, with both extraction, uploading (preferably 29 through approaches advocated by citizen science) and geospatial presentation capabilities;

• move towards organisation data sharing across boundaries, with greater free access to data for benchmark sites;

• development of a computationally simple user interface toolbox, within which hydrological series comprising of different data types, lengths and completeness can be assessed together;

• development of a set of practices for the treatment of data uncertainty associated with historical records; and,

• a forum for the sharing and review of best practice at a European level.

Inevitably an assessment of the data has to be made by the individual undertaking the analysis and the purpose for which the data is compiled, but the above proposals would facilitate a more rapid and structured approach to the compilation and analysis of the data, overcoming a number of the obstacles currently cited as prohibiting expansion in the application of historical data.

Conclusions

There is increasing recognition that historical records of flooding provide a valuable means by which extreme rare events can be better understood, facilitating more enlightened flood frequency analysis where interest is focused on extreme events (events with a return period in excess of 100 years).

As evidenced within this research (Table 1 and2 Author-produced version of the article published in Journal of Hydrology (2014), vol. 517, p. 963-973 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.jhydrol.2014.06.038 a number of countries if not actively incorporating historical flood records into flood frequency analysis considering how they can be used, in compliance with the EU Floods Directive (2007/60/EC). Whilst no single approach is uniformly applied to historical flood frequency analysis across Europe, a number of national and regional approaches exists. As historical evidence is often found in connection with large rivers, the use of this information could be a key driver in both academic and practical investigations of transboundary flood management. Dezileau, L., Terrier, B., Berger, J., Blanchemanche, P., Latapie, A., Freydier, R., Bremond, L., Paquier, A., Lang, M., Delgado, J., 2014

derived a 7 ,

 7 000-year flood chronology for the lake Mondsee in Upper Austria. Even the seasons of the palaeofloods could be precisely determined by the microstratigraphic position of a detrital layer within the annual succession of lake deposition. This flood chronology shows a striking variability in the flood occurrence from decadal to millennial time scales. There is a period of more than 200 years (21 B.C. 216 A.D.) without any flood documented, whereas the average frequency is 0.04 floods/year yielding 9 floods for such a time interval. 15 4. Questionnaire on use of historical data in flood frequency estimation As part of the COST Action ES0901 European procedures for flood frequency estimation a review was undertaken examining if, and how different European countries incorporate historical information into flood frequency analysis. Responses were collected from 15 European countries, representing the different participant countries of the COST Action; all participant countries were invited to contribute through the completion of a questionnaire, which was initially distributed to COST participants, who completed

  ), a number of examples of historical flood analysis are present within most European countries, with 30

  . A multidating approach applied to historical slackwater flood deposits of the gardon river, se france. Geomorphology 214, 56-68. DSI, 2012. Design Guidelines for Flood Hydrology -Taşkınlar Hidrolojisi Tasarım Rehberi. Guideline no. 008, State Hydraulic Works (DSI), Ankara, Turkey. Dub, O., Nemec, J., 1969. Hydrologie. technický pruvodce c.34. ( Hydrology. Technical Guidelines no 34.). Tech. rep., SNTL, Praha. DVWK, 1999. Wahl des Bemessungshochwassers. DVWK Schriften Heft 101, Deutscher Verband für Wasserwirtschaft und Kulturbau, Verlag Paul Parey, Hamburg. DWA, 2008. Erschließung und Einbeziehung historischer Informationen für die Ermittlung extremer Hochwasserabflüsse; Fallbeispiele und Empfehlungen. DWA-Themenheft 90 S, German Association for Water, Wastewater and Waste, Hennef. DWA, 2012. Ermittlung von Hochwasserwahrscheinlichkeiten (Estimation of flood probabilities). Merkblatt DWA-M 552, German Association for Water, Wastewater and Waste. El Adlouni, S., Ouarda, T., Zhang, X., Roy, R., Bobée, B., 2007. Generalized maximum likelihood estimators for the nonstationary generalized extreme value model. Water Resources Research 43 (3). 35

Figure 1 :

 1 Figure 1: Flood marks on the Loire river at Puy-en-Velay (France).

  49

Table 2 :

 2 Summary of historical flood records. Ratio in column four refers to the average ratio between length of instrumental record and the total length of the historical plus instrumental records.Author-produced version of the article published in Journal ofHydrology (2014), vol. 517, p. 963-973 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.jhydrol.2014.06.038

	Year of
	oldest recorded

Author-produced version of the article published in Journal ofHydrology (2014), vol. 517, p. 963-973 The original publication is available at http://www.sciencedirect.com/ doi : 10.1016/j.jhydrol.2014.06.038

Acknowledgement

The authors would like to thank COST Action ES0901 European procedures for flood frequency estimation for financial support. Two anonymous reviewers are acknowledged for their valuable comments on an earlier version of the paper.

Llasat, M.-C., Barriendos, M., Barrera, A., Rigo, T., 2005. Floods