T Bur

A Probst

A Bianco

L Gandois

Y Crouau
email: crouau@cict.fr

Determining cadmium critical concentrations in natural soils by assessing Collembola mortality, reproduction and growth $

Keywords:

The toxicity of cadmium for the Collembola Folsomia candida was studied by determining the effects of increasing Cd concentrations on growth, survival and reproduction in three cultivated and forested soils with different pH (4.5-8.2) and organic matter content (1.6-16.5%). The Cd concentration in soil CaCl 2 exchangeable fraction, in soil solution and in Collembola body was determined. At similar total soil concentrations, the Cd concentration in soil solutions strongly decreased with increasing pH. Reproduction was the most sensitive parameter. Low organic matter content was a limiting factor for reproduction. Effect of Cd on reproduction was better described by soil or body concentrations than by soil solution concentration. Values of EC 50-Repro expressed on the basis of nominal soil concentration were 182, 111 and 107 mg g À 1 , respectively, for a carbonated cultivated soil (AU), an acid forested soil with high organic matter (EPC) and a circumneutral cultivated soil with low organic content (SV). Sensitivity to Cd was enhanced for low OM content and acidic pH. The effect of Cd on reproduction is not directly related to Cd concentration in soil solution for carbonated soil: a very low value is found for EC 50-Repro (0.17) based on soil solution for the soil with the highest pH (AU; pH =8.2). Chronic toxicity cannot be predicted on the basis of soluble fractions. Critical concentrations were 8 Â 10 À 5 , 1.1, 0.3 mg mL À 1 , respectively, for AU, EPC and SV soils.

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The experiments were conducted in accordance with national and institutional guidelines for the protection of human subjects and animal welfare.

Introduction

Critical load (CL) was defined as ''the quantitative estimate of an exposure to one or more pollutants below which significant harmful effects on specified sensitive elements of the environment do not occur according to the present knowledge'' [START_REF] Nilsson | Critical loads for sulphur and nitrogen[END_REF]. CL has first been developed to evaluate and mitigate the effect of acid rain on forest ecosystems in Europe (De [START_REF] De Vries | Critical deposition levels for nitrogen and sulphur on Dutch forest ecosystems[END_REF][START_REF] De Vries | Assessment of critical loads and their exceedances on European forests using a one-layer steady-state model[END_REF][START_REF] Warfvinge | Calculating critical loads of acid deposition with profile-A steady-state soil chemistry model[END_REF][START_REF] Hornung | An empirical map of critical loads of acidity for soils in Great Britain[END_REF] and particularly in France [START_REF] Dambrine | De ´termination des ''charges critiques'' de polluants atmosphe ´riques pour les e ´cosyst emes naturels, en particulier forestiers. Bases the ´oriques -Projet d'application au cas des Vosges[END_REF][START_REF] Massabuau | Critical loads of acidity to streamwaters in the Vosges mountains (France): biological criteria[END_REF][START_REF] Party | Critical loads of acidity to France: sensitivity areas in the north-eastern France[END_REF][START_REF] Party | Charges critiques d'acidite én polluants atmosphe ´riques en France: conse ´quences vis a vis des sols et des peuplements forestiers[END_REF][START_REF] Moncoulon | Weathering, atmospheric deposition and vegetation uptake: role for ecosystem sensitivity to acid deposition and critical load[END_REF][START_REF] Moncoulon | Modeling acidification recovery on threatened ecosystems: application to the evaluation of the Gothenburg protocol[END_REF]. Since 1991, CL maps are used for international negotiations on air pollution abatement strategies [START_REF] Hettelingh | Chap. 3. Methods and data. in : Mapping Critical loads for Europe[END_REF]. It is now well admitted as a powerful tool to estimate ecosystem sensitivity to pollutant inputs.

As a first attempt, CL for heavy metals (HM) in soils (De [START_REF] Vries | Manual for calculating critical loads of heavy metals for soils and surface waters[END_REF] were estimated in a similar way [START_REF] Vries | Manual for calculating critical loads of heavy metals for soils and surface waters[END_REF]Probst et al., 2003a, b;[START_REF] Slootweg | Critical loads of cadmium, lead and Mercury in Europe[END_REF]. CL are based on the estimate of the highest concentration in soil solution (critical concentration, CC, De [START_REF] De Vries | Impact of soil properties on critical concentrations of cadmium, lead, copper, zinc and mercury in soil and soil solution in view of ecotoxicological effects[END_REF] supposed to have no effect on a soil function, community or population. Indeed this CC remains difficult to determine. Actually, models based on free ions concentrations are often used for that purpose [START_REF] Lofts | Deriving soil critical limits for Cu, Zn, Cd and Pb: a method based on free ion concentrations[END_REF]. But calibrations are still needed regarding toxicological impact on various soil organisms under different soil properties [START_REF] De Vries | Impact of soil properties on critical concentrations of cadmium, lead, copper, zinc and mercury in soil and soil solution in view of ecotoxicological effects[END_REF]. Bioassays using soil organisms might be useful tools to determine CC if they refer to ecologically relevant parameters like mortality, growth or reproduction. Molecular parameters (for example enzymatic activities) do not allow to determine the ecological impact of a specific chemical. Five standardized tests using soil animal models are used in Europe: Eisenia fetida (Annelide) mortality and reproduction tests (International Standard Organisation, ISO 11268-1, 1994, ISO 11268-2, 1997), Folsomia candida (Collembola) reproduction test (ISO 11267, 1998), Enchytraeids reproduction test (ISO 16387, 2001), and the assay for field testing with earthworm (ISO 11268-3, 1999). These assays usually concern normalised substrate rather than field soils.

Collembola are relevant target organisms to determine CC of HM in soils since (i) they are detritivorous, contribute to the nutrient cycle in soils and are widespread in most natural soils. Moreover, they have been extensively studied, particularly F. candida, which is commonly used as a biological model in laboratory test for pollutant toxicity assessment. The F. candida reproduction test is increasingly used because it is sensitive and because the breeding of F. candida is easy [START_REF] Riepert | ring test on a method for determining the effects of chemicals or soil contaminants on the reproduction of collembola[END_REF]. It was mainly used to assess the toxicity of pure metals [START_REF] Van Straalen | Population consequences of cadmium toxicity in soil microarthropods[END_REF][START_REF] Crommentuijn | Sublethall sensitivity index as an ecotoxicity parameter measuring energy allocation under toxicant stress-application to cadmium in soil arthropods[END_REF][START_REF] Crommentuijn | Bioavailability and ecological effects of cadmium on Folsomia candida (Willem) in an artificial soil substrate as influenced by pH and organic matter[END_REF][START_REF] Sandifer | Effects of pH on the toxicity of cadmium, copper, lead and zinc to Folsomia candida Willem, 1902 (Collembola) in a standard laboratory test system[END_REF][START_REF] Scott-Fordsmann | Sublethal toxicity of copper to a soil-dwelling springtail Folsomia fimetaria (Collembola: Isotomidae)[END_REF][START_REF] Smit | Effects of soil type, prepercolation, and ageing on bioaccumulation and toxicity of zinc for the springtail Folsomia candida[END_REF][START_REF] Crouau | The use of Folsomia candida (Collembola, Isotomidae) for the bioassay of xenobiotic substances and soil pollutants[END_REF][START_REF] Fountain | Continuous monitoring of Folsomia candida (Insecta: Collembola) in a metal exposure test[END_REF] or of organic chemicals [START_REF] Herbert | Comparison of instantaneous rate of population increase and critical-effect estimates in Folsomia candida exposed to four toxicants[END_REF][START_REF] Eom | Ecotoxicity of a polycyclic aromatic hydrocarbon (PAH)-contaminated soil[END_REF]. Application to complex mixtures such as polluted soils or wastes are less numerous [START_REF] Smit | Comparison of the toxicity of zinc for the springtail Folsomia candida in artificially contaminated and polluted field soils[END_REF][START_REF] Fountain | Biodiversity of Collembola in urban soils and the use of Folsomia candida to assess soil ''quality[END_REF][START_REF] Crouau | The use of Folsomia candida (Collembola, Isotomidae) in bioassays of waste[END_REF][START_REF] Crouau | Unexpected reduction in reproduction of Collembola exposed to an arsenic-contaminated soil[END_REF][START_REF] Crouau | Comparative ecotoxicity of three polluted industrial soils for the Collembola Folsomia candida[END_REF]. The effects of temperature [START_REF] Snider | The life history of Folsomia candida (Willem) (Collembola, Isotomidae) relative to temperature[END_REF], pH and soil moisture [START_REF] Holmstrup | Drought tolerance in Folsomia candida Willem (Collembola) after exposure to sublethal concentrations of three soil-polluting chemicals[END_REF][START_REF] Van Gestel | The influence of soil moisture content on the bioavailability and toxicity of cadmium for Folsomia candida Willem (Collembola: Isotomidae)[END_REF][START_REF] Van Gestel | The influence of soil characteristics on cadmium toxicity for Folsomia candida (Collembola: Isotomidae)[END_REF] as well as the variability between strains on test sensitivity have been studied [START_REF] Crommentuijn | Sublethall sensitivity index as an ecotoxicity parameter measuring energy allocation under toxicant stress-application to cadmium in soil arthropods[END_REF][START_REF] Chenon | The use of Folsomia candida (Collembola, Isotomidae) for the bioassay of xenobiotic substances and soil pollutants[END_REF][START_REF] Crouau | The relative sensitivity of growth and reproduction in the springtail, Folsomia candida, exposed to xenobiotics in the laboratory: an indicator of soil toxicity[END_REF].

Organic matter and pH have often been identified as key factors, which control the complexation and availability of metals, and thus influence metal toxicity, noticeably for Cd (see as example, [START_REF] Crommentuijn | Bioavailability and ecological effects of cadmium on Folsomia candida (Willem) in an artificial soil substrate as influenced by pH and organic matter[END_REF]Son et al., 2007).

To ensure their protection regarding agriculture and atmospheric inputs, CCs of HM must be determined for different kinds of soils with emphasis on Collembola as target living organisms. With that aim, processes and key factors of metal toxicity in ''natural'' soils must be better investigated. French soils present a large variety of conditions and show pollution by HM, noticeably Cd and Pb [START_REF] Hernandez | Heavy metal distribution in some French forest soils: evidence for atmospheric contamination[END_REF]Probst et al., 2003a, b).

In this paper, we used the reproduction of F. candida as an indicator of soil ecosystem sensitivity to cadmium and to determine CCs in soil solution. Moreover, we studied the mortality and the growth of F. candida to improve the understanding of Cd effects. To be as representative as possible of natural conditions, three spiked typical natural French soils with different pH and OM characteristics were used to perform toxicity tests. In these particular conditions, Cd LC 50 (lethal concentrations), LOEC (lowest efficient concentrations), EC 50 and EC 5 (efficient concentration) for reproduction were computed. Cd concentrations in organisms and in soil solution and CaCl 2 exchangeable Cd, were determined. The influence of the main soil parameters (pH, OM) on toxicity, was assessed. Finally, a method for estimating critical concentration from EC 5 values is presented.

Materials and methods

Soil characteristics

Experiments were performed using three soils : two cultivated soils from the South-West area of France (Aurade ´, AU and Saint-Victor, SV) and a forest soil (EPC, under spruce cover) from the centre part of France were chosen (Table 1). These soils were selected given their varying pH and OM contents (Table 1), to investigate the influence of these two parameters on F. candida reproduction. The two cultivated soils have a very low OM content and are circumneutral to basic (particularly the carbonated soil, AU) compared to the acidic forested soil (EPC). Soil moisture were set up to 25%, 30% and 20%, respectively, for AU, EPC and SV (50% water holding capacity, WHC), to enhance development of Collembola by creating an adequate crumbly structure. Cd concentrations were in the range of low contaminated soils [START_REF] Baize | Teneurs totales en e ´le ´ments traces me ´talliques dans les sols[END_REF].

The aim of the study was to compare the responses to Cd toxicity of various soils with different physico-chemical characteristics. Consequently, to match field conditions as closely as possible, the ISO 11267 guidelines were not appropriate.

Collembola cultures

A culture of F. candida was reared in the laboratory at 207 1 1C in darkness, in glass containers with a base of plaster of Paris/charcoal powder mixture (ratio 4/1). Distilled water and a small amount of dried Baker's yeast (as a food source) were added weekly. F. candida juveniles were collected two times a week with a suction apparatus in order to select synchronized populations.

Toxicity tests

The test consists in exposing juveniles to field soils contaminated by Cd and in comparing reproduction, growth and mortality with those of animals placed in non-contaminated control soil. For toxicity tests, plastic containers of approximately 100 mL were used. The natural soils were spiked with Cd(NO 3 ) 2 (0, 50, 100, 200, 400 mg Cd g À 1 dry soil) and were equilibrated for a week before starting the toxicity tests. Cd was dissolved in distilled water, which was used for soil moistening. For each soil and each spiking concentration, 8 test containers (12 for the control) were filled with 45 g of moist soil. Fifteen F. candida juveniles (8-12 days old juveniles) were introduced into each container. Indeed, we used 8-12 days old animals rather than 10-12 days (as recommended by the ISO guideline no. 11267). Young animals are more sensitive to metal toxicity and thus we think that animals as young as possible must be tested. The containers were aerated twice a week. Exogenous yeast was not added during testing in order to be closer to field conditions. The duration of exposure was 50 days, instead of the 28 days recommended in the ISO guideline (ISO no. 11267, 1998) in order to counterbalance the lack of added food during the assay. Indeed, this might lead to a lower reproduction rate than those of normalised assays with food addition. Moreover, a longer exposure duration increases the sensitivity of the assay (EC 50-repro for Cd after 6 weeks oEC 50-repro after 4 weeks; [START_REF] Van Gestel | The influence of soil characteristics on cadmium toxicity for Folsomia candida (Collembola: Isotomidae)[END_REF], decreases the variability of test results, and therefore increases the efficiency of the assay [START_REF] Crouau | What causes variability in the Folsomia candida reproduction test[END_REF]. Lastly, a longer exposure duration was more realistic because in field conditions, Collembola are exposed to pollutants for longer than 28 days. Moreover, increasing the assay duration allows to increase the number of individuals at the end of the assay and, on account of this, counterbalances the effect of none food addition, which would have decreased the number of individuals.

At the end of the exposure time (207 1 1C, in darkness), containers were flooded with deionised water and gently stirred in order to make all living animals to float at the water surface. The water surface of each container was photographed. Adults and juveniles were counted and their lengths (from the end of the posterior abdominal segment to the anterior margin of the head) were measured. All the animals were measured, but the animal number depended on the series and was the lowest for highest Cd concentration series. The limit length between juvenile and adult populations was defined as the length class presenting the lowest individual abundance (sum of the five concentration abundances), around the third quartile value.

Wilcoxon's two-sample test was used to assess significant differences of reproduction, mortality and length between exposed and control series. Nonparametric methods were used given the non-normal distribution of the data and the heterogeneity of variances. The EC 5 and EC 50 values were calculated by using the maximum likelihood-probit procedure (Toxcalc 5.0 software, Ives, 1996; EPA methods).

Chemical analyses

For each spiked concentration, Collembola were extracted (alive) and placed during 3 days in fasting containers with only a humid filter paper to control hygrometry. Collembola were then killed by freezing ( À 80 1C). For each soil and

Table 1

Physico-chemical properties of soils used for toxicity tests on reproduction of F. candida (OM: organic matter content; RMQS: French national network for soil quality measurement; RENECOFOR: French national network for forest ecosystems long-term survey, Ponette et al., 1997, data from Hernandez et al., 2003). digested (ultrapure HNO 3 , 90 1C) together with blank and standard samples in a clean room. Cd concentration measurements in Collembola were controlled by using the international reference material TORT-2 (Lobster Hepatopancreas).

Soils

After dissolution procedure, a single analytical measurement was done in a series including blank and reference material. Cd concentrations were analysed in Collembola with a Perkin-Elmer inductively coupled plasma-mass spectrometer (ICP-MS). In soil solutions and in exchangeable CaCl 2 solutions, Cd was analysed by inductively coupled plasma-optical emission spectrometry (ICP-OES). The main Cd isotope ( 114 Cd) was measured as it presented the lowest deviation during ICP-MS measurements. The detection limit of Cd measurements was 1.6 Â 10 À 3 mg L À 1 for body concentration and 1 mg L À 1 for water concentration. The significance of analytical interference was negligible (e.g. As and Co levels were lower with several orders of magnitude than Cd in spiked bodies and soil solutions).

ICP-MS and ICP-OES measurements were calibrated using a set of gradually concentrated external standards. For body concentration measurements, 3 calibration lines were performed for a 14 sample set analysis, using 4 standards for each (with Cd content from 0 to 55 mg L À 1 ). The correlation coefficient of the calibration line for 114 Cd was very elevated (r= 0.9999), which guaranties the quality of Cd measurement in bodies. During ICP-MS measurements, as a routine procedure, an In/Re mix was used as an internal standard for body concentration measurements.

Dissolved organic carbon (DOC) in soil solutions was analysed using a Shimatzu TOC 5000 Carbon Analyser. The detection limit of DOC measurements was 0.1 mg L À 1 . Pore water was extracted by soil centrifugation (2000g, 15 min).

Exchangeable Cd obtained by adding 10 À 2 mol L À 1 CaCl 2 (soil/solution = 1/10, w/w). Solutions were filtered (with 0.22 mm filter) before element and DOC analyses.

Results

Collembola and soil analyses

Cd concentrations in F. candida

Cd concentrations in body have been measured for all the experiment concentrations, except for 400 mg g À 1 condition because not enough animals were available for analytical determination (Fig. 1). Cd concentrations were high in all exposed animals. The highest Cd concentrations were found in Collembola of the SV soil (except for the 200 mg g À 1 condition) with a maximum value of 1100 mg g À 1 dry wt for the 100 mg g À 1 dry soil condition. The lowest concentration was measured in the Collembola of the AU soil, except for the 200 mg g À 1 condition for which the organisms concentrations in EPC and SV decreased.

Soil solution and exchangeable Cd concentrations, pH and DOC

Cd concentrations in the soil solutions and in the exchangeable fractions are summarised in Table 2. At the beginning of the assay (t1), soil solution concentrations increased with Cd nominal soil concentrations for the three soils. But, concentrations in the soil solutions and in the exchangeable fractions were much higher in the EPC and SV soils than in the AU soil. Cd in soil solution increased with time for SV and decreased for EPC.

Soil solution pH was circumneutral for AU and acidic for EPC and SV; pH was similar at t1 and t8 for AU, but it decreased slightly (half a unit) for EPC (except at 400 mg g À 1 ) and very much for SV. EPC showed DOC concentrations higher than those of AU and SV. This difference can be explained by the higher OM content of EPC (16.5% for EPC, 2% and 1.6%, respectively, for AU and SV). DOC did not change very much during the assay in AU, whereas it increased in EPC and decreased in SV for the highest Cd concentrations.

Collembola length

AU soil: Two groups of distinct lengths were observed for each soil concentration. The individuals added to the test containers at the beginning of the assay are the longest animals. The shortest group was composed of juveniles, which were born during the assay (Fig. 2a). The mean lengths of the two groups (juveniles and adults) were 0.45 and 1 mm, respectively. The limit point between the two populations was 0.75 mm. There is no significant difference between the lengths of the blank series and of the other series (adults and juveniles groups) except for the 100 mg g À 1 series (Fig. 2d).

EPC soil: The maximum number of individuals was observed for the 0.65 mm length. Contrary to what was observed for the AU and SV soils, Collembola length in EPC soil showed a single population distribution for all tested Cd concentrations (Fig. 2b). Applying the same method as for the other two soils, the limit between juveniles and adults was 0.85 mm. The increase of the soil Cd concentration did not change significantly the median of juvenile length, except for the 200 mg g À 1 series.

SV soil: Collembola of the SV soil showed two populations with different length ranges (Fig. 2c) for all series. The limit between juveniles and adults was 0.7 mm. Significant length differences of the blank series were only detected for the 100 mg g À 1 dry soil series (Fig. 2d). The lack of significant differences for the highest Cd concentrations (200 and 400 mg g À 1 ) could be due to the higher variability and the less numerous data for these two series.

Collembola reproduction and mortality

The EC 5 , EC 50 and LOEC for reproduction and mortality tests are given in Table 3. Comparison of the EC 50-repro of the three soils on the basis of soil concentrations indicated that Cd has the same toxicity for the SV and EPC soils and a lower toxicity for the AU soil. It was the opposite for the EC 50-repro calculated on the basis of soil solutions. A decrease in juveniles (effect on reproduction-Fig. 3a) and in adults (effect on mortality-Fig. 3b) populations with increasing Cd concentrations was observed for the EPC and SV soils. The AU soil showed a decrease in the juvenile number, but not in the adult number. A small increase in adults and juveniles was often observed for the lowest Cd concentrations, except in SV; the EPC and AU soils showed an increase in juvenile number for the 50 mg g À 1 series, followed by a regular decrease for the three highest concentrations.

Discussion

Juvenile productions were low when compared to litterature references [START_REF] Van Gestel | The influence of soil characteristics on cadmium toxicity for Folsomia candida (Collembola: Isotomidae)[END_REF][START_REF] Greenslade | A comparison of Collembola species for toxicity testing of Australian soils[END_REF] and the results of the assays did not fulfil validity criteria of the norm, probably due to differences in experimental conditions (no food addition, natural vs. artificial soil). Indeed, the objectives were not to strictly follow the norm but to fit as much as possible the field conditions. The lowest juvenile production in control series was observed for the SV soil (average of 1473 juveniles), which was nearly neutral. The two other soils are either calcareous (AU) or have a high organic matter content (EPC), which seems to increase the reproduction rate. The decrease in juveniles numbers in the SV and EPC soils (200 and 400 mg g À 1 series) could be partly due to the effect of Cd on mortality of adults (Fig. 3).

Values of EC 50 based on reproduction (EC 50-repro )

were 182, 111 and 107 mg g À 1 dry soil for AU, EPC and SV, respectively. These values were consistent with some studies [START_REF] Crommentuijn | Bioavailability and ecological effects of cadmium on Folsomia candida (Willem) in an artificial soil substrate as influenced by pH and organic matter[END_REF][START_REF] Crouau | The use of Folsomia candida (Collembola, Isotomidae) for the bioassay of xenobiotic substances and soil pollutants[END_REF][START_REF] Herbert | Comparison of instantaneous rate of population increase and critical-effect estimates in Folsomia candida exposed to four toxicants[END_REF], but two studies [START_REF] Van Gestel | The influence of soil moisture content on the bioavailability and toxicity of cadmium for Folsomia candida Willem (Collembola: Isotomidae)[END_REF][START_REF] Van Gestel | The influence of soil characteristics on cadmium toxicity for Folsomia candida (Collembola: Isotomidae)[END_REF] reported values which are about two times lower than the range of this study. High pH value (AU) increased EC 50 values based on nominal concentrations.

The EC 5-repro were 43, 56 and 15 mg g À 1 dry soil for AU, EPC and SV, respectively. The 95% confidence interval for AU overlapped that of EPC, indicating that the two values are almost equivalent.

For the AU soil, juvenile numbers decreased strongly with the increase in Cd concentration (Fig. 3b). Mortality of adults was low whatever the soil Cd concentrations. We did not observe a significant shift towards smaller lengths of juveniles with Cd concentration increase; therefore, in AU soil, Cd affected reproduction rather than mortality and growth of F. candida. Such a higher sensitivity of the reproduction parameter by comparison to mortality and growth parameters was previously observed [START_REF] Van Straalen | Population consequences of cadmium toxicity in soil microarthropods[END_REF][START_REF] Scott-Fordsmann | Sublethal toxicity of copper to a soil-dwelling springtail Folsomia fimetaria (Collembola: Isotomidae)[END_REF][START_REF] Fountain | Continuous monitoring of Folsomia candida (Insecta: Collembola) in a metal exposure test[END_REF].

For the SV soil, only the number of juveniles in the 200 mg g À 1 series differed significantly from the blank (p o0.01). This effect on reproduction was partly due to mortality (LOEC mortality = 200 mg g À 1 ;r= À0.57; p o0.01). Cd might delay juvenile growth for 200 and 400 mg g À 1 series (Fig. 2c). In contrast to the AU soil, for which juveniles were much more abundant than adults, animal numbers were quite similar between juvenile and adult groups for the SV soil. A low juvenile number was also found in control containers indicating that the SV soil did not favour F. candida reproduction. The low reproduction observed for the SV soil was not related to an indirect effect on mortality since more adults were counted in control containers for SV among the three soils. The low reproduction rate can be explained by the low OM content of the SV soil, which inhibits microbial activity and food production for F. candida.

Contrary to the AU and SV soils, juvenile and adult groups cannot be distinguished on length histogram of the EPC soil. The right part of the juvenile peaks (corresponding to the longest juveniles) was confounded with the left part of the adult peaks (shortest adults). Nevertheless, a separation between juvenile and adult populations was defined at 0.85 mm according to the procedure previously used for AU and SV. The overlap of juvenile and adult populations can be attributed to the high OM content in this soil: it enhanced growth rate of initially introduced individuals and caused consequently an early laying and a quick growth of produced juveniles.

Cd concentrations in organisms were lower for the AU soil than for the other soils at nominal Cd soil concentrations of 50 and 100 mg g À 1 . AU also had the lowest EC 50-repro on the basis of nominal concentrations. These results were consistent with the lowest soluble and exchangeable Cd concentrations found for the AU soil, if we consider that Cd measured in solution is representative of bioavailable Cd [START_REF] Van Gestel | Water-extractability, free ion activity, and pH explain cadmium sorption and toxicity to Folsomia candida. (Collembola) in seven soil-pH combinations[END_REF]. However, several results did not corroborate this hypothesis: (1) body concentrations for EPC and SV with 200 mg g À 1 nominal Cd were lower than for 50 and 100 mg g À 1 exposures, whereas Cd in solution was 2 or 3 times higher; (2) it is noteworthy that EC 50-repro values based on total soil concentrations were very close among the three soils whereas exchangeable Cd and Cd in solution were very different (more than 3500 times higher for EPC 50 gm g À1 and EPC 100 gm g À1 soil solution at t 1 than for AU 50 gm g À1 and AU 100 gm g À1 and more than 110 times higher for EPC 50 gm g À1 and EPC 100 gm g À1 exchangeable Cd than for the equivalent with AU soil). These last differences can probably be attributed to the effect of pH since it is well known that Cd availability in solution decreases with increasing pH (Van Gestel [START_REF] Van Gestel | The influence of soil characteristics on cadmium toxicity for Folsomia candida (Collembola: Isotomidae)[END_REF]. The results showed that Cd concentrations in soil solution and exchangeable fraction were not the only determining parameters for Cd toxicity on F. candida. Sources other than Cd contained in pore water must be considered to explain the results: (1) soil fungi are able to acidificate their close environment and to increase nutrient absorption, causing at the same time the solubilisation and absorption of trace elements [START_REF] Bago | Nitrate depletion and pH changes induced by the extraradical mycelium of the arbuscular mycorrhizal fungus Glomus intraradices grown in monoxenic culture[END_REF][START_REF] Casarin | Quantification of oxalate ions and protons released by ectomycorrhizal fungi in rhizosphere soil[END_REF][START_REF] Gadd | Geomycology: biogeochemical transformations of rocks, minerals, metals and radionuclides by fungi, bioweathering and bioremediation[END_REF][START_REF] Finlay | Ecological aspects of mycorrhizal symbiosis: with special emphasis on the functional diversity of interactions involving the extraradical mycelium[END_REF][START_REF] Van Scholl | Rock-eating mycorrhizas: their role in plant nutrition and biogeochemical cycles[END_REF]. When these organisms are consumed by Collembola, they represent a privileged route for trace metal absorption. This phenomenon should be more important for a carbonated soil as AU and would balance the very low Cd concentrations in pore water.

(2) Microorganisms consumed by F. candida constitute a first step in metal internalisation which leads to Cd ingested concentrations that are different from pore water Cd concentrations. As an example, [START_REF] Posthuma | Genetic ecology of metal tolerance in Collembola[END_REF] found that Cd concentrations in soil algae were equivalent to Cd concentrations in bulk soil for low values (0.009 mg g À 1 ) but were lower when bulk soil concentrations increased (0.046 mg g À 1 in algae for 0.56 mg g À 1 in soil). The Cd accumulation rate of these organisms would be more important for the AU soil than for the two other soils, relatively to pore water concentrations. (3)

Soil and exchangeable solutions were sieved with a 0.22 mm filter before analysis. This step eliminates Cd from solution when linked to suspended particles with diameter higher than 0.22 mm but which could be absorbed by Collembola (organic particles or clays). When such particles are consumed, Cd would be partly desorbed from particles in Collembola digestive system due to lowest pH (pH 6; [START_REF] Humbert | Etude du pH intestinal d'un Collembole (Insecta, Apte ´rygote)[END_REF] and consequently it would be absorbed through intestinal epithelium. A decrease of one pH unit reduces Cd sorption by about 75% [START_REF] Temminghoff | Speciation and calcium competition effects on cadmium sorption by sandy soil at various pH[END_REF]. Cd adsorbed onto these particles was not measured as Cd in soil solution. The process described above can only be observed when soil pH is very elevated (as in AU soil), but cannot occur in the EPC and SV soils with a lower pH. Fig. 4 shows the ratio of Cd concentrations in Collembola on Cd concentrations in pore water for the different nominal soil concentrations. Cd accumulation by F. candida relative to pore water concentration decreases with nominal concentration but is always higher for AU soil.

EC 50 and EC 5 give informations on Cd effects on F. candida. However, the final object of that study is the evaluation of the contamination level compatible with the protection of almost all the soil invertebrates community. We have kept the reproduction parameter because it is the most sensitive and ecologically relevant one. [START_REF] Crommentuijn | Sublethall sensitivity index as an ecotoxicity parameter measuring energy allocation under toxicant stress-application to cadmium in soil arthropods[END_REF]. Ideally, it would be necessary to test Cd effect on almost all the soil arthropods species. It is clearly impossible and we must try to correct the ECx that we get for F. candida on the basis of the relative sensitivities of F. candida and of the other soil invertebrates for which tests have been done. With this aim in mind, we tried to evaluate the Cd concentration preserving 95% of the reproduction of 95% of soil invertebrates (critical concentrations (CC)). Several authors consider that F. candida is less sensitive to trace metal than other species of the pedofauna [START_REF] Lubben | Influence of sewage sludge and heavy metals on the abundance of Collembola on two agricultural soils[END_REF][START_REF] Greenslade | A comparison of Collembola species for toxicity testing of Australian soils[END_REF]Son et al., 2007). EC 50-repro for Cd of some soil invertebrates are given in Table 4.

The EC 50-repro and LC 50 of soil invertebrates were approximated with the log-normal distribution applied to the data of Table 4. It allowed to quantify the sensitivity of F. candida in comparison with other soil invertebrates. This model has previously been used to study species distribution of Collembola in natural communities [START_REF] Syrek | Species abundance distribution of collembolan communities in forest soils polluted with heavy metals[END_REF] and NOEC distribution [START_REF] Aldenberg | Confidence limits for hazardous concentrations based on logistically distributed NOEC toxicity data[END_REF]. We get 20 and 37, respectively, for the EC 50-repro and LC 50 of the 5% more sensitive species. On this basis, F. candida would be about 9 times less sensitive for reproduction and 33 times for lethality than the 5% most sensitive group. So, the difference is larger for lethality than for reproduction. This observation is in agreement with the high sublethal sensitivity index (ratio between the lethal effect concentration and the sublethal effect concentration-SSI) previously found for F. candida [START_REF] Crommentuijn | Sublethall sensitivity index as an ecotoxicity parameter measuring energy allocation under toxicant stress-application to cadmium in soil arthropods[END_REF]. F. candida put a higher priority on survival than on reproduction. Applying the correction factors dealing with reproduction, the CC of the AU, EPC and SV soils would be, respectively, 8 Â 10 À 5 , 1.1 and 0.3 mg mL À 1 . These values can be compared to critical concentrations obtained according to the method exposed in De [START_REF] De Vries | Impact of soil properties on critical concentrations of cadmium, lead, copper, zinc and mercury in soil and soil solution in view of ecotoxicological effects[END_REF], which is based on modelling, using pH and MO content as prediction parameters: 1 Â 10 À 4 , 1.7 Â 10 À 3 , 5 Â 10 À 4 mg mL À 1 , respectively, [START_REF] Van Gestel | The influence of soil moisture content on the bioavailability and toxicity of cadmium for Folsomia candida Willem (Collembola: Isotomidae)[END_REF], [START_REF] Crommentuijn | Sublethall sensitivity index as an ecotoxicity parameter measuring energy allocation under toxicant stress-application to cadmium in soil arthropods[END_REF][START_REF] Crommentuijn | Bioavailability and ecological effects of cadmium on Folsomia candida (Willem) in an artificial soil substrate as influenced by pH and organic matter[END_REF], Sandifer andHopkin (1996, 1997) [START_REF] Greenslade | A comparison of Collembola species for toxicity testing of Australian soils[END_REF] the values determined by the mean of de Vries et al. method for AU but greatly higher for EPC and SV. Indeed, it means that for soils with a significant proton and organic matter content (EPC and SV), the model from De Vries et al. based on these parameters does not give suitable results. Thus, the apparent adequacy for critical limits obtained for carbonate soil (AU) might be coincidental.

Our results state that comparing critical limits determined by direct toxicological effect on soil organisms with those predicted by models based on soil parameter remain still difficult. Further investigations are needed.

Conclusion

This study confirms that Collembola reproduction is a more sensitive parameter than mortality and growth regarding Cd toxicity. It also shows that low organic matter content is a limiting factor for reproduction. Sensitivity to Cd was enhanced for low OM content and acidic pH. We succeed in determining EC 50 for Cd with three different natural soils and we show that effect of Cd on reproduction is better described by soil or body concentrations than by soil solution concentration. In spite of different Cd concentrations in soil solutions, EC 50 are rather similar. The critical limits determined in this study do not really fit those given by soil parameter modelling, which implies further investigations on coupled model particularly considering the influence of particulate matter and microorganisms.

Fig. 1 .

 1 Fig. 1. Cd concentrations in animals for the experimental concentrations (50, 100 and 200 mg g À 1 ) applied on the three considered soils (AU, EPC and SV), compared to the control Cd content in soils. (y axis: log unit).

Fig. 2 .

 2 Fig. 2. Number of juveniles and adults for each length class and each Cd soil concentration in AU (a), EPC (b) and SV (c) soils. (d) Medians, quartiles and mode of the lengths of juveniles (significant differences to control: n po 0.05; nn p o 0.01; nnn p o 0.001)

Fig. 3 .

 3 Fig. 3. Dose-effect relationship of Cd (nominal concentrations in soil) on the reproduction ((a) mean number of juveniles 7S.E.M.) and the mortality ((b) mean number of adults 7S.E.M.) of F. candida.

Fig. 4 .

 4 Fig. 4. Cd bioaccumulation factor relatively to pore water concentrations.

Table 2

 2 Cd concentrations in the three soils (nominal value, dry wt. basis), in corresponding soil solution (at t 0 + 1 week and t 0 +8 weeks) and in CaCl 2 exchangeable fraction. pH(CaCl 2 ) and pH(H 2 O) and DOC (at t 0 + 1 week and t 0 + 8 weeks) are also indicated.

	Cd soil	Cd solution (mg mL À 1 )	Cd CaCl 2 (mg mL À 1 )	pH soil solution	pH	DOC (mg mL À 1 )
	Nominal (mg g À 1 )	t1	t8		t1	t8	CaCl 2	t1	t8
	AU
	0	o DL	oDL	0.05	7.11	7.72	6.9	26	23
	50	0.003	oDL	0.24	7.25	7.65	7.04	25.6	20.2
	100	0.009	oDL	0.58	7.56	7.57	6.98	27.1	20.3
	200	0.47	0.43	2.07	7.45	7.45	7.03	31.4	30.1
	400	1.69	2.93	9.95	7.09	7.4	6.94	31.7	33
	EPC
	0	0.02	0.01	0.11	4.09	3.73	2.98	14.3	21.2
	50	10.60	5.21	29.85	3.85	3.58	2.96	24.5	24.9
	100	30.02	19.80	67.11	3.89	3.73	3.01	25.8	43.7
	200	90.54	45.28	112.65	3.4	3.1	3.05	26.3	66.2
	400	280.29	195.06	284.59	3.4	3.49	2.98	40	94.2
	SV
	0	o DL	0.04	0.67	4.16	2.57	4.44	30.2	28.8
	50	6.68	12.91	27.28	4.2	3.53	4.44	32.3	49.3
	100	18.45	35.04	47.33	4.05	3.3	4.47	43.2	26.1
	200	51.89	82.33	112.97	3.99	3.36	4.57	66.4	48.6
	400	143.13	185.23	264.47	3.91	3.19	4.64	72.7	59

o DL: inferior to detection limit.

Table 3

 3 Mean

		EC 5	EC 50	LOEC
	Juveniles
	AU
	Soil	43.5 (11-77)	182 (134-254) 400 (po 0.05)
	Soil solution 7 Â 10 À 4 (5 Â 10 À 6 -5 Â 10 À 3 ) 0.17 (0.05-0.6) 1.7 (p o0.05)
	Exchangea.	0.13 (0.012-0.32)	1.9 (1.1-3.8)	9.9 (p o0.05)
	EPC
	Soil	56 (26-72)	111 (96-133)	100 (po 0.05)
	Soil solution 9 (2.6-13.4)	22 (18-28)	30 (po 0.05)
	Exchangea.	42 (19-52)	72 (63-83)	67 (p o0.05)
	SV
	Soil	15	107	200 (po 0.01)
	Soil solution 2.6	36	52 (p o0.01)
	Exchangea.	8	57	113 (p o 0.01)
	Adults
	AU
	Soil	-	-	-
	Soil solution -	-	-
	Exchangea.	-	-	-
	EPC
	Soil	110 (47-137)	16 (118-177)	200 (po 0.05)
	Soil solution 22 (8-29)	35 (24-39)	45 (p o0.05)
	Exchangea.	72 (38-85)	95 (76-103)	77 (p o0.05)
	SV
	Soil	78 (29-113)	223 (178-280) 200 (po 0.05)
	Soil solution 26 (8-42)	93 (71-121)	82 (p o0.05)
	Exchangea.	35 (12-55)	129 (98-170)	113(p o 0.05)

and range (in brackets) EC 5 , EC 50 and LOEC for reproduction (juveniles number) and mortality (adults number) for the three soils (AU, EPC, SV) relatively to Cd concentrations in soil (nominal concentration, mg g À 1 ), in soil solution and to CaCl 2 exchangeable Cd(mg mL À 1 ).

Table 4

 4 EC 50-repro and LC 50 calculated on the basis of Cd soil concentrations for 12 soil invertebrates. (Bold types characters correspond to mean of several data.)

		EC 50-repro	LC 50	Reference
		(Cd soil)	(Cd soil)
	Aporrectodea caliginosa	35	540	Khalil et al. (1996)
	Caenorhabditis elegans		627	Donkin and Dusenbery (1994)
	Enchytraeus albidus	115	364	Lock and Janssen (2001)
	Eisenia andrei	33	417	Van Gestel et al. (1993)
	Eisenia fetida	116	1095	Spurgeon et al. (1994), Spurgeon and Hopkin (1995), Neuhauser et al. (1985), Fitzpatrick et al.
				(1996), Lock and Janssen (2001)
	Lumbricus terrestris		256	Fitzpatrick et al. (1996)
	Folsomia candida	180	1213

  [START_REF] Lock | Cadmium toxicity for terrestrial invertebrates: taking soil parameters affecting bioavailability into account[END_REF]

	Plectus acuminatus	321		Kammenga et al. (1996)
	Paronychiurus kimi	60	90	Son et al. (2007)
	Proisotoma minuta	125		Nursita et al. (2005)
	Sinella coeca	28	12	Menta et al. (2006)
	Sinella communis	50	374

Acknowledgments

This study benefited from the financial aids from ADEME, CNRS, INRA and Toulouse University.

The authors thank to A. Canut, A. Magro, F. Candaudap and A. Alric, for their help in field sampling, sample preparation, or analysis and to K. Dexter for checking the English.

T. Bur benefited from a joint fellowship Agence de l'Environnement et de la Maîtrise de l'Energie (ADEME)-Institut National de la Recherche Agronomique (INRA)/Re ´seau de Mesure de la Qualite ´des Sols (RMQS). L. Gandois benefited from a ADEME fellowship.


Samuel Grosdidier
email: grosdidiersamuel@hotmail.fr

Philippe Forget
email: philippe.forget@lseet.univ-tln.fr

Yves Barbin
email: yves.barbin@lseet.univ-tln.fr

Charles-Antoine Guérin

HF Bistatic Ocean Doppler Spectra: Simulation Versus Experimentation

Keywords: Bistatic high-frequency surface wave radar (HFSWR), Doppler spectrum [power spectral density (PSD)], ocean wave spectum, radar equation

We simulate the Doppler spectra that can be obtained under experimental conditions from bistatic highfrequency oceanic radar. For this, we combine the bistatic secondorder theory with the characteristics of the full radar system, such as antenna patterns, range attenuation, and postprocessing of the received signal. Because of the sharp variation of the bistatic geometry at short range, we show that it is crucial to take these effects into account for the correct interpretation of the first-order Bragg peaks. The second-order spectrum is more robust to the system characteristics but can under some conditions also suffer from its artifacts, especially in the vicinity of the secondary peaks. A comparison is made with experimental spectra acquired recently with a Wellen radar system on the Mediterranean coast. The Wave Watch III model is used to simulate directional wave height spectra after a preliminary validation with in situ buoy measurements. Experimental and simulated Doppler spectra agree generally well, except in the case where the directional wave spectrum has little energy in the line of sight of the radar.

I. INTRODUCTION

T ODAY, high-frequency surface wave radars (HFSWRs) are routinely used for the remote sensing of the ocean surface. As is well known, the analysis of the Doppler spectrum of the received signal allows the estimation of surface currents [START_REF] Barrick | First order theory and analysis of MF/HF/VHF scatter from the sea[END_REF], [START_REF] Barrick | Remote sensing of sea state by radar[END_REF] as well as wave spectra (e.g., [START_REF] Lipa | Extraction of sea state from HF radar sea echo-mathematical theory and modeling[END_REF]- [START_REF] Ramos | Observation of wave energy evolution in coastal areas using HF radar[END_REF]). HFSWRs have also proven to be potentially useful for target detection and tracking [START_REF] Gurgel | HF radar wave measurements in the presence of ship echoes-problems and solutions[END_REF], [START_REF] Sevgi | An integrated maritime surveillance system based on high-frequency surface-wave radars, part 1: Theoretical background and numerical simulations[END_REF]. Most of the HFSWR systems work with colocated transmitters and receivers. However, the monostatic mode raises practical issues such as the coastal space requirement to set up both the transmit and receive antenna arrays and the problem of mutual interference between antennas. These issues can be overcome by resorting to a bistatic radar system, where the emitter and receiver are sited at remote locations. In addition, the bistatic mode increases data product density and area of coverage for similar equipment. In this paper, we report on a bistatic HFSWR that has been recently installed on the coast of the Northwestern Mediterranean Sea. Although this dual system was primarily dedicated to surface current mapping using the MUSIC processing technique [START_REF] Lipa | Seasonde radial velocities: Derivation and internal consistency[END_REF], it is also possible to investigate with it the bistatic Doppler signature of a radar cell at the sea surface using a beamforming (BF) technique.

Several experimental studies have been made in the bistatic mode, such as estimation of the directional wave spectrum from first-order echoes [START_REF] Teague | Bistatic-radar techniques for observing long-wavelength directional ocean-wave spectra[END_REF], measurement of surface current velocities [START_REF] Teague | Bistatic-radar techniques for observing long-wavelength directional ocean-wave spectra[END_REF], [START_REF] Lipa | HF radar bistatic measurement of surface current velocities: Drifter comparisons and radar consistency checks[END_REF], vessel detection [START_REF] Roarty | Performance evaluation of seasonde high-frequency radar for vessel detection[END_REF], and wind measurement [START_REF] Huang | Measurement of sea surface wind direction using bistatic high-frequency radar[END_REF]. Likewise, there have been a number of theoretical works on the subject [START_REF] Barrick | Remote sensing of sea state by radar[END_REF], [START_REF] Gill | High-frequency bistatic cross sections of the ocean surface[END_REF]- [START_REF] Walsh | High-frequency radar cross section of the ocean surface for an FMCW waveform[END_REF]. They essentially come to the conclusion that the characteristics of the Doppler spectra under different sea states are similar to the monostatic case with some quantitative differences of geometrical origin.

The main objective of this paper is to assess the dependence of the Doppler simulation on the given experimental configuration. Our main finding is that it is of primary importance to take into account the characteristics of the whole radar system for a relevant simulation of the Doppler ocean bistatic echo in view of the interpretation and inversion of experimental data.

The theory of high-frequency (HF) bistatic Doppler radar cross section (RCS) is reviewed in Section II and adapted to take into account the characteristics of the radar system. The effects of antenna gains, attenuation along the propagation paths, range processing, and time processing are combined into a single radar equation (Section III). A description of the reference datasets is provided in Section IV, and the effect of the corresponding experimental configuration on the simulated data is discussed in Section V. The comparison between theoretical predictions and experimental measurements is presented and discussed in Section VI.

II. BISTATIC THEORY

Following a small-height small-slope analysis, a bistatic model for the scattering of vertically polarized HF radiation from a well-conducting rough sea surface has been developed in [START_REF] Gill | High-frequency bistatic cross sections of the ocean surface[END_REF], [START_REF] Gill | On the development of a secondorder bistatic radar cross section of the ocean surface: A high-frequency result for a finite scatering patch[END_REF], and [START_REF] Gill | The scattering of high-frequency electromagnetic radiation from the ocean surface: An analysis based on a bistatic ground-wave radar configuration[END_REF]- [START_REF] Gill | Bistatic form of the electric field equations for the scattering of vertically polarized high-frequency ground wave radiation from slightly rough, good conducting surfaces[END_REF]. Assuming a pulsed dipole, their approach produces the Doppler spectrum [power spectral density (PSD)], σ (ω), of the bistatic cross section for a finite patch. Here, these results are used assuming an infinite patch (2) and [START_REF] Lipa | Extraction of sea state from HF radar sea echo-mathematical theory and modeling[END_REF], which is equivalent to the incident monochromatic plane wave hypothesis. The geometry and notations of the scattering problem are depicted in Fig. 1. A radar cell on the sea surface can be labeled by its bistatic range R and its receiving angle φ c . It is also convenient to use the bistatic angle φ bi . The iso-ranges are ellipses with unit normal vector n. The Doppler spectrum can be written as the sum of two contributions of leading and corrective order σ = σ (1) + σ (2) .

(

The first term σ (1) is due to single-order Bragg scattering. It involves solely the so-called Bragg wave K B = K B n (and counter-Bragg wave, -K B ), where K B = 4π/λ E M cos φ bi is the Bragg wave number and λ E M is the electromagnetic wavelength. It writes

σ (1) (ω) = 2 6 π 2 K 4 B =±1 ( K B )δ(ω + ω B ) (2)
where ω B = √ gK B is the Bragg pulsation, and is the directional wavenumber spectrum of the elevations at the sea surface. The second term σ (2) includes under the same expression the second-order correction for both the electromagnetic and hydrodynamic processes. It can be written in a condensed form, as σ (2)

(ω) = 2 6 π 2 K 4 B 1,2 =± |B(K , 1 , 2 )| 2 ( 1 K ) ( 2 K 2 ) δ ω + 1 gK + 2 gK 2 dK (3)
where the wave vectors K , K 2 are linked by the Bragg condition

K + K 2 = K B . ( 4
)
The expression of the kernel B(K , 1 , 2 ) is recalled in Appendix VII. It can be verified that the expressions (2) and

(3) reduce to the monostatic formulation of [START_REF] Barrick | Remote sensing of sea state by radar[END_REF] when φ bi = 0. The above expressions for the first-and second-order PSD involve sharp resonance frequencies in the Dirac functions. This implies two singular peaks at plus or minus the Bragg pulsation (2) and reduces the twofold integral (3) to a single integral. In practice, the Dirac functions have to be replaced by peaks of finite width and amplitude because of several combined physical (e.g., variation of orbital velocity) and postprocessing effects (e.g., finite integration time at the receiver). This means that the actual PSD is a smoothed version of the theoretical one

σ (ω) = σ (ω )F(ω -ω )dω (5)
for some positive filter F. Correspondingly, the first-andsecond-order cross sections for finite integration time are given by σ

(1) (ω) = 4π 2 K 4 B =±1 ( K B )F(ω -ω b ) (6)
and

σ (2) (ω) = 4π 2 K 4 B 1,2 =±1 |B(K , 1 , 2 )| 2 F ω + 1 gK + 2 gK 2 ( 1 K ) ( 2 K 2 )dK . ( 7
)
A typical bistatic Doppler spectrum is illustrated in Fig. 2 for a mixed sea state (wind waves and swell) at the radar frequency 16 MHz and bistatic angle φ c = 30°. The omnidirectional wind wave spectrum is a standard Pierson-Moskovitz spectrum [START_REF] Pierson | A proposed spectal form for fully developed seas based upon the similarity theory of S. A. kitaigorodskii[END_REF] with a wind speed of 11 m/s at 19.5 m above the sea. This spectrum is combined with a classical spreading function (s = 4 and = 10 -2 , see the Appendix) in the cross-wind configuration (φ W = -90°). A Gaussian swell spectrum has been superimposed on the wind wave spectrum in a cross-swell configuration (the dominant direction of wave propagation is φ = -90°). The dominant wavelength of the swell is 230 m. The dominant swell amplitude is 1 m. The integration time has been set to T i = 4 min. The salient features of the Doppler spectrum are similar to those observed in the monostatic case. The first-order Bragg peaks (b) (ω = ± ω B ) provide the leading contribution. There are secondary peaks such as the so-called second-order hydrodynamic peaks (h) at

ω hyd = ± √ 2ω b ( 8
)
as well as the swell peaks (s). In addition to these peaks, there is a continuum arising from second-order contributions. The spectral peak of the omnidirectional wave spectrum appears as four local maxima (w) on both sides of each Bragg peak.

III. DOPPLER SPECTRUM UNDER EXPERIMENTAL CONDITIONS

The aforementioned analytical theory for first-and secondorder bistatic radar return is devised in the ideal mathematical case of an incident monochromatic plane wave impinging on an infinite statistically homogeneous surface. To be more consistent with experimental measurements, some authors have considered realistic emitted wave forms such as a pulsed wave [START_REF] Gill | High-frequency bistatic cross sections of the ocean surface[END_REF] or a frequency-modulated continuous wave (FMCW) [START_REF] Walsh | High-frequency radar cross section of the ocean surface for an FMCW waveform[END_REF] under the assumption of narrow beam and remote source and receiver. We employ here a different model, which allows us to simulate the average Doppler spectra for coarse beam resolution in the bistatic configuration at a short range. For this, we need to take the following effects into account.

1) For a given targeted cell, the entire illuminated area contributes to the received power. The contribution of a patch is given by the spatial resolution of the radar system.

2) The bistatic angle varies over the illuminated area.

3) In an FMCW radar, the range corresponds to a frequency shift in the received chirps. In order to reduce the effect of range sidelobes (Gibbs oscillations), each received chirp is multiplied by a weighting window prior to the Fourier transform [START_REF] Gurgel | The university of hamburg WERA HF radar-theory and solutions[END_REF]. It results in a smeared range resolution, which can be described by a spatial window W . 4) The time series corresponding to every discriminated range is coherently recorded and processed over a duration called the integration time (T i ). The PSD is obtained by averaging the periodogram over several integration times. Again, to avoid Gibbs oscillations, the signal is multiplied by a weighting window over the integration time. This results in spectral smearing [see [START_REF] Gill | Ocean surface wave measurement using a steerable high-frequency narrowbeam ground wave radar[END_REF] for the smoothed PSD]. From these considerations and the radar equation, we may write the experimental PSD at the output of the radar system as

σ exp (ω) = sea G σ (ω)dA. ( 9
)
We will refer to G as the "cell weighting function." It is given by

G = P e λ 2 E M (4π) 3 F t G t F r G r R 2 t x R 2 r x W ( 10
)
where Pe is the transmitted power. R t x and R r x are the distance from the patch to the transmitter and the receiver, respectively. The integration is in principle performed over an infinite surface, but the range processing window W and the antenna gains G t , G r limit the effective domain of integration. The terms F t , F r are the surface wave attenuation factor over the transmit and receive paths, respectively. They account for losses due to the finite conductivity of sea water, earth's curvature, sea surface roughness [START_REF] Barrick | Theory of HF and VHF propagation across the rough sea 1, the effective surface impedance for a slightly rough highly conducting medium at grazing incidence[END_REF], and island shadowing (see [START_REF] Wait | The ancient and modern history of EM ground-wave propagation[END_REF] for an overview on ground wave propagation theory). All the quantities involved in the integration implicitly depend on the bistatic range (R) and angle (φ) as well as on the central coordinates (R c , φ c ) of the targeted cell. The surface element of integration d A with respect to the coordinates (R, φ) is given in the Appendix.

IV. REFERENCE DATASETS

We now describe the reference datasets that have been used to assess the capabilities of the aforementioned simulator. The experiment was conducted with two Wellen Radar (WERA) systems [START_REF] Gurgel | The university of hamburg WERA HF radar-theory and solutions[END_REF], [START_REF] Gurgel | Wellen radar (WERA) a new ground-wave based HF radar for ocean remote sensing[END_REF] manufactured by Helzel Messtechnik GmbH, and the present data were acquired during a period of 3 weeks in December 2011. These radars are routinely operated at the Mediterranean Institute of Oceanography [START_REF]Mediterranean Institute of Oceanography[END_REF] for real-time sea surface current monitoring. They work at a carrier frequency f c = 16.150 MHz with a sweep bandwidth B = 50 kHz. Both receive and transmit systems use very stable master oscillators synchronized with GPS signals. Synchronization methods have already been successfully implemented for years in metrology and communication systems [START_REF] Osterdock | Gps synchronized frequency/time source[END_REF], and later in radio oceanography applications [START_REF] Barrick | Ocean surface current mapping with bistatic hf radar[END_REF], [START_REF] Barrick | Multi-station hf fmcw radar frequency sharing with gps time modulation multiplexing[END_REF].

The TX station is installed on the coastal ridge Cap Sicié at 190 m altitude and about 450 m away from the shore (43.06°N and 5.86°E, see Fig. 3). The radiated power is about 20 W. Two vertical resonant electric monopoles (and their ground planes) are fed in an end-fire configuration with the main wide lobe directed towards the sea. The RX array has been installed 40.4 km away from the TX station at Cap Bénat. It has been mounted over the hill slope amid the typical Mediterranean forest at an altitude 165 m and about 400 m away from the shore (43.092°N and 6.357°E, see Fig. 3). Eight vertical electric monopoles and their ground planes form an almost perfect periodic linear array (0.45 λ EM spacing). To ensure phase stability and to avoid variable influence of the surroundings, the antennas have been slightly resistively loaded. The global directional phase response of the array has been measured using a CW radio beacon aboard a ship IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING covering an area of about 270°around the station. Even though the extraction of the radial component of sea surface current is performed in real time at the RX station, the individual antenna signals are recorded and can be reprocessed on demand. A total of 183 Doppler spectra sampled every 3 h were selected. This sampling is the same as for the wave model described below (WW3 model). Each sample is computed by averaging 15 consecutive Doppler spectra. The integration time of each spectrum is 265 s corresponding to 1024 chirps with a pulse repetition period of 0.26 s.

The National Center for Archiving Swell (CANDHIS) [START_REF]CANDHIS[END_REF] provides measurement of sea elevations from a wave rider. We used data from a buoy located in deep water behind Porquerolles Island relative to the receiver (42.9667°N and 6.2048°E, Fig. 3). This location is in the short range of the radar system. The French institute PREViMer [START_REF]PREVIMER-Observations et Prévisions Côtières[END_REF] provided directional wave spectra 3.5 km southeast of the wave rider buoy (Fig. 3). These spectra have been simulated with the WaveWatch III model (WW3) [START_REF] Tolman | A mosaic approach to wind wave modeling[END_REF]- [START_REF] Ardhuin | Observation and estimation of lagrangian, stokes, and eulerian currents induced by wind and waves at the sea surface[END_REF]. The angular resolution of supplied wave spectra is 15°and the frequencies extend from 0.037 to 0.72 Hz. Wind forcing is provided by ECMF analysis at 0.5°resolution. Since the wind parameters considered here are from the WW3 dataset, they have been verified for reliability by comparison with wind measurements at Porquerolles Island.

V. EFFECT OF THE RADAR SYSTEM

The received periodic time series is usually multiplied by a Blackmann-Harris function. This process can be modeled by the convolution of the Doppler spectrum with the PSD of the function. To simplify the calculation in (5), the frequency filter F is assumed to be Gaussian instead of the PSD of the Blackmann-Harris function

F(ω) = 1 √ 2πs exp - ω 2 2s 2 . ( 11
)
The standard deviation s is chosen such that the 3-dB bandwidth (s 3d B ) coincides with the 3-dB bandwidth of the Blackmann-Harris PSD ( 4π/T i ), i.e., s = 1.7π/T i . The calculation of the integral in ( 9) is performed through a discretization of space in radar cells of widths R and φ. These parameters should be chosen small enough so as to assume a constant Bragg vector [consequently a constant σ (ω)] inside each cell. We found that the choice R = 1000 m and φ = 1°ensures this condition.

The antenna gains G t , G r in the direction of integration have been estimated using in situ ship measurements. For WERA, the range resolution window W can be approximated by the PSD of the Blackman-Harris function [START_REF] Gurgel | The university of hamburg WERA HF radar-theory and solutions[END_REF]. Equation ( 9) has been computed for short ranges (R ≤ 40 km) at the radar frequency 16 MHz. In this configuration, the total propagation attenuation F t F r along the free sea surface path is almost constant over the sea area where the weighting function is significant. The main variations of the attenuation functions are due to the island shadowing effect of the islands. These islands consist of rough topography with cliffs. Recently, advanced methods [START_REF] Sevgi | A mixed-path groundwave field-strength prediction virtual tool for digital radio broadcast systems in medium and short wave bands[END_REF]- [START_REF] Apaydin | Numerical investigations of and path loss predictions for surface wave propagation over sea paths including Hilly island transitions[END_REF] have been developed to simulate mixed path propagation losses. Simulation in [START_REF] Apaydin | A novel split-step parabolic-equation package for surface-wave propagation prediction along multiple mixed irregularterrain paths[END_REF] exhibits a strong loss behind a hilly island with sharp discontinuity. Therefore, as this mask effect dominates all other factors useful in our study, we decided to simply ignore the paths crossing the islands. Accordingly, we simply set the propagation factor to 0 for paths crossing the islands (and 1 otherwise).

The CANDHIS buoy is situated at bistatic coordinates R = 24.3 km and φ = -132°. However, it is difficult to simulate the radar return at such small ranges for two reasons. First, the Bragg frequency varies sharply with the aiming direction. Second, some points of the iso-bistatic range ellipse can be close to the transmitter or receiver. The corresponding large values of (R t x R r x ) -2 can pollute the signal when combined with a secondary antenna lobe. An additional difficulty is that the buoy is hidden from the transmitter by the Porquerolles Island. Therefore we chose to focus on another target cell (R c = 27 km and φ c = -120°), assuming that the sea state has not changed from one location to another.

The different terms involved in the radar equation ( 9) are plotted in Fig. 4 for this target cell. The terms are given as a function of azimuth at the range of the target cell. Superimposed is the angular variation of the cell weighting function [START_REF] Lipa | Seasonde radial velocities: Derivation and internal consistency[END_REF] times the surface element, G A. As seen, the azimuthal resolution of the radar system is very poor. This means that the variations of the local Bragg vector within the cell cannot be ignored and ( 6) and [START_REF] Ramos | Observation of wave energy evolution in coastal areas using HF radar[END_REF] based on a plane wave formalism no longer hold. Furthermore, strong sidelobes are visible around the direction φ = -153°. These weaknesses can limit the capability to estimate waves and currents from experimental Doppler spectra, as most of the inversion methods rely on these equations [START_REF] Wyatt | Limits to the inversion of HF radar backscatter for ocean wave measurement[END_REF]. A salient feature of real spectra is the broadening of the Bragg peaks with respect to the theoretical prediction. This can be explained by the diagram of Fig. 5, which shows that the Bragg frequency varies in the vicinity of the processed target cell. Therefore, the broadening of the peaks reflects the actual width of the main lobe of the radar system. It is an important issue raised by the bistatic configuration. The variation of the Bragg frequency inside the main azimuthal lobe can be much larger than the frequency shift due to the presence of usual surface currents (several tens of centimeters per second) and then hinders the estimation of the surface current. It is commonly observed in the monostatic case that the width of the Bragg peaks can exceed the width predicted by the finite integration time. This is usually attributed to various phenomena such as wave orbital velocities [START_REF] Essen | On the accuracy of current measurements by means of HF radar[END_REF] and finite area and time illumination [START_REF] Hisaki | VHF and HF sea echo doppler spectrum for a finite illuminated area[END_REF], [START_REF] Zhang | Inherent limitations in highfrequency radar remote sensing based on bragg scattering from the ocean surface[END_REF]. These mechanisms still apply to the bistatic configuration.

Another feature is the existence of peak at -0.4 Hz. This peak originates from scattering effect due to the secondary lobe located around φ = -50°and R = 26 km, where f B is close to -0.4 Hz. Here too, this interpretation is specific to the bistatic configuration for which the Bragg frequency cannot be considered constant as in the case of monostatic radar systems. The amplitude of the peak is smaller than the Bragg peak by only -20 dB. This value is much greater than the gain ratio between secondary and main lobes (-30 dB). This difference (10 dB) is due to the change of geometry yielding stronger Bragg waves in the secondary lobe than in the main lobe. For particular sea state condition, the ratio between this peak and Bragg peak can be much larger. This analysis has been conducted in absence of surface currents. Currents can significantly modify the position of secondary peaks relative to the Bragg peaks.

Following our observations, the introduction of antenna gains in the calculation of the PSD modifies the theoretical first-order peaks both in position and amplitude. This can limit their use at short range (due to the strong variability of the Bragg frequency) for the estimation of surface currents based on the shift of the Bragg peaks and the estimation of wind wave direction based on the ratio of positive and negative Bragg peaks [START_REF] Huang | HF radar wave and wind measurement over the eastern china sea[END_REF], [START_REF] Wyatt | Short wave direction and spreading measured with HF radar[END_REF]. In addition, the presence of secondary lobes can also mask the sharp swell peaks at short range. The cell weighting function has only a small effect on the secondorder Doppler spectrum (see Fig. 6) except in the vicinity of the hydrodynamic and electromagnetic peaks (Section II) which are smoothed. Hence, the second-order spectrum is more robust to the effects of antenna gains and could be used for oceanographic purposes such as wave spectrum inversion.

VI. EXPERIMENTAL COMPARISON

A. Bragg Ratio

We begin with the analysis of the Doppler signal through the Bragg line ratio (BLR), which is the ratio of amplitude of the first-order peaks in the Doppler spectrum. According to (2), the Bragg peaks are generated by short waves ( f B = 0.34 Hz at the selected radar cell) and the BLR reflects the directional properties of these waves. Since short waves are likely to be aligned with the wind, except in calm conditions, BLR can be considered as a proxy of the wind direction relative to the radar aiming direction as defined in Fig. 1 [START_REF] Huang | HF radar wave and wind measurement over the eastern china sea[END_REF], [START_REF] Stewart | Radio measurements of oceanic winds at long ranges: An evaluation[END_REF]- [START_REF] Shen | Wind-speed inversion from HF radar first-order backscatter signal[END_REF]. Fig. 7 shows the BLR measurements versus the relative wind direction φ w (taken in absolute value) for wind speed larger than 6 m/s. The variation of the BLR with φ w is consistent with many previous HF and VHF observations in the monostatic mode [START_REF] Wyatt | Short wave direction and spreading measured with HF radar[END_REF], [START_REF] Gurgel | An empirical method to derive ocean waves from second-order bragg scattering: Prospects and limitations[END_REF]. The values of the BLR are found to be close to -15 dB in downwind and -5 dB in cross-wind condition.

The experimental BLR have been compared with simulated values using WW3 spectra according to the bistatic theory with (σ exp ) and without ( σ ) the cell weighting function. In the former case, large differences between experimental and theoretical BLR values are observed, e.g., of 30 dB in up/down wind condition. Such high differences can be significantly reduced (to 13 dB) but not suppressed when the cell weighting function is considered. Possible explanations for this discrepancy are spatial inhomogeneity of the wave spectrum over the radar coverage and the validity of WW3 wave spectrum, especially for short waves propagating in the upwind direction. A better agreement is found for relative wind directions in the angular sector 0-45°.

Note that the dependence of the BLR on the relative wind direction can been modeled using a classical spreading function (see Appendix VII). A cardioid model with s = 8.5 and = 0.027 provides a satisfactory fit with the data.

B. Doppler Spectrum

We now compare experimental Doppler spectra and simulations using WW3 model. The 183 spectra defined in Section IV were analyzed. We have observed that omnidirectional WW3 spectra can noticeably differ from the CANDHIS buoy spectra. The difference between in situ and modeled wave estimation is mainly due to the grid of resolution of WW3, which is probably too large a coastal area to accurately match the measurements at a specified location. We therefore decided to select the dates at which WW3 and experimental spectra agree best. This agreement was evaluated according to four distinct criteria: 1) wind speed at Porquerolles station larger than 6 m/s; 2) relative difference of significant height (H s ) smaller than 20%; 3) difference in peak frequency (F p ) smaller than 20%; and 4) difference in BLR between radar data and simulation using WW3 wave spectrum smaller than 4 dB. Criterion 1 eliminates weak sea states for which secondorder Doppler spectrum is in general badly detected. Criteria 2 and 3 check the correctness of the large waves components in the omnidirectional spectrum. Criterion 4 ensures the proper directionality of the model spectrum at the Bragg waves. This criterion leads to a wind direction lying in the 0-45°sector .s)

Candhis WW3

Fig. 8. Comparison between omnidirectional spectrum from WW3 model (solid line) and CANDHIS buoy (dashed line) on 16:06 (Table I).

(see Section VII). After selection according to these criteria, we obtained 15 cases as detailed in Table I. For the 15 selected cases, the omnidirectional WW3 and in situ spectra are in good agreement for short waves (i.e., smaller than the peak wave). An example is shown on Fig. 8 on date 16:06. The WW3 directional wave spectra are typical of a wind wave system propagating in the direction of the wind (Fig. 9). An analysis (not detailed here) of the relationship between H s , F p , and wind speed shows that the fetches are relatively large (≥ 60 km).

Figs. 10-13 show the Doppler spectra for four generic cases. Again, a comparison is given between theoretical spectra (thin solid lines), simulated spectra in experimental conditions (dashed lines), and experimental measurement (thick solid lines). As before, directional height spectrum used in the simulation is based in WW3. The horizontal dashed line indicates the background noise floor estimated with the method of [START_REF] Hildebrand | Objective determination of the noise level in doppler spectra[END_REF].

The largest differences between modeled and experimental Doppler spectra are observed at the dates 12:12, 16:21, 17:03 (Fig. 10), 17:09, 17:12, 17:15, 20:12, 20:15, and 24:00. They correspond to the highest negative BLR values and will be referred to as the down cross wave (DCW) cases. For these cases, the BLR values are strongly affected by the cell weighting function. Since the latter is not always well characterized (attenuation factor, island shadowing effects, etc.,) this suggests that the criterion 4 based on BLR can fail for the DCW cases. A closer investigation of these cases shows that the characteristics of the radar system as modeled by the cell weighting function G have an important impact on the Doppler spectrum whenever the directional wave spectrum is weak in the upwind direction as is the case here with WW3 model. As a result, only the negative Doppler frequency part of the spectrum should be relevant for wave inversion purpose. Such an issue is not encountered in the other configurations.

Save for these differences, a good agreement has been generally found between experimental and simulated Doppler spectra. The radar system characteristics have little influence on the second-order spectrum except at the secondary peaks (swell and hydrodynamic peaks), which are smoothed. A broadening of the first-order peaks is observed (e.g., Fig. 11) and has already been explained by the effects of antenna gain in Section V. The appearance of a physically nonexpected secondary peak in the vicinity of the Bragg peak (e.g., at f d = -0.4 Hz in Figs. 11 and12) has also been explained in this section. Note that this undesirable peak is awkward when it comes to the estimation of the swell peaks because they occur in the same range of Doppler frequency.

According to the results of the bistatic RCS model presented in Section II, the spectral peak of the omnidirectional wave spectrum appears as four local maxima on both sides of each Bragg line with a relative position almost equal to F p . This phenomenon is well known in the monostatic configuration. It was theoretically predicted in [START_REF] Hasselmann | Determination of ocean wave spectra from doppler radio return from the sea surface[END_REF] and has been often reported in experiments [START_REF] Lipa | HF radar measurements of long ocean waves[END_REF]- [START_REF] Broche | VHF radar for ocean surface current and sea state remote sensing[END_REF]. These spectral maxima are generally IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING well identified in our Doppler spectra (e.g., Fig. 11) and behave as expected, i.e., they move closer to the Bragg lines as F p decreases. This is observed in Figs. 11-13 corresponding to F p = 0.13, 0.11, and 0.10 Hz, respectively. At low F p , i.e., for high sea states (Fig. 12), the maxima, due to the dominant waves tend to merge into the first-order peaks. In these cases, the second-order Doppler spectrum can be difficult to use for wave inversion purposes. It should be noted that the overall asymmetry of Doppler spectra in Figs. 11-13 reflects the change of wind from up-cross to down-cross direction (I). We also note the influence of surface currents that shifts both first-and second-order Doppler spectra (e.g., Fig. 10).

In the regions | f d | > f B , the maxima, due to the dominant waves, can be difficult to discriminate from the hydrodynamic peaks at ± √ 2 f B because of the smoothing effect of the system gains (e.g., Fig. 11 in the vicinity of √ 2 f B ). An important parameter governing the validity of the second-order bistatic RCS is the roughness parameter m = k 0 H s /4. In principle, it must be less than 1 for the applicability of the perturbation method on which (1) relies. Evidence of departures from the theory were found for m = 0.4 [START_REF] Wyatt | High order nonlinearities in HF radar backscatter from the ocean surface[END_REF]. Our m values are less than this limiting value, and we actually observed good agreements between experimental and simulated Doppler spectra, whereas they can differ in severe storm condition [START_REF] Kingsley | Analysis of second order HF radar sea spectra recorded in storm conditions[END_REF] or in shallow waters [START_REF] Broche | Shallow water waves observed by a VHF groundwave Doppler radar[END_REF].

C. Effect of Islands

We have assessed the relevance and limitations of a bistatic simulator in a specific experimental configuration in the coastal area of Toulon. One important point is the presence of islands in the short-range field of view of the radar, namely, Porquerolles island and the Giens Peninsula (see the map in Fig. 3). We could not precisely evaluate the attenuation due to these islands and simply ignored the masked directions. However, the presence of these islands is probably a favorable factor for the interpretation of Doppler spectra, as it can block undesirable side lobes of the emitting antenna pattern when the main lobe is aimed at some other unmasked direction (this is the case for the chosen grid point of the WW3 model, see Fig. 3). Hence, islands can be used as natural side lobe rejectors and therefore improve the performance of the bistatic system in neighboring areas.

VII. CONCLUSION

In this paper we developed a bistatic HF Doppler spectrum simulator based on the second-order theory in [START_REF] Gill | On the development of a secondorder bistatic radar cross section of the ocean surface: A high-frequency result for a finite scatering patch[END_REF] and including the characteristics of the radar, such as antenna gains and propagation effects. We have run this simulator in the configuration of a WERA system recently used over the Mediterranean coast. Using the spectral model WW3 validated by in situ buoy measurements, we were able to compare the simulated and experimental Doppler spectra.

We found that the effects of the radar system are significant for the first-order peaks. In bistatic configuration, experimental artifacts, such as antenna side lobes, can smear the firstorder echo over a frequency interval corresponding to the Bragg frequency variation in azimuth and range. The firstorder Bragg peaks are broadened, not only by the finite integration time, but also by undesirable echoes originating from nontargeted cells. Moreover, the actual gains can modify the BLR ratio in such a way that BLR values no longer reflect the Bragg wave properties. This holds particularly true when the wave spectrum presents little energy in the up-/down-wind sector. In addition, for high sea states, the broadening of Bragg peaks can mask the second-order signature long waves.

The second-order Doppler spectrum is less affected by system gains except possibly at second-order peaks. The swell peaks can be masked by the wind-driven Doppler spectrum. The hydrological peaks are smoothed. We analyzed the simulations for which the modeled directional wave spectra were most realistic. These simulations accurately reproduced the experimental data, indicating that the bistatic theory is relevant and could be used for the purpose of wave spectrum inversion.

APPENDIX A BISTATIC KERNELS

The expression of the kernel in (3) is ) e and h are the hydrodynamic and electromagnetic coupling coefficients, respectively. The electromagnetic coupling coefficients used here are

B(K , 1 , 2 ) = e (K ) + h (K , 1 , 2 ). ( A1
e = (K .u i )(K 2 .(K -k 0 u i )) 2k 0 cos 2 (φ bi ) √ K .(K -2k 0 u i ) + ik 0 (A2)
with u i the unit vector from the transmitter to the radar cell (see Fig. 1). is the normalized surface impedance given by [START_REF] Wait | The ancient and modern history of EM ground-wave propagation[END_REF]

] = 1 N 1 - 1 N 2 (A3)
where N is the refractive index of the surface

N = r + i σ s 0 ω 0 (A4)
r is the relative permittivity and σ s the conductivity of sea, and ω 0 is the radar pulsation. The expression (A2) differs from its counterpart appearing in [START_REF] Gill | On the development of a secondorder bistatic radar cross section of the ocean surface: A high-frequency result for a finite scatering patch[END_REF] by the presence of a term involving ik 0 . This "correction" appears for the monostatic coefficient in [START_REF] Lipa | Extraction of sea state from HF radar sea echo-mathematical theory and modeling[END_REF], [START_REF] Walsh | High-frequency radar cross section of the ocean surface for an FMCW waveform[END_REF], and [START_REF] Robson | Simplified theory of first-and second-order scattering of HF radio waves from the sea[END_REF] and is justified by the finite conductivity of the sea. In the bistatic case, we have introduced this term in a heuristic way to avoid nonintegrable singularities. A rigorous derivation of this result, which remains to be established, would take us too far from the main objectives of this paper. The deep water expression of the hydrodynamic coupling coefficients is used in this paper (see [START_REF] Walsh | High-frequency radar cross section of the ocean surface for an FMCW waveform[END_REF] and [START_REF] Weber | On the nonlinear theory for gravity waves on the ocean's surface. Part I: Derivations[END_REF]). A general expression can be found in [START_REF] Walsh | Model development for evaluation studies of ground wave radar[END_REF].

APPENDIX B CALCULATION OF THE CELL SURFACE ELEMENT

In a frame of reference centered at the receiver with polar coordinates R r x and φ (φ the receiver azimuthal angle and R r x the distance from the receiver to the cell, see Fig. 9), the differential dA is given by

d A = R r x (R, φ)dR r x dφ. (B1)
In these coordinates, R r x is given by

R r x (R, φ) = R(1 -e 2 ) 1 + ecos(φ) (B2)
where e = f /R is the ellipse eccentricity and f is the halfdistance between the two focus (see Fig. 1). It follows that dA can be written as The directional spectrum is given by the product of the unidirectional spectrum and the spreading function

dA = R r x (R, φ) δ R r x δ R dRdφ (B3) with δ R r x δ R = R 2 + 2R f cos(φ) + f 2 (a + f cos(φ)) 2 . ( B4
S(K ) = S u (K )D(φ). (C1)
In this paper, we used as S u (K ) the semiempirical model given in [START_REF] Pierson | A proposed spectal form for fully developed seas based upon the similarity theory of S. A. kitaigorodskii[END_REF] for a saturated sea (infinite fetch). It depends on U 19.5 , which is the wind speed at 19.5 m above sea.

A commonly used model of spreading function D(φ) was proposed by [START_REF] Longuet-Higgins | Observation of the directional spectrum of sea waves using motions of a floating buoy[END_REF], which is

D(φ) = + (1 -)cos s ( φ 2 ) N(s, ) (C2)
where φ is the angular direction relative to the wind direction, and N(s, ) is a normalization factor such that 2π 0 D(φ) dφ = 1. The parameter s characterizes the width of the angular distribution, while was first introduced by [START_REF] Tyler | Wave directional spectra from synthetic aperture observations of radio scatter[END_REF] to fit HF radar measurements. Physically, represents the fraction of energy that propagates against the wind direction.

Models for s can be found in the literature [START_REF] Mitsuyasu | Observations of the directional spectrum of ocean waves using a cloverleaf buoy[END_REF], [START_REF] Hasselmann | Directional wave spectra observed during JONSWAP 1973[END_REF] under the assumption of unimodal wave propagation. However, unimodality is not always valid and many studies support bimodality, especially at the early stage of wave development (e.g., [START_REF] Yuan | A reappraisal of ocean wave studies[END_REF], [START_REF] Gagnaire | Analysis of the structure of ocean wave directional spectrum inferred from quasi-exact computations of non-linear wave-wave interactions[END_REF]). In order not to deviate too far from the main objective of the paper, we chose to use the simple cardioid model with constant s and values. These parameters were fitted with the experimental data in the mean-square sense using the BLRs and found to be s = 8.5 and = 0.027 (-15.7 dB), respectively. The value of s is consistent with the classical models described above, e.g., s = 8.5 corresponds to a Bragg to peak frequency ratio f B / f p = 1.7 in Mitsuyasu's model for a fully developed sea and also to the estimations given in [START_REF] Wyatt | Short wave direction and spreading measured with HF radar[END_REF]. Recently, the sech 2 functional form was proposed to replace the cardioid model to fit HF/VHF radar measurement [START_REF] Wyatt | Short wave direction and spreading measured with HF radar[END_REF], [START_REF] Shen | Wind-speed inversion from HF radar first-order backscatter signal[END_REF]. We did not, however, use this model, which we found less performing in our context. Yves Barbin received the Degree and Masters degrees from University Paris 6, Paris, France, and the Ph.D. degree in signal processing applied to geophysics from Institut National Polytechnique de Grenoble, Grenoble, France.

He had been involved in radar applications for space science. He designed the Mars96 radar for the in-situ deep EM sounding of planet Mars, and the Concert instrument for the cometary ESA-mission Rosetta. He has been with MIO (formerly LSEET) since 2001, where he has been developing radio oceanagraphy activity. His background, technical reports, and papers concern electromagnetism, signal processing, space sciences, electronics, applied mathematics, embedded computers, real-time systems, instrument designs, and cognitive science.

Charles-Antoine Guérin received the B.Eng. degree from the Ecole Nationale Supérieure de l'Aéronautique et de l'Espace, Toulouse, France, in 1994, and the Ph.D. degree in theoretical physics from the University of Aix-Marseille, France, in 1998.

He is currently a Professor and Researcher with the Mediterranean Institute of Oceanography, University of Toulon, Toulon. He specializes in electromagnetic wave theory and its application to ocean remote sensing.

Fig. 1 .

 1 Fig. 1. Bistatic geometry. RX and TX are the receiving and transmitting antenna, respectively. The bistatic range R and the receiving angle φ are the spatial coordinates of the current point used for (9). The area d A refers to the integration variable in (9).

Fig. 2 .

 2 Fig. 2. Bistatic cross-wave Doppler spectrum at radar frequency 16 MHz and bistatic angle φ bi = 30°. (b) Bragg peaks, (h) second-order hydrodynamic peaks, (w) local maxima generated by wind waves, and (s) swell peaks.

Fig. 3 .

 3 Fig. 3. Map of the experiment. The emitter is located at Cap Sicié (red point on the left) and the receiver at Cap Bénat (red point on the right). The CANDHIS buoy is close to the Porquerolles Island (yellow point) and to the grid point of WW3 model (cross). The iso-range ellipses are shown for R = 24 km, R = 27 km, and R = 30 km. The red line indicates the radar aiming direction φ = -120°.

Fig. 4 .

 4 Fig. 4. Azimuthal variation of the different factors in the cell weighting function for a target cell at R c = 27 Km and φ c = 120°. All quantities have been normalized by their maximum.

Fig. 6 2 GΔAFig. 5 .Fig. 6 .

 6256 Fig. 5. Azimuthal and range variation of the amplitude g A in the radar equation for a target cell at R c = 27 km and φ c = 120°. The cross indicates the target cell position (R c = 27 km and φ c = 120°). White curves correspond to different Bragg frequencies (in Hz). The side lobes observed around -150°c an be minimized using a basic rejector process.

Fig. 7 .

 7 Fig. 7. Bragg line ratio versus relative wind direction φ w as obtained with (a) our radar measurements, (b) theoretical bistatic model using a WW3 spectrum, (c) simulated model in experimental conditions using a WW3 spectrum, and (d) simple cardioïd model.

Fig. 9 .Fig. 10 .

 910 Fig. 9. Directional WW3 spectrum (in dB) for date 16:06 (Table I). Black arrow indicates the Bragg vector at R c = 27Km and φ c = 120°. Green arrow indicates the peak wave direction. Write arrows indicates the WW3 forcing wind direction (φ w = 99°).

Fig. 11 .Fig. 12 .

 1112 Fig. 11. Comparison of simulated and measured Doppler spectra on date 16:06.

Fig. 13 .

 13 Fig. 13. Comparison of simulated and measured Doppler spectra on date 16:18.

Samuel

  Grosdidier received the Masters degree in environmental oceanography and remote sensing from the Université du Sud Toulon Var', Toulon, France, in 2007, and the Ph.D. degree in electrical engineering and signal processing from the the Université de Brest, Brest, France, in 2010. He has a Post-Doctaral position at the Mediterranean Institute of Oceanography (MIO), Toulon, France, since 2011. His current research interests include remote sensing of ocean surface wave by high-frequency radar. Philippe Forget received the B.Eng. degree from the École Nationale Supérieure des Techniques Avancées', Paris, France, in 1974, the 'Thèse de 3e Cycle' in oceanography from Paris VI University, Paris, in 1979, and the 'Thèse de Doctorat d'Etat' in oceanography from Sud Toulon-Var University, La Garde, France, in 1983. He is currently a Director of Research at CNRS, Mediterranean Institute of Oceanography (CNRS/IRD/Aix-Marseille and Sud Toulon-Var Universities), Nicosia, France. He has worked in various fields of coastal oceanography (surface waves, coastal dynamics, internal waves, ocean-atmosphere interactions), electromagnetism (scattering by the sea surface, radio wave propagation), ocean optics, and remote sensing (HF/VHF radars, SAR and other microwave techniques, optical sensors). He has been involved in several mission projects of Centre National d'Etudes Spatiales (CNES), Toulouse, France, and has conducted several oceanographic and remote sensing (airborne) field campaigns.

TABLE I DESCRIPTION

 I OF THE 15 SELECTED DATES. W S AND φ W S ARE THE FORCING WIND PARAMETERS OF WW3. H s AND F p ARE FROM THE BUOY, AND m = k 0 H s /4 IS THE ROUGHNESS PARAMETER. THE BLR WAS ESTIMATED FROM RADAR DATA AND

			SIMULATION USING WW3. VALUES IN
			PARENTHESIS ARE FROM WW3
	Date	W	φ w		H s	F p	BLR	m
	(dd:hh)	(m/s)	(°)		(m)	(Hz)	(dB)
	12:12	11.1	-57		1.3(1.2)	0.20(0.23)	-12.4(-13.6)	0.11
	14:18	9.2	-45		1.9(1.8)	0.12(0.12)	-3.1(-6.6)	0.16
	16:06	12.4	-103		2.3(2.3)	0.13(0.14)	11.7(11.8)	0.19
	16:09	12.9	-102		3.0(3.1)	0.11(0.12)	10.7(13.1)	0.25
	16:12	12.1	-105		3.9(3.5)	0.11(0.11)	11.8(12.8)	0.33
	16:15	13.9	-92		4.0(3.9)	0.11(0.11)	9.4(10.2)	0.34
	16:18	16.3	-46		4.3(4.3)	0.10(0.10)	-2.9(-4.5)	0.36
	16:21	16.7	-52		4.4(4.2)	0.10(0.10)	-12.4(-13.4)	0.37
	17:03	15.5	-43		3.3(4.0)	0.11(0.11)	-13.3(-16.1)	0.28
	17:09	10.7	-40		2.6(2.8)	0.11(0.11)	-11.6(-15.1)	0.22
	17:12	11.9	-43		2.4(2.7)	0.11(0.12)	-14.8(-17.4)	0.20
	17:15	14.1	-46		2.4(2.7)	0.11(0.12)	-15.9(-19.2)	0.21
	20:12	11.5	-54		1.9(1.9)	0.15(0.14)	-9.4(-13.3)	0.16
	20:15	11.8	-42		2.1(2.2)	0.15(0.13)	-13.0(-14.5)	0.18
	24:00	8.8	-59		1.0(0.9)	0.21(0.25)	-9.8(-8.8)	0.09
		0
		-10
	Sp(f) (m 2	-30 -20
		-40
		-50	10	-1	Frequency (s -1 )

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

This work was supported in part by the Stradivarius Project (FUI and Région PACA).