Adrien Jacotot
email: adrien.jacotot@protonmail.com

Simon Gensous

Cyril Marchand

Michel Allenbach

Effects of elevated atmospheric CO2 and increased tidal flooding on leaf gas-exchange parameters of two common mangrove species: Avicennia marina and Rhizophora stylosa

Keywords: Mangrove, CO 2 enrichment, Photosynthetic activity, Stomatal density, Climate change, Sea-level rise

Introduction

Mangroves are considered to be major ecosystems involved in the carbon cycle along tropical and subtropical coastlines. Due to their high ability to fix and store CO 2 [START_REF] Donato | Mangroves among the most carbon-rich forests in the tropics[END_REF][START_REF] Alongi | Carbon cycling and storage in mangrove forests[END_REF], they are among the most efficient blue carbon sinks [START_REF] Kauffman | Ecosystem carbon stocks of micronesian mangrove forests[END_REF]. Besides providing many ecosystem services [START_REF] Lee | Ecological role and services of tropical mangrove ecosystems: a reassessment[END_REF], mangroves are characterized by a limited number of plant species because of a stressful environment (e.g., salinity, anoxia, soil instability). In addition, future climate change could affect the functioning of mangrove ecosystems, such as their productivity and carbon sequestration capacities, or even their ability to conquer new available spaces. Sea-level rise will probably induce an even more stressful environment for mangrove plants, while temperature and atmospheric CO 2 increases would favor their growth.

Atmospheric CO 2 concentrations have been rising continuously from 280 ppm at the preindustrial age to more than 400 ppm currently [START_REF] Betts | El Nino and a record CO 2 rise[END_REF]. By the end of the twenty-first century, atmospheric CO 2 concentrations could range from 794 to 1150 ppm, with the uncertainty depending on which model is consulted [START_REF] Collins | Long-term climate change: projections, commitments and irreversibility pages 1029 to 1076[END_REF]. The effects of elevated atmospheric CO 2 concentrations on temperate plant species are well documented, usually an enhancement of photosynthesis and water-use efficiency is observed [START_REF] Urban | Physiological impacts of elevated CO 2 concentration ranging from molecular to whole plant responses[END_REF][START_REF] Karnosky | Impacts of elevated atmospheric CO 2 on forest trees and forest ecosystems: knowledge gaps[END_REF][START_REF] Ainsworth | What have we learned from 15 years of free-air CO 2 enrichment (FACE)? A meta-analytic review of the responses of photosynthesis, canopy properties and plant production to rising CO2[END_REF]. Photosynthesis responses of tropical plants, especially mangroves, are less well studied, although stimulation of photosynthesis and net primary productivity has been reported [START_REF] Farnsworth | Elevated CO 2 alters anatomy, physiology, growth, and reproduction of red mangrove (Rhizophora mangle L.)[END_REF][START_REF] Reef | The effect of atmospheric carbon dioxide concentrations on the performance of the mangrove Avicennia germinans over a range of salinities[END_REF].

Climate change is not a single parameter but a combination of numerous ones, which may have opposing effects on mangrove plants. Sea-level rise is considered to be the major climate change threat to mangrove ecosystems because of their development in the intertidal areas [START_REF] Ellison | Vulnerability assessment of mangroves to climate change and sea-level rise impacts[END_REF]. Global mean sea level increased over recent decades and is predicted to increase from 0.26 to 0.98 m by 2100 [START_REF] Church | Sea Level Change. In: Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change[END_REF]. All mangroves may not be able to keep pace with sea level and will have to migrate landward to maintain their preferred hydroperiod [START_REF] Gilman | Threats to mangroves from climate change and adaptation options: a review[END_REF]). However, both natural and artificial barriers will strongly limit the inland migration of mangroves [START_REF] Mcleod | A blueprint for blue carbon: toward an improved understanding of the role of vegetated coastal habitats in sequestering CO 2[END_REF][START_REF] Lovelock | The vulnerability of Indo-Pacific mangrove forests to sea-level rise[END_REF]. If mangroves cannot migrate or keep pace with sea-level rise, they will be subjected to greater depth and duration of tidal flooding. When grown outside their optimum flood duration, mangrove trees respond by a decrease in photosynthetic activity and in net primary productivity [START_REF] Krauss | Environmental drivers in mangrove establishment and early development: a review[END_REF].

Major advances in the comprehension of the evolution of the ecosystem have been made recently by studying the effects of elevated atmospheric CO 2 in combination with other environmental parameters such as salinity [START_REF] Reef | The effect of atmospheric carbon dioxide concentrations on the performance of the mangrove Avicennia germinans over a range of salinities[END_REF], nutrient availability [START_REF] Mckee | Where temperate meets tropical: multifactorial effects of elevated CO 2 , nitrogen enrichment, and competition on a mangrove-salt marsh community[END_REF][START_REF] Reef | The effects of CO 2 and nutrient fertilisation on the growth and temperature response of the mangrove Avicennia germinans[END_REF], or species competition [START_REF] Mckee | Where temperate meets tropical: multifactorial effects of elevated CO 2 , nitrogen enrichment, and competition on a mangrove-salt marsh community[END_REF]. However, to our knowledge, although the interactive effect of elevated CO 2 and tidal flooding duration was tested on brackish marshes [START_REF] Cherry | Elevated CO 2 enhances biological contributions to elevation change in coastal wetlands by offsetting stressors associated with sea-level rise[END_REF], no study tested these effects on mangrove physiology and specifically on photosynthesis.

Within this context, the main objective of this study was to evaluate the long-term effects of elevated CO 2 and tidal flooding duration on the leaf gas-exchange parameters (assimilation, transpiration, dark respiration, stomatal conductance, water-use efficiency) of seedlings of Avicennia marina and Rhizophora stylosa, the most widespread mangrove species throughout the Indo-Pacific region [START_REF] Buchmann | Avicennia marina. The IUCN Red List of Threatened Species[END_REF][START_REF] Ellison | Rhizophora stylosa: The IUCN Red List of Threatened Species 2010[END_REF]. We were also interested in the seasonal variations of leaf net photosynthetic rates. Our main hypotheses were (i) atmospheric CO 2 enrichment will lead to a stimulation of photosynthetic activity, (ii) tidal flooding duration will reduce the photosynthesis response due to waterlogging stress. To reach our goals, we used a closed chamber experiment, where more than 1000 two-year-old mangrove seedlings were grown at two CO 2 concentrations (400 vs. 800 ppm), over two semi-diurnal tidal flooding durations (3h15 vs. 4h45 for A. marina, 6h00 vs. 7h45 for R. stylosa), during one complete year. Leaf gasexchange parameters were measured monthly during the whole year of experiment, and chlorophyll fluorescence was determined only for the last 6 months. Light curve responses, stomatal density, and specific leaf area were assessed at the end of the experiment.

Materials and methods

Description of the facility

The experiment was conducted in the City of Mont-Dore in New Caledonia (22°13′49″S, 166°31′09″E) from June 2016 to May 2017. The facility consists of three semi-open greenhouses of 72 m 2 each (12 m × 6 m, 6 m height). Inside each greenhouse, a circular closed chamber of 36 m 2 (2.4 m height) was built to maintain elevated atmospheric CO 2 concentrations. The atmospheric CO 2 concentrations in each of the three closed chambers were continuously monitored during the experiment using CO 2 probes connected to a CO 2 central unit, which controlled the entire system (MAXICLIM NG 08/3Z, Anjou Automation). Pure CO 2 gas was supplied from 5:00 a.m. to 7:00 p.m. at the top of the chambers by brief pulses from a high-pressure cylinder.

HOBO temperature and humidity sensors (Onset, Cape Cod, Massachusetts, USA) were installed inside the greenhouse and the closed chamber. Air temperature and humidity were recorded every 5 min. Temperature and humidity were allowed to fluctuate naturally inside the greenhouses, however, air cooling units were installed in the closed chambers to prevent high variations of temperatures. Mean temperatures and relative humidity for the experiment period are given in Table 1.

Mangrove seedlings were placed on custom-built tidal tables, each working individually. Each tidal table included a 700-l polypropylene tank (1 m 2 area over 0.7 m height), surmounted by a 300-l planting tray (1 m 2 area over 0.3 m height). Fresh seawater was pumped from the adjacent lagoon (20 m) and stored in the tanks, which was replaced twice a month during the entire study. To simulate high tide periods, an aquarium pump, placed in each tank, sent the water to the planting tray. A siphon pipe allowed the planting tray to completely drain the water back to the reserve to reproduce low tide periods. To control the tidal treatment attributed to each tank, the aquarium pumps were connected to three custom-built current controllers (one per greenhouse). Controllers were constructed from Arduino open source plans available for free under public licenses and were programed according to the needs of the experiment.

Water quality (pH, salinity, DO) in the reservoir was checked periodically using YSI probes.

Plant material

Mature propagules of Avicennia marina and Rhizophora stylosa were collected from the natural mangrove of Oundjo, in New Caledonia (21°4′8″S, 164°42′51″E). The propagules were collected from multiple trees, between February and March 2014, during the optimum fruiting period. They were then planted in 2.5-l polyethylene bags in a 1:1 hand mixed mangrove peat and sand. During the 2 years preceding the experiment, the seedling mortality was high, resulting in a different number of seedlings used for the experiment. This high mortality may be explained by a lack of water during the first stages of development of the juveniles. Indeed, the semi-arid climate of New Caledonia induces a stressful and constraining environment for the development of juveniles due to high heat and reduced rainfalls. After their installation within the greenhouses, the tidal system was fully operational and was maintained until the end of the experiment. A total of 720 and 400 two-year-old R. stylosa and A. marina, respectively, were followed for this study.

During the year of experiment, the mortality dropped to less than 1%. Prior to the experiment, mean heights were 172.4 ± 40.17 and 90.91 ± 23.33 mm, and mean basal diameters 4.81 ± 0.98 mm and 5.54 ± 0.65 mm for A. marina and R. stylosa, respectively. For all seedlings, height measurements were made along the main axis, from the soil for A. marina, and from the top of the hypocotyl for R. stylosa. Basal diameters were taken at 0.5 cm above these two limitations.

Experimental design

The experiment was setup as a split-plot design with CO 2 atmospheric concentrations as the whole-plot (Ambient, 400 ppm vs. Elevated, 800 ppm) and tidal flooding duration (TFD) as the split-plot nested within CO 2 (Natural vs Longer). Elevated atmospheric CO 2 concentrations were maintained between 780 and 820 ppm CO 2 . CO 2 concentrations were periodically checked using two different portable infra-red CO 2 analyzers (a G2131-i CRDS analyzer from Picarro Inc., Santa Clara, USA; and a Li-8100A from LI-COR Biosciences, Lincoln, USA). Natural TFD were setup according to the average flooding duration observed in New Caledonian mangroves for both species (unpublished data). These tidal duration may be different and variable according to the geographical position of the studied mangrove (e.g., [START_REF] Van Loon | Hydrological classification in mangrove areas: a case study in Can Gio, Vietnam[END_REF]. In New Caledonia, mangroves develop in semi-arid conditions with a specific zonation of the ecosystem: Rhizophora spp. colonizes the seaward side, while Avicennia marina develops at higher elevations. Previous studies suggested that the main factor controlling the distribution of mangrove species in New Caledonia was soil salinity, which in turn was controlled by the duration of tidal inundation and thus by the soil elevation [START_REF] Marchand | Redox conditions and heavy metals distribution in mangrove forests receiving effluents from shrimp farms (Teremba Bay, New Caledonia)[END_REF][START_REF] Marchand | The partitioning of transitional metals (Fe, Mn, Ni, Cr) in mangrove sediments downstream of a ferralitized ultramafic watershed (New Caledonia)[END_REF]. As a result, the flooding duration for Rhizophora trees is higher than for Avicennia. Consequently, in the experiment, natural TFD was 3h15 for A. marina and 6h00 for R. stylosa for each high tide. Simulated tidal cycles were semi-diurnal, meaning that there were two high tides each day, separated by a low tide period of 8h30 and 5h45 for A. marina and R. stylosa, respectively. We hypothesized that an increase in mean sea level will similarly affect the flooding duration of both species; thus, in the experiment, longer TFD was simulated by increasing the natural times by 1h45, which corresponds to a high tide of 5h00 and 7h45 for A. marina and R. stylosa, respectively. Consequently, low tides periods were reduced to 6h45 and 4h00 for A. marina and R. stylosa, respectively. This increase in flooding duration has been randomly defined but, however, remains realistic given the expected sea-level rise at the end of the century. Although we chose a similar increase in flooding duration for both species, we are aware that this may be not the case, and that the flooding duration may increase differently in both stands within the natural system. Nevertheless, an increase of 1h45 of tidal duration will have different implication for both species, as it corresponds to an increase of 45% of the natural tidal duration of A. marina, whereas it is only 25% for R. stylosa. During high tide, the water level in the planting trays was identical for all tidal tables, 5 cm above sediment surface to submerge the root system.

The mangrove seedlings were allocated randomly between the tidal tables, with 25 A. marina or 30 R. stylosa on each tidal table, resulting in 100 A. marina (4 tidal tables) and 180 R. stylosa (6 tidal tables) for each of the four treatments. The tidal tables were then distributed between the three greenhouses as true experimental replicates, and then either inside or outside the closed chambers according to their CO 2 treatment. During the experiment, the mangrove seedlings were regularly rotated within each tidal table and were rotated three times between the greenhouses to minimize the greenhouse effect.

Leaf gas-exchange measurements

Gas-exchange parameters were performed during low tides using a semi-open gas-exchange analyzer (CO-650, Qubit Systems, Canada). In this system, CO 2 is pulled from ambient air, which serves as a baseline for measurements. Prior to each measuring periods, air samples with either 400 or 800 ppm of CO 2 at 15-20% of relative humidity (RH) were prepared. These air samples were then stored in specific gas plastic bags (from Qubit Systems) and maintained at a temperature of ~ 25 °C. They were then connected to the inlet of the CO-650, which allowed to have a similar air baseline all along the year of measurements. Assimilation (P n ) and transpiration (T) rates, as well as the stomatal conductance (g s ), were determined every month from June 2016 to May 2017. Measurements were performed in the morning (8:00-12:00 a.m.), on 30 different fully expanded leaves for the two species and the four treatments with a Photosynthetic Photon Flux Density (PPFD) of 1200 µmol m -2 s -1 . The instantaneous wateruse efficiency (WUE) was then calculated as WUE = P n /T. Dark respiration (D r ) measurements were made at night (8:00-10:00 p.m.) on three different seedlings for each species and treatment. No dark respiration measurements were made in July and September 2016.

Light curve responses (P n /PPFD curves) were generated at the end of the experiment on three leaves per species and per treatment. Eight PPFD intensities of 1200, 800, 400, 200, 100, 50, 25, and 0 µmol m -2 s -1 were chosen. Transitions between PPFD levels were made once photosynthesis was stable and lasted between 4 and 10 min. CO 2 concentrations were maintained at 400 ppm or 800 ppm, depending of the CO 2 treatment, with a relative humidity ranging from 15 to 20%. Air temperature was maintained to 25 °C. Curve fitting was resolved using the solver function of Microsoft Excel [START_REF] Lobo | Fitting net photosynthetic light-response curves with Microsoft Excel-a critical look at the models[END_REF][START_REF] Lobo | Erratum to: Fitting net photosynthetic light-response curves with Microsoft Excel-a critical look at the models[END_REF], and the best fitting was chosen according to the lower sum of the squares of the errors. The model, which best fitted with our data, was the rectangular hyperbola Michaelis-Menten based model [START_REF] Kaipiainen | Parameters of photosynthesis light curve in Salix dasyclados and their changes during the growth season[END_REF].

Specific leaf area

At the end of the experiment, 30 mature and fully expanded leaves per species and treatment were scanned and analyzed for leaf area (SLA) using ImageJ [START_REF] Schneider | NIH image to ImageJ: 25 years of image analysis[END_REF]. Then, all leaves were dried at 60 °C for 72 h before being weighed for dry mass (g). SLA (cm 2 g -1 ) was calculated as the ratio of leaf area to the corresponding leaf dried mass.

Chlorophyll fluorescence measurements

Chlorophyll fluorescence was measured using a portable chlorophyll fluorometer (FluorPen FP 100, Photon Systems Instruments, Czech Republic). The maximum quantum efficiency of PSII photochemistry (F v /F m ) was measured on the abaxial leaf surface at night from 8:00 p.m. to 10:00 p.m., using a PPFD of 3000 µmol m -2 s -1 as saturating flash for a duration of 1 s. Measurements were done only for the warm season, from November 2016 to May 2017 on 30 young fully expanded leaves of both species and each of the four treatments.

Stomatal density

Five fully expanded leaves for each species and treatment were randomly collected to determine the stomatal density. For A. marina, because of a dense layer of trichomes obscuring stomata, the leaves were macerated in a 5:1 solution of hydrogen peroxide and glacial acetic acid for 1 h at 70 °C. Then, the abaxial epidermis was peeled and stained with Safranin O. The number of stomata was counted from the interior surface of the epidermis [START_REF] Nguyen | Growth responses of the mangrove Avicennia marina to salinity: development and function of shoot hydraulic systems require saline conditions[END_REF]. For R. stylosa, nail varnish imprints of the abaxial side of the leaves were taken. The number of stomata was then counted under a light microscope (Leica DM500B, Leica Microsystems, Wetzlar, Germany) on three fields of view per leaf at a ×200 magnification.

Statistical analysis

Normality and equality of variance were analyzed using Shapiro and Levene tests, respectively. Following results, a two-way analysis of variance (ANOVA), followed by a Tukey's HSD test was applied to identify significant differences (p ≤ 0.05), between treatments of gas-exchange parameters, SLA, F v /F m , and stomatal density. In addition, significant differences between real and estimated values of dark respiration were analyzed using Student's t test after verification of normality and equality of variance using Shapiro and Fisher tests. Both species were Fig. 1 Mean values ± SEM (n = 360) of leaf gas-exchange parameters for A. marina and R. stylosa grown in ambient (400 ppm) or elevated (800 ppm) CO 2 , and under normal (dark-gray bars) and longer TFD (gray bars), for 12 months. a, f photosynthetic rates (µmol m -2 s -1 ), b, g transpiration rates (µmol m -2 s -1 ), c, h water-use efficiency, d, i stomatal conductance (µmol m -2 s -1 ), and e, j dark respiration rates (µmol m -2 s -1 ). Analyses were realized between species by an ANOVA. Different letters indicate significant differences (p < 0.05) ◂ analyzed independently. All statistical analyses were performed using XLSTAT version 2016.3.

Results

Leaf gas-exchange response to elevated CO 2 and flooding

The results of leaf-gas exchanges for A. marina and R. stylosa are presented in Fig. 1. For A. marina, mean annual net photosynthesis rate (P n ) was significantly higher under elevated CO 2 than under ambient CO 2 concentrations (Table 2), either with normal or longer TFD. Within each CO 2 treatment, longer TFD slightly decreased P n , however, this effect is only significant under elevated CO 2 (Fig. 1a; Table 2). Furthermore, transpiration rates (T r ) were significantly reduced under elevated CO 2 in comparison to the ambient CO 2 treatment (Fig. 1b; Table 2). Consequently, elevated CO 2 significantly increased water-use efficiency (WUE) for both TFD treatments. Under elevated CO 2 , WUE was significantly lower with longer TFD than with normal TFD (Fig. 1c; Table 2). In addition, only the longer TFD treatment in combination with elevated CO 2 had a significant effect on stomatal conductance (g s ) with lower values than for the others treatments (Fig. 1d; Table 2). No significant differences (Table 2) were observed for dark respiration rates (R d ) with CO 2 or TDF treatments (Fig. 1e).

For R. stylosa, elevated CO 2 significantly increased P n for both natural and longer TFD treatments (Fig. 1f; Table 2); however, longer TFD significantly reduced P n only under elevated CO 2 . Furthermore, within each TFD treatments, transpiration rates were significantly reduced under elevated CO 2 , while within each CO 2 treatment, TFD had no significant effect (Fig. 1g; Table 2). As a result, WUE for R. stylosa was significantly higher for trees grown under elevated than under ambient CO 2 concentrations. In addition, longer TFD significantly increased WUE in trees grown under elevated CO 2 (Fig. 1h; Table 2). Stomatal conductance was significantly increased under elevated CO 2 and normal TFD, however, it was significantly reduced under elevated CO2 and longer TFD (Fig. 1i; Table 2). No significant differences (Table 2) were observed for dark respiration rates (R d ) between treatments (Fig. 1j).

Seasonal response of the net photosynthetic rates

Different seasonal responses of net photosynthetic rates were observed between the cool season and the warm season (Fig. 2). From June to November, mean temperature was 22.3 °C, whereas from November to May, it was 26.7 °C (Table 1). For A. marina, elevated CO 2 enhanced P n by 32 and 33% for natural and longer TFD during the cool season, whereas during the warm season, P n was enhanced by 40 and 39% for natural and longer TFD, respectively (Fig. 2a). For R. stylosa, a similar response as for A. marina was observed. During the cool season, an increase in P n of 40 and 37% was observed for natural and longer TFD, whereas an increase of P n of 45% was observed during the warm season, for both TFD treatments (Fig. 2b).

Specific leaf area after 12 months of enrichment

Specific leaf area (SLA) was significantly higher for both species under elevated CO 2 , either with natural or longer TFD (Fig. 3a,b; Table 2). Within each CO 2 treatment, no significant effects of longer TFD on SLA were observed, either for A. marina and for R. stylosa (Fig. 3a,b; Table 2).

Net photosynthesis light curve responses (Pn/PPFD)

The net photosynthesis response to light was similar for both species (Fig. 4a,b). From 0 to 100 µmol photon m -2 s -1 , P n showed no difference between all the four treatments either for A. marina or R. stylosa. For PPFD values higher than 100 µmol photon m -2 s -1 , both A. marina and R. stylosa showed higher P n values when growing under elevated than under ambient CO 2 concentrations. When compared to natural TFD, longer TFD slightly reduced P n under ambient CO 2 concentrations, whereas under elevated CO 2 , P n was higher from 100 to 800 µmol photon m -2 s -1 , but lower at 1200 µmol photon m -2 s -1 . Regarding the light saturation points, for A. marina, they were, under ambient CO 2 concentrations, 872 and 785 µmol photon m -2 s -1 for natural and longer TFD, respectively, whereas under elevated CO 2 concentrations, they were 1490 and 1224 µmol photon m -2 s -1 . For R. stylosa, the light saturation points were, under ambient CO 2 concentrations, 751 and 676 µmol photon m -2 s -1 , and under elevated CO 2 concentrations, 1591 and 1283 µmol photon m -2 s -1 , for natural and longer TFD, respectively. In addition, dark respiration estimated from the light curves was systematically higher from 5 to 20% than real values measured at night during the same period of the year (Table 3); however, these differences were not significant in both species and in any of the four treatments.

Maximum quantum efficiency of PSII photochemistry (F v /F m ) during the warm season

For

Stomatal density

The results of stomatal density for A. marina and R. stylosa are presented in Fig. 5. For both species, stomatal density was significantly reduced under elevated CO 2 in comparison to ambient CO 2 concentrations, whereas within each CO 2 treatment, no significant differences in stomatal density were observed under natural or longer TFD (Fig. 5a,b; Table 2).

Discussion

Future sea-level rise will affect mangrove photosynthesis

Sea-level rise will result in an increase of the tidal flooding duration for mangroves. In our experiment, applying a longer tidal duration to Avicennia marina and Rhizophora stylosa seedlings resulted in a decrease of 5% and 3% in photosynthesis, and of 23% and 2% in WUE, for A. marina and R. stylosa, respectively. However, these reductions were lower than those reported for other stressing factors, such as for example, salinity, as demonstrated by [START_REF] Ball | Growth and water use of the mangroves Rhizophora apiculata and R. stylosa in response to salinity and humidity under ambient and elevated concentrations of atmospheric CO 2[END_REF] on R. stylosa and R. apiculata. Tidal flooding may induce a rapid deficit in oxygen in the soil due to and microorganisms respiration [START_REF] Naidoo | Gas exchange responses of a mangrove species, Avicennia marina, to waterlogged and drained conditions[END_REF]. In this study, no oxygen measurements were performed, however, depending on other studies, a decrease of 28% of oxygen could be observed after 6 h of flooding [START_REF] Skelton | Oxygen and pressure changes measured in situ during flooding in roots of the Grey Mangrove Avicennia marina (Forssk.) Vierh[END_REF], or of 100% after 3.5 h, as reported for A. marina seedlings [START_REF] Hovenden | Ventilation and respiration in roots of one-year-old seedlings of grey mangrove Avicennia marina (Forsk.) Vierh[END_REF].

In this later case, the deficit of oxygen led to a complete anoxia of the root system. During flooding events, mangrove roots may use all their internal oxygen content, and then start to metabolize anaerobically [START_REF] Krauss | Environmental drivers in mangrove establishment and early development: a review[END_REF]. Mangroves are well-adapted to waterlogging condition of their soil, and generally respond by producing lenticels on basal stems or root structures to help offset the effects of low soil oxygen levels [START_REF] Krauss | Environmental drivers in mangrove establishment and early development: a review[END_REF]. However, in our study, A. marina and R. stylosa were 3 years old at the end of the experiment, and their number of lenticels was limited due to their size and only a few seedlings started to produce pneumatophore or prop roots. Similar results of a decrease in photosynthesis and water-use efficiency with increasing tidal flood duration were previously observed on seedlings but also on mature mangrove trees [START_REF] Youssef | Anatomical adaptive strategies to flooding and rhizosphere oxidation in mangrove seedlings[END_REF][START_REF] Naidoo | Gas exchange responses of a mangrove species, Avicennia marina, to waterlogged and drained conditions[END_REF][START_REF] Chen | Photosynthetic and physiological responses of Kandelia candel L. Druce seedlings to duration of tidal immersion in artificial seawater[END_REF]. In their work on Kandelia candel, [START_REF] Chen | Photosynthetic and physiological responses of Kandelia candel L. Druce seedlings to duration of tidal immersion in artificial seawater[END_REF] showed that during anaerobic conditions, the production of abscisic acid (ABA) increased. The latter stimulates stomatal closure, and thus reduces photosynthesis (Kozlowski 1984). No hormone measurements were made in our study, but we suggest that a similar mechanism may be involved in the observed decrease of photosynthesis for A. marina and R. stylosa when subjected to longer tidal flooding, as observed by [START_REF] Chen | Photosynthetic and physiological responses of Kandelia candel L. Druce seedlings to duration of tidal immersion in artificial seawater[END_REF]. Reduced photosynthesis during longer immersion time may also result from the inhibition of the RuBisCO enzyme activity [START_REF] Ellison | Simulated sea level change alters anatomy, physiology, growth, and reproduction of red mangrove (Rhizophora mangle L.)[END_REF][START_REF] Pezeshki | Carbon assimilation and biomass partitioning in Avicennia germinans and Rhizophora mangle seedlings in response to soil redox conditions[END_REF]). Further study should now examine precisely these hypotheses.

All F v /F m values reported in our study for A. marina and R. stylosa, with either elevated CO 2 or longer tidal flooding, indicated that leaves were photosynthetically actives, with ratios between 0.77 and 0.81, indicative of healthy photosystems and absence of significant stressing factors damaging the photosynthetic functions [START_REF] Lichtenthaler | How to correctly determine the different chlorophyll fluorescence parameters and the chlorophyll fluorescence decrease ratio R Fd of leaves with the PAM fluorometer[END_REF][START_REF] Sobrado | Leaf characteristics and diurnal variation of chlorophyll fluorescence in leaves of the 'Bana'vegetation of the Amazon region[END_REF][START_REF] Orekhov | The use of parameters of chlorophyll a fluorescence induction to evaluate the state of plants under anthropogenic load[END_REF]. In addition, in their study on Rhizophora stylosa in Australia, [START_REF] Cheeseman | Photosynthesis and photoprotection in mangroves under field conditions[END_REF] observed mean values of F v /F m of 0.801, which is similar to the values we found in our study. In their study, [START_REF] Cheeseman | Photosynthesis and photoprotection in mangroves under field conditions[END_REF] observed a decrease in the PSII efficiency at high level of irradiance, and they suggested that downregulation of PSII efficiency, rather than damage, is responsible of this decrease, as indicated by the values of F v /F m . Consequently, we suggest that downregulation of PSII is also responsible of the decrease of the photosynthetic efficiency observed in this study for high irradiance levels (Fig. 4). We further suggest that the 5-20% differences between dark respiration rates estimated from the light curves and the one measured at night may be due to temperature variation between day and light, as respiration rates are also temperature depend [START_REF] Tjoelker | Modelling respiration of vegetation: evidence for a general temperature-dependent Q10[END_REF][START_REF] Atkin | Thermal acclimation and the dynamic response of plant respiration to temperature[END_REF][START_REF] Smith | Plant respiration and photosynthesis in global-scale models: incorporating acclimation to temperature and CO 2[END_REF].

Elevated atmospheric CO 2 concentrations will increase mangrove net productivity

According to our initial hypothesis, elevated CO 2 significantly stimulated photosynthesis, which was enhanced by more than 37% for A. marina and by more than 45% for R. stylosa. In our study, the initial increase of photosynthesis was maintained after 1 year of enrichment, and no downregulation was observed, contrary to some previous observations of photosynthetic acclimation after long-term exposure to elevated CO 2 [START_REF] Farnsworth | Elevated CO 2 alters anatomy, physiology, growth, and reproduction of red mangrove (Rhizophora mangle L.)[END_REF]. In addition, dark respiration was not affected by elevated CO 2 concentrations, either for A. marina or for R. stylosa, which is different from the results of [START_REF] Farnsworth | Elevated CO 2 alters anatomy, physiology, growth, and reproduction of red mangrove (Rhizophora mangle L.)[END_REF] who observed a slight decrease of dark respiration with elevated CO 2 . Consequently, elevated CO 2 induced a stimulation of photosynthesis but did not influence plant dark respiration, suggesting that the productivity of mangroves seedlings may be further enhanced with future climate change, which is in accordance with previous studies showing increase of the net CO 2 exchange rate [START_REF] Farnsworth | Elevated CO 2 alters anatomy, physiology, growth, and reproduction of red mangrove (Rhizophora mangle L.)[END_REF][START_REF] Ball | Growth and water use of the mangroves Rhizophora apiculata and R. stylosa in response to salinity and humidity under ambient and elevated concentrations of atmospheric CO 2[END_REF][START_REF] Reef | The effect of atmospheric carbon dioxide concentrations on the performance of the mangrove Avicennia germinans over a range of salinities[END_REF].

Surprisingly, SLA increased for both species under elevated CO 2 (Fig. 3), oppositely to the results of other studies [START_REF] Ball | Growth and water use of the mangroves Rhizophora apiculata and R. stylosa in response to salinity and humidity under ambient and elevated concentrations of atmospheric CO 2[END_REF][START_REF] Mckee | Where temperate meets tropical: multifactorial effects of elevated CO 2 , nitrogen enrichment, and competition on a mangrove-salt marsh community[END_REF][START_REF] Reef | Historical analysis of mangrove leaf traits throughout the 19th and 20th centuries reveals differential responses to increases in atmospheric CO 2[END_REF]. This is an important result, as an increase in SLA will lead to a higher potential for carbon acquisition by photosynthesis but also for light interception. Consequently, even if elevated CO 2 had no effect on photosynthesis in low light conditions, the increase of SLA may promote the growth of A. marina and R. stylosa seedlings in shaded area. Finally, light response of both species to elevated CO 2 was consistent with previous studies [START_REF] Ziska | Long-term photosynthetic response in single leaves of a C3 and C4 salt marsh species grown at elevated atmospheric CO 2 in situ[END_REF][START_REF] Drake | Canopy photosynthesis of crops and native plant communities exposed to long-term elevated CO 2[END_REF][START_REF] Kubiske | Effects of elevated CO 2 and light availability on the photosynthetic light response of trees of contrasting shade tolerance[END_REF][START_REF] Herrick | Effects of CO 2 enrichment on the photosynthetic light response of sun and shade leaves of canopy sweetgum trees (Liquidambar styraciflua) in a forest ecosystem[END_REF], having higher effect of elevated CO 2 at high irradiance (Fig. 4). Photosynthesis was stimulated by elevated CO 2 from low lights levels in both species, suggesting that not only sun exposed leaves, but also shaded leaves will fix more CO 2 in the future, therefore further increasing mangroves productivity. Seedlings recruitment may be also promoted, as it was demonstrated that seedlings survivorship is strongly affected by light availability [START_REF] Tamai | Early growth and growth of mangrove seedlings in mangrove forests of south Thailand[END_REF][START_REF] Smith | Effects of light quantity and quality on early seedling development in the red mangrove, Rhizophora mangle L[END_REF][START_REF] Lopez-Hoffman | Salinity and light interactively affect neotropical mangrove seedlings at the leaf and whole plant levels[END_REF].

Increase in temperature will raise the beneficial effect of elevated CO 2

We observed a clear difference in the photosynthetic response to elevated CO 2 between the cool season and the warm season, which increased from 32 to 40% and from 38 to 45% for A. marina and R. stylosa, respectively (Fig. 2). Although photosynthesis of tropical C3 species such as A. marina and R. stylosa can operate between 15 and 45 °C, there is a temperature optimum for which it will be maximal [START_REF] Sage | The temperature response of C3 and C4 photosynthesis[END_REF]. In their review, [START_REF] Gilman | Threats to mangroves from climate change and adaptation options: a review[END_REF] indicated that this optimum lies between 28 and 32 °C for mangroves species, however, it appears to be species-specific, as lower values of 24.5 °C have been reported for A. germinans [START_REF] Reef | The effects of CO 2 and nutrient fertilisation on the growth and temperature response of the mangrove Avicennia germinans[END_REF]) and of 26.8 °C for A. marina [START_REF] Leopold | Net ecosystem CO 2 exchange in the "Coeur de Voh" mangrove, New Caledonia: effects of water stress on mangrove productivity in a semi-arid climate[END_REF]). In our study, mean monthly temperatures increased from 22.3 to 26.7 °C during the warm season, which is close to the optimal temperatures reported above, therefore confirming the hypothesis of temperature as a limiting factor for photosynthesis during the cool season under elevated CO 2 . With future climate change, the global temperatures are predicted to rise by 0.3 to 4.8 °C, depending on prediction models [START_REF] Stocker | climate change 2013: the physical science basis[END_REF], and our work suggests that the combination of elevated CO 2 with the increase of temperature may further promote the CO 2 fixation by mangrove trees. However, it seems that this beneficial effect may be inhibited if temperatures increase to more than 40 °C [START_REF] Andrews | Photosynthetic gas exchange properties and carbon isotope ratios of some mangroves in North Queensland[END_REF][START_REF] Gilman | Threats to mangroves from climate change and adaptation options: a review[END_REF][START_REF] Reef | The effects of CO 2 and nutrient fertilisation on the growth and temperature response of the mangrove Avicennia germinans[END_REF], which may happen with future climate changes, particularly in the actual arid or semi-arid regions.

Elevated CO 2 will help mangroves trees to resist drought

We observed that growth under elevated atmospheric CO 2 resulted in a significant reduction of stomatal density, with more than 19% and 23% for A. marina and R. stylosa, respectively. The more likely is that this effect was induced by the decrease of stomatal conductance, as previously reported by [START_REF] Lammertsma | Global CO 2 rise leads to reduced maximum stomatal conductance in Florida vegetation[END_REF], which was already observed in mangrove trees grown under elevated CO 2 [START_REF] Snedaker | Stomatal conductance and gas exchange in four species of Caribbean mangroves exposed to ambient and increased CO 2[END_REF][START_REF] Reef | The effect of atmospheric carbon dioxide concentrations on the performance of the mangrove Avicennia germinans over a range of salinities[END_REF]. Decrease in stomatal density, and thus in stomatal conductance, probably contributed to the decrease in transpiration rates (Fig. 1). The combination between higher net photosynthetic rates and lower transpiration rates leaded to an increase in water-use efficiency, and our results showed that this parameter was enhanced by more than 45% for A. marina and more than 50% for R. stylosa under elevated CO 2 , consistently with previous observations [START_REF] Reef | The effect of atmospheric carbon dioxide concentrations on the performance of the mangrove Avicennia germinans over a range of salinities[END_REF]. As atmospheric CO 2 concentrations will continue to rise in the future [START_REF] Collins | Long-term climate change: projections, commitments and irreversibility pages 1029 to 1076[END_REF], it is possible that the stomatal density will continue to decline, thereby preventing water loss by further reduction of transpiration rates. Improving water-use efficiency might be a key for mangroves to resist drought episodes, which will increase in frequency with future climate change [START_REF] Dai | Increasing drought under global warming in observations and models[END_REF]. Due to the semi-arid climate, mangrove trees in New Caledonia are often stunted in growth. They suffer from the elevated salt concentration within the sediment due to the high evaporation of the water and the low inputs by rain or river discharges [START_REF] Marchand | Redox conditions and heavy metals distribution in mangrove forests receiving effluents from shrimp farms (Teremba Bay, New Caledonia)[END_REF]. Consequently, they have a limited productivity [START_REF] Leopold | Net ecosystem CO 2 exchange in the "Coeur de Voh" mangrove, New Caledonia: effects of water stress on mangrove productivity in a semi-arid climate[END_REF]. Enhancement of water-use efficiency with future climate change will, in return, promote growth and productivity of these trees, and finally will improve their carbon fixation and as so, their role in climate change mitigation. Expanding mangrove forests within arid and semi-arid regions is another major challenge, as it could be the case, for example, on the west coast of South Africa. In this region, mangrove expansion is limited to the tropics, notably due to the aridity of the Sahara Desert in the north, and the Namib Desert in the south [START_REF] Ward | Impacts of climate change on mangrove ecosystems: a region by region overview[END_REF] preventing mangrove seedlings from colonizing the northern and southern subtropical areas. Mangrove plants distribution is affected by many parameters, including temperature, precipitation, pore-water salinity, length of tidal immersion, etc [START_REF] Duke | Factors influencing biodiversity and distributional gradients in mangroves[END_REF]. The results presented herein suggest that climate changes will enhance mangrove photosynthesis and will allow mangrove juveniles to colonize new areas, which was recently observed with either a poleward migration or a landward migration of mangroves depending on the region [START_REF] Gilman | Threats to mangroves from climate change and adaptation options: a review[END_REF][START_REF] Saintilan | Mangrove expansion and salt marsh decline at mangrove poleward limits[END_REF].

Conclusions

Our results highlight that future climate changes, and particularly elevated CO 2 and increased tidal flooding duration, will strongly affect mangroves physiology. In this study, elevated CO 2 (800 ppm) significantly enhanced photosynthesis by more than 37% and 45% for A. marina and R. stylosa. However, our results do not support the previous observations of a downregulation of photosynthesis. Additionally, dark respiration was not affected by elevated CO 2 , therefore implying a higher carbon gain for the mangrove seedlings studied. Season was also a key driver of the leaf-gas exchanges, with an increase of photosynthesis during the warm period for both species. Consequently, future increase in global temperatures with climate change will further enhance the productivity of the trees, as long as it does not exceed the species-specific optimal temperature for photosynthesis. When increasing tidal flooding duration, photosynthetic rates were slightly reduced but not enough to offset the carbon gain induced by the elevated CO 2 concentrations. Additionally, elevated CO 2 reduced transpiration rates, leading to a significant increase in water-use efficiency, which may favor mangrove expansion, specifically in arid or semiarid regions. As both species responded similarly to the experiment, we suggest that climate changes may not favor the development of one species over the other, and thus may not affect their relative repartition along the intertidal areas. This study thus provided useful information about the response of mangrove seedlings to future climate change. Further research will now be needed to evaluate the effects of future climate change on the carbon storage capacities of the whole ecosystem. Indeed, mangroves are recognized for their role in sequestering carbon both in their biomass and in their soils. Therefore, understanding how elevated CO 2 and prolonged water flooding will affect mangrove plant tissues composition, and thus the diagenesis of mangrove-derived organic matter in soils could help to understand the future role of mangrove ecosystems in climate change mitigation.

Fig. 2

 2 Fig. 2 Annual evolution (± SEM) of leaf net photosynthetic rates (P n , µmol m -2 s -1 ) for a A. marina, and b R. stylosa. Colored markers: ambient CO 2 concentrations, white markers: elevated CO 2 concentrations. Shaded area represents the warm season

Fig. 4 Fig. 5

 45 Fig. 4 Pn/PPFD curves for A. marina (a) and R. stylosa (b) at the end of the experiment. (n = 3 ± SEM). Colored markers: ambient CO 2 concentrations, white markers: elevated CO 2 concentrations

Table 1

 1

	Mean annual and seasonal temperatures (°C) and relative humidity (%) ± standard deviations (SD) inside the	Parameters (means ± SD)	Annual	Cool season (June-November)	Warm season (December-May)
	greenhouses and the closed chambers	Greenhouse temperature (°C) Chamber temperature (°C)	25.1 ± 2.9 25.0 ± 3.3	23.1 ± 2.6 22.3 ± 3.0	26.4 ± 3.2 26.7 ± 3.5
		Greenhouse relative humidity (%)	82.6 ± 13.6	85.8 ± 12.6	80.7 ± 14.2
		Chamber relative humidity (%)	79.9 ± 12.6	78.4 ± 12.2	80.8 ± 12.8

Table 2

 2

	Significance values reported by two-way analysis of		Avicennia marina		Rhizophora stylosa
	variance (ANOVA), followed by a Scheffe post hoc test or a Kruskal-Wallis test	P n T r	CO 2 667.70*** 45.78***	TFD 8.86** 0.718 NS	Interaction 0.55 NS 1.304 NS	CO 2 1401.48** 28.33***	TFD 10.37*** 3.919*	Interaction 2.63 NS 2.511 NS
		WUE	155.64***	0.76 NS	8.75**	285.17***	8.17**	10.63***
		g s	16.01***	7.46**	12.25***	0.001 NS	25.07***	19.54***
		D r	0.05 NS	0.01 NS	0.07 NS	1.77 NS	0.017 NS	0.241 NS
		SLA	114.49***	1.260 NS	2.75 NS	51.61***	1.35 NS	18.00 NS
		F v /F m	3.96*	9.26**	7.45**	25.04***	2.32 NS	4.50*
		SD	94.97***	0.426 NS	0.05 NS	83.06***	0.535 NS	0.05 NS
		NS non-significant
		***, **, * indicates significant effects at p < 0.001, 0.01, and 0.05, respectively

Acknowledgements This research was supported by the Province Sud of New Caledonia, the City of Mont-Dore, KNS Koniambo Nickel SAS, and Vale NC. We are grateful to the IFRECOR Committee for having attributed to this study the IFRECOR Palme National Distinction. We thank Eric Gay, the mayor of Mont-Dore, for his continuous support during the study. We also thank Jacky Mermoud and Diana Burns for assistance with managing the facilities, as well as Laure Barrabe, Tracy Rolland, and Inès Gayral for their help in field work. We are also very grateful to Karen L. Mckee, Scientist Emeritus with the U.S. Geological Survey for her helpful comments on the manuscript.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


Andreea Laczko
email: andreea.laczko@mae.utcluj.ro

Stephane Brisset
email: stephane.brisset@centralelille.fr

Mircea Radulescu
email: mircea.radulescu@mae.utcluj.ro

Stéphane Brisset

Design of a

Keywords: barycenter method, brushless DC permanent-magnet generator, design, optimization, wind cycle

Introduction

Brushless direct current (DC) permanent magnet machines have become widely used in various industrial applications due to the advantages that define them and their ease of control. The lack of brushes in their configuration yields several benefits for this topology as improved efficiency, better reliability, longer life with less maintenance, higher power density and higher torque to weight ratio [START_REF] Singh | PMBLDCG based stand-alone wind energy conversion system for small scale applications[END_REF], [START_REF] Rim | Modeling, simulation, and analysis of variable-speed constant frequency power conversion scheme with a permanent magnet brushless DC generator[END_REF]. The optimal design of a brushless DC permanent magnet (BLDCPM) generator for the considered architecture of the wind energy conversion system to be studied in order to minimize a specific objective function, i.e. total power losses over one year wind-speed cycle operation, depends on the appropriate selection of the multiple design parameters. The structure presented in Fig. 1 can be considered as a good example of a complex wind energy conversion system (even if limited to the DC bus) as it incorporates subsystems belonging to different physical domains with strong interference between each other, imposing to consider the globalism of the system in the design process, rather than exploring them separately. Therefore, the approach based on design optimization is justified and even necessary for achieving optimal results in a short amount of time. Due to the many operating points within the wind speed profile and because the optimization process requires many evaluations of the objective function, adapted models have to be considered in terms of results accuracy and simulation time. The most preferred is the one based on finite element analysis, because of its high precision. However, it is well known for its huge evaluation time making it a displeasing strategy to be considered in optimization. Nevertheless, it can be used outside the optimization loop as a validation model in order to refine the obtained results. But, when dealing with few initial specifications and many unknown parameters specific analytical and/or semi-analytical models are preferred over the numerical ones, as they perform much faster. This paper describes the considered optimization methodology used in the search of the optimal design of a directdriven BLDCPM generator with trapezoidal induced electromotive force (back-EMF) voltages for use in microwind turbine applications. The optimization process is based on two modeling levels of different time scales and of different approaches, in order to calculate the generator's performances. As the optimization will be performed over a long term wind speed profile, adequate simplification method of the profile is proposed and applied to the power losses calculation of the overall wind energy system. In order to achieve feasible solution several constraints have to be analyzed on the input/outputs of the model, resulting in a constrained mono-objective optimization. Due to the wind speed cycle operation, suitable algorithm and optimization strategy are also considered in order to find the global optimum of the objective function and to reduce the probability of falling into a local minimum.

Modeling description of the wind energy system components

Wind speed profile and wind turbine model

The long-term wind speed profile considered is represented by the mean value taken over one hour of wind measurements, every hour for one year, resulting into 8759 operating points. A problem that can appear when Fig. 1. Architecture of the wind energy conversion system under study designing the generator over such a long term wind speed profile is linked to the direct-driven variable speed operation, meaning that the many fluctuations in the wind speed are visible in the power and frequency of the generator. As the wind turbine power changes with the cube of the wind speed, its expression emphasizes the importance that the dynamic properties of the wind speed have upon the wind energy conversion system. Hence, the three-bladed horizontal axis wind turbine chosen for this study provides the assessment of the available power in the wind speed [START_REF] Manwell | Wind Energy Explained: Theory, Design and Application[END_REF] as:

𝑃 𝑤𝑡 = 0.5𝜌 𝑎𝑖𝑟 𝜋𝑅 𝑤𝑡 2 𝐶 𝑝 (𝜆)𝑣 𝑤 3 (1)
with ρair being the air density (kg/m 3 ), Rwt denotes the radius of the turbine-rotor blades (m), 𝜆, the tip-speed coefficient, vw, the wind speed (m/s), and Cp the power coefficient of the turbine, which provides an idea about how many of the kinetic energy from the air mass can be converted into mechanical energy by the wind turbine. This coefficient can be calculated through interpolation based on the factors provided in [START_REF] Belouda | Design methodologies for sizing a battery bank devoted to a stand-alone and electronically passive wind turbine system[END_REF].

Simulation models of the generator-rectifier assembly

Two simulation models have been developed to characterize the behavior of the wind energy conversion system. Both of them depend on the sizing characteristics [START_REF] Brisset | Analytical model for the optimal design of a brushless DC wheel motor[END_REF] of the generator (Fig. 2a) that is determined beforehand and works as a background function for each of the simulation model during the optimization.

A) Analytical simulation model [START_REF] Laczko | Modeling approaches to brushless DC permanent-magnet generator for use in micro-wind turbine applications[END_REF]: This model is based on the sizing characteristics of the generator, whereas its electromagnetic parameters are derived from the circuit equations of the machine by considering only the amplitude of the involved quantities. It is characterized as the fastest of the models, being very suited for the initial stage of design upon which the optimization could be performed. To be noted that no control is implemented for this model as the commutation of the phases is not explicitly taken into consideration.

B)

Semi-analytical simulation model [START_REF] Laczko | Modeling approaches to brushless DC permanent-magnet generator for use in micro-wind turbine applications[END_REF], [START_REF] Laczko | Modeling and simulation of a brushless DC permanent-magnet generator-based wind energy conversion system[END_REF]: This second model (Fig. 2b) is developed to take into account the switching pattern that depends on rotor angular position, the hysteresis current-control, as well as the commutation and conduction intervals of the controlled pulse width modulation (PWM) rectifier. It provides a better precision of the output solution than the analytical one, but it engages a long time for the simulation of all the points within the wind speed profile. In order to speed up its evaluation a wind speed cycle partition technique based on barycenter method is adapted to the maximum power point tracking (MPPT) operation area of the wind turbine and implemented in terms of wind energy system power losses. The adopted MPPT control strategy corresponds to an operation of the wind turbine at optimal power coefficient (𝐶 𝑝_𝑜𝑝𝑡 ) and optimal tip-speed ratio (𝜆 𝑜𝑝𝑡 ) [START_REF] Laczko | Modeling and simulation of a brushless DC permanent-magnet generator-based wind energy conversion system[END_REF]. The barycenter method divides the wind speed profile into a chosen number of regions (Fig. 3a), each region (r) being represented by its barycenter and the necessary parameters (Fig. 3b) needed for the losses calculation. The required parameters are derived by assuming, depending on the corresponding power loss expression, the electromagnetic power of the BLDCPM generator proportional to the cube of the wind speed and the rotational angular speed, Ω, linked to the wind speed through the equation of the tip-speed ratio. Accordingly, the electromagnetic torque of the generator is considered proportional to the square of the wind speed, being also expressed as a current dependent characteristic. An explicit description of the determination process of the power losses equations based on the barycenter method is reported in [START_REF] Laczko | Modeling approaches to brushless DC permanent-magnet generator for use in micro-wind turbine applications[END_REF]. The expressions for these power losses are based on the equations provided in [START_REF] Belouda | Design methodologies for sizing a battery bank devoted to a stand-alone and electronically passive wind turbine system[END_REF], [START_REF] Andrada | Power Losses in Outside-Spin Brushless D.C. Motors[END_REF], [START_REF]V, 250-W, High Efficiency BLDC Motor Drive with DC-Bus Voltage Ripple Compensation[END_REF] and reformulated afterwards in connection to the barycenter method in order to calculate them for each region as follows:  Mechanical losses [START_REF] Belouda | Design methodologies for sizing a battery bank devoted to a stand-alone and electronically passive wind turbine system[END_REF], [START_REF] Andrada | Power Losses in Outside-Spin Brushless D.C. Motors[END_REF] due to friction phenomena :

𝑃 𝑚𝑒𝑐ℎ ,𝑟 = 𝑓 𝑤𝑡 Ω 𝑟 2 𝑁 𝑟 〈𝑣 𝑤 2 〉 𝑟 〈𝑣 𝑤 〉 𝑟 2 (2)
with 𝑓 𝑤𝑡 the friction coefficient (N.m/rad), 𝑁 𝑟 the number of points in the region, Ω 𝑟 the corresponding rotational speed (rad/s) of the region in cause, and 〈•〉 𝑟 denotes the mean value in the region.  Copper losses [START_REF] Andrada | Power Losses in Outside-Spin Brushless D.C. Motors[END_REF] caused by the induced currents in the stator windings :  Iron losses [START_REF] Andrada | Power Losses in Outside-Spin Brushless D.C. Motors[END_REF] based on the magnetic properties of the materials :

𝑃 𝑗 ,𝑟 = 3𝑅𝐼 𝑅𝑀𝑆 ,𝑟 2 𝑁 𝑟 〈𝑣 𝑤 4 〉 𝑟 〈𝑣 𝑤 〉 𝑟 4 (3)
𝑃 𝐹𝑒_ℎ𝑦𝑠 ,𝑟 = 𝑘 ℎ𝑦𝑠 𝑁 𝑝 2𝜋 (𝐵 ̂𝑡ℎ 𝛼 + 𝐵 ̂𝑠𝑦 𝛼 ) Ω 𝑟 𝑁 𝑟 〈𝑣 𝑤 〉 𝑟 〈𝑣 𝑤 〉 𝑟 (4) 𝑃 𝐹𝑒_𝑒𝑑𝑑𝑦 ,𝑟 = 𝑘 𝑒𝑑𝑑𝑦 𝑁 𝑝 2 𝜋 3 (𝐵 ̂𝑡ℎ 2 + 2𝐵 ̂𝑠𝑦 2 ) Ω 𝑟 2 𝑁 𝑟 〈𝑣 𝑤 2 〉 𝑟 〈𝑣 𝑤 〉 𝑟 2 (5)
where 𝑘 ℎ𝑦𝑠 and 𝑘 𝑒𝑑𝑑𝑦 are hysteresis, respectively eddy current loss coefficients which can be calculated from manufacturer data, 𝑁 𝑝 the pole pairs number and 𝐵 ̂𝑡ℎ and 𝐵 ̂𝑠𝑦 are the peak values of the stator tooth and yoke flux densities.

 Conduction and switching losses [START_REF]V, 250-W, High Efficiency BLDC Motor Drive with DC-Bus Voltage Ripple Compensation[END_REF] in the three-phase power converter based IGBT devices with anti-parallel diode units: with 𝑓 𝑚𝑜𝑑 the modulation factor, 𝑉 𝐶𝐸 the collector-emitter voltage of the insulated gate bipolar transistor (IGBT) (V), 𝑉 𝐶𝐸0 is the ON-state, zero current collector-emitter voltage (V) which can be obtained from the manufacturer datasheet, 𝐼 𝑛_𝐼𝐺𝐵𝑇 represents the nominal current of the transistors, 𝐼 𝐶_𝑅𝑀𝑆 is the current during the 120 • switch conduction period, 𝐸 𝑂𝑁 and 𝐸 𝑂𝐹𝐹 denote the turn-on and turn-off switching losses (J) of the transistors, 𝑉 𝐶𝐶(𝑡𝑒𝑠𝑡) and 𝐼 𝐶𝐶(𝑡𝑒𝑠𝑡) describe the test voltage (V) and current (A), 𝐼 𝐶_𝑝𝑘 is calculated for a 110% overload of the generator winding current, 𝑓 𝑠𝑤 is the switching frequency (Hz), 𝑉 𝐹 the forward ON voltage in the diodes (V), 𝑇 𝑐𝑜𝑚𝑚 and 𝑓 𝑒𝑙𝑒 express the phase commutation time (s) and the fundamental frequency of the machine (Hz), respectively and finally 𝐼 𝐹_𝐴𝑉𝐺 is the average forward current of the diode during phase commutation.

𝑃 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑜𝑛_𝐼𝐺𝐵𝑇 ,𝑟 =

Optimization problem description

Mono-objective function

The objective function proposed for resolution is represented by the minimization of the overall power losses (𝑃 𝑡𝑜𝑡𝑎𝑙_𝑙𝑜𝑠𝑠 ) in the system, based on the power flow presented in Fig. 4, during one year wind speed cycle operation, which indirectly implies the maximization of the output useful power. Other possible objectives could be the manufacturing cost, the reliability of the system, the lifetime expectancy, etc. but the amount of renewable energy provided by the wind turbine is preferred as it is correlated with major environmental concerns such as energy depletion and climate change.

𝑂𝑃 1 = 𝑚𝑖𝑛(𝑃 𝑡𝑜𝑡𝑎𝑙_𝑙𝑜𝑠𝑠 ) = 𝑚𝑖𝑛(𝑃 𝑚𝑒𝑐ℎ_𝑡 + 𝑃 𝑗_𝑡 + 𝑃 𝐹𝑒_𝑡 + 𝑃 𝑐𝑜𝑛𝑣_𝑡 ) (10)

Design variables and constraints

The continuous (c) and discrete (d) type variables of the wind energy system considered to be optimized are presented in Table 1, along with their associated variation domain. The performance operating points of the wind turbine, i.e. the cut-in, rated and cut-off wind speeds are also set as variables to be optimized in order to provide the optimal turbine power curve and consequently the nominal power of the generator. As they strongly influence the length of the wind profile to be considered in the calculation of the wind energy system power losses and due to the nature of the employed optimization algorithm, their range of definition is slightly narrowed so that the turbine to start its operation at a cut-in wind speed less than the average wind of the profile. The cut-off wind speed is chosen to prevent the forces acting on the turbine structure at high wind speeds to damage the rotor. Depending on the design cost of the wind turbine a lower value can be set for this parameter, however for this study its proposed definition domain was favored to assess the large amount of data within the wind speed profile. The many design variables to be optimized may lead to non-feasible configurations as results of the optimization process. To resolve this difficulty several constraints were imposed on the:  Useful (output) power at cut-in wind speed:

𝑃 𝑜𝑢𝑡_𝑣 𝑖𝑛 > 0 [W] (11)
 Generator inner diameter:

𝐷 𝑖𝑛𝑡 ≥ 80 [mm] (12)
 Permanent magnet thickness:

ℎ 𝑝𝑚 ≤ 6 [mm] (13)
 Maximum temperature of the copper windings:

𝑇 𝐶𝑢,𝑟 ≤ 130 [℃] (14)
 Generator efficiency over the long-term wind cycle, obtained as the ratio between the total output power (∑ 〈𝑃 𝑜𝑢𝑡_𝑔𝑒𝑛 〉 𝑖 𝑁 𝑖=1

) of the generator and the total input power given by the wind turbine (∑ 〈𝑃 𝑖𝑛_𝑤𝑡 〉 𝑖 𝑁 𝑖=1

), with 𝑁 being the number of wind speeds within the considered wind profile:

𝜂 𝑔𝑒𝑛_𝑐𝑦𝑐𝑙𝑒 ≥ 0.9

Equations ( 14)-( 17) are set of constraints that apply to all regions. The above problem formulation becomes a constrained mono-objective optimization that is solved by using a stochastic method, in particular the genetic algorithm (GA) [START_REF] Golberg | Genetic algorithms in search, optimization, and machine learning[END_REF] from the MATLAB® environment to find the geometrical and electrical parameters that satisfy the problem constraints while performing the minimization of the power losses of the wind energy system over one year wind speed profile. The considered control parameters of the genetic algorithm are those listed in Table 2.

Optimization methodology and results

Single-level optimization approach

The first attempt is to perform the optimization upon the analytical simulation model based on few initial data and specifications, so that a first design that respects all the constraints could be generated. The workflow of the global design optimization process for the single level approach is depicted in Fig. 5. After 11 minutes and 526,001 model evaluations, the optimization upon the analytical model is finished and the optimum design variables are further used for verifying the obtained results by evaluating with them the semianalytical model over complete wind cycle operation and also the semi-analytical model associated to the barycenter method. It is to be noted that the simulations of the semi-analytical model account for electrical dynamics, as they analyze the generator behavior during one electrical period (0 ≤ t ≤ T), but for mechanical steady-state, since only one wind speed value (i.e. the average wind speed over one hour wind speed measurements for the complete cycle and the wind speed value corresponding to the barycenter of one region for the barycenter method, respectively) is set as input for each simulation.

Previous work [START_REF] Laczko | Modeling approaches to brushless DC permanent-magnet generator for use in micro-wind turbine applications[END_REF] established that just six regions are enough to partition the wind cycle and approximate, with an acceptable relative error, the total power losses in the wind energy system, as also noticeable in Fig. 6. The relative errors between the (i) analytical (𝐴𝑁 𝑐𝑦𝑐𝑙𝑒 ) model with complete cycle (red) and (ii) the semi-analytical (𝑆𝐴 𝑏𝑎𝑟𝑦 ) model with barycenter method (blue), for several quantities, are provided. A comparison in terms of computation time and operating points is also given in Table 3.

Two-level optimization approach

For a refining of the optimization results with analytical model, a correction strategy that uses evaluations of the semi-analytical model associated to the barycenter method is proposed and implemented in the two level optimization approach, as presented in Fig. 7. As seen in the previous section, some differences arise between the output parameters of the analytical and semi-analytical models under complete cycle operation. This issue is fixed by building a surrogate model that includes the analytical model and a correction on its outputs. The optimization process is started again until the discrepancy between the surrogate (SU) model and the semianalytical model with barycenter method is small enough. The correction is based on output space-mapping technique [START_REF] Bakr | An Introduction to the Space Mapping Technique[END_REF].

The stop criterion of the correction loop (Fig. 7) is:

100 |𝑃 𝑙𝑜𝑠𝑠_𝑡𝑜𝑡𝑎𝑙_𝑆𝐴 𝑏𝑎𝑟𝑦 𝑘 -𝑃 𝑙𝑜𝑠𝑠_𝑡𝑜𝑡𝑎𝑙_𝑆𝑈 𝑘 | |𝑃 𝑙𝑜𝑠𝑠_𝑡𝑜𝑡𝑎𝑙_𝑆𝐴 𝑏𝑎𝑟𝑦 𝑘 | < 0.1% (20)
where the indexes 𝑆𝐴 𝑏𝑎𝑟𝑦 and SU correspond to the semi-analytical model associated to the barycenter method and surrogate model, respectively, while k denotes the iteration. The convergence history for some particular output variables are displayed in Fig. 8. The optimal results found at the 6 th iteration were then used to compare the electromagnetic behavior of the BLDCPM generator with the semi-analytical model and finite element (FE) method. The cross-sectional model of the machine was thus created and subjected to transient magnetic field analysis by means of JMAG Designer software [12]. To visualize also the electromagnetic torque response of the generator and the stator-winding phase currents for the base operating point, a 2D FE time-stepping analysis was carried out, the obtained waveforms being displayed in Fig. 10 and compared to the ones given by the semi-analytical model. A dissimilarity can be noticed between the electromagnetic torque waveforms of the two models, as well as a relative error of 6% among their average values. This may be justified by the fact that neither the cogging torque (resulting from the interaction of the magnets with the slotted stator), nor the magnetic saturation have been considered in the semi-analytical model.

Conclusions

In this paper the optimal design of a direct-driven BLDCPM generator for use in micro-wind turbine applications has been investigated. The design optimization process is based on two simulation models, one more accurate and the other faster but not so precise and relies on the use of an evolutionary optimization algorithm to find the geometrical and electrical parameters that satisfy the problem constraints while performing the minimization of the power losses of the wind energy system over a long-term wind speed profile. For refined results, an adjustment of the analytical model based on output space-mapping has been implemented by comparison to the semi-analytical one associated to a barycenter method that allows easy exploitation of large amount of data available from the wind cycle. Comparative analysis have also been carried out through semi-analytical model and FE simulations for the optimal design of the BLDCPM generator found at the last iteration in the two level optimization approach.

Fig. 2 .

 2 Fig. 2. a) Geometric features of the BLDCPM generator and b) Semi-analytical simulation model implementation in MATLAB/Simulink environment

Fig. 4 .

 4 Fig. 4. Power flow in the wind energy conversion system

Fig. 5 .Fig. 6 .

 56 Fig. 5. Semi-analytical simulation model implementation in Matlab/Simulink environment

Fig. 7 .Fig. 8 .

 78 Fig. 7. Correction process of the analytical model by means of output space mapping

Fig. 9 .Fig. 10 .

 910 Fig. 9. Magnetic flux-line distribution and flux density representation in FE (a) and comparative FE-computed and semianalytically-modeled back-EMF waveforms of the optimal BLDCPM generator (b)

Table 1 .

 1 Wind turbine system design variables

	Variable	Notation	Type	Definition domain
	Cut-in wind speed [m/s]	𝑣 𝑖𝑛	c	[1÷4]
	Nominal wind speed [m/s]	𝑣 𝑛	c	[4÷20]
	Cut-off wind speed [m/s]	𝑣 𝑚𝑎𝑥	c	[20÷27]
	Number of pole pairs	𝑁 𝑝	d	{2,…,20}
	Stator bore diameter [mm]	𝐷 𝑠	c	[100÷500]
	Magnetic length [mm]	𝐿 𝑚	c	[50÷500]
	Air gap thickness [mm]	𝑔	c	[0.5÷5]
	Ratio length rotor/stator Peak magnetic induction in the airgap [T]	𝑟 𝑟𝑠 𝐵 ̂𝑔	c c	[1÷1.2] [0.5÷1]
	Peak magnetic induction in the rotor yoke [T]	𝐵 ̂𝑟𝑦	c	[0.6÷1.6]
	Peak magnetic induction in the stator yoke [T]	𝐵 ̂𝑠𝑦	c	[0.6÷1.6]
	Peak magnetic induction in the stator teeth [T]	𝐵 ̂𝑡ℎ	c	[0.6÷1.8]
	Current density [A/mm 2 ]	𝛿 𝑑𝑒𝑛𝑠	c	[0.5÷8]
	Ratio DC voltage/EMF	𝑘 𝑣	c	[0.5÷10]
	Commutation frequency [kHz]	𝑓 𝑠𝑤	c	[1÷30]
	DC bus voltage [V]	𝑉 𝑑𝑐	c	[48÷300]

Table 2 .

 2 Genetic algorithm control parameters

	Population size			500
	Number of generations			100*number of design variables
	Crossover Probability			0.8
	Mutation Rate			1/ number of design variables
	 Maximum current in the phase windings to avoid magnets demagnetization:
	𝐼 𝑅𝑀𝑆,𝑟 ≤ 𝐼 𝑑𝑒𝑚𝑎𝑔 3 ⁄		(15)
	 Rising time of the phase current:
	𝑡𝑖𝑚𝑒_𝐼 𝑅𝑀𝑆,𝑟 ≤	1 30 𝑓 𝑒𝑙𝑒	[s]	(16)
	 Relative hysteresis band-width of stator current:
	∆𝑖 𝑟 𝐼 𝑅𝑀𝑆,𝑟	≤ 0.1			(17)
	 Generator total mass:
	𝑀 𝑔𝑒𝑛_𝑡 ≤ 20 [kg]

Table 3 .

 3 Analytical and semi-analytical models comparison

Analytic with complete cycle Semi-analytic with barycenter method Semi-analytic with complete cycle

	No. of operating points	8,759	6	8,759
	Simulation time	< 1 [s]	≈ 16 [s]	≈ 2 [h]

Appendix

Wind Energy System Parameters

The optimal design parameters (in bold) of the wind energy system found at the last iteration in the two level approach are listed below in Table 4, along with several other parameters considered fixed during the optimization process: