Flavia Dory
email: flavia.dory@imbe.fr

Laurent Cavalli
email: laurent.cavalli@imbe.fr

Evelyne Franquet
email: evelyne.franquet@imbe.fr

Magalie Claeys-Bruno
email: magalie.claeys-bruno@imbe.fr

Benjamin Misson
email: benjamin.misson@mio.osupytheas.fr

Thierry Tatoni
email: thierry.tatoni@imbe.fr

Céline Bertrand
email: celine.bertrand@imbe.fr

Summer dynamics drive the microbial response to DOC additions in a high-altitude lake Running head: DOC additions on planktonic interactions

Keywords: DOC additions, phytoplankton-bacterioplankton relationship, high-altitude lakes, summer phytoplankton dynamics, co-limitation, mixotrophy

1. The predicted increase in allochthonous dissolved organic carbon (DOC) in high-altitude lakes is expected to alter the phytoplankton-bacterioplankton relationship. However, few studies address the influence of summer phytoplankton dynamics on planktonic responses to DOC additions.

2. We sampled natural plankton assemblages during two contrasting periods of summer in a high-altitude lake in the French Alps and subjected them to DOC inputs and nutrient enrichments under two light conditions (dark or light) and two temperature conditions (10°C or 18°C).

3. Our results indicate that DOC use by bacteria differs over the summer, depending on the availability of autochthonous DOC and the nutrient limitation. DOC was consumed by bacteria more in early summer but was assimilated into biomass more in late summer. This pattern likely arose from the greater availability of phytoplankton-derived DOC in late summer, reducing the need for alternative carbon sources in late summer, when phytoplankton biomass was high. We found greater competition between bacteria and phytoplankton in late summer after DOC addition, linked to the summer nutrient limitation pattern. Mixotrophic taxa were stimulated after DOC additions both in early summer and in late summer. Our study thus highlights a differential response depending on the timing of summer DOC inputs.

4. The global changes forecast for the French Alps should increase heterotrophic and mixotrophic processes in planktonic communities of shallow high-altitude lakes with vegetated catchments. This experimental study provides insights that will be useful in predicting ecological trajectories and in refining predictions of sentinel lakes' responses to global changes.

Introduction

Dissolved organic carbon (DOC) inputs associated with terrestrial dissolved organic matter (DOM) have substantially increased in recent decades in lake ecosystems, and will likely continue to evolve [START_REF] Solomon | Ecosystem consequences of changing inputs of terrestrial dissolved organic matter to lakes : Current knowledge and future challenges[END_REF]. DOC acts as a major regulator of lakes' functioning [START_REF] Williamson | Dissolved organic carbon and nutrients as regulators of lake ecosystems : Resurrection of a more integrated paradigm[END_REF]. DOC concentration and quality have been shown to alter water transparency and thermal stratification [START_REF] Solomon | Ecosystem consequences of changing inputs of terrestrial dissolved organic matter to lakes : Current knowledge and future challenges[END_REF], modify pH and alkalinity [START_REF] Evans | Long-term increases in surface water dissolved organic carbon : Observations, possible causes and environmental impacts[END_REF] and attenuate harmful ultraviolet radiation in lakes [START_REF] Warner | Differences in the Effects of Storms on Dissolved Organic Carbon (DOC) in Boreal Lakes during an Early Summer Storm and an Autumn Storm[END_REF]. By changing the lakes' pool of available nutrients, DOC acts as an important driver of bacterioplankton biomass [START_REF] Schulhof | Sierra Nevada mountain lake microbial communities are structured by temperature, resources and geographic location[END_REF], phytoplankton biomass [START_REF] Hazukova | Under Ice and Early Summer Phytoplankton Dynamics in Two Arctic Lakes with Differing DOC[END_REF][START_REF] Isles | Trade-offs Between Light and Nutrient Availability Across Gradients of Dissolved Organic Carbon Lead to Spatially and Temporally Variable Responses of Lake Phytoplankton Biomass to Browning[END_REF] and their relationships in lake ecosystems. Allochthonous DOC inputs are consequently directly related to the degree of net heterotrophy in lakes [START_REF] Jansson | Links between Terrestrial Primary Production and Bacterial Production and Respiration in Lakes in a Climate Gradient in Subarctic Sweden[END_REF]. Through its effects on planktonic processes, allochthonous DOC regulates energy transfer to higher trophic levels [START_REF] Jansson | Allochthonous Organic Carbon and Phytoplankton/Bacterioplankton Production Relationships in Lakes[END_REF], food web dynamics and lake metabolism [START_REF] Mitrovic | Allochthonous dissolved organic carbon in river, lake and coastal systems : Transport, function and ecological role[END_REF]. However, its influence depends on the trophic nature of lake ecosystems [START_REF] Dorado-García | Quantification of Carbon and Phosphorus Co-Limitation in Bacterioplankton : New Insights on an Old Topic[END_REF].

In oligotrophic ecosystems, bacteria have an inherent advantage over phytoplankton in assimilating inorganic nutrients [START_REF] Currie | A comparison of the abilities of freshwater algae and bacteria to acquire and retain phosphorus1[END_REF][START_REF] Jansson | Bacterioplankton growth and nutrient use efficiencies under variable organic carbon and inorganic phosphorus ratios[END_REF] but their growth is usually limited by C (Fouilland et al., 2014). Inputs of allochthonous DOC can increase bacterioplankton biomass and lead to more competitive dynamics between bacteria and phytoplankton for inorganic nutrients (Carney et al., 2016a;[START_REF] Hitchcock | Different resource limitation by carbon, nitrogen and phosphorus between base flow and high flow conditions for estuarine bacteria and phytoplankton[END_REF]. These changes benefit mixotrophs, who acquire organic carbon and/or mineral nutrients from their bacterial prey (Caron, 1994), allowing them to eliminate their main competitors for inorganic nutrients [START_REF] Thingstad | On the Strategy of 'Eating Your Competitor' : A Mathematical Analysis of Algal Mixotrophy[END_REF]. As different mixotrophic taxa have different ingestion rates (Flynn et al., 2018), the types of mixotrophs that constitute the communities and their proportions could directly modify predation pressure on bacteria after allochthonous DOC inputs.

However, it has also been observed in temperate lakes that autochthonous DOC derived from phytoplankton is preferentially consumed and incorporated into biomass over allochthonous DOC, owing to its greater accessibility and nutritional quality [START_REF] Guillemette | Differentiating the degradation dynamics of algal and terrestrial carbon within complex natural dissolved organic carbon in temperate lakes[END_REF]. The quantity of phytoplankton biomass and primary production, which together regulate the bioavailability of autochthonous organic carbon, condition the C-limitation of bacteria and thus bacterial abundance and production in lakes [START_REF] Ejarque | Climate-induced hydrological variation controls the transformation of dissolved organic matter in a subalpine lake[END_REF][START_REF] Gasol | Comparative analyses in aquatic microbial ecology : How far do they go?[END_REF][START_REF] Kritzberg | Does autochthonous primary production drive variability in bacterial metabolism and growth efficiency in lakes dominated by terrestrial C inputs?[END_REF][START_REF] Morán | Total and phytoplankton mediated bottom-up control of bacterioplankton change with temperature in NE Atlantic shelf waters[END_REF]. As an illustration, in oligotrophic ecosystems where phytoplankton-derived organic carbon was sufficient to support bacterial demands, bacteria did not experimentally respond to C additions like sucrose because of primary limitation by inorganic nutrients [START_REF] Dorado-García | Quantification of Carbon and Phosphorus Co-Limitation in Bacterioplankton : New Insights on an Old Topic[END_REF]. The quantity of phytoplankton biomass, by regulating the quantity of autochthonous DOC bioavailable for bacteria, could therefore modify the microbial response to allochthonous DOC inputs. In addition, evidence suggests that the nature of the molecules liberated in the water differs among phytoplankton species (Romera-Castillo et al., 2010;Sarmento & Gasol, 2012) and the uptake of autochthonous DOC by bacteria varies according to the phytoplankton species composing the bulk of the community (Sarmento et al., 2013). Thus, phytoplankton biomass and composition, by exercising a dual bottom-up and top-down control over bacteria, could impact the microbial response to allochthonous DOC inputs in oligotrophic lakes. However, little is known about the mechanisms through which phytoplankton biomass and composition regulate the microbial response to DOC additions in oligotrophic ecosystems.

In high-altitude lakes, DOC concentrations are generally low (< 1 mg C/L, see [START_REF] Laurion | Attenuation of ultraviolet radiation in mountain lakes : Factors controlling the amongand within-lake variability[END_REF], and these ecosystems could respond significantly to increased flux from the surrounding catchments. In mountain lakes, most DOC is of autochthonous origin during summer [START_REF] Reche | Photoreactivity of Dissolved Organic Matter from High-Mountain Lakes of Sierra Nevada, Spain. Arctic[END_REF][START_REF] Sadro | The effect of an extreme rain event on the biogeochemistry and ecosystem metabolism of an oligotrophic high-elevation lake[END_REF]. However, the observed upward shift in the treeline [START_REF] Elliott | Multiscale Influences of Climate on Upper Treeline Dynamics in the Southern Rocky Mountains, USA : Evidence of Intraregional Variability and Bioclimatic Thresholds in Response to Twentieth-Century Warming[END_REF][START_REF] Harsch | Are treelines advancing? A global meta-analysis of treeline response to climate warming[END_REF] and the predicted increase in extreme precipitation events [START_REF] Ipcc | Climate change 2013 : The Physical Science Basis[END_REF] are likely to increase allochthonous DOC fluxes to high-altitude lakes. Recent studies highlight the sensitivity of mountain lakes to climate changes [START_REF] Moser | Mountain lakes : Eyes on global environmental change[END_REF][START_REF] Sadro | Climate warming response of mountain lakes affected by variations in snow[END_REF][START_REF] Smits | Snowpack determines relative importance of climate factors driving summer lake warming[END_REF]. Higher DOC values associated with wetter periods were observed between 2015 and 2017 in subalpine [START_REF] Ejarque | Climate-induced hydrological variation controls the transformation of dissolved organic matter in a subalpine lake[END_REF] and mountain lakes [START_REF] Moser | Mountain lakes : Eyes on global environmental change[END_REF]. This increased carbon flux may cause dramatic changes in mountain lakes' metabolism [START_REF] Sadro | The effect of an extreme rain event on the biogeochemistry and ecosystem metabolism of an oligotrophic high-elevation lake[END_REF].

In high-altitude lakes, rapid environmental changes usually induce rapid modifications of phytoplankton community composition over a short period [START_REF] Tiberti | Ecological dynamics of two remote alpine lakes during ice-free season[END_REF][START_REF] Ventura | The main features of seasonal variability in the external forcing and dynamics of a deep mountain lake (Redó, Pyrenees)[END_REF]. For example, [START_REF] Jacquemin | Growth rate of alpine phytoplankton assemblages from contrasting watersheds and Ndeposition regimes exposed to nitrogen and phosphorus enrichments[END_REF] observed changes in the structure and composition of phytoplankton communities, associated with an evolution of limitation patterns, during summer in alpine lakes. Due to poor light conditions, mixotrophic species dominate autotrophic ones during the ice-covered period [START_REF] Leppäranta | Ice-Covered Lakes Environment[END_REF] and are still dominant in phytoplankton assemblages in early summer [START_REF] Waibel | Importance of mixotrophic flagellates during the ice-free season in lakes located along an elevational gradient[END_REF]. Rapid changes in chemical parameters are also conditioning biomass dynamics in high-altitude lakes [START_REF] Bergström | Changes in nutritional quality and nutrient limitation regimes of phytoplankton in response to declining N deposition in mountain lakes[END_REF][START_REF] Oleksy | The role of warm, dry summers and variation in snowpack on phytoplankton dynamics in mountain lakes[END_REF]. A bimodal pattern in phytoplankton biomass dynamics has been observed, with a first peak immediately after the snowmelt and a second one occurring at the end of the summer period [START_REF] Tiberti | Ecological dynamics of two remote alpine lakes during ice-free season[END_REF]. Since phytoplankton is an important regulator of bacteria in ecosystems receiving few allochthonous inputs, phytoplankton communities' seasonal dynamics in terms of biomass and composition should regulate the impact of DOC inputs on PBR in high-altitude lakes. However, few studies address the influence of summer phytoplankton dynamics on PBR in response to DOC additions in high-altitude lakes.

This study examines how shifts in phytoplankton community structure and composition impact the microbial response to DOC additions. We sampled natural plankton assemblages during two contrasting periods of summer in a high-altitude lake in the French Alps. These samples received DOC inputs in the form of glucose and nutrient enrichments (N and P) under controlled laboratory conditions in microcosms. To characterize the influence of phytoplankton on bacteria, the assemblages were subjected to two light conditions: a dark: light cycle condition (LIGHT) and a total darkness condition (DARK). The planktonic organisms were maintained at two temperatures, one reproducing the average temperature of high-altitude lakes during summer (10°C) and the other that accelerates metabolic processes (18°C). Firstly, we hypothesised that the effect of DOC additions on planktonic communities depends on the initial phytoplankton biomass. This means that DOC additions should stimulate bacteria more in early summer when the initial phytoplankton biomass is expected to be low. Secondly, we assumed that the communities' response to DOC additions depends on the initial phytoplankton composition. This means that mixotrophs should benefit less from DOC additions in late summer, when they are expected to represent a lower proportion of the initial community than autotrophs.

Methods

Study area and sampling

Water for experiments was sampled in Lake Cordes, an oligotrophic high-mountain lake located in the French Alps, adjacent to the Queyras regional natural park. enriched with N and P. N was added as NH4NO3 sufficient to increase N concentrations to 335 μg/L and P was added as KH2PO4 sufficient to increase P concentrations to 35 μg/L. In LIGHT conditions, the microcosms were placed under a circadian cycle (Light: dark cycle = 14:10), at a fixed irradiance (45 ± 2 μmol m -2 s -1 ). In DARK conditions, the microcosms were placed in the dark in growth chambers, surrounded by aluminium, to target heterotrophic processes while minimising the influence of autotrophs. Finally, the microcosms were subjected to temperatures of either 10°C, the average summer temperature, or 18°C, sufficient to accelerate the metabolic processes of organisms without representing a threat to the planktonic organisms [START_REF] Jacquemin | Growth rate of alpine phytoplankton assemblages from contrasting watersheds and Ndeposition regimes exposed to nitrogen and phosphorus enrichments[END_REF]. Thus, the experimental set-up consisted of a 4

x 2 x 2 x 2 factorial design (32 treatments in triplicate) implemented for 10 days, as in our previous study [START_REF] Dory | Microbial consortia in an ice-covered high-altitude lake impacted by additions of dissolved organic carbon and nutrients[END_REF], allowing the estimation of the coefficients of the interaction effects.

Physico-chemical analysis

Average in situ temperatures were calculated from the mean temperatures measured every metre on the water column during the sampling dates (hourly observations). Subsamples for dissolved inorganic nitrogen (DIN = NH4 + + NO2 + + NO3 2-), soluble reactive phosphorus (SRP = PO4 2-), and dissolved organic carbon (DOC) concentrations were filtered through pre-combusted 25 mm glass filters (Whatman GF/F, 0.7 mm) prior to launching the experiments. The dissolved fraction for DIN and SRP was stored in a 125 ml HDPE bottle, and frozen (-18°C) until analysis. DIN and SRP were determined by ionic chromatography (Metrohm, 930 Compact IC Flex combined with 863 Compact Autosampler). Dissolved organic carbon was measured under initial conditions and at the end of the experiments.

Subsamples stored in 24 ml pre-combusted (4 hr at 450℃) glass tubes (Wheaton equipped with Teflon/silicone septa) and preserved in 30 μl of sodium azide solution (1 M NaN3) at +4℃. DOC concentration was determined using a TOC-VCSH analyzer (Shimadzu, TOC-V).

Consumed DOC is the difference between the initial DOC concentrations after carbon additions and the final DOC concentrations measured at the end of the experiments.

Biological variables

Phytoplankton

Phytoplankton were enumerated and identified via microscopy. Phytoplankton communities were analysed under initial conditions and at the end of the experiments. The samples destined for phytoplankton composition analysis were fixed with alkaline Lugol solution (0.5%) and stored in 150 ml HDPE bottles at +4℃. Phytoplankton counts were performed according to the [START_REF] Utermöhl | Methods of collecting plankton for various purposes are discussed[END_REF] method, at 40-fold magnification under an inverted microscope (Olympus IX 70). Phytoplankton samples were identified at genus level and species level when possible, using appropriate taxonomic guides.

We checked for any development of predators in our microcosms by estimating ciliate abundances via the Utermöhl method, under initial conditions and at the end of the experiments.

Picoplankton

Sub-samples of 1.5 ml were taken under initial conditions and thereafter every 2 experimental days in the microcosms for picoplankton analyses by flow cytometry.

Subsamples were fixed with glutaraldehyde (0.25% final concentration) and stored at -80℃ until flow cytometry analysis. Picoplankton was characterised and enumerated using an Accuri C6 flow cytometer equipped with a blue laser (488 nm) and using BD Accuri CFlow Plus Analysis software (BD-Biosciences). For picophytoplankton, 500 µl of sample were run at fast speed (66 µl/min). Picophytoplankton were identified according to size (FSC), complexity (SSC) and fluorescence (emissions in the orange and red wavelength ranges, respectively 585 ± 20 and >670 nm). Non-fluorescent polystyrene microspheres (Flow Cytometry Size Calibration Kit, Thermo Fisher Scientific) were used as a size standard. Flow cytometer analysis distinguished between two picophytoplanktonic groups. Small cells (<2 μm) with high orange fluorescence and low complexity were classified as phycoerythrin-rich picocyanobacteria (picocyanobacteria). A picoeukaryote group was identified by its high red and low orange fluorescence, small size (<2 μm) but higher complexity than the picocyanobacteria. For heterotrophic prokaryotic plankton (HPP), samples were stained with 1:10,000 (vol/vol) SYBR® Green II and incubated 20 min in darkness. 50 µl of stained samples were run at medium speed (35 µl/min). We checked for any double-counting in cytometry and microscopy by calculating the average size of each picophytoplankton and phytoplankton group, as described in [START_REF] Dory | Microbial consortia in an ice-covered high-altitude lake impacted by additions of dissolved organic carbon and nutrients[END_REF]. HPP were identified by their small size (low FSC), low complexity (low SSC), high green fluorescence (530 ± 15 nm), and lack of red (> 670 nm) fluorescence. Picoplankton data were acquired and analysed using BD Accuri CFlow Plus Analysis software (BD-Biosciences).

Cellular carbon biomass calculation

Abundances were transformed into carbon content based on the literature. Cell abundance (cells/ml) of HPP was converted to biomass (μg C/L) using 20 fg C/cell as constant conversion factor [START_REF] Ducklow | Bacterial production and biomass in the oceans[END_REF][START_REF] Linacre | Distribution pattern of picoplankton carbon biomass linked to mesoscale dynamics in the southern gulf of Mexico during winter conditions[END_REF]. A conversion factor of 237 fg C/cell was used for picocyanobacteria [START_REF] Gerea | Grazing impact and prey selectivity of picoplanktonic cells by mixotrophic flagellates in oligotrophic lakes[END_REF] and a conversion factor of 183 fg C/µm 3 for picoeukaryotes [START_REF] Lagaria | Phytoplankton Response to Saharan Dust Depositions in the Eastern Mediterranean Sea : A Mesocosm Study[END_REF]. For phytoplankton, biovolume was estimated by shape assimilation to defined geometric forms and direct measurement of the main cell dimensions. Mean biovolume was calculated for each class of phytoplankton and then converted into biomass using the particular carbon content defined for each class by [START_REF] Wetzel | Composition and Biomass of Phytoplankton[END_REF].

Data analysis

Quantitative analysis

For initial conditions, all biological and physico-chemical variables were checked for normality using the Shapiro-Wilk test [START_REF] Shapiro | An Analysis of Variance Test for Normality (Complete Samples)[END_REF]. Mean values were compared between early summer and late summer using Student or Welch t-tests. To test the DOC addition effect on all response variables (phytoplankton biomass, HPP biomass, consumed DOC and mixotrophs/autotrophs ratio) at the end of the experiments, and to determine whether DOC additions interacted with the other experimental factors (nutrients, temperature, light and campaign), Design of Experiments (DOE) was used. Design of Experiments combines mathematical and statistical techniques that optimise the relevance of the data obtained by quantifying the relationship between output and input variables [START_REF] Box | Statistics for experimenters[END_REF][START_REF] Montgomery | Design and Analysis of Experiments[END_REF]. Contrary to a one-factor-at-a-time approach, DOE involves simultaneous variation of all the factors so that their effects can be estimated by considering the interactions between them. We considered the result of each experiment to be a linear combination of the main effects and interaction effects among the five factors (interaction order = 4, bijklm), considering two levels for each experimental factor. Thus, the linear models were performed three times for each combination of two glucose additions. This model could be written as follows:

Y = b0 + biXi + bijXiXj + bijkXiXjXk + bijklXiXjXkXl + bijklmXiXjXkXlXm i = 1 to 5 j = 1 to 5, j > i k = 1 to 5, k > j l =

Multivariate analysis

We performed multivariate analyses on the phytoplankton biomass to detect any changes in phytoplankton community structure between early summer and late summer under initial conditions, and between treatments at the end of the experiments. Multivariate analyses were performed with the vegan package on R software (v. 3.6.3). Permutational multivariate analysis of variance (PERMANOVA) with 999 permutations (p = 0.05) on the Bray-Curtis dissimilarity matrix (ADONIS function in R) was used to test the hypothesis that the campaign (under initial conditions) or DOC additions (at the end of the experiments) structured the distribution of phytoplankton communities.

Results

Initial conditions

Initial concentrations of dissolved organic carbon (DOC), soluble reactive phosphorus (SRP) and dissolved inorganic nitrogen (DIN) were low in both campaigns (Table 1).

Average DOC concentrations were significantly lower in early summer (0.61 ± 0.02 mg/L) than in late summer (1.04 ± 0.09 mg/L) (t = -9.4, df = 3.53, p = 0.001). Average SRP concentrations were low (below 10 µg/L) and were not significantly different between campaigns (t = -0.44, df = 7.9, p = 0.67). Average DIN concentrations were significantly higher in early summer (0.60 ± 0.06 mg/L) than in late summer (0.15 ± 0.04 mg/L) (t = 16.22, df = 10.42, p < 0.001). Water temperature was significantly lower in early summer (8.9°C) than in late summer (14.6°C) (t = -99.56, df = 15.62, p < 0.001).

Concerning biotic parameters, the initial HPP biomass did not significantly differ between early summer and late summer (t = 1.61, df = 7.96, p = 0.14), being close to 17 µg C/L in both campaigns. Initial phytoplankton biomass was almost 7-fold greater in late summer than in early summer (t = -17.45, df = 6.19, p < 0.001). The initial phytoplankton community differed significantly between campaigns (permanova, F1,9 = 214, p = 0.004). In early summer, diatoms dominated the community (37%), followed by chrysophytes (23%), cryptophytes (17%), dinoflagellates (15%) and picocyanobacteria (6%). In late summer, diatoms were even more predominant (47%), followed by picocyanobacteria (22%), chrysophytes (16%) and dinoflagellates (13%). The mixotrophs/autotrophs (M/A) ratio was higher in early summer (1.13 ± 0.44) than in late summer (0.45 ± 0.05) (t = 3.04, df = 3, p = 0.05). Finally, ciliates were almost thirty-fold more abundant in late summer than in early summer (t = -3.00, df = 11.19, p = 0.01).

Plankton responses to experiments in microcosms

Based on the linear model, the response of all biotic variables (phytoplankton biomass, HPP biomass, consumed DOC and M/A ratio) to experiments varied between early summer and late summer (CAMP effect, Table S1). Moreover, CAMP effect interacted with at least three other factors for each variable, which means that the effects of DOC, nutrients, light, and temperature on planktonic communities varied between early summer and late summer.

Consumed DOC

At the end of the experiments, DOC was consumed more in the GLUCOSE treatments (2C, 4C, 6C) than in the C-control treatments (0C), in both early (Figure 1) and late summer (Figure 1). The exceptions were treatment 6C0NP at 10°C_LIGHT in early summer, and treatments 4C0NP and 6C0NP at 10°C (DARK and LIGHT) in late summer. DOC was consumed more in early summer than in late summer with glucose added at 2 mg/L, 4 mg/L and 6 mg/L (DOC*CAMP interaction, Table S1), the average consumed DOC in all GLUCOSE treatments reaching 49.2 % in early summer and 13.9 % in late summer. For example, in the 6CNP treatment, the average consumed DOC reached 5.03 mg/L in early summer but only 2.63 mg/L in late summer. In both campaigns, the maximum values for consumed DOC were reached at 18°C_DARK.

DOC was consumed more in NP treatments than in 0NP treatments when glucose was added at 2 mg/L, 4 mg/L, and 6 mg/L (DOC*NUT interaction, Table S1). DOC was consumed more at 18°C than at 10°C when glucose was added at 4 mg/L and 6 mg/L (DOC*T interaction, Table S1).

Finally, DOC was consumed more in DARK conditions than in LIGHT conditions, when glucose was added at 4 mg/L and 6 mg/L (DOC*LIGHT interaction, Table S1). This effect was higher in late summer than in early summer (DOC*LIGHT*CAMP interaction, Table S1).

HPP biomass

A fivefold interaction was detected on HPP biomass (COD*NUT*LU*T°*CAMP, Table S1), particularly on the 8 th day for all glucose concentrations.

HPP biomass dynamic differed between early and late summer: in early summer, HPP biomass rapidly decreased in almost all treatments except the CNP treatments (Figure 2). In late summer however, HPP biomass increased in almost all treatments, including controls (0CNP and 0C0NP) especially in the DARK conditions. A smaller and briefer increase in HPP biomass in the controls was observed in the LIGHT conditions (Figure 2).

Glucose additions stimulated HPP biomass more in late summer than in early summer (COD*CAMP, Table S1) from the 4 th experimental day until the end of the experiments.

In early summer, under 10°C_DARK, 18°C_DARK and 10°C_LIGHT conditions, HPP biomass increased in the CNP treatments until the 4 th or 6 th day compared to 0CNP, then declined until the end of the experiment (Figure 2). At 18°C_LIGHT, HPP biomass increased in all the CNP treatments until the 2 nd day and then declined; however, biomass remained higher in the CNP treatments than in the 0CNP treatments.

In late summer, at 10°C_DARK, HPP biomass increased more in all the CNP treatments than in the 0CNP treatment and continued to increase until the end of the experiment (Figure 2). Under 18°C_DARK, 10°C_LIGHT and 18°C_LIGHT conditions, HPP biomass increased more in the CNP treatments than in the 0CNP treatment, but only until the 4 th or 6 th day, then declined until the end of the experiments. In 0NP treatments, glucose additions stimulated HPP biomass only at 18°C_DARK.

Shifts in phytoplankton community biomass, structure and composition

Total phytoplankton biomass differed strongly between campaigns (CAMP effect, Table S1), and was higher in late summer than in early summer in all conditions and treatments (Figure 3). Nutrient addition significantly stimulated phytoplankton biomass in both campaigns (NUT effect, Table S1). A quadruple interaction was detected on phytoplankton biomass at the end of the experiments (NUT*LU*T°*CAMP, Table S1).

However, DOC additions had almost no effect on phytoplankton biomass, neither alone nor in interaction. At the end of the experiments, DOC additions significantly modified community composition in early summer, but DOC addition effect was weak (permanova, F1,94 = 5.19, p = 0.004). DOC additions significantly didn't modified community composition in late summer (permanova, F1,94 = 0.94, p = 0.41). However, phytoplankton community composition differed significantly among conditions and treatments, both in early summer (permanova, F31,64 = 10.83, p < 0.001) and in late summer (permanova, F31,64 = 17.02, p < 0.001) (Figure 3). Based on the linear model, a quadruple interaction was detected on the mixotrophs/autotrophs (M/A) ratio at the end of the experiments (DOC*NUT*LU*CAMP, Table S1), when glucose was added at 4 mg/L and 6 mg/L.

Concerning autotrophic taxa, diatoms mainly consisted of

In early summer, the relative and absolute biomass of cryptophytes and dinoflagellates increased with DOC additions in DARK conditions, both in 0NP and in NP treatments (Figure 3 and Figure S2). Consequently, the proportion of mixotrophs increased in DARK conditions after DOC additions, with an accentuated effect in NP treatments where DOC was added at 4 and 6 mg/L, at 10°C and 18°C (Figure S1). In LIGHT conditions, the relative biomass of cryptophytes, chrysophytes and dinoflagellates increased with DOC additions in the 0NP treatments at 10°C, and the relative and absolute biomass of chrysophytes increased with DOC additions in the 0NP treatments at 18°C (Figure S3). Consequently, the proportion of mixotrophs increased with DOC additions in LIGHT conditions in the 0NP treatments (Figure S1).

In late summer, the relative and absolute biomass of choanoflagellates increased with DOC additions in DARK conditions at 18°C, mainly in the NP treatments (Figure 3 and

Figure S4

). The relative and absolute biomass of cryptophytes increased with DOC additions in NP treatments at 18°C_DARK. Thus, the proportion of mixotrophs increased after DOC additions in DARK conditions at 18°C in NP treatments (Figure S1). In LIGHT conditions, the relative biomass of chrysophytes increased with DOC additions in 0NP treatments, and their absolute and relative biomass increased with DOC additions at 18°C in NP treatments (Figure S5). The relative and absolute biomass of dinoflagellates increased with DOC additions at 18°C in NP treatments. Thus, the proportion of mixotrophs increased in LIGHT conditions with DOC additions, at 10°C in 0NP treatments and at 18°C in NP treatments.

(Figure S1).

Finally, the biomass of autotrophs decreased with DOC in one condition in early summer (average decrease of 14.4 µg C/l compared to 0C treatments, data not shown) and in two conditions in late summer (average decrease of 45.8 µg C/l compared to 0C). The biomass of mixotrophs increased with DOC in three conditions in both campaigns, but the average increase compared to 0C treatments was higher in late summer (31.6 µg C/l) than in early summer (7.8 µg C/l).

Ciliate abundance

In early summer, ciliate abundance increased in the 4CNP and 6CNP treatments at 10°C_DARK, and in all the CNP treatments at 18°C_DARK (Figure S6). In late summer, ciliate abundance increased in the 4CNP treatments at 10°C_LIGHT, and in the 6CNP treatments at 18°C_LIGHT (Figure S6). There was no difference in DOC-stimulated increase in ciliate abundance between early summer and late summer, except in the dark, where ciliates increased more in early summer than in late summer in the 4CNP (p = 0.018) and 6CNP treatments (p = 0.02).

Discussion

Dissolved organic carbon (DOC) acts as a major control of high-altitude lakes' functioning [START_REF] Moser | Mountain lakes : Eyes on global environmental change[END_REF]. Allochthonous DOC can be assimilated by microbial organisms, changing interactions between them. However, the summer dynamics of phytoplankton biomass and composition could also impact planktonic responses to DOC inputs. Our study aimed to assess how changes in the phytoplankton community between early summer and late summer modify these microbial responses.

Differential prokaryotic assimilation of DOC over the summer

In our microcosms, bacterial response was higher when glucose and nutrients were added jointly than after glucose addition alone. Moreover, HPP were able to develop only when provided with inorganic nutrients, especially in late summer. These two results suggest limitation primarily by nutrients and co-limitation by C of bacteria. This pattern of colimitation has already been observed in high-latitude lakes [START_REF] Dorado-García | Quantification of Carbon and Phosphorus Co-Limitation in Bacterioplankton : New Insights on an Old Topic[END_REF] and in Lake Cordes in the ice-covered period [START_REF] Dory | Microbial consortia in an ice-covered high-altitude lake impacted by additions of dissolved organic carbon and nutrients[END_REF]. Both the present study and the previous one found evidence that bacterioplankton in Lake Cordes were co-limited by nutrients and C from April to August.

We observed that glucose was consumed more in early summer than in late summer (Figure 4), whatever the conditions of temperature and light and the nutrient treatments. Initial DOC concentrations were lower in early summer (0.61 mg/l) than in late summer (1.04 mg/l).

As the magnitude of plankton response to nutrient additions depends on the nutrient limitation [START_REF] O'donnell | Nitrogen and phosphorus colimitation of phytoplankton in Lake Baikal : Insights from a spatial survey and nutrient enrichment experiments[END_REF], it could be that the greater glucose consumption observed in early summer resulted in greater C limitation of bacteria. Initial DOC concentrations measured in both campaigns varied with phytoplankton biomass, DOC concentrations being higher when the phytoplankton biomass was higher in late summer. The contrasting glucose consumption between campaigns could also be related to changes in DOC lability over the summer.

Phytoplankton biomass was far lower in early summer (16.25 µg/l) than in late summer (111.94 µg/l), and the increased phytoplankton biomass could result from greater availability of autochthonous DOC in late summer [START_REF] Ejarque | Climate-induced hydrological variation controls the transformation of dissolved organic matter in a subalpine lake[END_REF]. This interpretation of the phytoplankton biomass influence is also supported by the finding of greater differences in DOC consumed in DARK versus LIGHT conditions in late summer than in early summer.

Our findings are consistent with the conclusions of [START_REF] Kritzberg | Influence of dissolved organic matter source on lake bacterioplankton structure and functionimplications for seasonal dynamics of community composition[END_REF], namely that the bacterial growth efficiency and production were higher with amendments of algae leachates than with more refractory substrates in oligotrophic lakes. In addition, it has been established that phytoplankton-derived DOC is more quickly and efficiently consumed by bacteria than allochthonous DOC [START_REF] Guillemette | Differentiating the degradation dynamics of algal and terrestrial carbon within complex natural dissolved organic carbon in temperate lakes[END_REF]. To conclude, in early summer, HPP actively consumed the glucose added to the microcosms likely because phytoplankton-derived DOC was low. In late summer, phytoplankton-derived DOC was more available and HPP probably needed less glucose, which resulted in lower glucose consumption.

Based on our linear model, glucose in interaction with nutrient additions was consumed more in early summer than in late summer, but glucose additions stimulated HPP biomass more in late summer than in early summer (Figure 4). The possibility that the discrepancies regarding glucose consumption and HPP biomass production are related to a top-down regulation of bacteria by predators in our microcosms cannot be excluded. In fact, ciliates and mixotrophs developed in the microcosms after glucose additions, and a previous study under the same experimental conditions demonstrated the strong influence of predator development on the bacterial response to glucose [START_REF] Dory | Microbial consortia in an ice-covered high-altitude lake impacted by additions of dissolved organic carbon and nutrients[END_REF]. However, biomasses measurements on the 4 th experimental day confirm that DOC was assimilated by HPP more in late summer. Seasonal modifications in bacterial communities' composition have previously been described in oligotrophic lakes, linked to qualitative and quantitative changes in allochthonous or autochthonous organic substrates [START_REF] Kritzberg | Influence of dissolved organic matter source on lake bacterioplankton structure and functionimplications for seasonal dynamics of community composition[END_REF]. In our study, lake conditions differed strongly between early summer and late summer, as demonstrated by the campaign effect detected by the linear model. In early summer, frequent storms associated with high turbidity likely constituted stressful environmental conditions for heterotrophic bacteria. Such environmental conditions have been linked to increased respiration of dissolved organic carbon by heterotrophic bacteria in high-altitude lakes [START_REF] Sadro | The effect of an extreme rain event on the biogeochemistry and ecosystem metabolism of an oligotrophic high-elevation lake[END_REF]. Thus, in our experiments, the bacterial metabolism probably changed over summer, related to the increased stability of environmental conditions and the more available autochthonous DOC in late summer. Unfortunately, our results do not permit us to determine whether the observed change was due to a taxonomic modification of the bacterial community, a functional modification of the bacterial community, or both.

In summary, our results indicate that DOC was consumed by bacteria more in early summer than in late summer but was assimilated more in late summer. In agreement with our first hypothesis, these seasonal changes in bacterial metabolism could be linked to environmental changes, especially phytoplankton biomass dynamics over the summer.

Changes in competition and predation after glucose addition over the summer

Our results indicate more competitive processes for inorganic nutrients between bacteria and phytoplankton in late summer in the GLUCOSE treatments. This competition resulted in a greater decrease in autotroph biomass and a greater increase in mixotroph biomass in late summer after glucose additions. The latter was likely related to the decline in HPP biomass observed from the 4th experimental day. In addition, we observed a decrease in initial DIN concentrations over the summer (Figure 4), consistent with the findings of [START_REF] Jacquemin | Growth rate of alpine phytoplankton assemblages from contrasting watersheds and Ndeposition regimes exposed to nitrogen and phosphorus enrichments[END_REF] on the evolving nutrient limitation pattern in Lake Cordes during summer 2016. Our results support the findings of [START_REF] Carney | Lotic bacterioplankton and phytoplankton community changes under dissolved organic-carbon amendment : Evidence for competition for nutrients[END_REF], who observed increased competition between bacteria and phytoplankton depending on limitation by inorganic nutrients in mesocosms. In our microcosms, it is therefore possible that the more pronounced increase in HPP biomass in the DARK conditions in late summer than in early summer can also be explained by reduced competition with phytoplankton for nutrients in the DARK conditions.

Based on the linear model, our results indicate that top-down predatory control by ciliates and mixotrophs increased after glucose additions, both in early summer and in late summer. In phytoplankton communities, we observed differences in the stimulation of the different mixotrophs, depending on light and temperature conditions, between early summer and late summer. We were able to identify common trends in the relative increase in mixotrophic groups between early and late summer: chrysophytes were consistently stimulated more than autotrophs after glucose additions only in the LIGHT treatments, while choanoflagellates were consistently stimulated more by glucose additions in the DARK treatments. [START_REF] Rottberger | Influence of nutrients and light on autotrophic, mixotrophic and heterotrophic freshwater chrysophytes[END_REF] highlighted the inability of the chrysophyte species Dinobryon divergens to develop in the dark through prey ingestion alone. However, this earlier study also pointed out major differences in general nutritional preferences between different mixotrophs. In our microcosms, all species of chrysophytes were unable to develop in the dark through prey ingestion alone, whatever the campaign. Our results therefore indicate that the nutritional strategy of chrysophytes in Lake Cordes remains relatively stable over the summer.

In our microcosms, the biomass of cryptophytes increased mainly in early summer in the DARK conditions after glucose additions. By contrast, in late summer cryptophytes increased only in relative biomass. It is therefore possible that a change in the nutritional preferences of cryptophytes occurs between early summer and late summer. Light availability has been shown to be a crucial factor in the proportions of mixotrophs in high-altitude lakes.

In these ecosystems, the highest proportion of mixotrophs is usually observed after snowmelt, because the mixotrophic strategy is advantageous under ice-cover, when nutrients and light are limiting factors [START_REF] Waibel | Importance of mixotrophic flagellates during the ice-free season in lakes located along an elevational gradient[END_REF]. A recent microcosm study on Lake Cordes demonstrated that under-ice species of cryptophytes were able to develop in the dark by ingesting bacterial prey [START_REF] Dory | Microbial consortia in an ice-covered high-altitude lake impacted by additions of dissolved organic carbon and nutrients[END_REF]. Conversely, other studies positioned cryptophytes towards the autotrophic end of an increasing trophic state gradient [START_REF] Saad | Influence of lake trophic conditions on the dominant mixotrophic algal assemblages[END_REF]. These conclusions highlight the controversy surrounding the nutritional strategies of cryptophytes, which may differ in their degree of heterotrophy due to specific environmental limitations like light, nutrients, prey availability or a combination of these [START_REF] Bergström | Occurrence of mixotrophic flagellates in relation to bacterioplankton production, light regime and availability of inorganic nutrients in unproductive lakes with differing humic contents[END_REF]. In addition, proportions of choanoflagellates in DARK conditions were higher in late summer than in early summer. The observed differential response of cryptophytes to glucose additions in the dark could also result from evolving competition with other groups for prey. To sum up, in our study cryptophytes were only able to develop through prey ingestion in early summer, not in late summer, probably due to changes in environmental conditions or competition mechanisms.

Overall, we clearly observed a stimulation of mixotrophic taxa after glucose additions in our experiments. Contrary to our hypothesis, however, no difference in the magnitude of mixotroph stimulation was observed between campaigns. This might be because there was little difference in the mixotrophic assemblage's composition between early summer and late summer, with a relatively similar mixotrophic potential in the communities over the season.

Conclusion

High-altitude lakes are particularly vulnerable to the combined action of DOC and nutrients. In our experimental study, DOC in combination with inorganic nutrients rapidly modified the relationship between bacterioplankton and phytoplankton. We show here that DOC was incorporated differently into the food web in early summer and in late summer, depending on the availability of autochthonous DOC and the nutrient limitation. In general, DOC additions promoted heterotrophic and mixotrophic pathways in the planktonic food web.

Thus, our findings contribute information that can help predict the ecological trajectories of shallow high-altitude lakes with large, vegetated catchments: more heterotrophic and mixotrophic communities can be expected in the future under the environmental changes forecast for these ecosystems. Table S1: Simple effects and interaction effects detected with the linear model from Design of Experiments on abiotic and biotic variables. Phyto_Total: total phytoplankton biomass on the 10 th day; HPP2… 10: Biomass of heterotrophic prokaryotic plankton on the 2 nd , 4 th , 6 th , 8 th and 10 th day; Consumed_DOC: DOC consumed at the end of the experiment; M/A: mixotrophic / autotrophic ratio. DOC: dissolved organic carbon; NUT: inorganic nutrients; LU: light; T: temperature; CAMP: campaign.

  1 to 5, l > k m = 1 to 5, m > l With 1 = glucose, 2 = nutrients, 3 = light, 4 = temperature, 5 = campaign Quantitative analyses were performed with R (v. 3.6.3), and Azurad (version Expert, AZURAD SAS, Marseille, France, 2019) software.

Figure 1 :

 1 Figure 1 : DOC variation in the microcosms between initial conditions and end of experiments, in early summer and late summer. Concentrations are shown for each DOC*nutrient treatment under the four temperature*light conditions. Error-bars represent standard error (n = 3).

Figure 2 :

 2 Figure 2: Heterotrophic prokaryotic plankton (HPP) biomass per experimental day, in early summer and late summer. Biomass is shown for each DOC*nutrient treatment under the four temperature*light conditions. Error-bars represent standard error (n = 3).

Figure 3 :

 3 Figure 3 : Phytoplankton groups' relative biomass and total absolute biomass (black points) at the end of experiments, in early summer and late summer. Biomass is shown for each DOC*nutrient treatment under the four temperature*light conditions.

Figure 4 :

 4 Figure 4: Scheme of the phytoplankton regulation of bacterial response to glucose addition in early summer and late summer. Black lines represent processes that are reinforced (heavy line) or weakened (light line). Dashed lines represent variables or processes not measured. GLU = glucose; DOC = dissolved organic carbon; CL = ciliates; MX = mixotrophs; AT = autotrophs; HPP BioM = Heterotrophic prokaryotic plankton biomass; Phyto BioM = phytoplankton biomass; DOC PHYTO = phytoplanktonderived DOC.

  *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** **

Figure S1 :

 S1 Figure S1 : Mixotrophs / autotrophs ratio and phytoplankton absolute biomass (black points) at the end of the experiments, in early summer and late summer. Ratio and biomass are shown for each DOC*nutrient treatment under the four temperature*light conditions. Error-bars represent standard error (n = 3)

. Enrichment experiments under controlled conditions 2.2.1. Experimental design

	on 7 th July 2019 (early summer) and on 28 th August 2019 (late summer). The campaigns were
	characterized by highly contrasting turbidity. Turbidity was high in early summer (average
	turbidity = 7 NTU), related to frequent previous storms, but low in late summer (average
	turbidity = 0.5 NTU). Water samples totalling 42 L were collected using a Niskin Bottle every
	metre to sample the entire water column and were filtered through a 50 µm mesh to exclude
	any larger grazers on food web components. Filtered water was stored in 8 L HDPE
	containers and transported in a cool box to the laboratory.
	2.2Microbial community was acclimatized overnight in 10 L sterilised transparent
	polycarbonate plastic bottles (Nalgene®) at 10°C. Physico-chemical and biological variables
	were measured in each bottle to define initial conditions before the start of the experiments.
	Then water from each bottle was manually homogenised and transferred to 96 microcosms.
	Transparent sterilised polycarbonate plastic bottles (Nalgene®) were filled with 350 ml of
	sampled water. In C treatments, glucose was added to the microcosms as an available DOC
	source at four different concentrations: no addition [0C], + 2 mg/l [2C], + 4 mg/l [4C] and + 6
	mg/l [6C]. In NP treatments, planktonic communities were either not enriched [0NP] or
	The lake is
	located at an elevation of 2446 m.a.s.l. It is shallow (maximum depth = 9 m) and small (1.8
	ha) but has a large catchment area (140 ha) with developed soil and meadows (approximately
	60% alpine grass cover). Water sampling campaigns were conducted twice over the summer,

Table 1 :

 1 Biotic and abiotic parameters measured under initial conditions before each experiment.Mean ± standard error. DOC: Dissolved organic carbon; SRP: Soluble reactive phosphorus; DIN:

	Dissolved inorganic nitrogen; HPP: Heterotrophic prokaryotic plankton. Significant P-values:
	<0.001***; <0.01**; <0.05*.
		Early summer Late summer
	DOC (mg/L)	0,61 ± 0,02	1,04 ± 0,09
	SRP (µg/L)	5 ± 0,14	3 ± 0,03
	DIN (mg/L)	0,60 ± 0,06	0,15 ± 0,04***
	Temperature (°C)	8,98 ± 0,08	14,60 ± 0,18***
	Phytoplankton biomass (µg C/L)	16,25 ± 1,41	111,94 ± 14,55**
	HPP biomass (µg C/L)	17,51 ± 1,39	16,56 ± 0,64
	Mixotrophs/autotrophs ratio	1,13 ± 0,44	0,45 ± 0,05**
	Ciliate abundance (cell/ml)	0,12 ± 0,41	3,98 ± 4,43***

Acknowledgments

We are grateful to the members of the French Biodiversity Office, especially René Conraud, for their help in the field. DOC analyses were carried out by the Mediterranean Institute of Oceanography. Data used in this study were partly produced through the technical facilities of the Biological and Chemical Analysis (IMBE, Marseille). We thank Marjorie Sweetko for improving the English of this manuscript. This work was supported by the French National program EC2CO (Ecosphère Continentale et Côtière). Flavia Dory received a PhD fellowship from the Ministère de l'Enseignement Supérieur et de la Recherche and this paper is part of her Ph.D.

Data availability statement

The datasets generated and analysed during the current study are available from the corresponding author on reasonable request.

Conflict of interest

The authors declare no conflicts of interest.

Supplementary information


Sonja Kallio

Monica Siroux
email: monica.siroux@insa-strasbourg.fr

Photovoltaic power prediction for solar micro-grid optimal control

Keywords: Solar energy, Photovoltaics, Prediction model, Multiple linear regression, Artificial neural network, Machine learning

In a solar micro-grid, a hybrid renewable energy system generates electricity for a building's onsite use. The battery storage and the main power grid connection are used to facilitate the matching between the demand and production. To control energy flows optimally, an accurate day-ahead prediction of the photovoltaic (PV) panels output is required. However, this is a challenging task due to the fluctuating nature of solar radiation availability. The accuracy of the prediction is influenced by the modelling method and input parameters. In this study, the measured power and weather data is gathered from an experimental installation of PV panels to predict PV output for a 24-hours horizon in 15 min intervals. The multiple linear regression (MLR) and artificial neural network (ANN) methods are considered in the prediction modelling and compared using performance indicators. The micro-inverter technology is used to gather the individual PV panel output in addition to the overall system output. The results show that the modelling methods have different accuracy performances and the ANN model built with the individual PV output data results in the highest accuracy. Utilizing the micro-inverter technology leads to an advantage of having more accurate PV prediction for the control purpose.

Introduction

Solar energy is an inexhaustible source of renewable energy. Additionally, it is free of charge and any emissions. However, the availability of solar energy is strongly fluctuating and depends on the changing weather conditions, time of the day and location. That creates significant uncertainty in the power output of solar systems. The photovoltaic panel is a silent device without moving parts and can convert sunlight into electricity through the photovoltaic effect.

The electrical efficiency of the crystalline silicon PV panels varies from 11% to 22% [START_REF] Wang | Hybrid solar-assisted combined cooling, heating, and power systems: A review[END_REF]. An increasing amount of distributed PV installations in the building sector enables building owners to act as a prosumer by generating and storing their own electricity onsite or selling it to the grid [START_REF] Barbu | Analysis of a residential photovoltaic-thermal (PVT) system in two similar climate conditions[END_REF]. A solar micro-grid can be used to generate profit

Nomenclature

GHI

global horizontal irradiation, W/m 2 GTI global tilted irradiation, W/m 2 P power, W p pressure, hPa RH relative humidity, % T temperature, • C WS wind speed, m/s for the building owner, and through the optimal control of hybrid renewable energy systems reviewed in [START_REF] Kallio | Hybrid renewable energy systems based on micro-cogeneration[END_REF], the profit and self-consumption can be maximized. However, PV power output has uncontrollable and abrupt nature. Thus, an accurate forecast of the output is required for optimal energy management in the solar micro-grid as well as in the other levels of the electric grid [START_REF] Gupta | PV power forecasting based on data-driven models: a review[END_REF].

In the literature, different PV power prediction methods have been proposed with different data inputs. The most used methods are deterministic, machine learning (ML) and hybrid techniques [START_REF] Mas | Comparison of three machine learning models for the prediction of hourly PV output power in Saudi Arabia[END_REF][START_REF] Theocharides | Comparative analysis of machine learning models for day-ahead photovoltaic power production forecasting[END_REF]. The deterministic methods are based on the physical model of the PV to predict the power output, and the artificial intelligence-based ML methods, such as multiple linear regression (MLR), artificial neural network (ANN) and support vector machine (SVM), aim to form a relationship between input and output without any further knowledge of the system [START_REF] Mas | Comparison of three machine learning models for the prediction of hourly PV output power in Saudi Arabia[END_REF]. Kalogirou [START_REF] Kalogirou | Artificial neural networks in renewable energy systems applications: a review[END_REF] conducted a comprehensive review on the ANN method in renewable energy systems considering PV systems. Zazoum [START_REF] Zazoum | Solar photovoltaic power prediction using different machine learning methods[END_REF] compared different ML techniques for PV power prediction. He concluded that the ML methods are suitable and fast to predict the PV power of any system.

The scientific literature has aimed to improve the accuracy of the PV power forecasting models in terms of different prediction algorithms and input data. Different sets of weather and PV operation parameters have been investigated to increase the accuracy [START_REF] Alshafeey | Evaluating neural network and linear regression photovoltaic power forecasting models based on different input methods[END_REF]. However, to the best of the author's knowledge, there is no work focusing on the different ML methods using as an input parameter the PV power data measured by the individual microinverters to increase the accuracy of the day-ahead power prediction. In this study, the MLR and ANN prediction models are built for each PV panel and the overall system using the input data measured from the micro-inverter and aggregated system level. The study aims to reveal if using the data of the micro-inverter level can increase the prediction accuracy of the whole PV system.

Methodology

A comparative study of different PV power prediction models is conducted. First, the experimental set-up of PV panels is presented with data gathering methods. Next, the monitored data is pre-processed and used to create different data-driven models for the PV power prediction. The first method is a multiple linear regression (MLR) with interaction terms which is compared to a method called Artificial Neural Network (ANN). Both models are regression models, and the monitored data from the PV installation and weather station are used to train and validate the models in the MATLAB environment. The training data was collected from 27.9.2021 to 31.3.2022 and includes large variation of different weather conditions. The different prediction models are built by using as input the weather data and power output data from the micro-inverter and aggregated system level.

Experimental set-up

The installation of four PV panels in Fig. 1 was realized on the rooftop of the INSA ICUBE Laboratory in Strasbourg, France (48 • N and 7 • E) in September 2021. Strasbourg is classified to have an oceanic and semicontinental climate according to the Köppen climate classification [START_REF] Kallio | Energy analysis and exergy optimization of photovoltaic-thermal collector[END_REF]. Each PERC (Passivated Emitter & Rear Contact) monocrystalline PV panel has a peak power of 300 W, and micro-inverters are used to convert each panel's DC output to AC power individually. The energy production is maximized by a Maximum Power Point Tracking (MPPT) of each micro-inverter. Two of the panels have a tilt angle of 7 • , and the rest is set to an 18 • angle. The PV panels were installed on the available roof area which has a clear face with the sun during a part of the day. The shading from the surrounding buildings during the day cannot be avoided. However, the micro-inverter technology enables the independent operation of each panel and partial shading has an impact only on the shaded panels. Using the micro-inverter technology has also several other advantages over traditional inverters discussed in [START_REF] Mundada | A review of technical requirements for plug-and-play solar photovoltaic microinverter systems in the United States[END_REF].

The four micro-inverters are connected to a gateway which is used to communicate measured system data to the web-based monitoring and analysis software provided by Enphase company [12]. The power output of each panel (P inv,1-4 ) and the whole system (P agg ) is measured every 15 min and uploaded into Excel file from the online software. The installation includes also Lithium-Ion AC battery storage to store the PV production if not used directly in the building. The optimal battery use is managed by the gateway.

In addition to the PV panels, the installation includes a weather station to measure the local weather parameters global horizontal irradiance (GHI), ambient temperature (T a ), dew point temperature (T d ), pressure ( p at ), wind speed (WS) and relative humidity (RH) in 15 min intervals. A data logger is used to transfer the weather data to a computer for further analysis.

Correlation analysis

The PV power production correlates with the surrounding weather conditions. The Pearson correlation analysis was used to find out the correlation between the PV power output and individual weather variables. Generally, this analysis method reveals how strong are the linear relationship between the different variables in a given data set. The analysis shows the correlation coefficients that vary from -1 to 1. The magnitude of the absolute value of the coefficient indicates the strength of proportionality between two variables. This indicator is used to select the most significant variables for the prediction model. The high number of parameters can result in lower accuracy of the model.

Multiple linear regression model

In this study, the measured historical data of both the PV power output and weather variables were used as an input to create a multiple regression model with interaction effects. The interaction effect occurs when the effect of the independent weather variable on the PV production changes depending on the other weather variables. This interaction is presented as a product of the independent weather variables. The regression model with interaction effects is an extension of the general regression presented as follows [START_REF] Mas | Comparison of three machine learning models for the prediction of hourly PV output power in Saudi Arabia[END_REF]:

ŷ = β 0 + β 1 x 1 + β 2 x 2 + • • • + β n x n + ε (1)
where β 0 is the intercept and x represents each independent weather variables. The other β parameters present the slope coefficient of the variable. All β parameters are defined in the model creation process to minimize the error ϵ. The interaction effects are added to the general form of the multiple regression model as follows:

ŷ = β 0 + β 1 x 1 + β 2 x 2 + β 3 x 1 x 2 . . . + β n x n + β l x n x m + ε (2)
where x 1 x 2 is the interaction between two variables.

Artificial neural network model

The ANN algorithms are commonly used to solve time series prediction tasks because they have the ability to learn the behaviour of variables from historical measurements, such as PV power output and weather data in terms of the PV prediction modelling [START_REF] Dolara | Comparison of training approaches for photovoltaic forecasts by means of machine learning[END_REF]. The ANN is based on supervised learning, and the prediction performance increases with the amount of historical data used in the training of the model. In addition to the training dataset, a part of the historical dataset is used only for the test and validation of the model to show the generalization capability of the prediction model. The learning or training process is based on continuously improving the weights and biases within the neural network to reach the desired output, which minimizes MSE in Eq. ( 2) (or RMSE in Eq. ( 3)) between the actual and predicted output. This is performed by using a learning algorithm, such as gradient descent, error back-propagation or Levenberg-Marquardt [START_REF] Dolara | Comparison of training approaches for photovoltaic forecasts by means of machine learning[END_REF]. The back-propagation algorithms are the most used and powerful in terms of learning [START_REF] Kalogirou | Solar energy engineering[END_REF]. In this study, the MATLAB software is used to train the ANN model and the limited-memory Broyden-Fletcher-Goldfarb-Shanno quasi-Newton (LBFGS) optimization algorithm is used to minimize the MSE [START_REF]Regression neural network[END_REF].

The number of inputs to the ANN model indicates the "neurons" in the input layer presented in Fig. 2. The layer structure includes the input layer, a certain number of hidden layers with hidden neurons and the output layer. In the case of PV power prediction, the input layer includes the selected weather variables (x 1 , x 2, x 3 . . . , x n ), and the output is the power prediction. Generally, the ANN model can include any number of hidden layers and neurons. However, the accuracy of the model depends on the right number of layers and neurons. In this study, the Multi-Layer-Feed-Forward Neural Network (MLFFNN) structure is used in which the information flows only in one direction from the input to the output layer. The outputs of the previous layer are the inputs for each neuron on the next layer. The inputs of each neuron are multiplied by weights (w 1 , w 2 , w 3 . . . , w n ) and combined using a weighted linear combination [START_REF] Alshafeey | Evaluating neural network and linear regression photovoltaic power forecasting models based on different input methods[END_REF]. Before the outputs of the neurons are ready, a nonlinear activation function f ac , such as Hyperbolic tangent or Sigmoid function, is applied to the results of the layer. In this study, the Rectified linear unit function is used to perform a threshold operation on the input values to set the values less than zero to be zero [START_REF]Regression neural network[END_REF]. After training, the ANN is a quick method to provide predictions for complex non-linear problems and it can reach good accuracy also with smaller data set used in the training and validation [START_REF] Alshafeey | Evaluating neural network and linear regression photovoltaic power forecasting models based on different input methods[END_REF].

Model performance indicators

To conduct a comparative study between different models, certain performance indicators are used to evaluate the accuracy of the prediction models. In addition to a simple absolute error between the actual and predicted value, the following commonly used performance indicators for the forecasting models are used in this study: Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Square Error (RMSE) and Coefficient of Determination (COD) [START_REF] Alshafeey | Evaluating neural network and linear regression photovoltaic power forecasting models based on different input methods[END_REF][START_REF] Nageem | Predicting the power output of a grid-connected solar panel using multi-input support vector regression[END_REF].

M AE = 1 n n ∑ i=1 ⏐ ⏐ y i -ŷi ⏐ ⏐ (3)
M S E = 1 n n ∑ i=1 ( y i -ŷi ) 2 (4) R M S E = √ M S E =    √ 1 n n ∑ i=1 ( y i -ŷi ) 2 (5) C O D = R 2 = 1 - ∑ ( y i -ŷi ) 2 ∑ (y i -y) 2 ( 6
)
where n is the number of observations, y is the mean value of the observations, y and ŷ are the actual and predicted values of the PV power, respectively.

In the regression analysis, the COD is used to present how close the prediction model output is compared to the observed data and it results in values between zero and 1. To evaluate the overfitting of the prediction model, the COD requires the other indicators alongside it. In the evaluating process, the COD should be closer to 1 and the other indicators closer to zero [START_REF] Alshafeey | Evaluating neural network and linear regression photovoltaic power forecasting models based on different input methods[END_REF].

Results and discussion

In this section, the performance results of the MLR and ANN model are presented. The training data was collected from the PV installation between September 2021 and March 2022. In addition to the performance indicators, a representative day in April was selected and the prediction was computed and compared to the actual power output of the system.

Correlation coefficient analysis

To evaluate the significance of the individual weather variables to the PV power, a correlation coefficient analysis was conducted. The results of the analysis were used to select the most relevant weather variables for the modelling. The weather variables under the investigation were the ambient temperature T a , relative humidity RH, dew point temperature T d , wind speed WS, atmospheric pressure p at , global horizontal irradiance GHI and global tilted irradiation GTI for both panel arrays in the tilt angle of 7 • and 18 • . The GTI values were calculated based on the measured GHI, number of a day, latitude and tilt angle of the panels. The PV power output P was recorded per panel and overall system. The correlation coefficients between the weather variables and PV power output are presented in Table 1. The highest correlation was recognized between solar irradiation on the horizontal and tilted surface (GHI and GTI) and the PV power. The coefficient for each solar irradiation variable was 0.94. The second highest significance was shown by the RH followed by the ambient temperature. The impact of the RH was negative, which decreased PV power when the RH increased. This was caused by the increased amount of water vapour particles in the air reducing the solar insolation such as dust. The dew point temperature T d showed the lowest significance by the value of 0.01 and was excluded from the modelling. The other variables in Table 1 were included in the prediction modelling by MLR and ANN.

Multiple linear regression model performance

To predict the PV power, an MLR model was trained in the MATLAB software environment. The performance indicators presented in Section 2.5 were used to evaluate the accuracy of the model.

First, the regression model was trained with the weather data and the aggregated PV power output of the system. Next, the PV power output data of each micro-inverter was used to predict the output of each panel. The predictions of each panel were summed up to have a prediction of the whole system. The performance of the prediction models generated by the aggregated PV output data and by the individual micro-inverter data was compared.

The overall performance results in Table 2 show that the MLR, which was based on the micro-inverter data, showed better performance with 13.86 MAE, 1438 MSE, 37.92 RMSE and 0.938 COD than the model based on the aggregated PV power data with 16.32 MAE, 2160 MSE, 46.48 RMSE and 0.907 COD. The results revealed that a more accurate prediction model was achieved if the micro-inverter data was used first to model each panel output and then summed up to have PV power prediction for the whole system. This method can help to predict more accurately the PV power of the system if all the panels are not positioned equally to the sun during the day, for example, if some shading occurs. The MLR model based on the micro-inverter data was used to predict the PV power for the representative day in April, shown in Fig. 3a. This day was not used in the training dataset. Fig. 3b presents the correlation between the actual and predicted values. In this case, the model was able to perform as follows: 43.4 MAE, 7552 MSE, 86.9 RMSE and 0.91 COD.

Artificial neural network model performance

The same dataset, as for the MLR model, was used to train an ANN model. Again both aggregated and microinverter based PV power data were used to train the model to see if the micro-inverter data can be used to have a more accurate prediction model for the installation.

The overall performance results in Table 2 show that the ANN model, which was based on the micro-inverter data, showed again better performance with 9.87 MAE, 930 MSE, 30.497 RMSE and 0.9596 COD than the model based on the aggregated PV power data with 13.34 MAE, 1517 MSE, 38.96 RMSE and 0.935 COD. However, in both cases, the ANN model showed the better overall performance than the MLR models.

The ANN model based on the micro-inverter data was used to predict the PV power for the representative day in April, shown in Fig. 4a. Fig. 4b presents the correlation between the actual and predicted values. The model was able to perform as follows: 32.26 MAE, 4632 MSE, 68.06 RMSE and 0.9471 COD.

Conclusion

In this paper, the PV panel installation using micro-inverter technology was realized in INSA ICUBE Laboratory in Strasbourg to build a PV power prediction model using two different methods: multiple linear regression and artificial neural network. The weather station was used to collect the weather data. The correlation analysis was used to select the most significant weather parameters correlating with the PV power output. The parameters were the ambient temperature, relative humidity, pressure, wind speed and solar irradiation.

In addition to the two different modelling methods, the prediction models were built using two different approaches to collect the PV power output data from the installation. First, the aggregated PV power was used in the modelling process. Next, the PV power data, detected by each individual micro-inverter, was used to model each PV panel output to get a more accurate model of the whole system.

The results showed that the overall performance of the ANN models was better than the MLR models resulting in lower MAE, RMSE and MSE and higher COD. Additionally, the results revealed that building a model of each panel by using the PV power data from the micro-inverters resulted in more accurate prediction models. Due to this, it is recommended to use the micro-inverter technology in the PV installations to facilitate the prediction of the system output power.

For future work, the PV prediction model based on the ANN and micro-inverter data will be enhanced by collecting more data from the installation. The comparison between different models will be extended with other methods, such as Support Vector Machine, Fuzzy prediction and Regression Tree. Additionally, the prediction model will be used in the model predictive control of a hybrid renewable energy system.

Fig. 1 .

 1 Fig. 1. The PV installation with the weather station and data collection process.

Fig. 2 .

 2 Fig. 2. The structure of a simple ANN model with one hidden layer.

Fig. 3 .

 3 Fig. 3. (a) The predicted and actual PV power using the micro-inverter based MRL model. (b) Actual vs. predicted PV power correlation with the linear trendline from the MRL model.

Fig. 4 .

 4 Fig. 4. (a) The predicted and actual PV power using the micro-inverter based ANN model. (b) Actual vs. predicted PV power correlation with the linear trendline from the ANN model.

Table 1 .

 1 The correlation coefficients.

	Variable	Correlation with PV power
	Ambient temperature	0.27
	Relative humidity	-0.39
	Dew point temperature	0.01
	Wind speed	0.15
	Atmospheric pressure	0.11
	GHI	0.94
	GTI_up	0.94
	GTI_down	0.94

Table 2 .

 2 The overall performance comparison of the models based on the different methods and PV data input.

	Model		Performance indicator
			MAE	MSE	RMSE	COD (R 2 )
	Multiple regression	Overall	16.32	2161	46.485	0.9074
		Micro-inv.	13.86	1438	37.919	0.9376
	ANN	Overall	13.34	1517	38.96	0.935
		Micro-inv.	9.87	930	30.497	0.9596

Acknowledgements

The authors would like to thank Interreg V Rhin supérieur, France for their support and funding of this research.

Data availability

The authors do not have permission to share data.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.