New Caledonia is located in the Pacific Ocean at 22°S and 165°E and is subject to tropical or subtropical meteorological conditions. Winds are characterized by two main directions [14]. Trade winds blowing from 60°to 160°at speed higher than 4 m s⁻¹ represent 69% of yearly wind occurrence ($\sim 250\text{d}{\text{yr}}^{\mathrm{-1}}$) around Nouméa. Westerly winds blowing from 220°to 300°at speeds higher than 2 m s⁻¹ represent less than 12% of yearly wind occurrence. The study area is the Southwest (SW) lagoon of New Caledonia, delimited by the land and the barrier reef between the Mato pass in the South, and the Uitoe pass in the North (Fig. 1). It receives freshwater runoffs from three main rivers (Pirogues, Coulée, and Dumbéa), but river flow rates are usually low, with 5 m³ s⁻¹ (yearly average) for the largest one, the Dumbéa River [13]. The central part of the lagoon is characterized by oligotrophic to mesotrophic waters (yearly average $0.25\pm 0.01\text{μg}$ $\text{Chl}a$ l⁻¹, [15]), whereas a local eutrophication is perceptible near the city of Nouméa (146 000 inhabitants). In addition to this local enrichment due to urban effluents, nickel industry delivers industrial effluents [16]. In this lagoon, phytoplankton biomass displays a weak seasonality, associated with marked short-term (week) variations [15] and interannual differences [17].

Hydrodynamic studies have been conducted in New Caledonia for over 25 years [18,19]. Recently, a model of the water circulation in the Southwest lagoon was developed and validated [20–23]. In these papers, model description, circulation analysis, vertical structure of the currents, and the initial and boundary conditions were presented in details. In this study, we use a $\mathrm{\Delta }x=\mathrm{\Delta }y=500\text{m}$ grid spacing and $10\sigma$-levels.

The first biogeochemical model was developed by Bujan et al. [24] and Pinazo et al. [13]. An improved version was implemented by Faure [25] by adding an explicit microbial loop. The structure of the whole model is described in Fig. 2. The structure is typical of NPZD models (nutrients–phytoplankton–zooplankton–detritus). However, the zooplankton is considered as a theoretical population, undifferentiated and static, and no state variable is associated to it. Thus, the model is closed by a function of predation. Each compartment is expressed in carbon and nitrogen units, leading to 11 state variables (Table 1). One particularity of the model is the expression of the growth rate of phytoplankton based on the formulation of cell quota [26,27]. The variable stoichiometry allows taking into account the nutritional status of the cells, the nutrient limitation of phytoplankton growth, and the computation of nutrients uptake. Primary production is limited by temperature, light and nutrients (ammonium (NH₄) and nitrate (NO₃)). Bacterial production (BP) is also modelled with the cell quota concept [28]: BP is limited by the cell internal quota in carbon and nitrogen. All state variables equations could be found in Pinazo et al. [13] and Faure [25]. Here, we present only the pertinent equations (Table 2).

Three different formulations were tested in order to model the $\text{Chl}a$ concentration (CHL_CST, CHL_ST, CHL_DYN). In Table 2, Eqs. (1) to (4) were the same for each formulation, describing the trend of phytoplankton carbon and the carbon specific nitrogen uptake (on NH₄ and NO₃).

In CHL_CST, modelled $\text{Chl}a$ concentration was computed using a constant $\text{Chl}a$:C ratio equal to 0.24 g $\text{Chl}a$ (mol C)⁻¹ (Table 2, Eq. (5)).

As the model simulated a variable phytoplankton N:C ratio, the second formulation chosen (CHL_ST) was a stationary equation from Smith et al. [7] (Table 2, Eq. (6)). This equation calculated the $\text{Chl}a$:C ratio of phytoplankton depending on their internal N:C ratio. The $\text{Chl}a$:C ratio is positively correlated with the N:C ratio. In CHL_ST, $\text{Chl}a$ is not a state variable, but a diagnostic variable, and permitted to diminish computation time.

In CHL_DYN, $\text{Chl}a$ is an explicit state variable in the ecosystem model. The $\text{Chl}a$ synthesis is modelled with a dynamic equation from Geider et al. [11] and Lefèvre et al. [29] (Table 2, Eqs. (7)–(8)). Carbon-specific $\text{Chl}a$ synthesis is determined by the rate of nitrogen assimilation (Table 2, Eq. (4)), and a regulatory term (Table 2, Eq. (8)).

Eq. (1) gives the standard three-dimensional equation for each of the biogeochemical concentration (Conc). BIO_TEND represents the gain and losses of the considered variable:

The standard structure of three-dimensional biogeochemical equations is presented in Eq. (1). The left-hand side of the equation accounts for temporal variability, vertical and horizontal advection, and settling velocity of particles. The right-hand side of the equation accounts for biogeochemical gain and loss (BIO_TEND), and turbulent diffusivities. The current velocities ($U,V,W$) and the diffusivity coefficients ($K_X,K_Y,K_Z$) calculated by the hydrodynamic model were used as forcing variables for the biogeochemical model.

The hydrodynamic model was forced by tide and by realistic wind with a time step of 10 min. It was dynamically coupled with the biogeochemical model [25]: the scheme of advection–diffusion calculated the evolution of biogeochemical variables in parallel to the execution of the physical code, with the same time step of 50 s. The biogeochemical model was forced by irradiance measured each hour, and calculated the trends of biogeochemical variables, with a time step of 20 min.

Initialization conditions were established thanks to a campaign during which 90 stations were sampled over the lagoon (Camecal 5, 19–27 June 2003). Boundary conditions were adjusted to field measurements and published data (Table 5). Freshwater inputs from the three main rivers were introduced in the model. The strong trophic gradient between the bays around Nouméa and the central part of the lagoon led us to consider the inputs in nitrogen from human sewages in three bays of Nouméa (Sainte-Marie, Koutio and Grande Rade, see Fig. 1). Moreover, coupling between pelagic processes and benthic mineralization could represent a source of nitrogen in coastal areas of the lagoon (C. Grenz, unpublished data). We added a constant positive flux of ammonium and nitrate into the pelagic water column along the coastline (NH₄: 15 μmol m⁻² h⁻¹; NO₃: 5 μmol m⁻² h⁻¹; Grenz, unpublished data).

A 34-day realistic simulation of the model was run in order to examine the biogeochemical response of the Southwest lagoon to the transient meteorological conditions measured during June and July 2003 (Fig. 3). The simulation began on 19 June and ended on 23 July; it permitted to illustrate the model behaviour under different meteorological events. Firstly, a low irradiance (lower than 600 J cm⁻² d⁻¹) occurred around 27 June and 16 July, whereas the mean irradiance for this period is 1257 J cm⁻² d⁻¹; strong rains came with the second decrease of irradiance, leading to river flows in each river, up to 300 m³ s⁻¹ for the Dumbéa River. Secondly, a shift from a low northwest to a strong southeast wind took place around the 7 July. The duration of the simulation was chosen in order to compare model outputs with field data.

Several lagoon surveys demonstrated that, on average, the water column is nearly homogeneous and that 3-m-depth samples are well representative of the whole water column [13,15]. For an easier presentation, results will be discussed after distinguishing three stations with increasing trophic status (Fig. 1): M40 represents the central part of the lagoon, B08 an open bay and D47 a semi-closed bay around Nouméa.

Experimental data were collected on 8 and 22 July at 3-m-depth on M40, B08 and on 10 and 23 July on D47. Chlorophyll $a(\text{Chl}a)$ concentration was fluorometrically determined on 7-ml methanol extracts of 300-ml samples collected onto Whatman GF/F filters according to Holm-Hansen [30]. Ammonium concentration was fluorometrically determined on three 40-ml replicates on a Turner TD-700, using the o-phtaldialdehyde method [31].

The simulated variables appeared to be consistent with usual observations in the Southwest lagoon of New Caledonia [15–17,19]. The gradient of primary production between the central part of the lagoon and the bays was well reproduced. The average simulated values (Table 4) appeared to be coherent with the measured data, with a yearly averaged PP of 8.1 and 45.3 mg C m⁻³ d⁻¹ at M33 (close to M40) and N12 (in a semi-closed bay of Nouméa), respectively [15]. The measured value of $\text{Chl}a$ and NH₄ concentrations were well reproduced by the model, especially when using the CHL_ST model (Fig. 4). The simulated $\text{Chl}a$:C ratios ranged from a minimum value of 0.07 g $\text{Chl}a$ (mol C)⁻¹ to a maximum of 0.375 g $\text{Chl}a$ (mol C)⁻¹. These values fall within the range reported in experimental studies on microalgal culture (0.036 to 1.2 g $\text{Chl}a$ (mol C)⁻¹) [4], in subtropical Atlantic Ocean waters (0.15 to 0.36 g $\text{Chl}a$ (mol C)⁻¹) [5] and in English Channel waters (0.12 to 0.96 g $\text{Chl}a$ (mol C)⁻¹) [6]. The simulated phytoplankton N:C ratio ranged from 0.076 to 0.19 mol N (mol C)⁻¹. These values are consistent with the 0.08–0.164 range reported in the North Pacific Central Gyre [32], or with the 0.07–0.14 range observed in the Atlantic Ocean (BATS) [29].

As shown by a previous modelling study [13,23], the lagoon channel is deeply influenced by hydrodynamics resulting from trade winds. Oceanic waters enter the lagoon by the southern sector end, and very short flushing times of water are computed in the central part of the lagoon [23]. In our simulation, the different model formulations did not show large differences in M40, therefore under strong hydrodynamical forcings (strong trade winds), the complexity of a biogeochemical model does not significantly change the outputs [33].

However, flushing times of waters in areas like bays around Nouméa are longer [23], and therefore these zones are more controlled by biogeochemical processes. In B08 and D47, each model formulation clearly produced different outputs. During the first part of the simulation (19 June to 7 July), using CHL_CST, $\text{Chl}a$ remained very high in B08 and D47, thanks to a high carbon production. At the opposite, using CHL_ST or CHL_DYN, $\text{Chl}a$ started to decrease on 27 June, when the NH₄ concentration was too low to maintain the N:C ratio. Using these two model formulations, during the rain event and nitrogen inputs on 16 July, the N:C and $\text{Chl}a$:C ratios increased, leading to an increase of $\text{Chl}a$ (slight for CHL_DYN). It appeared that a constant $\text{Chl}a$:C ratio could lead to overestimate the $\text{Chl}a$ concentration in low nutrient conditions, since $\text{Chl}a$ could also be dependent upon the N:C ratio and thus on the nutrient resources. As a consequence, even if the carbon primary production could be well described and modelled, the conversion of phytoplankton carbon into $\text{Chl}a$ using a constant ratio would produce significant inaccuracy on the value of the $\text{Chl}a$ concentration.

Using the CHL_DYN simulation, the $\text{Chl}a$:C ratio was low, leading to unrealistically low values of $\text{Chl}a$ in comparison with measured data (Fig. 4). Lefèvre et al. [29] showed that some parameters as ${\mu }_{\max }(T)$ or ${\alpha }_{\mathrm{Chl}a}$ (Tables 2 and 3) could have a pronounced effect on the simulated value of $\text{Chl}a$ and perhaps a better estimation of our parameters could improve the outputs of the dynamic model. The difficulty could be to establish a set of parameters able to describe contrasted trophic status such as those encountered in the Southwest lagoon of New Caledonia.