The Mediterranean Sea BGC-Argo array operating in the period 2012–2016 (Fig. ) was composed of 31 floats that acquired 1314 vertical profiles of temperature (T) and salinity (S), chlorophyll a concentration (Chl, mgm-3), derived from fluorescence measurements between 0 and 1000 m see, and radiometric quantities, such as downward planar irradiance (Ed, µW cm-2 nm-1), at three different wavelengths (λ=380, 412, and 490 nm) and photosynthetically available radiation (PAR, µmol photons m-2 s-1) integrated between 400 and 700 nm . Radiometric measurements were obtained in the upper 250 m, with vertical resolution of 1 m between 10 and 250 m and 0.20 m between 0 and 10 m. All profiles were acquired around local noon.

The quality control (QC) procedure of radiometric profiles was specifically designed to identify and remove the dark signal, atmospheric clouds, and wave focusing at the surface . Note that the operational definition of PAR used by the BGC-Argo community takes into consideration the planar irradiance Ed rather than the scalar one Eo, therefore differing from its theoretical definition and leading to an underestimation of Eo values by 30 % or more . The scalar values of PAR were thus derived according to , although the correction related to the irradiance scattering was neglected due to the lack of information on IOPs (see Sect. S1 in the Supplement).

Vertical profiles of Chl concentration were quality-controlled according to the procedure of the international BGC-Argo programme that removes spikes and corrects for non-zero deep values and non-photochemical quenching at the surface . Due to a factory calibration bias for WET Labs ECO series Chl fluorometers, Chl concentrations were corrected by a factor of 0.5 .

All the data used in this study are freely available and compiled into the database published by . Seven variables (T, S, Chl, Ed(380), Ed(412), Ed(490), PAR) were vertically interpolated to a resolution of 1 m in the upper 400 m. Finally, we partitioned the profiles geographically into 13 (out of 16) subbasins (Fig. ), with the majority of profiles located in the northwestern Mediterranean (NWM, 332 profiles), followed by northern Ionian (ION3, 172 profiles) and southern Tyrrhenian (TYR2, 162 profiles) seas. No data were available for the southwestern Ionian (ION1) and the eastern Levantine (LEV4) seas and only one profile was present in the northern Adriatic Sea (ADR1), as well as in the western Levantine Sea (LEV1). The WMO code specification for each BGC-Argo float (along with their operational periods) is provided in the Sect. S2 in the Supplement.

Biogeochemical processes have been simulated according to the voxel approach (“volume element with biological content and processes”; ), discretized along the vertical direction in order to resolve vertical irradiance attenuation and nutrient gradients. Each voxel replicated light and mixing conditions according to the trajectory and measurements of the corresponding BGC-Argo float, thus simulating a pseudo-Lagrangian experiment. No exchanges of mass between voxel and the surrounding field have been considered, which implies smaller mass exchanges due to horizontal diffusion and baroclinic components of the (upper ocean) advection field compared to vertical processes and biogeochemical dynamics. Conversely, a voxel exchanges heat with the atmosphere and receives light in accordance with its moving position. Such an approach, similar to the one adopted by , has already been successfully applied by in order to analyse BGC-Argo floats in the North Atlantic.

Furthermore, it is assumed that major biogeochemical transformations can be described by the Biogeochemical Flux Model (BFM) parametrizations, properly driven by a bio-optical model, which has been validated by contrasting model results and experimental data. The model is formulated through a system of partial differential equations: ∂tCi(z,t)=∂z[Dv(z,t)∂zCi(z,t)]+vsink,i∂zCi(z,t)1+BFMi(T,S,PAR,C‾(z,t)), where Ci is the ith biogeochemical tracer simulated (i=1, 50), Dv is the vertical eddy diffusivity derived with the vertical mixing model described in Sect. , vsink is the sinking velocity, and BFMi is the reaction term corresponding to the tracer Ci. T, S, and PAR are the data measured by BGC-Argo floats. Since the surfacing of BGC-Argo floats is programmed at around local noon, the variability related to diurnal variation in solar irradiance is taken into consideration according to .

The biogeochemical model BFM is a biomass-based numerical model that simulates the biogeochemical fluxes of carbon, phosphorus, nitrogen, silicon, and oxygen, characterizing the lower trophic level (producers, consumers, and recyclers) of the marine ecosystem. Its application is based on the coupled transport–biogeochemical model OGSTM-BFM . It includes four phytoplankton functional types (diatoms, nanoflagellates, picophytoplankton, and dinoflagellates), carnivorous and omnivorous mesozooplankton, bacteria, heterotrophic nanoflagellates, and microzooplankton. Each variable is described in terms of internal carbon, phosphorus, and nitrogen concentrations. Particulate and dissolved organic matter are also included, with the latter partitioned in labile, semi-labile, and semi-refractory phases (for parameters' specifications see Sect. S3 in the Supplement). The present study is focused mainly on Chl, reserving for future analysis (according to data availability and optical model complexity) a study of plankton functional type (PFT) resource competition dynamics .

In particular, the Mediterranean Sea Monitoring and Forecasting Centre (Med-MFC) has operatively produced analyses, forecasts, and reanalyses of a series of biogeochemical state variables (e.g. Chl, nutrients, pCO2) for Copernicus Marine Environment Monitoring Services (CMEMS) since 2015 using the MedBFM model , which embeds the OGSTM-BFM and assimilates surface Chl from satellite observations .

We tested a total of 17 classes of simulations (summarized in Tables  and ).

In the first set of simulations, the biogeochemical model was forced with PAR from BGC-Argo floats. Experimental values of temperature and density (computed from float profiles) were also taken into consideration. A simulation for each of the BGC-Argo float trajectories was performed with this set-up, hereafter abbreviated as REF.

Initial conditions for all biogeochemical variables of BFM are provided by the CMEMS reanalysis of Mediterranean Sea biogeochemistry period 1999–2015; produced by the MedBFM model system. The initialization profiles for our 1-D configuration are extracted from the MedBFM model output array, taking the nearest model point to the BGC-Argo position in time and space.

The simulations' timescale corresponds to a typical BGC-Argo time-series length during the period 2012–2016, i.e. 11 months on average, with a vertical resolution of 1 m. After being initialized, the model evolves without further assimilation of biogeochemical data from the 3-D configuration.

Vertical eddy diffusivity coefficient profiles Dv(z) are represented as Gaussian-shaped functions, thus allowing a gradual increase in vertical mixing through the pycnocline. Approaches and impacts of using different parametrizations to reconstruct mixing along the water column are shown and discussed in Sect. .

According to the work's objectives, four classes of simulations were considered, which correspond to the following subsections: the reference simulation, a subset with perturbed vertical mixing models, tests with different optical configurations, and a last group of additional analyses involving CDOM description and diurnal variability. Outputs are validated qualitatively and quantitatively in terms of profile shapes and the deep chlorophyll maximum (DCM) depth. The DCM definition is based on the absolute maximum of Chl, excluding results of DCM shallower than 40 m or deeper than 200 m, as well as the ones with concentrations lower than 0.1 mgm-3. All results, for both model and BGC-Argo floats, are averaged on a weekly basis. Model outputs are compared with a match-up shown as target and Taylor diagrams . The former evaluates results with root-mean-square distance (RMSD) as the main statistical parameter, which was calculated following Eq. (): 6RMSD=1nΣi=1n(mi-oi)2, where n is the number of data, m are the model values, and o are the observables.

Due to the various sources of possible uncertainties in the fluorescence-to-Chl conversion of BGC-Argo profiles, we chose to focus our study on DCM depth rather than DCM magnitude. This is additionally justified with the BFM statistical sensitivity analyses (see Sect. S4 in the Supplement), which considered DCM width, DCM magnitude, and surface Chl. Results indicate that DCM depth is the most effective feature the model is able to reproduce.

The assimilation of PAR profiles helped to accurately estimate the DCM depth (Fig. ). Measured and modelled DCM depth showed high correlation (r=0.83, p value < 0.005). Both model and measurements indicate that DCM depth varies typically between 50 and 70 m in western areas (ALB, SWM1, SWM2, NWM, TYR) and is generally deeper in eastern areas (ADR2, ION3, LEV2, LEV3), between 100 and 140 m. The model tends to slightly underestimate the DCM depth variability (Fig. , regression slope = 0.81<1): the deepest simulated DCMs are around 125 m depth, whereas data from floats reach 140 m (e.g. lovbio018c).

Chl patterns display high variability at both temporal and vertical scales (Figs.  to ). The subsurface Chl pattern is formed by patchy structures and it is generally deepening eastward during stratification periods (Fig. ). BGC-Argo observations indicate that DCM is further eroded by vertical mixing occurring predominantly in autumn and early winter. At the ocean surface, the increase in Chl is triggered by rather shallow mixing (≤75 m). Simulations provide an adequate reproduction of the Chl mixing timing and therefore of the DCM erosion. By comparing Hovmöller maps of all 31 floats (considering both depth and time variability) for measured and simulated Chl, a significant average correlation coefficient (r) of 0.75 is obtained: such a result quantitatively confirms that the alternation of mixing and stratification phases, as seen from BGC-Argo Chl measurements, is well reproduced.

Simulated Chl also reproduces episodic signals, such as Chl deepening due to specific mixing events. For example, a mixing event in the NWM subbasin, reaching approximately 200 m depth during winter 2015, triggers an intrusion of Chl (0.2 mgm-3) in deeper layers consistent with BGC-Argo float measurements (float lovbio067c, Fig. ). Similar dynamics are reproduced in winter 2014 (Fig. ) for the lovbio035b float drifting from NWM toward the ALB subbasin.

Considering float trajectories, two kinds of situations are possible: the BGC-Argo float trajectory is relatively stationary in the deployment area (Figs. , , and ), or the float migrates extensively by following a given water mass (Fig. ). Results confirm that in the second case, when lateral advection processes could play an important role in the float dynamics, the applied approach also allows an adequate representation of measured Chl patterns. The present multi-float simulation, however, does not include trajectories comprising both west and east Mediterranean basins, where strong gradients between deep water nutrient inventories could invalidate the approach. In such cases, nudging or more sophisticated techniques would be required .

REF results further demonstrate that irradiance along the water column is the driving mechanism controlling DCM depth in addition to mixing, which is proven by a significant correlation between DCM and euphotic depths for both measured and simulated Chl (Fig. a). Such findings were already established in , indicating that the DCM is located at a fixed PAR value, oscillating near the 5.8 µmol photons m-2 s-1 isolume (Fig. b, blue line). Data and model outputs in the present study show a higher variability of critical PAR values in the case of shallower DCM (Fig. b).

The Mediterranean Sea is a nutrient-limited basin (e.g. ); therefore an insight into the role played by nutrients requires further investigation. Phosphate dynamics show an increase in surface Chl driven by nutrient uptake in upper layers due to convective mixing (Figs.  to ). During stratification periods, the phosphocline follows the euphotic layer threshold. Results from the sensitivity analyses (Sect. S4 in the Supplement) illustrate that the role of nutrients is significant in regulating Chl concentration in DCM.

The REF simulation is forced by PAR measurements; hence it is possible to evaluate the direct impact of nutrients' vertical fluxes compared to light on DCM properties. The effect of self-shading by Chl and CDOM can increase the role of nutrients in terms of DCM depth modulation, which can be evaluated only by using bio-optical models where attenuation is regulated by Chl or CDOM as presented in Sect. .

As shown in the previous section, the vertical distribution of Chl displays a distinct variability, which can be at least partially ascribed to mixing. Typically, higher vertical eddy diffusivity values imply smoother structures. During the stratification phase, when DCM forms, the controlling mixing parameter is the background diffusivity Dvbackground.

Simplified theoretical models, such as KiSS , can provide rough quantitative scales in order to determine the minimum vertical length scales (L0) that allow the formation of stable biomass patches , including the DCM, in a steady-state hypothesis: 7L0∝Dvμ, where Dv is the vertical diffusivity coefficient and μ is the growth rate (in stratified conditions Dv=Dvbackground). An increase in background diffusion over a critical value will produce a dispersal of patchy structures (i.e. a relative maximum of Chl concentration), whereas an increase in growth rate μ can drive the formation of finer-scale structures.

The dynamics presented in this study are, however, more complex than KiSS, in terms of both BGC-Argo data and the 1-D BFM model. Vertical eddy diffusivity can simultaneously affect nutrients, phytoplankton, and mesozooplankton with intricate interactions, which in turn make it difficult to derive analytical solutions. Moreover, unlike KiSS, both the model and environment are hardly ever in a steady-state condition, as a result of daily and seasonal oscillations in physical forcings, which are essentially due to variability in diel irradiance and vertical mixing.

Several simulations, labelled MLD1, MLD2, MLD3, and MLD4, were carried out by changing the background vertical eddy diffusivity coefficient values (Dvbackground) by 2 orders of magnitude, i.e. from 10-6 to 10-4 m2 s-1 (Table ). This subset of simulations (with float-derived PAR) clusters at a correlation of approximately 0.8 with RMSD of DCM depth between 10 and 15 m, the same order of what was found by . Perturbing Dvbackground over 2 orders of magnitude (from REF to MLD4) shows that the impact on DCM position is lower than 10 m (Fig. b), with an uplift of DCM depth with higher Dvbackground . The direct impact of eddy diffusivity appears lower compared to direct light modulation on DCM depth.

The alternative bio-optical models (OPT1, OPT2, OPT3) were slightly less accurate compared to REF, with correlation decreasing from 0.8 to 0.6–0.5 (Fig. a). The OPT3 simulation showed a bias very close to zero, thus suggesting an intermediate skill compared to assimilated PAR simulations (e.g. REF) and the bio-optical models (OPT1 and OPT2). OPT1 and OPT2 cluster of simulations shows slightly lower correlations and an increase in bias (almost zero for OPT1 and from 6 to -14 m for OPT2a to OPT2d) with a RMSD of approximately 20 m in all cases.

Some of the bio-optical models considered, in particular OPT1, OPT2a, and OPT2b, reproduce the DCM depth gradient between western and eastern subbasins with a tolerance of ±10 m (Fig. ). In previous studies , the correct simulation of the DCM depth longitudinal gradient was obtained by forcing the system with a space-time-dependent light attenuation parameter based on Secchi disc climatology or on satellite Kd(490) data. Both empirical approaches prevent us from understanding whether the origin of such gradients is directly related to external forcings or if it can be interpreted as a self-emerging property (i.e. related to the appearance of features which are not directly and explicitly imposed from the choice of boundary conditions or model parameters used in the numerical experiment; ). Results suggest that a gradient in DCM depth could be partially reproduced and explained in terms of internal biogeochemical processes and partially due to external forcings (i.e. downward irradiance and nutrient initial conditions), even without considering lateral dynamics (Fig. a, b).

A direct analysis of the impact of alternative bio-optical models on light attenuation (Fig. c) indicates that the simulated eastern basin waters present generally lower Kd values (and lower dispersion around the median) for REF and OPT3. In other cases, where self shading is included, the variability is driven by Chl (from OPT1 to OPT4c) or by Chl and CDOM (OPT5), as bio-optical model parameters do not depend on space and time explicitly. West–east gradients are higher for maximum light attenuation along the water column (cross mark, Fig. c) where Chl concentration is higher. For OPT3, the average and maximum Kd overlap since Kd is parametrized as constant along the water column.

The average surface PAR of the data set considered is higher in eastern areas, especially during the months of January (40 %), September (15 %), October (22 %), November (36 %), and December (16 %), probably due to clearer atmospheric conditions (image not shown). During summer, when DCM stabilizes, the west–east differences in measured surface PAR are lower and oscillate around 10 %; however they still contribute to increasing irradiance penetration at deeper layers.

The western and eastern subbasins are also different in terms of nutrient regimes that in turn impact biogeochemical dynamics and the DCM depth gradient in non-trivial ways. The role of nutrients can be evaluated by perturbing initial conditions for the trajectories starting in the western subbasin (see Sect. S4 in the Supplement). Results indicate that increased nutrients in the western subbasin cause an amplification of the west–east light attenuation gradients (Fig. d) due to the increase in Chl.

The emerging conceptual scheme is that the first-order controlling mechanism for DCM depth is related to light propagation along the water column, as shown in REF and OPT3 simulations. Other tests indicate that nutrients modulate Kd consistently with gradients simulated in REF. The decadal temporal scale of subsurface nutrient variability controlling self-shading mechanisms is longer than that of simulations, suggesting that the role of nutrients in DCM positioning is especially regulated through initial conditions chosen for the present simulations.

Another key factor pertains to shorter wavelengths (400–450 nm) in the visible part of the spectrum: when light penetrates deeper along the water column, compounds like CDOM are more effective in absorbing light and might in turn enhance spatial gradients in irradiance regimes, which could synergistically contribute to a deeper DCM in eastern subbasins. However, with a current mono-spectral formulation, such aspects still cannot be addressed. Multispectral configurations linked with specific PFT and CDOM absorption terms are thus needed for future in-depth studies of the questions raised in the present work .

The use of daily averaged irradiance (i.e. with continuous light, CL1, and CL2) was compared against REF that includes the diurnal variability. A consistent reduction of surface Chl concentrations was observed in the former case (Fig. ), with a correlation lower than REF, affecting (in relative terms) the values around DCM much less (Fig. ).

Near the surface, phytoplankton is limited by low nutrients (especially in eastern subbasins), whereas closer to DCM the trophic limitation is weaker, sometimes nonexistent . One possible explanation could be that light limitation at the DCM at low irradiance values is almost linear; thus the PAR daily averaging effects have a larger impact at the surface, where light limitation is highly non-linear due to saturation. Furthermore, the BFM formulation for Chl acclimation in the case of diurnal variability generates an increase in Chl-to-carbon (Chl:C) ratio. This could in turn have important consequences in operational applications, where data assimilation is employed for model skill improvement: at the surface, the adoption of a diurnal cycle formulation could reduce corrections made by the assimilation scheme and therefore minimize possible spurious trends introduced by it .

Combining daily-averaged irradiances with the lowest diffusivity rates (Dvbackground=10-6 m2 s-1, simulation CL2) results in additional relative Chl maxima at surface layers (Fig. , panel “T=33 weeks”), as well as in increased patchiness of the whole vertical profile. Similar Chl profiles with multiple subsurface maxima were identified in a comprehensive fluorescence data analysis in the Mediterranean Sea . Theoretical considerations predict different maxima along the water column based on the Tilman resource competition theory applied to a heterogeneous system . At this stage, however, it is difficult to assess whether the patchy structures observed in data and model are, for various reasons, realistic or artefactual. Nonetheless, it can be ascertained that the background diffusion needed to maintain such structures in model simulations is very low. As a result, within the framework of currently used mathematical formulations in the 1-D BFM model, the inclusion of diurnal variability tends to reduce the formation of fine-scaled structures that could be interpreted in terms of a reduction in diel growth (μ) or seen as a possible perturbation that has an equivalent effect of an increased diffusion.

OPT4 and OPT5 simulations take into consideration CDOM dynamics by including an additional term in OPT2a, where light attenuation by PAR was described only in terms of Chl. In OPT4a, b, and c, CDOM is parametrized as dead Chl by changing only the rate of Chl decay from 1 d to 1 month. Such a simplified dynamics description derives from the high correlation observed between Chl and CDOM in . However, no analysis was carried out within the present data set to corroborate findings from due to a lack of information on CDOM fluorescence. In all three model configurations, the dead Chl accumulation results in higher turbidity levels that in turn reduce light penetration depths. This is quantified by significantly negative DCM biases (over 40 m in OPT04c), which result in shallower DCM compared to BGC-Argo-derived profiles since the attenuation of Chl is overestimated even when considering the fastest degradation rates (Fig. ). The experiment OPT5 mimics the CDOM dynamics described in where a lower bias is observed compared to the (over)simplified OPT4 tests (where correlation coefficients range from 0.6 to less than 0.1 for OPT4a to OPT4c respectively). OPT5 still results in a negative bias of around 10 m compared to the values from -25 to -40 m for OPT4a to OPT4c. The model, regardless of initial conditions, correctly drives CDOM absorption coefficients in deeper layers to low values, while an enhanced surface production reinforces mineralization and bleaching (Fig. ). Results of CDOM variability from the BOUSSOLE site (northwest Mediterranean; ) show that CDOM absorption ranges to a maximum value of 0.07 m-1 and indicate that there is a temporal delay between phytoplankton bloom and a maximum in CDOM absorption (Fig. 3 in ), whereas deeper layers (below 100 m) have generally lower CDOM absorption. The data set shown in evidences that cycles of CDOM accumulation are followed by depletion in the upper 10 m due to photodegradation in summer. In the model results presented here, bleaching has a deeper effect over the entire CDOM “productive” layer (see red and blue lines, Fig. ), while the subsurface CDOM maximum is not reproduced. The lack of CDOM accumulation in deeper layers for the OPT5 configuration hinders a proper analysis of mechanisms related to the emergence of CDOM from subsurface dark layers. Improving model dynamics calibrations could possibly be achieved by utilizing information on CDOM light absorption from BGC-Argo float measurements .