For the study, we used data from biogeochemical Argo profiles for the period 2011-2022 in the North Atlantic, including the Mediterranean and subpolar areas, i.e., 0-80°N (Argo, 2000; Bittig et al., 2022). All profiles included nitrate observations were selected via the Argo data selection tool ( Figure 1 ). The data set contained pressure, temperature, salinity, chlorophyll a (referred to as chlorophyll) and nitrate. A set of quality requirements was defined for each profile such that location and time of transmissions were well defined (i.e., a QC flag of 1 or 8) and the data coverage of pressure, temperature and salinity was at least 75% (i.e., a QC flag of either A or B) of all profile levels with good data (Argo, 2021). Individual quality checks were applied to all measurements (i.e., a QC flag of 1 or 2) and accepted chlorophyll measurements also included adjusted data due to non-photochemical quenching (i.e., a QC flag of 5). An additional set of criteria was applied for removing profiles with insufficient data coverage: the first pressure measurement should be in the upper 10 m and the upper 200 m of each profile should contain a minimum of 20 observations of all the variables applied in the analysis.

In total, 4108 profiles were included in the data set of which 3680 were used for calculating PP and with a seasonal coverage between 707 - 1356 ( Table 1 ). The data had a broad latitudinal distribution with more than 1000 profiles in each of the 20-degree latitude bands between 20-80°N and with a minimum coverage (n=190) in the tropical area between 0-20°N. Each three month period during the year included between 56 - 825 profiles in each 20-degree latitude band except for the tropical region (0-20°N), where the number of profiles ranged between 40-54. In total, 1395 profiles of the entire data set were obtained from the Mediterranean Sea between 35.2 - 43.8°N, and given the general oligotrophic nature of the area (e.g., Siokou-Frangou et al., 2010), these profiles were considered as representative for mid-latitude conditions and included in the analysis. Thus, all seasons and latitude bands were well represented by the data set.

Surface PAR (SPAR) was extracted from MODIS-satellite data binned in 8-day intervals and in 9x9 km resolution (Frouin et al., 1989; NASA Ocean Biology Processing Group, 2017). SPAR for each float was extracted from the corresponding 8-day period in the binned satellite data set that included the date of the profile transmission. Satellite values were extracted from the four center values in the geographical grid surrounding the location of the Argo float and their average value was assumed to represent the conditions at the location of the float. Missing values were disregarded and if all four nearest neighbors to the float were missing, then the SPAR value for the float was not defined. Similarly, sea surface temperature (SST) and surface chlorophyll a (Hu et al., 2012) were extracted from the MODIS data for calculating PP-parameters based on satellite derived surface values.

Four characteristic depth scales were applied in the analysis of the float profiles: the mixed layer depth (D_Ml), the depth of the euphotic zone (D_Eup), the nutricline depth (D_Nut) and the depth of the deep chlorophyll maximum (DCM).

The D_Ml was defined from a temperature difference of 0.2 °C between 10 m depth and the bottom of the mixed layer (de Boyer Montégut et al., 2004). The mixed layer depth characterizes the upper well mixed surface layer where properties of temperature and salinity are relatively constant.

A constant light attenuation (k_d) for photosynthetic available radiation (PAR) was parameterized from the average chlorophyll concentration in the mixed layer (Morel and Maritorena, 2001; Morel et al., 2007) and the PAR-profile was calculated according to Beer’s law: PAR(z) = SPAR exp(k_d z), where z is the vertical coordinate (i.e., positive upwards, z ≤ 0). The euphotic depth (D_Eup), i.e., the depth range where photosynthesis is assumed to take place, was defined by the depth level where PAR was 0.1% of the surface value (Laws et al., 2014).

The depth of the nutricline (D_Nut) characterizes the vertical nutrient profile in relation to the euphotic zone. The nutricline depth was estimated from the nitrate distribution below the surface layer. When nitrate is the limiting nutrient for PP, the nitracline (D_NO3) will define D_Nut. However, conditions may exist where other nutrients, e.g., silicate (Hátún et al., 2017), iron (Nielsdóttir et al., 2009; Ryan-Keogh et al., 2013), etc., limit PP. Under these circumstances, the nutricline is not related to the nitrate concentration but nitrate will still be consumed in the nitrate-replete surface layer. Therefore, the nitracline below the nitrate-rich surface layer may indicate the depth extent of whatever nutrient(s) is limiting. This appeared possibly to be the case especially with respect to profiles collected at high latitudes, e.g., in the Baffin Bay, where profiles with high nitrate concentrations at the surface exhibited a DCM. In most of these profiles, the depth of the DCM was closely related to a gradient in the nitrate profile. Thus, D_Nut was calculated from two criteria: (1) if the surface concentration of nitrate was less than 1 μmole kg^-1 the nutricline depth was found at the most shallow depth where the nitrate concentration was greater than 1 μmole kg^-1, or (2) the vertical gradient of D_Nut was a maximum. D_Nut was only calculated from profiles with nitrate data above 15 m. The concentration was determined by applying a linear interpolation and the vertical gradient was obtained from the slope of a linear regression of 10 m segments of nitrate.

The DCM was determined by the maximum value of the low-pass filtered (i.e., a 10 m running mean) chlorophyll fluorescence profile. In some areas, the DCM was centered around the depth interval with a significantly elevated chlorophyll concentration and, in those cases, the increased biomass was well-represented by the DCM. However, in some profiles, the DCM was found from a weakly stratified chlorophyll profile in relatively homogeneous mixed layers and, in these profiles, the DCM was not associated with a significant maximum of chlorophyll. This was particularly the case during the fall and winter seasons where chlorophyll variations in the deep mixed layers were relatively small. This was taken into account in the analysis. Here, the DCM is used for expressing the depth of the “deep” chlorophyll maximum. However, in many cases the maximum is located near or at the surface, in particular outside the growth season or in well mixed areas. Thus, we refer to the DCM also in such profiles, as a general term expressing the maximum chlorophyll concentration.

Profiles were also analyzed with respect to the vertically integrated chlorophyll (ΣChl, in units of mg chl m^-2) integrated from D_Eup to the surface. The Argo profiles were analyzed in four latitudinal bands, i.e., 0-20, 20-40, 40-60 and 60-80°N, which are referred to as the tropical, subtropical, mid-latitude and high-latitude areas, respectively. In general, R (R Core Team, 2021) was applied for the statistical analyses.

The total daily primary production in the water column (PP, in units of mg C m^-2 d^-1) was estimated from the vertical distributions of satellite derived PAR and in situ observations of chlorophyll (chl) from the Argo-profiles, i.e., PP_Prof (Webb et al., 1974; Jassby and Platt, 1976):

where t is time and the time integral is integrated during a 24 hour period accounting for the daily solar insolation curve, and vertically from D_Eup to the surface.

The photosynthetic parameters describe the maximum photosynthetic rate ( P max B ) and the initial slope (α^B) of the chlorophyll-normalized PP versus PAR, respectively. The maximum photosynthetic rate was parameterized in terms of SST as originally formulated for the P opt B parameter in the VGPM-model (Behrenfeld and Falkowski, 1997). This parameterization has been shown to represent the general variation of P max B in different oceanic regions although they have been obtained by different incubation methods, i.e., in situ with natural insolation versus incubations in the laboratory (Bouman et al., 2005). Photosynthetic parameters obtained more recently from a global data set showed relatively large variation of P max B in comparison with the VGPM-parameterization (Richardson et al., 2016) and similarly, relatively large variation was found for values in the subpolar North Atlantic (Richardson and Bendtsen, 2021). Despite these concerns, the VGPM-parameterization is applied here as being representative of P max B .

The VGPM-parameterization of P max B implies that P max B increases from 1.3 to 6.6 mg C (mg chl)^-1 h^-1 between 0 °C and 20 °C and gradually decreases towards higher temperatures (Behrenfeld and Falkowski, 1997). It should be noted that this temperature dependence implicitly covers a wide range of hydrographic regions and, therefore, also to some extent accounts for variability in other factors influencing P max B , e.g., phytoplankton community composition.

The parameterization of α^B applied is based on an analysis of surface and DCM values of α^B in different D_NO3 intervals from the global ocean (Richardson and Bendtsen, 2019) and ranges between 1.6 and 4.6·10^-2 μg C (μg chl h μE m^-2 s^-1)^-1. The largest values are associated with the DCM, thus indicating a more efficient use of photons for photosynthesis under the dim light conditions below the surface than at higher light intensities. However, variations of photosynthetic parameters may depend on local nutrient and light conditions (Babin et al., 1996) and co-variation between α^B and P max B are to some extent already considered in the VGPM-parameterization of P opt B (Behrenfeld and Falkowski, 1997; Bouman et al., 2005). Therefore, we apply a constant value of α^B of 3.1·10^-2 μg C (μg chl h μE m^-2 s^-1)^-1, corresponding to the mid-point between the largest and smallest value in the study of Richardson and Bendtsen (2019), as a representative value. In general, total PP estimates are about twice as sensitive to the value of P max B than the value of α^B (Morel et al., 1996). Thus, the applied parameterization of P max B is a critical component in the analysis of the large-scale distribution of PP.

The general relationship between PP, light and nutrients estimated from Argo-profiles was compared with similar relationships obtained from two different PP-models based on surface observations, i.e. the VGPM-model (PP_VGPM; Behrenfeld and Falkowski, 1997), and the VPP-model (PP_VPP; Richardson and Bendtsen, 2019).

PP in the VGPM-model is calculated as: PP_VGPM = P opt B chl(surf) f(SPAR) D’_eu, and depends on P opt B derived from surface observations of SST, surface chlorophyll (chl(surf)), a light function depending on SPAR (f(SPAR)) and the euphotic depth ( D eu ' ). This model was analyzed in two cases where surface fields were extrapolated from Argo-measurements of SST and chlorophyll near the surface and the estimated D_Eup or from satellite observations of SST and chlorophyll and a parameterization of D’_eu that was representative for case 1 waters (Morel et al., 2007). The general distribution of the two cases was similar and only results of the PP_VGPM based on Argo-profiles are shown.

PP in the VPP-model is calculated as: PP_VPP = PP_10m/γ. This model estimates PP from primary production calculated from Eq. (1) but only in the upper 10 m, i.e. PP_10m. The ratio between total PP and PP_10m was calculated from a global data set of PP and analyzed in three nutricline depth intervals: D_nut< 20 m, 20-90 m and > 90 m, and the corresponding values of γ were 0.31, 0.19 and 0.11, respectively, e.g., 31% of total PP on average occurs in the upper 10 m in areas where the nutricline depth is less than 20 m. Here, we apply the same photosynthetic parameters of P max B and α as for calculating PP_prof and PP_VGPM.

PP_VGPM and PP_VPP are thus used here as two examples of a family of models estimating PP on the basis of surface optical characteristics observed by satellites against which PP-model estimates employing vertical distribution data for light, nutrients and chlorophyll could be compared.

The DCM was generally located below the D_Nut except in areas with a shallow nutricline (<30 m) or in profiles obtained during winter time ( Figure 2 ). Relatively shallow DCMs associated with deep nutriclines (D_Nut>90m) were also mainly found during the winter period ( Figure 2 , triangles). The average depth of all DCMs in areas with a D_Nut less than 20 m was 32 m and it increased to 88 m in areas where D_Nut was larger than 90 m ( Table 2 ). During the growth season from April-November the average DCM, binned in 20 m depth intervals, was generally located below D_Nut, except for areas with a shallow nutricline, i.e., less than 20 m ( Figure 2 , black circles). The latitudinal distribution of the DCM depth (colors, Figure 2 ) also showed a gradual increase from high latitudes (~35 m, Table 2 ) towards the tropics (~112 m). This increase in the depth of the DCM with latitude was associated with the deepening of the D_Nut towards subtropical and tropical areas.

Phytoplankton biomass was approximated by vertically integrating chlorophyll (ΣChl) in the water column. The greatest biomass was found at high latitudes (60-80 °N) where ΣChl typically varied between 20 - 100 mg chl a m^-2 ( Figure 2 , blue circles) with an average of 38 mg chl a m^-2 ( Table 2 ). Values lower than 20 mg chl a m^-2 were associated with profiles made during periods of low light intensities during the winter season ( Figure 2 , triangles) while the highest values (>50 mg chl a m^-2) were associated with phytoplankton blooms in the growth season at high- and midlatitudes. Mid-latitude areas exhibited a relatively large range of biomass (10-100 mg chl a m^-2) with an average value of 35 mg chl a m^-2, i.e., comparable to that found at high latitudes. Significantly lower phytoplankton biomass was found in subtropical and tropical areas with an average ΣChl of 19 and 17 mg chl a m^-2, respectively.

The distribution of DCM and ΣChl in relation to nutricline depth and latitude motivated an analysis of the combined influence of light (represented by SPAR) and nutricline depth, i.e., representing the availability of nutrients. The distribution of DCM in a diagram spanned by D_Nut and SPAR showed a characteristic large-scale pattern, where a shallow DCM (<20 m) was associated with a relatively shallow D_Nut, whereas the deepest DCMs were found in oligotrophic areas with a deep D_Nut and a high SPAR ( Figure 3 ). The vertically integrated chlorophyll distribution also showed a characteristic pattern with a well-defined maximum in areas of a relatively shallow D_Nut (<50 m) and modest insolation (SPAR ~ 40 E m^-2 d^-1), and a gradual decrease of ΣChl with deeper D_Nut ( Figure 3 ).

The distribution of PP_Prof in relation to D_Nut had some similarity to that found for ΣChl ( Figure 4 ). The greatest PP_Prof was found at high latitudes and in subpolar areas with average values of 571 and 676 mg C m^-2 d^-1, respectively ( Table 2 ). The observed range (0 to >2 g C m^-2 d^-1) at high and mid-latitudes ( Figure 4 , blue circles) was associated with low PP_Prof during the dark winter months and relatively high PP_Prof during the growth season. PP_Prof showed a gradual decrease towards subtropical and tropical areas where PP_Prof in general ranged between 50-500 mg C m^-2 d^-1 with average values of 332 and 296 mg C m^-2 d^-1, respectively.

The entire PP_prof data set was analyzed in a manner similar to the approach used for chlorophyll in a diagram spanned by light and nutricline depth ( Figure 5 ). PP_Prof had a maximum of ~1.4 g C m^-2 d^-1 for SPAR ~58 E m^-2 d^-1 and D_Nut ~10 m depth ( Figure 5 ). Only a few profiles had a D_Nut less than ~10 m. Thus PP_prof generally decreased with increasing D_Nut for all light levels. PP_Prof at low light levels (<10 E m^-2 d^-1) was less than 400 mg C m^-2 d^-1 and decreased below 200 mg C m^-2 d^-1 in areas with a D_nut deeper than ~90 m depth. In general, the lowest PP_Prof-values were seen in areas with a deep D_nut and low light levels, i.e., in areas with the deepest DCM ( Figure 3 ). The majority of profiles with D_nut< 50 m were located at high- and mid-latitudes, whereas deep nutriclines and high light levels were mainly occupied with profiles from the subtropical and tropical areas. The lowest light levels (SPAR< 10 E m^-2 d^-1) were recorded at high latitudes and represented conditions from the dark winter season. The tilted shape of the highest PP-values were shifted upward towards higher SPAR compared with the corresponding tilted distribution of ΣChl ( Figure 3 ), showing the influence of light on the PP-estimate. Thus, the data suggest a general pattern that would be expected, i.e., water column PP_Prof decreasing gradually with increasing nutricline depth and increasing with increasing SPAR.

The general PP-distribution was analyzed further by considering the statistical variation of PP in the diagram spanned by SPAR and D_nut ( Figure 6 ). The diagram was divided into equidistant intervals of SPAR of 5 E m^-2 d^-1 and D_nut of 20 m depth, and the corresponding values of the mean and standard deviation of PP were calculated. On average, there were 29 PP-values in each cell and cells with less than 5 PP-values were not considered. The PP-diagram based on the gridded average distribution of PP ( Figure 6 ) was in accordance with the diagram based on all data (e.g., Figure 5 ). The diagram showed a similar peak value in areas with a shallow nutricline and high light levels, a general decrease towards deeper nutricline depths, and a general increase with increasing light levels. The relative error within each cell was defined from the ratio between the standard deviation of PP and the mean of the total PP ( Figure 6 ) and was in general less than 60%. Areas with a shallow nutricline were in general associated with a relative error above 50%, whereas the relative error was less in areas with a deep nutricline. However, the largest variability of 50 - 80% was found in areas with nutricline depths between ~80 - 120 m depth and with relative high light levels between ~35 - 50 E m^-2 d^-1.

In the shallow nutricline interval (<50 m), the PP_VGPM and PP_VPP also showed a maximum at ~58 E m^-2 d^-1. The minimum PP in the two models were seen in areas with a deep nutricline (>120 m) and relatively high light levels (>40 E m^-2 d^-1). Thus, the two PP-models yielded significantly different estimates in regions characterized by a deep nutricline: PP_Prof showed an increase in PP with increasing light-levels while the two surface-based models showed a significant decrease. The structure of the two models was also different in areas with a shallow nutricline and low light levels, where a more gradual increase of PP with increasing light was seen in the PP_Prof than in the VGPM estimate.

The general relationship between the depth of the DCM and D_Nut showed that some DCMs tended to be located deeper than D_Nut at high latitudes. These profiles were generally made during winter ( Figure 2 , triangles). Otherwise, DCMs tended to be located deeper than D_Nut, where DCMs from the growth season were more closely related to D_Nut than during winter time. During the growth season, the depth levels of the DCM and D_Nut in the intermediate depth range between 20 - 90 m were in general accordance. Thus, this distribution from the entire North Atlantic of DCM and D_nut is in good accordance with previous findings (Herbland and Voituriez, 1979; Cullen, 1982; Cullen, 2015) and supports the hypothesis that the chlorophyll maximum is closely related to the nutrient distribution. In areas with a nutricline deeper than ~90 m, DCMs were generally located above D_Nut. This general pattern is also in accordance with previous studies and can be explained by light limitation when D_Nut becomes too deep to support growth (Richardson and Bendtsen, 2019).

Some profiles at high and mid-latitudes showed that the DCM was deeper than D_nut in areas with D_nut less than 50 m also during the growth season ( Figure 2 ). The binned average DCMs during the growth season was only deeper than D_nut in the depth range between 0 - 20 m. The relation between DCM and D_nut was thus weaker in these areas, suggesting that processes other than nutrient limitation could be important here. Fluorescence, and the ratios between fluorescence and chlorophyll, and carbon and chlorophyll can be affected by nutrient and light conditions (Westberry et al., 2016). The effects of light on phytoplankton are considered when estimating chlorophyll from fluorescence and chlorophyll concentrations are corrected in the adjusted BGC-Argo data (Roesler et al., 2017). Iron stress also causes increases in fluorescence (Behrenfeld and Milligan, 2013; Schallenberg et al., 2022) and decreases in the carbon to chlorophyll ratio (Westberry et al., 2016), which would ultimately appear as high chlorophyll from the floats. While iron limitation is not well-studied in the North Atlantic, it is possible that the reduction in chlorophyll at high latitudes during high SPAR ( Figure 3 ) may be a result of growth limitation by micronutrients (e.g., Westberry et al., 2016) or due to photoinhibition (Yang et al., 2022). The photoprotective strategy in phytoplankton has been seen in Arctic phytoplankton species (Lacour et al., 2018) and is a prominent feature in polar waters (Kauko et al., 2017). A response from phytoplankton to iron limitation or excessive light could explain the relatively few profiles with a weak relation between DCM and D_Nut during the growth season at high latitudes. In summary, the location of the DCM, as well as the vertically integrated chlorophyll, generally showed a strong relationship to D_Nut.

The relationships between PP_Prof, nutricline and latitude ( Figure 4 ) suggested that D_Nut could be associated with nutrient availability in large areas of the ocean, and the latitudinal distribution indicated that part of the PP_Prof variation could be described by light conditions. This motivated the combined analysis in a diagram showing PP_prof versus D_nut calculated from Argo-profiles and PAR obtained from satellite observations ( Figure 5 ). These two variables are only proxies for the in situ drivers of phytoplankton growth: PAR in the water column is modified by local attenuation and this is not accounted for by SPAR, and D_Nut only indirectly represents nutrient supply by mixing to the euphotic zone. However, both variables are closely related to light and nutrient supply for primary production and this is supported by the corresponding distributions of chlorophyll ( Figure 3 ).

PP_Prof increases relatively quickly as SPAR increases in areas with a shallow nutricline, generally at high latitudes ( Figure 6 ). In these areas, light is expected to be the primary limiting factor for PP, given availability of all other limiting micro-nutrients. Thus, light availability could explain the steady increase of PP_Prof with increasing light levels up to ~58 E m^-2 d^-1. PP_Prof decreases at higher light levels (>60 E m^-2 d^-1) in areas with a relatively shallow D_nut (<50 m). The reduced PP_Prof at the highest PAR may be explained by reduced photosynthesis due to photoinhibition (Falkowski and LaRoche, 1991; MacIntyre et al., 2002; van de Poll et al., 2011), or the limitation by another micro-nutrient such as iron (Behrenfeld and Milligan, 2013; Westberry et al., 2016). However, more profiles in high light and shallow nutricline conditions are required for analyzing this further. Areas characterized by low light levels and a deep D_Nut (i.e., SPAR<10 E m^-2 d^-1 and D_Nut>40 m) were only covered by few PP_Prof-data. indicating that D_Nut was in general less than ~40 m at high latitudes during winter.

The highest PP_Prof estimates (>1 g C m^-2 d^-1) were seen in areas with a relatively shallow nutricline (<50 m) and were mainly located at mid- and high latitudes. This can be explained by the combination of high nutrient concentrations where D_Nut was shallow, and high light levels during the growth season. Low PP_Prof estimates in areas with a shallow D_nut can be explained by low light levels during the winter season. PP in the intermediate nutricline depth range (50-90 m) was generally below 1 g C m^-2 d^-1 and was mainly associated with profiles from mid-latitudes and the subtropical areas. Subtropical and tropical profiles were mainly available for areas where D_Nut was below 90 m.

The PP_Prof distribution was in good accordance with the expected variation with light and nutrient availability. In areas with a deep D_Nut (>100 m), PP_Prof increased steadily with light. Similarly, areas with a shallow D_Nut, i.e., mainly located at mid- and high-latitudes, showed an expected but also stronger increase of PP with increasing light at light levels below ~50 E m^-2 d^-1. PP_Prof is proportional to the chlorophyll concentration (Eq. 1) and some similarity is also seen between PP_Prof and ΣChl ( Figure 3 ). However, the consistent increase of PP with SPAR for any D_Nut depth level suggests a general relationship between PP_Prof, SPAR and nutrients in oligotrophic areas. PP_Prof was also found to gradually decrease with increasing D_Nut at all light levels.

The associated error-distributions showed that PP could be estimated with a relative error of less than 50% in large parts of the PP-diagram, in particular in areas with a deep nutricline depth. PP in these areas appears to be well constrained by light and nutricline depth. In areas with a shallow nutricline (<50 m), the relative error was between 50 - 60% and the largest variability was seen with modest to high light levels (20 - 40 E m^-2 d^-1). These profiles were generally encountered at high latitudes ( Figure 5 ), suggesting that the estimation of PP is more variable in the PP-diagram during spring and/or fall whereas the relative error decreases towards higher (summer) and lower (winter) light levels. The maximum variability is seen in the intermediate range of nutricline depths (~80 - 120 m) and light levels (~35 - 50 E m^-2 d^-1), and this shows that PP estimated from this part of the PP-diagram is less well determined by light and nutricline depth. Profiles from this part of the diagram are mainly from the subtropical and tropical areas of the ocean, and the variability indicates that PP is also influenced by other processes.

Some of this variability could be explained by short-term variability in PP due to vertical mixing by mesoscale eddies (Johnson et al., 2010). Increased nutrient inputs from ocean eddies will tend to increase the PP-rate for a relatively long period, whereas nutricline depth levels tend to increase relatively quickly after a mixing event (e.g., Richardson and Bendtsen, 2017). Thus, profiles obtained from these areas may include measurements made both before and after such mixing events. This might explain some of the variability in this part of the PP-diagram. In addition, while PP is calculated from float-based chlorophyll, it is important to take into account other factors that influence chlorophyll and fluorescence measures. Part of the variability in PP could be attributed to a sum of factors from iron limitation, to a change in community structure and species composition (Roesler et al., 2017). However, while the influence of these factors varies with area, the same chlorophyll measures were used to model PP, which would remove variability between profiles, leaving the relative variance the same.

There is only an indirect relationship between PP_Prof and D_Nut, however, the PP-diagram indicates that PP_Prof can be directly related to nutrient availability for a given level of SPAR. This is in line with earlier local studies showing relationships between PP and nutrient distributions (e.g., Herbland and Voituriez, 1979). The general distribution of PP_Prof shows a well-defined maximum in areas with a shallow nutricline (< 60 m) and SPAR-levels between ~40 - 50 E m^-2 d^-1 where PP_Prof reaches an average value of ~1 g C m^-2 d^-1, and a general decrease of PP_Prof towards deeper nutriclines with typical PP values between 200 - 400 mg C m^-2 d^-1. PP estimated from the averaged PP-diagram ( Figure 6 ) has a relative error of about 50% compared with PP_Prof.

The PP-diagram provides a method for comparing estimates of the large-scale distributions of PP from different models in relation to light and nutricline depth. The VGPM-model (Behrenfeld and Falkowski, 1997) was parameterized from a large data set of in situ PP-measurements and has been applied in several studies and its strengths and shortcomings have been evaluated in previous studies (e.g., Carr et al., 2006). The VPP-model also depends on surface observations alone and was based on a simple relationship between PP and nutricline depths in a global data set (Richardson and Bendtsen, 2019). Therefore, we apply these two models as examples of a comparison in the PP-diagram of different surface-based PP-models with PP_Prof, i.e., PP estimated explicitly from in situ observations in the entire euphotic zone. The two models can be driven by observed satellite fields alone. However, in order to make a direct comparisons between PP_Prof, PP_VGPM and PP_VPP, all are here calculated from surface chlorophyll and surface temperature extrapolated from the uppermost measurement in the Argo-profile.

The PP_VGPM and PP_VPP-distributions showed a maximum at shallow nutricline depths and light levels between 30 - 60 E m^-2 d^-1. The decrease in PP noted with increasing nutricline depth was in general accordance with PP_Prof ( Figure 7 ). However, the maximum values in the PP_Prof distribution were ~1200 mg C m^-2 d^-1 whereas the corresponding maxima were ~1400 and 2000 mg C m^-2 d^-1 for the PP_VGPM and PP_VPP, respectively. Thus, both models resulted in a significantly higher peak value than PP_Prof. Both the PP_VGPM- and the PP_VPP-distributions decreased steadily with increasing SPAR-levels above ~20 E m^-2 d^-1 in areas with a deep nutricline (>130 m). This is not in accordance with the expected photosynthetic response for an increase in PAR and indicates that these models may underestimate PP in this part of the PP-diagram.

Previous analyses of PP estimated from the VGPM-model indicated that it underestimates PP in oligotrophic areas when compared to other PP-models (Westberry et al., 2008; Emerson, 2014) and the distributions in Figure 7 suggest that this could be an issue relevant for both surface-based PP-models due to a general underestimation of PP in tropical and subtropical areas with a deep nutricline. Oligotrophic areas with a deep nutricline are generally characterized by low surface concentrations of chlorophyll a (e.g., Richardson and Bendtsen, 2017), and these low chlorophyll values can explain the low estimates in this part of the PP-diagram.

Thus, we find a general structural difference between the two surface-based models and PP_Prof, where PP_Prof shows a more gradual increase with D_nut< 50 m and an expected increase with light in areas with a deep nutricline. It should be noted that both models show the same tilted structure as seen in the vertically integrated chlorophyll distributions for D_Nut less than ~90 m ( Figure 3 ). This comparison demonstrates the applicability of the PP-diagram for identifying structural differences between PP-models in relation to observed fields of nutrients and light.

The comprehensive BGC-Argo data archive with high-resolution vertical nitrate profiles provides a new opportunity to include nitrate or, more generally, nutrients in the evaluation of PP-estimates from different models. Using this data archive, PP-estimates can be analyzed in relation to in situ observations of nutrient availability and satellite observations of SPAR, i.e., the two most critical factors for photosynthesis and biological production. The distribution of PP_Prof in relation to light and nutrient availability suggest that universal relations exist between large-scale PP, light and nutricline depth, and these relations may then be applied in the analysis of different PP-models and, more generally, for estimating large-scale patterns of PP from information about light and nutrients alone.

The general distribution of the PP-estimate versus light and nutrient availability showed that a PP-diagram can be applied for evaluating different PP-models. The differences between the two surface-based PP-models and PP_Prof examined in this study showed the potential of using nutrient information in the evaluation of global PP-patterns. At high latitudes characterized by shallow nutriclines, it is important to acknowledge the interchanging effects of light and nutrients between the seasons: where light is the dominant limiting factor in the winter and nutrients become limiting in the summer, when light is sufficient. Future work should include a distinction for high nutrient, low chlorophyll (HNLC) areas like the Southern Ocean, where iron and light primarily limit phytoplankton growth and primary production (Martin et al., 1990; Boyd et al., 2007).

Light and nutrient-based estimates of PP may also elucidate large-scale distributions of new production (NP), i.e., the fraction of PP based on newly available nitrate or nitrite (Dugdale and Goering, 1967). NP balances the export of organic matter on longer timescales (> month - years) and the fraction of PP exported out of the euphotic zone (i.e., the f-ratio; Eppley and Peterson, 1979) has been found to increase with PP and decrease with SST (Laws et al., 2011). Thus, the PP-diagram indicates that the corresponding NP-distribution would tend to have an even more steep gradient between areas with a shallow and a deep nutricline.

The models applied in this study represent examples among a suite of PP-models (e.g., Carr et al., 2006). PP-models may be solely driven by satellite observations (Westberry et al., 2008; Uitz et al., 2010; Silsbe et al., 2016), derived from ocean circulation models (Kwiatkowski et al., 2020) or by data-assimilation by combining observations and circulation models (Gregg and Rousseaux, 2019). However, the access to information about location, light and in situ nutrient conditions makes evaluations in a PP-diagram possible with these other model-products.