Biogeochemical (BGC) tracers and their interactions with upper-ocean physical processes, from basin-scale circulations to millimeter-scale turbulent dissipation, are critical for understanding the role of the ocean in the global carbon cycle. These interactions cause multi-scale spatial and temporal heterogeneity in tracer distributions that can greatly affect carbon exchange rates between the atmosphere and interior ocean, net primary productivity, and carbon export . There are still significant gaps, however, in our understanding of how these biophysical interactions develop and evolve, thus limiting our ability to accurately predict critical exchange rates.

Better understanding these interactions requires accurate physical and BGC models that can be coupled together. The exact equations that describe the physics (e.g., the Navier–Stokes or Boussinesq equations) are often known and physically accurate solutions can be obtained given sufficient spatial resolution and computational resources. Due to the vast diversity and complexity of ocean ecology, however, even when only considering the lowest trophic levels, accurately modeling BGC processes can be quite difficult. Put simply, there are no known first-principle governing equations for ocean biology.

As such, two different approaches to modeling BGC processes are often used when faced with this challenge. The first is to increase model complexity and include equations for every known BGC process. Often, these models include species functional types or multiple classes of phytoplankton and/or zooplankton that each serve specific functional roles within the ecosystem, such as calcifiers or nitrogen fixers. The justification for this approach is that particular phytoplankton and zooplankton groups serve as important system feedback pathways, and that without explicit representation of these feedbacks, there is little hope of accurately representing the target ecosystem . In many cases, these models also contain variable intra- and extracellular nutrient ratios, which are important when accounting for different nutrient regimes within the global ocean and species diversity of non-Redfield nutrient ratio uptake .

Although these more complex models are typically highly adaptable and are often able to capture different dynamics than those for which they were calibrated , these more complex models contain many more parameters than their simplified counterparts. Moreover, many of the parameters, such as phytoplankton mortality, zooplankton grazing rates, and bacterial remineralization rates, are inadequately bounded by either observational or experimental data . Because of the increased complexity of such models, it is also often difficult to ascertain which processes are responsible for the development of a particular event (e.g., a phytoplankton bloom), and so these models can be ill suited for process studies. Lastly, while these highly complex models are regularly used within global Earth system models (ESMs), they are typically prohibitively expensive to integrate within high-fidelity, high-resolution physical models. Examples of such models are those used to enhance fundamental understanding of subgrid-scale (SGS) physics in ESMs and to assist in the development of new SGS parameterizations .

In broad terms, the second common BGC modeling approach is focused on substantially decreasing model complexity and severely truncating the number of equations used to describe the dynamics of an ecosystem. Such approaches include the well-known nutrient–phytoplankton–zooplankton–detritus class of models. These models have significantly fewer unknown parameters and can be more easily integrated within complex physical models. Their simplicity also enables greater transparency when attempting to understand the dominant forcing or dynamics underlying a particular event. While they are often capable of reproducing the overall distributions of chlorophyll, primary production, and nutrients , such simplified models have been shown to underperform at capturing complex ecosystem dynamics, and often struggle in regions of the ocean for which they were not calibrated .

Although both of these general BGC modeling approaches have their respective advantages, particularly given their different objectives, the difference between lower-complexity BGC models used in small-scale studies and the more complex BGC models used in global ESMs poses a problem. In particular, the difficulty in directly comparing the two types of models makes the process of “scaling up” newly developed parameterizations or “downscaling” BGC variables within nested-grid studies much more challenging. This motivates the need for a new BGC model that is reduced enough to be usable within high-resolution, high-fidelity physical simulations for process, parameterization, and parameter optimization studies but is still complex enough to capture important ecosystem feedback dynamics, as well as the dynamics of vastly different ecosystems throughout the ocean, as required by ESMs.

To begin addressing this need, here we present a new upper-thermocline, open-ocean, 17-state-variable Biogeochemical Flux Model (BFM17) obtained by reducing the larger 56-state-variable Biogeochemical Flux Model (BFM56) developed by . Most high-fidelity, high-resolution physical models are capable of integrating 17 additional tracer equations with limited additional computational cost. Following the approach used in BFM56 , a biological and chemical functional family (CFF) approach underlies BFM17, where matter is exchanged in the model through units of carbon, nitrate, and phosphate. This permits variable non-Redfield intra- and extracellular nutrient ratios. Most notably, BFM17 includes a phosphate budget, the importance of which has historically been underappreciated even though observational data have indicated its potential importance as a limiting nutrient, particularly in the Atlantic Ocean . To reduce model complexity, we parameterize certain processes for which field data are lacking, such as bacterial remineralization.

In the present study, we outline, in detail, the formulation of BFM17 and its development from BFM56. We couple BFM17 to the 1-D Princeton Ocean Model (POM) and validate the model for upper-thermocline, open-ocean conditions using observational data from the Sargasso Sea. We also compare results from BFM17 and the larger BFM56 for the same upper-thermocline, open-ocean conditions. As a result of the focus on upper-thermocline, open-ocean conditions, further assumptions have been made in deriving BFM17 from BFM56, such as the exclusion of any representation for the benthic system and the absence of limiting nutrients such as iron and silicate.

It should be noted that the primary focus of the present study is to introduce the viability of BFM17 as an accurate BGC model for high-resolution, high-fidelity simulations of the upper ocean used in process, parameterization, and parameter optimization studies. This is accomplished here by comparing results from BFM17 to results from observations and BFM56; as such, here we only consider one open-ocean location (i.e., the Sargasso Sea). Although the model must also be applied at other locations to determine its general applicability, its ability to reproduce important and difficult key behaviors in the Sargasso Sea supports its use as a process study model. The correspondence between BFM17 and the more general BFM56 also provides confidence that the reduced model will prove effective at modeling other ocean locations and conditions, and exploring the range of applicability of BFM17 remains an important direction for future research. We also emphasize that relatively limited calibration of BFM17 parameters has been performed in the present study. Most parameters are set to their values used in the larger BFM56 , and optimization of these parameters over a range of ocean conditions is another important direction of future research, for which BFM17 is ideally suited.

Finally, we note that other similarly complex BGC models have been calibrated using data from the Sargasso Sea, such as those developed in , , , , , , , , and . However, each of these models employs less than 10 species and none use a CFF approach or include oxygen, a tracer that is historically difficult to predict. Although some of these models employ data assimilation techniques (e.g., ) and produce relatively accurate results, most leave room for improvement. With a minimal increase in the number and complexity of the model equations, such as those associated with tracking phosphate in addition to carbon and nitrate, and by including both particulate and dissolved organic nutrient budgets, we anticipate that a significant increase in model accuracy and applicability might be achieved over previous models of similar complexity. Additionally, with this increase in model complexity, the disparate gap between the complexity of BGC models used in small- and global-scale studies is reduced, thereby simplifying up- and down-scaling efforts. This last point is emphasized here by the good agreement between results from BFM17 and BFM56.

In the following, BFM17 is introduced in Sect. , with detailed equations and parameter values provided in Appendix . Results from a zero-dimensional (0-D) test of BFM17 are provided in Appendix . In Sect. , BFM17 is coupled to the 1-D POM physical model. A discussion of the methods used to calibrate and validate the model with observational data collected in the Sargasso Sea is presented in Sect. . Model results, a skill assessment, a comparison to results from BFM56, and a brief comparison to other similar BGC models are discussed in Sect. .

The 17-state equation (BFM17) is an upper-thermocline, open-ocean BGC model derived from the original 56-state equation model (BFM56) , which is based on the CFF approach. In this approach, functional groups are partitioned into living organic, non-living organic, and non-living inorganic CFFs, and exchange of matter occurs through constituent units of carbon, nitrogen, and phosphate. To date, there are no other BGC models with this order of reduced complexity using the CFF approach, making BFM17 unique and able to accurately reproduce complex ecosystem dynamics.

BFM17 is a pelagic model intended for oligotrophic regions that are not iron or silicate limited and is obtained from the more-complete BFM56 by omitting quantities and processes assumed to be of minor importance in these regions. We have developed BFM17 primarily for use with high-resolution, high-fidelity numerical simulations, including large eddy simulations (LESs) used in process, parameterization, and parameter optimization studies. As such, we do not validate the efficacy of BFM17 as a global BGC model, and note that it is missing potentially important processes for such an application, which we elaborate on shortly. We also note that we compare BFM17 to the original BFM56 in Sect.  to demonstrate that, although it is reduced in complexity, BFM17 is equally appropriate for use in seasonal process, parameterization, and optimal parameter estimation studies for which a more complex model such as BFM56 may be too computationally expensive. Nevertheless, given the agreement between the BFM17 and BFM56 results in Sect. , there is reason to believe that BFM17 may have potential as a global BGC model, and the examination of the broader applicability of BFM17 is an important direction for future research.

In BFM17, the living organic CFF is comprised of single-phytoplankton and zooplankton living functional groups (LFGs); these two groups are the bare minimum needed within a BGC model and already account for six state equations (corresponding to carbon, nitrogen, and phosphate constituents of both groups). The baseline parameters used in BFM17 are those detailed in , and a complete list of the model parameters is provided in Appendix . Parameters used in the representation of phytoplankton loosely correspond to the flagellate LFG in BFM56, while the zooplankton parameters correspond to the micro-zooplankton LFG. The only relevant difference with respect to is related to the choice of the phytoplankton specific photosynthetic rate (rP(0) in Table  of Appendix ); in this case, the new value was chosen according to the control laboratory cultures of .

Within BFM17, we track chlorophyll, dissolved oxygen, phosphate, nitrate, and ammonium, since their distributions and availability can greatly enhance or hinder important biological and chemical processes. Dissolved oxygen is of particular interest, because it is historically difficult to predict using BGC models of any complexity. This is likely due, in part, to missing physical processes in the mixing parameterizations used in global and column models. This provides motivation for the present study, since a primary goal in the development of BFM17 is to create a BGC model that can be used in combination with high-resolution, high-fidelity physical models (e.g., those found in LES) to understand the effects of these physical processes and how they can be more accurately represented in mixing parameterizations.

Dissolved and particulate organic matter, each with their own partitions of carbon, nitrogen, and phosphate, are also included in BFM17 to account for nutrient recycling and carbon export due to particle sinking. Another primary goal of developing BFM17 is to explore how spatially decoupled (or “patchy”) processes, such as the sinking of organic matter and the subsequent upwelling of multiple recycled nutrients (not just nitrate) affect the fate and distribution of a phytoplankton bloom.

Lastly, remineralization of nutrients is provided by parameterized bacterial closure terms, thereby reducing complexity while still maintaining critical nutrient recycling. The related parameter values (see Table  in Appendix ) were chosen according to , who carried out sensitivity tests to evaluate the many parameter values found in the literature.

Iron is omitted from BFM17, limiting the applicability of the model in regions where iron components are important, such as the Southern Ocean and the tropical Pacific. Thus, if used in such regions, at least a fixed concentration of iron may be needed (although this method has not yet been validated within BFM17). Top-down control of the ecosystem in the form of explicit predation of zooplankton is also not included. Instead, a simple constant zooplankton mortality is used, as this is a complicated process and understanding where to add this closure and where to feed the particulate and dissolved nutrients from this process in a lower-complexity model is not well understood. However, the addition of a top-down closure term was tested, and no major differences were observed in the model results. Consequently, it was assumed that the constant mortality term was sufficient for this model, similar to other models of this complexity . Additionally, the benthic system within BFM56 has been removed. It is assumed that within the upper thermocline of the open ocean, the ecosystem is not substantially influenced by a benthic system and any water-column influences from depth can be taken into account using boundary conditions (such as those discussed in Sect. ). As such, we cannot attest to the accuracy of BFM17 in shelf or coastal regions.

In summary, notable novel attributes of BFM17, in comparison to other models of comparable complexity, are the use of (i) CFFs for living organisms, including two LFGs for phytoplankton and zooplankton, (ii) CFFs for both particulate and dissolved organic matter, (iii) a full nutrient profile (i.e., phosphate, nitrate, and ammonium), and (iv) the tracking of dissolved oxygen. A summary of the 17 state variables tracked in BFM17 is provided in Table , and a schematic of the CFFs and LFGs used in BFM17, along with their interactions, is shown in Fig. . The detailed equations comprising BFM17, as well as all associated parameter values, are presented in Appendix . Results from an initial 0-D test of BFM17 are provided in Appendix .

As a demonstration of BFM17 for predicting ocean biogeochemistry in oligotrophic pelagic zones, here we couple the model to a 1-D physical mixing parameterization and make comparisons with available observational data in the Sargasso Sea. In order to focus on the upper-thermocline, open-ocean regime for which BFM17 was developed, the physical model only extends 150 m in depth and diagnostically calculates diffusivity terms based upon prescribed temperature and salinity profiles from the observations. While a 1-D physical model is unlikely to resolve all processes relevant for biogeochemistry in the upper thermocline, we have made additions, such as large-scale general circulation and mesoscale eddy vertical velocities, as well as relaxation bottom boundary conditions for nutrient upwelling, to better represent missing processes.

For all equations here and in Appendix , we adopt the same notation style used for BFM56 in , , and the BFM user manual for consistency and clarity. The coupled physical and BGC model is a time–depth model that integrates in time the generic equation for all biological state variables, denoted Aj, given by 1∂Aj∂t=∂Aj∂tbio-W+WE+v(set)∂Aj∂z+∂∂zKH∂Aj∂z, where Aj are the 17 state variables of BFM17, the first term on the right-hand side accounts for sources and sinks within each species due to biological and chemical reactions (as represented by the equations comprising BFM17 and outlined in Appendix ), W and WE are the vertical velocities due to large-scale general circulation and mesoscale eddies, respectively, v(set) is the settling velocity, and KH is the vertical eddy diffusivity. Although the BFM17 formulation and model results are the primary focus of the present study, we also perform coupled physical–BGC simulations using BFM56 for comparison. Equation () applies to all 17 state variables in BFM17, as well as to all 56 state variables in BFM56. Consequently, the only differences between the biophysical models with BFM17 and BFM56 are the number of state variables being tracked and the equations used to calculate the biological forcing terms. The specific forms of Eq. () for each of the 17 species in BFM17 are discussed in Appendix , and the specific forms of this equation for each of the 56 species in BFM56 were previously discussed in . The parameters used in BFM56 correspond to the values provided in Tables – of Appendix , with the remaining undefined parameters (since BFM56 includes many more model parameters than BFM17) based on values from .

The range of values for W and WE in Eq. () is included in Table  and the corresponding depth profiles are discussed in Sect. . The settling velocity, v(set), in Eq. () is only non-zero for the three constituents of particulate organic matter, and its value is given in Table . We assume v(set)=0 for zooplankton, since zooplankton actively swim and oppose their own sinking velocity. Finally, KH in Eq. () is calculated by the model and is described in more detail later in this section.

To obtain the complete 1-D biophysical model, BFM17 has been coupled with a modification of the three-dimensional (3-D) POM that considers only the vertical (specifically, the upper 150 m of the water column) and time dimensions; that is, the evolution of the system in the (z,t) space. It is well known that the primary calibration dimension in marine ocean biogeochemistry is along the vertical direction, as shown in several previous calibration and validation exercises .

The 1-D POM solver (POM-1D) is used to calculate the vertical structure of the two horizontal velocity components, denoted U and V, the potential temperature, T, salinity, S, density, ρ, turbulent kinetic energy, q2/2, and mixing length scale, ℓ. In this model adaptation, vertical temperature and salinity profiles are imposed from given climatological monthly profiles obtained from observations, as previously done in and . POM-1D directly computes the time evolution of the horizontal velocity components, the turbulent kinetic energy and the mixing length scale, all of which are used to compute the turbulent diffusivity term, KH, required in Eq. (). In this configuration, POM-1D is called “diagnostic” since temperature and salinity are prescribed. Furthermore, pressure effects are neglected in the density equation and the buoyancy gradients and temperature are used in place of potential temperature since we consider only the upper water column.

A detailed description of POM can be found in , and in the following we simply provide a description of the physical model and equations solved in POM-1D. In diagnostic mode, as used in the present study, POM-1D solves the momentum equations for U and V given by 2∂U∂t-fV=∂∂zKM∂U∂z,3∂V∂t+fU=∂∂zKM∂V∂z, where f=2Ωsin⁡ϕ is the Coriolis force, Ω is the angular velocity of the Earth, and ϕ is the latitude. The vertical viscosity KM and diffusivity KH are calculated using the closure hypothesis of as 4KM=qlSM,5KH=qlSH, where q is the turbulent velocity and SH and SM are stability functions written as 6SM1-9A1A2GH-SH(18A12+9A1A2)GH=A11-3C1-6A1/B1,7SH1-(3A2B2+18A1A2)GH=A21-6A1/B1. The coefficients in the above expressions are (A1,B1,A2,B2,C1)=(0.92,16.6,0.74,10.1,0.08), with 8GH=l2q2gρ0∂ρ∂z, where ρ0=1025 kg m-3, g=9.81 m s-2. Following , GH is limited to have a maximum value of 0.028. The equation of state relating ρ to T and S is non-linear and given by 9ρ=999.8+(6.8×10-2-9.1×10-3T+1.0×10-4T2-1.1×10-6T3+6.5×10-9T4)T+(0.8-4.1×10-3T+7.6×10-5T2-8.3×10-7T3+5.4×10-9T4)S+(-5.7×10-3+1.0×10-4T-1.6×10-6T2)S1.5+4.8×10-4S2, where the polynomial constants have been written only up to the first digit. For a more precise reproduction of these constants, the reader is referred to . Finally, the governing equations solved to obtain the turbulence variables q2/2 and ℓ are 10∂∂tq22=∂∂zKq∂∂zq22+KM∂U∂z2+∂V∂z2+gρ0KH∂ρ∂z-q3B1ℓ,11∂∂tq2ℓ=∂∂zKq∂∂zq2ℓ+E1ℓKM∂U∂z2+∂V∂z2+E1ℓgρ0KH∂ρ∂z-q3B1W̃, where Kq=κKH is the vertical diffusivity for turbulence variables, κ=0.4 is the von Karman constant, and W̃=1+E2ℓ2/κ2(1/|z|+1/|z-H|)2 with (E1,E2)=(1.8,1.33). In Eqs. () and (), the time rate of change of the turbulence quantities is equal to the diffusion of turbulence (the first term on the right-hand side of both equations), the shear and buoyancy turbulence production (second and third terms), and the dissipation (the fourth term). This is a second-order turbulence closure model that was formulated by as a particular case of the model for upper-ocean mixing.

Boundary conditions for the horizontal velocities U=(U,V) and the turbulence quantities are 12KM∂U∂z|z=0=τw,13KM∂U∂z|z=zend=0,14q2,q2ℓz=0=B12/3|τw|Cd,0,15(q2,q2ℓ)|z=zend=0, where τw=Cd|uw|uw is the surface wind stress, uw is the surface wind vector, Cd is a constant drag coefficient chosen to be 2.5×10-3, and z=0 and z=zend denote the locations of the surface and the greatest depth modeled, respectively.

For all variables except oxygen, surface boundary conditions for the coupled model variable Aj are 16KH∂Aj∂zz=0=0. By contrast, the surface boundary condition for oxygen has the form 17KH∂O∂zz=0=ΦO, where ΦO is the air–sea interface flux of oxygen computed according to . The bottom (i.e., greatest depth) boundary conditions for phytoplankton, zooplankton, dissolved organic matter, and particulate organic matter are 18KH∂Aj∂zz=zend=0. This boundary condition was chosen since it allows removal of the scalar quantity Aj through the bottom boundary of the domain. This can be seen by integrating Eq. () over the boundary layer depth using the boundary condition above, giving 19∂∂t∫z=zendz=0Ajdz=W+WE+v(set)Ajz=zend, where the biological part of Eq. () has been neglected and the resulting temporal change in the integrated scalar Aj is negative since |(W+WE)|<|v(set)|, as shown in Table . For oxygen, phosphate, and nitrate, the bottom boundary conditions are 20KH∂Aj∂zz=zend=λjAjz=zend-Aj*, where λj and Aj* are the corresponding relaxation velocity and observed at-bottom boundary climatological field data value, respectively, of that species. Base values for the relaxation velocities are included in Table . Lastly, the bottom boundary condition for ammonium is 21KH∂N(3)∂zz=zend=0. Since observations of ammonium concentration in the observational area are not available, this choice is based on the assumption that the nitrogen diffusive flux from depth to the surface (euphotic) layers occurs mostly in the form of a nitrate flux, consistent with the concepts of “new” and “regenerated” production, as described by and .

The coupled BFM17-POM-1D model was run using the parameter values from Tables , , and –, which were decided on the basis of standard literature values . The simulations were allowed to run out to steady state, and multi-year monthly means were calculated as functions of depth for chlorophyll, oxygen, nitrate, phosphate, particulate organic nitrogen (PON), and net primary production (NPP), each of which was measured at the BATS/BTM site. The model PON is defined as the sum of nitrogen contained within the phytoplankton, zooplankton, and particulate detritus, and NPP is defined as the net phytoplankton carbon uptake (or gross primary production) minus phytoplankton respiration.

Figure  qualitatively compares the BATS data (top row) with the results from BFM17 (middle row). The model is able to capture the initial spring bloom between January and March brought on by physical entrainment of nutrients, the corresponding peak in net primary production and PON around the same time, and the subsequent subsurface chlorophyll maxima during the summer (evident in Fig.  as a larger chlorophyll concentration at depths close to 100 m during the summer months). The predicted oxygen levels are lower than observed values; however, the overall structure predicted by BFM17 is not completely dissimilar to that of the BATS oxygen field. These results are consistent with those from BFM56 (bottom row of Fig. ), suggesting that the two models are in generally close agreement. Correlation coefficients between the two models are 0.85 for chlorophyll, 0.56 for oxygen, 0.99 for nitrate, 0.99 for phosphate, 0.95 for PON, and 0.97 for NPP. Differences in chlorophyll and oxygen are likely due to the removal in BFM17 of specific phytoplankton and zooplankton species in favor of general LFGs, to the removal of denitrification, and to the parameterization of remineralization using new closure terms that were calibrated to give reasonable agreement with the observational data.

As mentioned previously, oxygen is historically difficult to predict using BGC models of any complexity. It is likely that this is due, in part, to inaccuracies in the mixing parameterizations used in POM-1D and other physical models. For example, BFM17 struggles to accurately predict oxygen, in part, because the second-order mixing scheme of lacks sufficient resolution of the winter mixing using just the monthly mean temperature and salinity. However, since it is often not included or presented at all in models of similar complexity to BFM17 (i.e., models reduced enough to reasonably couple to a high-fidelity, high-resolution physical model), studies that explore this hypothesis have been difficult to undertake. Thus, we include oxygen in BFM17 and present our results here to illustrate this exact point and to lend motivation to developing and using a model such as BFM17 to study the effects of physical processes missing from mixing parameterizations and how they can be better represented.

To obtain a first indication of the performance of BFM17, a model assessment was performed for each target field. The same assessment was performed for BFM56 to compare the two models. The results are summarized by the Taylor diagram in Fig. . This diagram can be used to assess the extent of misfit between the models and observations by showing the normalized root mean square errors (RMSEs), normalized standard deviation, and the correlation coefficient between each of the model outputs and the BATS target fields.

The normalized RMSEs were calculated as εrms/σobs, where εrms is the RMSE between the model and the observation fields and σobs is the standard deviation of the observation field. The normalized standard deviation was calculated as σmod/σobs, where σmod is the standard deviation of the model fields. The normalized RMSEs, normalized standard deviation, and the correlation coefficients each give an indication of the relative similarities in amplitude, variations in amplitude, and structure of each modeled field compared to the BATS target fields, respectively. For each variable, these statistics were calculated over all months and all depths shown in Fig. .

The Taylor diagram in Fig.  shows that BFM17 and BFM56 produce similar results. For most variables, errors in the amplitudes are within roughly one standard deviation of the observations. Additionally, the structures of the model fields for chlorophyll, nitrate, phosphate, PON, and NPP have high correlations with that of the BATS target fields. The correlation values range from 0.63 for chlorophyll to 0.94 for nitrate in BFM17 and from 0.60 for chlorophyll to 0.93 for phosphate and nitrate in BFM56. For BFM17, variabilities in amplitude for nitrate, phosphate, oxygen, and NPP are closest to those of the corresponding BATS target fields, while the chlorophyll and PON have too much variability. For BFM56, nitrate, phosphate, oxygen, and chlorophyll have similar variability in amplitude to the BATS data, while NPP and PON have too little and too much variability, respectively.

Table  provides a comparison of correlation coefficients and un-normalized RMSEs, calculated with respect to the observational fields, from BFM17 and BFM56, as well as from other models. Comparisons were only made to models that were calibrated using the same BATS/BTM data, employed some kind of parameter estimation technique, and reported correlation and RMSEs. included six biological tracers, while both and included seven. The study used data assimilation, while the and studies used only optimization to determine a select set of parameters. All models used climatological monthly mean forcing from the BATS region and reported climatological monthly means for their results. Care was taken to ensure that the same variable definition was compared between all models. used a similar 1-D physical model to the one that was used here, while and used a time-dependent box model of the upper-ocean mixed layer. As such, correlations and RMSE values for comparison to were computed over the entire domain (, calculated their metrics over the top 168 m of their domain). For comparison to and , correlations and RMSEs were calculated only within the mixed layer (defined as the depth at which the density is 0.2 kgm-3 greater than the surface density) and are shown as separate columns in Table .

The correlation coefficients and RMSEs for both BFM17 and BFM56 are comparable to the study for chlorophyll, while they outperform this study for nitrate, PON, and NPP. The study, which used data assimilation and is therefore naturally more likely to perform better, does in fact do so for predictions of chlorophyll and nitrate. However, the nitrate correlation values for BFM17 and the model are both high, although the latter model does have a lower RMSE value. As compared to the model, BFM17 has higher correlation values for both PON and NPP but a larger RMSE for NPP. Lastly, both BFM17 and BFM56 outperform the study for all fields for both correlation coefficient and RMSE values.

These results show that, with a relatively small increase in the number of biological tracers as compared to similar models, BFM17 is generally able to increase correlation coefficient values and decrease RMSE values for many of the target fields in comparison to similar models. Moreover, BFM17 approaches the accuracy of models that use data assimilation to improve agreement with the observations, such as the model. The extra biological tracers in BFM17, as compared to the and models, account for variable intra- and extracellular nutrient ratios with the addition of phosphorus.

Finally, a key benefit of the chemical functional family approach used by BFM17 is the ability of the model to predict non-Redfield nutrient ratios. Figure  shows the constituent component ratios normalized by the respective Redfield ratios for BFM17. The figure includes the component ratios of carbon to nitrogen, carbon to phosphorous, and nitrogen to phosphorous for phytoplankton, dissolved organic matter (DOM), and POM. Zooplankton nutrient ratios were not included because the parameterization of the zooplankton relaxes the nutrient ratio back to a constant value. The normalized ratio values are uniform non-unity-valued fields.

Ultimately, Fig.  shows that BFM17 is able to capture the phosphate-limited dynamics that characterize the BATS/BTM region . In particular, Fig.  shows that all results comparing carbon or nitrogen to phosphorous for BFM17 produce normalized values greater than 1, where the normalization is carried out using the Redfield ratio (i.e., a normalized value greater than 1 indicates that the field is denominator limited). Figure  also shows that the ratios are not uniform for phytoplankton, DOM, and POM, with the ratios decreasing with depth as a result of the increased availability of nitrogen and phosphate.

In this study, we have presented a new upper-thermocline, open-ocean BGC model that is complex enough to capture open-ocean ecosystem dynamics within the Sargasso Sea region, yet reduced enough to integrate with a physical model with limited additional computational cost. The new model, named the Biogeochemical Flux Model 17 (BFM17), includes 17 state variables and expands upon more reduced BGC models by incorporating a phosphate equation and tracking dissolved oxygen, as well as variable intra- and extracellular nutrient ratios. BFM17 was developed primarily for use within high-resolution, high-fidelity 3-D physical models, such as LES, for process, parameterization, and parameter optimization studies, applications for which its more complex counterpart (BFM56) would be much too costly.

To calibrate and test the model, it was coupled to the 1-D Princeton Ocean Model (POM-1D) and forced using field data from the Bermuda Atlantic test site area. The full 56-state-variable Biogeochemical Flux Model (BFM56) was also run using the same forcing. Results were compared between the two models and all six of the BATS target fields – chlorophyll, oxygen, nitrate, phosphate, PON, and NPP – and a model skill assessment was performed, concluding that the BFM17 captures the subsurface chlorophyll maximum and bloom intensity observed in the BATS data and produces comparable results to BFM56. In comparison with similar studies using slightly less complex models, BFM17-POM-1D performs on par with, or better than, those studies.

In the future, a sensitivity study is necessary to assess the most sensitive model parameters, both in BFM17 as well as in the 1-D physical model. After identification of these most sensitive model parameters, an optimization can be performed to reduce discrepancies between the BATS observational biology fields and the corresponding model output fields. Additionally, it would be useful to study the efficacy of using BFM17 in a global context, to reproduce the ecology in other regions of the ocean, and its sensitivity under various physical forcing scenarios. Finally, BFM17 is now of a size that it can be efficiently integrated in high-resolution, high-fidelity 3-D simulations of the upper ocean, and future work will examine model results in this context.