Nutrient-phytoplankton-zooplankton-detritus Research Articles

The XSO framework (v0.1) and Phydra library (v0.1) for a flexible, reproducible, and integrated plankton community modeling environment in Python

Abstract. Plankton community modeling is a critical tool for understanding the processes that shape marine ecosystems and their impacts on global biogeochemical cycles. These models can be of variable ecological, physiological, and physical complexity. Many published models are either not publicly available or implemented in static and inflexible code, thus hampering adoption, collaboration, and reproducibility of results. Here we present Phydra, an open-source library for plankton community modeling, and Xarray-simlab-ODE (XSO), a modular framework for efficient, flexible, and reproducible model development based on ordinary differential equations. Both tools are written in Python. Phydra provides pre-built models and model components that can be modified and assembled to develop plankton community models of various levels of ecological complexity. The components can be created, adapted, and modified using standard variable types provided by the XSO framework. XSO is embedded in the Python scientific ecosystem and is integrated with tools for data analysis and visualization. To demonstrate the range of applicability and how Phydra and XSO can be used to develop and execute models, we present three applications: (1) a highly simplified nutrient–phytoplankton (NP) model in a chemostat setting, (2) a nutrient–phytoplankton–zooplankton–detritus (NPZD) model in a zero-dimensional pelagic ocean setting, and (3) a size-structured plankton community model that resolves 50 phytoplankton and 50 zooplankton size classes with functional traits determined by allometric relationships. The applications presented here are available as interactive Jupyter notebooks and can be used by the scientific community to build, modify, and run plankton community models based on differential equations for a diverse range of scientific pursuits.

Nutricline adjustment by internal tidal beam generation enhances primary production in idealized numerical models

When the barotropic tide encounters variable bathymetry, fluctuating flow along a topographic slope generates baroclinic tides, or internal tides. There is growing evidence that these internal tides can affect primary production in the euphotic zone, though the dominant mechanisms are unclear. Internal tides move passive phytoplankton through an exponentially varying light field, enhancing primary production near the base of the euphotic zone. In addition internal tides also increase primary production through vertical nutrient advection into the euphotic zone. Topographically generated internal tides can be separated into two regimes: 1) the often highly nonlinear near-field regime where tidal beams are observed and 2) the more linear far-field regime. This study examines the primary production response to these internal tide processes using the Regional Ocean Modeling System (ROMS) coupled to a simple Nutrient, Phytoplankton, Zooplankton, Detritus (NPZD) model configured for an oligotrophic system with the nutricline positioned below 50 m depth. These idealized simulations generate internal tide beams with an oscillating, horizontal body force at the M2 tidal frequency that is applied to domains with a bathymetric step and uniform stratification. Sensitivity of the primary production response to the energy content of the tidal beam is obtained by adjusting the height and slope of the bathymetric step. Simulation results reveal that primary production intensifies along tidal beams due to the local enhancement of parcel vertical displacement (light effect) and nutrient advective flux divergence (nutrient effect). In the near-field regime across the range of step heights and slopes in this study, the nutrient effect is an order of magnitude larger and explains 92% of the variance in primary production versus only 14% for the light effect. The geometry of the generating feature sets the kinematics of the tidal beam. The light effect is limited in the euphotic zone across our domains because realized changes in light experienced over a tidal cycle are small relative to the amount of light available at a particular depth. In contrast, the magnitude of the nutrient effect increases more substantially with tidal beam energy.

Forward hysteresis and Hopf bifurcation in an Npzd model with application to harmful algal blooms.

Nutrient-Phytoplankton-Zooplankton-Detritus (NPZD) models, describing the interactions between phytoplankton, zooplankton systems, and their ecosystem, are used to predict their ecological and evolutionary population dynamics. These organisms form the base two trophic levels of aquatic ecosystems. Hence understanding their population dynamics and how disturbances can affect these systems is crucial. Here, starting from a base NPZ modeling framework, we incorporate the harmful effects of phytoplankton overpopulation on zooplankton-representing a crucial next step in harmful algal bloom (HAB) modeling-and split the nutrient compartment to formulate an NPZD model. We then mathematically analyze the NPZ system upon which this new model is based, including local and global stability of equilibria, Hopf bifurcation condition, and forward hysteresis, where the bi-stability occurs with multiple attractors. Finally, we extend the threshold analysis to the NPZD model, which displays both forward hysteresis with bi-stability and Hopf bifurcation under different parameter regimes. We also examine ecological implications after incorporating seasonality and ecological disturbances. Ultimately, we quantify ecosystem health in terms of the relative values of the robust persistence thresholds for phytoplankton and zooplankton and find (i) ecosystems sufficiently favoring phytoplankton, as quantified by the relative values of the plankton persistence numbers, are vulnerable to both HABs and (local) zooplankton extinction (ii) even healthy ecosystems are extremely sensitive to nutrient depletion over relatively short time scales.

Evaluating Alternate Methods of 4D-Var Data Assimilation in a Coupled Hydrodynamic—Four-Component Biogeochemical Model of the California Current System

Assimilating biogeochemical (BGC) data into ocean models using traditional four-dimensional variational data assimilation (4D-Var) includes the technical challenge of constructing tangent-linear (TLM) and adjoint (ADJ) models corresponding to the non-linear BGC model. This hurdle can be time-consuming, particularly for non-linear BGC models experiencing active development, with regular updates to functional types or representation of key BGC processes. We evaluate two alternate approaches that greatly simplify TLM and ADJ construction and eliminate the need for code updates when the underlying, non-linear BGC model changes. One form of model-reduced data assimilation represents BGC interactions as a linear combination of orthogonal modes; we use empirical orthogonal functions and refer to this as the BioEOFs method. The second approach treats BGC variables as passive tracers that experience advection and diffusion by TLM and ADJ physics over an assimilation cycle, but are biochemically inactive. We evaluate the efficacy of these methods in a realistically configured, data-assimilative implementation of the Regional Ocean Modeling System with a simple nutrient–phytoplankton–zooplankton–detritus (NPZD) BGC model for the U.S. west coast. In a series of sequential data-assimilative model cycles, observations of temperature, salinity, sea-level anomaly, and phytoplankton biomass constrain the modeled state over the period spanning January–June 2019. We perform the assimilation in both physical and logarithmic-transformed space and compare results of the two approximate methods to traditional 4D-Var using TLM and ADJ models with BGC processes corresponding explicitly to the BGC model. While the full-adjoint 4D-Var results in the best correction to phytoplankton fields for analyses and forecasts, the BioEOFs and passive-tracer approaches also significantly reduce the model-observation misfit compared to a non-assimilative run and do so at reduced computational expense. The passive tracer performs generally better than BioEOFs, whose corrections exhibit large-scale structure across the domain. While the most accurate state estimate will result from development and application of the full TLM and ADJ, the log-transformed passive-tracer approach may be a viable alternative for performing BGC 4D-Var for state estimation when a full-adjoint option is not yet available.

ECOSMO II(CHL): a marine biogeochemical model for the North Atlantic and the Arctic

Abstract. ECOSMO II is a fully coupled bio-physical model of 3D hydrodynamics with an intermediate-complexity NPZD (nutrient, phytoplankton, zooplankton, detritus) type biology including sediment-water column exchange processes originally formulated for the North Sea and Baltic Sea. Here we present an updated version of the model incorporating chlorophyll a as a prognostic state variable: ECOSMO II(CHL). The version presented here is online coupled to the HYCOM ocean model. The model is intended to be used for regional configurations for the North Atlantic and the Arctic incorporating coarse to high spatial resolutions for hind-casting and operational purposes. We provide the full descriptions of the changes in ECOSMO II(CHL) from ECOSMO II and provide the evaluation for the inorganic nutrients and chlorophyll a variables, present the modelled biogeochemistry of the Nordic Seas and the Arctic, and experiment on various parameterization sets as use cases targeting chlorophyll a dynamics. We document the performance of each parameter set objectively analysing the experiments against in situ, satellite and climatology data. The model evaluations for each experiment demonstrated that the simulations are consistent with the large-scale climatological nutrient setting and are capable of representing regional and seasonal changes. Explicitly resolving chlorophyll a allows for more dynamic seasonal and vertical variations in phytoplankton biomass to chlorophyll a ratio and improves model chlorophyll a performance near the surface. Through experimenting with the model performance, we document the general biogeochemisty of the Nordic Seas and the Arctic. The Norwegian and Barents seas primary production show distinct seasonal patterns with a pronounced spring bloom dominated by diatoms and low biomass during winter months. The Norwegian Sea annual primary production is around double that of the Barents Sea while also having an earlier spring bloom.

Cyclone Hudhud-eddy induced phytoplankton bloom in the northern Bay of Bengal using a coupled model

The present study explored the role of the pre-existing cyclonic eddy on the chlorophyll-a (Chla) bloom after a cyclone pass over the northern Bay of Bengal (BoB). We used a high-resolution (~9 km) Regional Ocean Modeling System (ROMS) coupled with an established Nutrient-Phytoplankton-Zooplankton-Detritus (NPZD) model. In the study, we have considered cyclone Hudhud (category-4), which passed over a cyclonic eddy in the BoB during 7–12 October 2014. Before the passage of cyclone Hudhud, strong stratification in the upper ocean inhibited eddy-driven upwelling of nutrients to the mixed layer and limited the phytoplankton production. However, when cyclone Hudhud interacted with the cyclonic eddy, which further reduced the water column stability (one order less) of the upper ocean and initiated the wind-driven upwelling. This mechanism resulted in the easy upwelling of cold nutrient-rich water to the mixed layer. A case study presented here demonstrates ocean–atmosphere (eddy-cyclone) interaction and its influence on the mixed layer Chla production in the northern BoB. Our study showed that column integrated Chla value in the upper 100 m increased by 70% when cyclone Hudhud passed over a cyclonic eddy region in the BoB. The present study suggested that cyclonic eddy accompanied by cyclone Hudhud induced the Chla bloom in the Northern Bay during the post-monsoon season of 2014.

Drivers and impact of the seasonal variability of the organic carbon offshore transport in the Canary upwelling system

Abstract. The Canary upwelling system (CanUS) is a productive coastal region characterized by strong seasonality and an intense offshore transport of organic carbon (Corg) to the adjacent oligotrophic offshore waters. There, the respiration of this Corg substantially modifies net community production (NCP). While this transport and the resulting coupling of the biogeochemistry between the coastal and open ocean has been well studied in the annual mean, the temporal variability, and especially its seasonality, has not yet been investigated. Here, we determine the seasonal variability of the offshore transport of Corg, its mesoscale component, latitudinal differences, and the underlying physical and biological drivers. To this end, we employ the Regional Ocean Modeling System (ROMS) coupled to a nutrient–phytoplankton–zooplankton–detritus (NPZD) ecosystem model. Our results reveal the importance of the mesoscale fluxes and of the upwelling processes (coastal upwelling and Ekman pumping) in modulating the seasonal variation of the offshore Corg transport. We find that the region surrounding Cape Blanc (21∘ N) hosts the most intense Corg offshore flux in every season, linked to the persistent, and far reaching Cape Blanc filament and its interaction with the Cape Verde Front. Coastal upwelling filaments dominate the seasonality of the total offshore flux up to 100 km from the coast, contributing in every season at least 80 % to the total flux. The seasonality of the upwelling modulates the offshore Corg seasonality hundreds of kilometers from the CanUS coast via lateral redistribution of nearshore production. North of 24.5∘ N, the sharp summer–fall peak of coastal upwelling results in an export of more than 30 % of the coastal Corg at 100 km offshore due to a combination of intensified nearshore production and offshore fluxes. To the south, the less pronounced upwelling seasonality regulates an overall larger but farther-reaching and less seasonally varying lateral flux, which exports between 60 % and 90 % of the coastal production more than 100 km offshore. Overall, we show that the temporal variability of nearshore processes modulates the variability of Corg and NCP hundreds of kilometers offshore from the CanUS coast via the offshore transport of the nearshore production.

The Meridionally Averaged Model of Eastern Boundary Upwelling Systems (MAMEBUSv1.0)

Abstract. Eastern boundary upwelling systems (EBUSs) are physically and biologically active regions of the ocean with substantial impacts on ocean biogeochemistry, ecology, and global fish catch. Previous studies have used models of varying complexity to study EBUS dynamics, ranging from minimal two-dimensional (2-D) models to comprehensive regional and global models. An advantage of 2-D models is that they are more computationally efficient and easier to interpret than comprehensive regional models, but their key drawback is the lack of explicit representations of important three-dimensional processes that control biology in upwelling systems. These processes include eddy quenching of nutrients and meridional transport of nutrients and heat. The authors present the Meridionally Averaged Model of Eastern Boundary Upwelling Systems (MAMEBUS) that aims at combining the benefits of 2-D and 3-D approaches to modeling EBUSs by parameterizing the key 3-D processes in a 2-D framework. MAMEBUS couples the primitive equations for the physical state of the ocean with a nutrient–phytoplankton–zooplankton–detritus model of the ecosystem, solved in terrain-following coordinates. This article defines the equations that describe the tracer, momentum, and biological evolution, along with physical parameterizations of eddy advection, isopycnal mixing, and boundary layer mixing. It describes the details of the numerical schemes and their implementation in the model code, and provides a reference solution validated against observations from the California Current. The goal of MAMEBUS is to facilitate future studies to efficiently explore the wide space of physical and biogeochemical parameters that control the zonal variations in EBUSs.

Response of Algae Bloom to the Variation of Nutrient and Suspended Sediments in the Bohai Bay: A Model Study

Liu, H.; Zhang, Z.-K., and Yin, B.-S., 2020. Response of algae bloom to the variation of nutrient and suspended sediments in the Bohai Bay: A model study. In: Bai, X. and Zhou, H. (eds.), Advances in Water Resources, Environmental Protection, and Sustainable Development. Journal of Coastal Research, Special Issue No. 115, pp. 676-681. Coconut Creek (Florida), ISSN 0749-0208.A nutrient-phytoplankton-zooplankton-detritus (NPZD) biological model is developed and coupled to an ocean circulation model to simulate the annual cycle of nutrient and phytoplankton dynamics in the Bohai Bay. It is found that the nutrient concentration shows the high and low level in winter and summer, respectively, and has a negative correlation with the algae biomass which reaches the summit and declines to the lowest in summer and winter, respectively. Based on the validated model results, the nutrient and phytoplankton dynamics is investigated by means of a series of numerical experiments. It is found that the nitrogen limi-tation is dominant in this sea region, though the phosphate limitation may appear in the mouth of Haihe River. Additionally, the influence of the suspended sediment on the nutrient and phytoplankton dynamics is exam-ined. It can be seen that the increase of the suspended sediment concentration can effectively restrict the algae photoproduction and maintain the high level of the nutrients in the Bohai Bay.

Model Study on the Impact of Petroleum Hydrocarbons and Suspended Solids on a Marine Ecosystem

A Nutrient-Phytoplankton-Zooplankton-Detritus (NPZD) type of model is developed, and coupled to a three-dimensional ocean circulation model (POM) to simulate the annual cycle of the biogenic elements in a marine ecosystem. The impact of petroleum hydrocarbons and suspended solids are also examined. A series of numerical experiments are conducted to investigate how the marine ecosystem responds to the concentration variation of petroleum hydrocarbons and suspended solids in the sea waters. It is found that as the concentration of suspended solids increases, the diatom bloom occurs for a long time, and meanwhile the dinoflagellate bloom is significantly weakened. As a consequence, the total phytoplankton biomass decreases and the nutrient concentration increase in the water column. Contrary to the SS situation, as the concentration of petroleum hydrocarbons changes, the algae biomass and the nutrient concentration don’t show the obvious differences in the water column.

Effects of the 2013–2016 Northeast Pacific warm anomaly on physical and biogeochemical variables off northwestern Baja California, derived from a numerical NPZD ocean model

Interannual climatic anomalies have important physical and biological consequences for the southern part of the California Current System (CCS). Two examples of these anomalies are “The Blob” and El Niño phenomena. The Blob was an anomalously warm water mass that formed in the Gulf of Alaska during fall 2013 and then affected most of the eastern North Pacific, including the waters off Baja California, Mexico. In this work we use a biogeochemical nutrient-phytoplankton-zooplankton-detritus (NPZD) model coupled to a three-dimensional hydrodynamic model, which allowed the simulation of some of the physical and biological consequences of the anomalous warm 2013–2016 period (The Blob was observed in 2014 and El Niño by mid-2015). A model-observation comparison showed that in some cases the model solution deviates substantially from the observed vertical thermal structure, but the temporal evolution of the spatially-averaged variables diagnosed by the model shows good agreement with the observations, except for the period from late 2015 to mid-2016, when the sea surface temperature (SST) is underestimated and the model failed to reproduce the correct sign of the surface chlorophyll-a (sCHL) anomalies. An EOF analysis of the 15-year (2003–2017) record of monthly mean modeled variables allowed the identification of two main contributions to the model variability: one mode mostly correlated with the Multivariate El Niño-Southern Oscillation (ENSO) Index (MEI), explaining ~50% of the variance of temperature (T) and dissolved nitrogen (N) and ~10% of the variance of chlorophyll-a (CHL), and another mode mostly correlated with the Coastal Upwelling Index (CUI) anomaly, explaining ~50-70% of variance of CHL and only ~10-20% of variance of T and N. In the 2013–2016 period, an El Niño signal diagnosed by the MEI induced a remarkable warming off northwestern Baja California. As a consequence, the thermocline and the nutricline deepened during this period and caused a deepening and weakening of the subsurface CHL maximum (SCM). Around the southern region of the study area (near Punta Baja) these effects were more intense at the surface over the shelf, but in the northern region (south of Southern California Bight) the effects were more intense subsurface seaward of the shelf break. This ENSO-modulated subsurface warming tends to weaken the Southern California Eddy during El Niño events, and intensify it during La Niña episodes. During the 2013–2015 period there was also a weakening of the upwelling-favorable winds, which caused a prolonged negative anomaly of the wind forcing, reducing the nutrient flux and causing negative CHL anomalies. Finally, in addition to the partial relation between the ENSO and the warming observed along the Baja California coast, the anomalies were observed in this area 4–6 months before the onset of the El Niño conditions (MEI>0.5) period, when the Blob was affecting the southern part of the CCS.

Simulating phytoplankton growth during the spring thermal bar in a deep lake

Phytoplankton growth in Lake Baikal was simulated during thermal bar events using meteorological data from June 1–30, 2017. Dynamics of the thermal bar and the plankton population were reproduced by the coupled physical–biological model that describes hydrodynamic processes and interactions of the components of the nutrient–phytoplankton–zooplankton–detritus system. The key point of the model is consideration of atmospheric impact on the lake surface, taking into account the intraday variability of wind forcing and fluxes of shortwave and longwave radiation and latent and sensible heat. Numerical modeling showed that a combination of cabbeling instability, associated with the thermal bar, and wind-driven currents lead to sinking of the phytoplankton biomass from the surface area to the lower layers of the lake. The increase in phytoplankton results in a degradation of the nutrients in the corresponding water environment. Simulations demonstrated that the maximum concentrations of phytoplankton are localized in the inshore side of the thermal bar. At the same time, the thermal bar acted as a barrier preventing the horizontal propagation of the biological substances into open waters. A comparative analysis of the calculated temperature and phytoplankton distributions with available field data was performed. • Plankton dynamics during the spring thermal bar in a deep lake were simulated. • The thermal bar acts as a barrier to horizontal propagation of the plankton biomass. • Wind forcing plays a significant role in the time-space distribution of the phytoplankton. • Wind contributes to sinking of the phytoplankton to the lower layers of the lake.

Quantifying top-down control and ecological traits of the scyphozoan Aurelia aurita through a dynamic plankton model

Aurelia aurita (Linneaus, 1758) is a cosmopolitan scyphozoan, probably the most investigated jellyfish in temperate and highly productive coastal ecosystems. Despite a prominent top-down control in plankton food webs, a mechanistic understanding of A. aurita population dynamics and trophic interactions has been barely addressed. Here we develop a food web dynamic model to assess A. aurita role in the seasonal plankton dynamics of the Kiel Fjord, southwestern Baltic Sea. The model couples low trophic level dynamics, based on a classical Nutrient Phytoplankton Zooplankton Detritus (NPZD) model, to a stage-resolved copepod model (referencing Pseudocalanus sp.) and a jellyfish model (A. aurita ephyra and medusa) as consumers and predators, respectively. Simulations showed the relevance of high abundances of A. aurita, which appear related with warm winter temperatures, promoting a shift from a copepod-dominated food web to a ciliate and medusa dominated one. The model captured the intraspecific competition triggered by the medusae abundance and characterized by a negative relationship between population density and individual size/weight. Our results provide a mechanistic understanding of an emergent trait such as size shaping the food web functioning, driving predation rates and population dynamics of A. aurita, driving its sexual reproductive strategy at the end of the pelagic phase.

A Hybrid Lagrangian–Eulerian Particle Model for Ecosystem Simulation

Current numerical methods for simulating biophysical processes in aquatic environments are typically constructed in a grid-based Eulerian framework or as an individual-based model in a particle-based Lagrangian framework. Often, the biogeochemical processes and physical (hydrodynamic) processes occur at different time and space scales, and changes in biological processes do not affect the hydrodynamic conditions. Therefore, it is possible to develop an alternative strategy to grid-based approaches for linking hydrodynamic and biogeochemical models that can significantly improve computational efficiency for this type of linked biophysical model. In this work, we utilize a new technique that links hydrodynamic effects and biological processes through a property-carrying particle model (PCPM) in a Lagrangian/Eulerian framework. The model is tested in idealized cases and its utility is demonstrated in a practical application to Sandusky Bay. Results show the integration of Lagrangian and Eulerian approaches allows for a natural coupling of mass transport (represented by particle movements and random walk) and biological processes in water columns which is described by a nutrient-phytoplankton-zooplankton-detritus (NPZD) biological model. This method is far more efficient than traditional tracer-based Eulerian biophysical models for 3-D simulation, particularly for a large domain and/or ensemble simulations.

A modelling approach to assess the effects of atmospheric nitrogen deposition on the marine ecosystem in the Bohai Sea, China

Atmospheric deposited nitrogen (AD-N) approximates or exceeds riverine input in many coastal ecosystems, such as the Bohai Sea (BHS) which is one of the most eutrophic coastal waters in China. We construct a three-dimensional (3D) physical-biogeochemical model to understand the influence of atmospheric dissolved inorganic nitrogen (DIN) on the intra- and inter-annual variations of phytoplankton blooms and nutrient dynamics in the BHS. The biological component, which is coupled to the Regional Ocean Modelling System (ROMS), is a simple but widely used Nutrient-Phytoplankton-Zooplankton-Detritus (NPZD) model with eight state variables. The model simulation successfully reproduces the spatial and temporal variations of observed DIN and dissolved inorganic phosphorus (DIP) and the climatological features of phytoplankton biomasses (chlorophyll a), which confirms the major role of air-transported nutrients in controlling standing stocks and nutrient limitations. The modelling results show that the relative contributions of deposited nitrogen to the total DIN in the seawater for the Bohai, Laizhou and Liaodong Bays and Central Bohai Basin reach 84.8%, 49.3%, 37.4% and 44.4% on average, respectively. The relative contribution ratio is approximately 54% for the entire Bohai region, causing a 56.5% increase in the phytoplankton biomass on average. These results also indicate that the effects of AD-N on nutrient and phytoplankton dynamics vary widely in regional areas because of the uneven spatial distribution of nitrogen deposition fluxes and also partially because of the hydrodynamic conditions, shortwave radiation and water temperatures.

Evaluation of the complexity and performance of marine planktonic trophic models.

Planktonic models represent a powerful tool for creating hypotheses and making predictions about the functioning of marine ecosystems. Their complexity varies according to the number of state variables and the choice of functional forms. We evaluated plankton models during the last 15 years (n =145) with the aims of understanding why they differ in complexity, evaluating model robustness, and describing studies of plankton modelling around the globe. We classified models into four groups: Nutrient-Phytoplankton-Zooplankton (NPZ), Nutrient-Phytoplankton-Zooplankton-Detritus (NPZD), Size-Structured (SS) and Plankton-Functional-Type (PFT). Our results revealed that the number of state variables varied according to the question being addressed: NPZ models were more frequently applied in physical-biological studies, while PFT models were more applied for investigating biogeochemical cycles. Most models were based on simple functional forms which neglect important feedback related to control of plankton dynamics. Modelling studies sometimes failed to describe sensitivity analysis, calibration and validation. The importance of testing different functional forms was commonly overlooked, and the lack of empirical data affected the verification of model robustness. Lastly, we highlight the need to develop modelling studies in the Southern Hemisphere, including Brazil, in order to provide predictions that assist the management of marine ecosystems.

Data assimilation in a coupled physical-biogeochemical model of the California Current System using an incremental lognormal 4-dimensional variational approach: Part 2—Joint physical and biological data assimilation twin experiments

Coupled physical and biological data assimilation is performed within the California Current System using model twin experiments. The initial condition of physical and biological variables is estimated using the four-dimensional variational (4DVar) method under the Gaussian and lognormal error distributions assumption, respectively. Errors are assumed to be independent, yet variables are coupled by assimilation through model dynamics. Using a nutrient-phytoplankton-zooplankton-detritus (NPZD) model coupled to an ocean circulation model (the Regional Ocean Modeling System, ROMS), the coupled data assimilation procedure is evaluated by comparing results to experiments with no assimilation and with assimilation of physical data and biological data separately. Independent assimilation of physical (biological) data reduces the root-mean-squared error (RMSE) of physical (biological) state variables by more than 56% (43%). However, the improvement in biological (physical) state variables is less than 7% (13%). In contrast, coupled data assimilation improves both physical and biological components by 57% and 49%, respectively. Coupled data assimilation shows robust performance with varied observational errors, resulting in significantly smaller RMSEs compared to the free run. It still produces the estimation of observed variables better than that from the free run even with the physical and biological model error, but leads to higher RMSEs for unobserved variables. A series of twin experiments illustrates that coupled physical and biological 4DVar assimilation is computationally efficient and practical, capable of providing the reliable estimation of the coupled system with the same and ready to be examined in a realistic configuration.

Annual plankton dynamics in a coupled physical–biological model of the Strait of Georgia, British Columbia

A three-dimensional coupled biophysical model was developed to study the dynamics of the plankton ecosystem in the Strait of Georgia (SoG) estuary. The ocean circulation component is an implementation of the Regional Ocean Modeling System (ROMS) and the lower trophic level ecosystem is a nine-compartment Nutrient–Phytoplankton–Zooplankton–Detritus (NPZD) model that includes two types of phytoplankton and of zooplankton. A three year hindcast (2007–2009) is used to examine the mean annual seasonal cycle of the local plankton dynamics. For realistic values of irradiance, wind forcing and fresh water fluxes, the model predicts a seasonal cycle of salinity, nutrients and plankton in reasonable agreement with observations. In particular, the model reproduces the main features of the estuarine circulation, the marked increase in phytoplankton biomass during spring followed by intermittent less intense blooms during summer and fall, as well as the seasonal pattern of zooplankton biomass. Model results show that primary production fluctuates between low values in January and high values in April, with an annual production of 270±33 (gCm−2) in the SoG. Most primary production is fueled by nitrate (f-ratio of about 0.7). Upwelling is the main source of nitrate into the upper layer, while most of the nitrate entering the Strait is exported out by horizontal advection. Physical processes, such as freshwater inflow, wind events, tidal mixing, and horizontal transports are important in maintaining the high spatio-temporal variability of the local phytoplankton biomass and production. Horizontal variability is high during the growing season (March to September). In summer, phytoplankton concentrates near the surface, in the shallow mixed layer, resulting in sporadic nutrient limitation of phytoplankton growth. In the northern portion of the strait, weaker summer winds and tidal currents lead to increased near-surface stratification which restricts nutrient fluxes and limit phytoplankton growth. In the central region, nitrate and light limitation are equally important at limiting phytoplankton growth during the summer whereas, in the tidally mixed regions of the south, primary production is higher in summer than during the spring resulting in higher annual primary production in this region than elsewhere.

Data assimilation in a coupled physical–biogeochemical model of the California Current System using an incremental lognormal 4-dimensional variational approach: Part 1—Model formulation and biological data assimilation twin experiments

A quadratic formulation for an incremental lognormal 4-dimensional variational assimilation method (incremental L4DVar) is introduced for assimilation of biogeochemical observations into a 3-dimensional ocean circulation model. L4DVar assumes that errors in the model state are lognormally rather than Gaussian distributed, and implicitly ensures that state estimates are positive definite, making this approach attractive for biogeochemical variables. The method is made practical for a realistic implementation having a large state vector through linear assumptions that render the cost function quadratic and allow application of existing minimization techniques. A simple nutrient-phytoplankton-zooplankton-detritus (NPZD) model is coupled to the Regional Ocean Modeling System (ROMS) and configured for the California Current System. Quadratic incremental L4DVar is evaluated in a twin model framework in which biological fields only are in error and compared to G4DVar which assumes Gaussian distributed errors. Five-day assimilation cycles are used and statistics from four years of model integration analyzed. The quadratic incremental L4DVar results in smaller root-mean-squared errors and better statistical agreement with reference states than G4DVar while maintaining a positive state vector. The additional computational cost and implementation effort are trivial compared to the G4DVar system, making quadratic incremental L4DVar a practical and beneficial option for realistic biogeochemical state estimation in the ocean.

Research on stability and Hopf bifurcation of marine ecosystem dynamics models

The predictability of marine ecosystem dynamics models is one of the most vital factors to limit their practical applications, of which the stability is the fundamental condition. In order to discuss the stability and Hopf bifurcation of marine ecosystem dynamics models, an approach based on a theorem termed dimension reduction was proposed and further applied in the mass-conservative nutrient-phytoplankton-zooplankton-detritus (NPZD) model in this paper. Results showed that the nonsingular equilibrium point of NPZD model was analytically stable in use of the dimension reduction theorem and the Hopf bifurcation might occur when model parameters changed along the threshold values. The analytical results of the NPZD model were further verified by numerical simulation in this study. It can be concluded that this approach based on the dimension reduction theorem is well applicable to the theoretical analysis of a kind of stability problems and Hopf bifurcation of massconservative systems.