Progress Report: April 1999
Project Title: Linked Biophysical Modeling in the California Current System: The Influence of Circulation and Behavior on Prominent Mesozooplankton Species
Investigators: Thomas (Zack) Powell (PI), Hal Batchelder (Research Scientist), Chris Edwards (Post-Doc.), (All at Univ. Calif. Berkeley), and Dale Haidvogel (PI) and Mohamed Iskandarani (Asst. Res. Prof.) (Both at Rutgers University) (

This research developed detailed understanding of coupled physical/ecosystem models in relatively simple contexts in anticipation of more complete and complicated three-dimensional simulations of the California Current System (CCS). Our approach emphasizes a hierarchy of model capabilities, progressing through a series of numerical experiments of increasing complexity in one and two physical dimensions. The flowchart (Figure 1) depicts our strategy in linking physical, ecosystem and individual based models.

Figure 1. Flow-chart showing model interactions and how they contribute to our fundamental research questions.

Two-Dimensional Upwelling Ecosystem Study

We constructed a two-dimensional (x-z, vertical slice), finite-difference hydrodynamic model, subject to vertical mixing parameterized using the Large et al. (1994) algorithm. Physical fields were used to drive the Franks et al. (1986) NPZ ecosystem model. Conventional application of this ecosystem model (Franks and Walstad 1996; Wroblewski et al. 1988) assumes that macrozooplankton are the dominant herbivores. However, recent evidence (Strom and Morello 1988; Strom et al. 1993; Verity 1985) illustrates the substantial contribution of microzooplankton to the nitrogen cycle, and our approach examines how a quintessential ecosystem response changes when this arguably more realistic parameter range is considered. We modeled the coast off Newport, OR, during idealized upwelling-favorable wind conditions. Coastal upwelling injects nutrient rich water into the euphotic zone, and induces the development of phytoplankton blooms immediately offshore in both macro and microzooplankton scenarios. The vertical extent of primary production is controlled by the surface mixed layer physics. However, the horizontal scale of the bloom is determined by the biological dynamics specific to the parameters applied. Microzooplankton have rapid growth and respond quickly to phytoplankton blooms, shortening their duration, which in an offshore Ekman drift yields a limited zonal bloom. In addition to the quantitative changes to the duration of the phytoplankton maxima, qualititative changes in the model response are evident in the biological fields downstream. Specifically, the microzooplankton parameterization drives a roughly 20 day oscillatory behavior manifested as a narrow zooplankton maximum just downstream of the phytoplankton peak, with low biomass further offshore. Over long time-scales, this behavior leads to phytoplankton patchiness, both spatially, depending on the duration of the wind-stress forcing, and temporally, in the case of wind-relaxation. In contrast, the overdamped pendulum-like response of the macrozooplankton parameter model leads to a slow return to a sizeable steady zooplankton level offshore, and no phytoplankton patchiness. Denman and Abbott (1988) argue that biological productivity is predominantly determined by physical processes, but our model exemplifies a case in which biological processes play a fundamental role setting the spatial structure of the fields (Abbott and Letelier 1998). Results from this research have been presented at two conferences and are in preparation for a peer-reviewed journal (Edwards et al. 1999).

Effect of Realistic Ocean Mixing on NPZ Oscillations

The purpose of this work was to characterize the stability of the Franks et al. (1986) NPZ model in the presence of vertical mixing. Ecosystem models of the NPZ type are coupled nonlinear systems of equations that exhibit a well-known range of dynamical behavior from stable equilibria to limit cycles to chaos. The dynamical regime of a particular model is of course determined by the parameter set applied. What is not generally discussed is that even with a particular parameter set, some components of the model (e.g., uptake rate) are spatially dependent. This variation can lead to different dynamical regimes within the water column (Figure 1). We have performed a linear stability analysis of the Franks model and shown that both stable fixed points and limit-cycle dynamics are common features of even a single vertical profile. However, the addition of diffusion modifies this stability, by coupling the otherwise independent oscillators and stable points. For some parameter sets (e.g., the macrozooplankton parameters discussed above), this coupling stabilizes the vertical profile, whereas for others the dynamics remain unstable (e.g., the microzooplankton case). For still other (quite plausible) parameter sets, the dynamical regime of the coupled system can vary non-monotonically from stable to unstable states depending on the magnitude of the diffusion. Indeed, for very weak levels of diffusion, the model exhibits chaotic dynamics for both parameter sets explored, though this state does not appear for more realistic, natural levels. Understanding the dynamical regime of the model in the presence of mixing has important implications for the appropriate initialization of biological models, as well as toward the interpretation of numerical integrations in more complicated advective scenarios. This effort has led to the preparation of one paper (Edwards and Powell 1999) for a peer-reviewed journal and presentations at two academic conferences.

Figure 2. Time series at 4 depths using the Franks et al. (1986) model and macrozooplankton parameters. Model dynamical state varies with depth. Phytoplankton (dash-dot); Zooplankton (dashed); Nutrient (solid).

Individual-Based Modeling of Metridia pacifica

We coupled 2D Eulerian biophysical simulations of hydrodynamics and lower trophic levels (NPZ models) with Lagrangian particle tracking IBMs of larger zooplankton in the California Current ecosystem. Our primary goal was to evaluate how the interaction of extrinsic (environmental) and intrinsic (specific to the individual organism) factors control distribution and demography. We focused on the interactions of food concentration, advection, diffusion and light (extrinsic factors) with organism size, nutritional state, and behavior (intrinsic factors) in the copepod, Metridia pacifica. Extensive experimental data and field observations exist (Batchelder 1986a) for this species, and it has been modeled previously in 1D (Batchelder and Miller 1989; Batchelder and Williams 1995). We extended earlier population dynamics models in two respects: 1) by forcing the IBM using physics and food resources obtained from an idealized 2D Eulerian simulation; and, 2) by exploring more realistic, mechanistic models for diel vertical migration (DVM). We developed and tested a particle tracking model (PTM) to couple the Eulerian fields from the slice model to the Lagrangian IBM. The PTM moves animals by advection, diffusion, and vertical migration. The latter is affected by ambient light intensity and food concentration, proximity to the bottom and surface, and individual size and nutritional state.

We have identified four metrics for evaluating the response of organisms to their environment: 1) growth/development; 2) reproduction; 3) survival; and, 4) distribution, particularly nearshore retention. For an individual to be successful in an eastern boundary current upwelling system it must grow, reproduce and survive. Moreover, since ocean productivity is greatest nearshore, zooplankton production is enhanced by nearshore retention. We examined growth and nearshore retention only. Suitable habitat space is the region of the domain that favors nearshore retention and positive individual growth. Model results, using an idealized upwelling circulation, indicate that DVM interacts with the 2D flow fields to retain individuals nearshore when the amplitude of the vertical excursion places animals in near-bottom onshore flow during the day (Figure 3). This occurs more often and from a larger "volume" of the upwelling system for larger organisms than for smaller individuals, and is most effective deep and inshore (<40 km from shore). The spatial extent and magnitude of the phytoplankton bloom (food resources) strongly controls the volume of suitable habitat space for the copepods. Spatially-extensive and high concentration blooms (macrozooplankton scenario) provided a much larger suitable habitat than did smaller blooms (microzooplankton scenario). Rapid growth from small, nonmigratory life stages to larger, migrating stages provides greater opportunity for nearshore retention. This indicates that resource fields are important in determining not only growth rates, but also nearshore retention, and thus, argues for detailed descriptions of how resources vary in space and time. This research has been presented at one conference and one invited talk. Future work will extend the model to other targeted species (Calanus pacificus and Euphausia pacifica).

More detailed information about the IBM simulations and movies of results are available here.

Figure 3. The upper panel shows 13-day trajectories of four individual copepods in the nearshore region within an upwelling circulation. Three individuals nearest to shore experienced positive growth (lower panel). The individual located deep and furthest from shore experienced negative growth leading to mortality. Weight fluctuations result from size-dependent diel vertical migration between low (deep) and high food regions (shallow).

Large-Scale Physical Modeling

Two models initially developed at Rutgers University are in wide use within the U.S. GLOBEC program. They are the Regional Ocean Modeling System (ROMS) and the Spectral Element Ocean Model (SEOM). ROMS is the latest version of the S-Coordinate Rutgers University Model (SCRUM), recently reconfigured in collaboration with colleagues at UCLA for improved algorithmic performance and accuracy. System attributes include extensive restructuring for sustained performance on SMP-class parallel-computing platforms; high-order, weakly dissipative algorithms for tracer advection; a unified treatment of surface and bottom boundary layers, based on the Large et al. (1994) and Styles and Glenn (1999) algorithms; an integrated set of procedures for data assimilation (nudging, optimal interpolation, and the reduced-state Kalman filter); and advanced treatments of open boundary conditions. Coupled physical/biological models based upon SCRUM/ROMS are now in place in the Coastal Gulf of Alaska in support of GLOBEC NEP (see, e.g., Hermann and Stabeno 1996).

The primary engine for simulating the three-dimensional circulation of the Northern California/Oregon coastal region will be the spectral element ocean model (SEOM) developed by Iskandarani and Haidvogel (see below). Prior support from U.S. GLOBEC has enabled the continued development of SEOM, and its evaluation in both idealized and realistic, basin-scale settings. Recent technical improvements to the three-dimensional circulation model fall predominantly in the areas of sub-gridscale parameterization and multi-scale nesting/coupling. In the former area, the introduction of spatially adaptive horizontal diffusion operators and filters now allows scale- and process-selective viscous closure. In the vertical, the KPP (Large et al. 1994) vertical mixing algorithm has been implemented on the native (finite element) grid of SEOM, and shown to reproduce known mixed-layer responses to prescribed applied surface fluxes. Nearshore resolution for the Northeast Pacific regional SEOM model will be less than 5 km (Figure 4).

Figure 4. Elemental boundaries of Northeast Pacific regional SEOM grid. Colorbar indicates horizontal resolution (km).

Importantly for our GLOBEC applications, SEOM now offers a unified treatment of inter-regional (multi-scale) coupling, including in a single framework the capabilities for continuously variable grids, model/model nesting, and regional open boundary conditions. An important recent development is the implementation of an inter-grid nesting capability based on the mortar element method, which allows two-way exchange of information between grids of differing elemental partition and/or spectral truncation. As a proof-of-concept of this mortar element capability, we are currently testing a two-way coupled version of a SEOM-based North Atlantic Basin model with the GLOBEC Georges Bank model developed at Dartmouth College by Prof. Dan Lynch.

Finally, intercomparative testing of numerical models -- including MOM and MICOM, as well as SEOM -- has shown the considerable advantages of the higher-order SEOM code in the limit of idealized, process-oriented test problems, including the large-scale wind-drive ocean circulation, flow around coastal canyons, and gravitational adjustment and downslope flows.

Two peer-reviewed publications (Levin et al. 1998; Curchitser et al. 1998), and a forthcoming monograph (Haidvogel and Beckman 1999), describe our progress in these areas.

Publications

Curchitser, E. N., D. B. Haidvogel, and M. Iskandarani. On the transient adjustment of a mid-latitude basin with real geometry: the constant depth limit. Dyn. Atm. Ocean. (Submitted).

Edwards, C. A., H. P. Batchelder, and T. M. Powell. On microzooplankton and macrozooplankton dynamics within an upwelling ocean ecosystem. (To be submitted to Marine Research)

Edwards, C. A., and T. M. Powell. The stability of a NPZ model subject to realistic ocean mixing. (To be submitted to Marine Research)

Haidvogel, D. B., and A. Beckmann. 1999. Numerical Ocean Circulation Modeling. Imperial College Press, London.

Levin, J. G., M. Iskandarani, and D. B. Haidvogel. A non-conforming spectral element ocean model. Int. J. Num. Meth. Fluids. (Submitted)

Stacey, M. T., H. P. Batchelder, T. M. Powell, and S. Twombly. Estimation of biological vital rates using an augmented Kalman filter. (Submitted to Limnol. Oceanogr.)