Future Directions in Bioluminescence Research

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ABSTRACT

Coupled Physical-Biological Modeling and Prediction

Dennis J. McGillicuddy, Jr.

Woods Hole Oceanographic Institution, Woods Hole, MA 02543

Interaction of planktonic ecosystem dynamics with oceanic circulation can create enormously complex patterns in organism abundance. Even an ocean at rest could accommodate significant spatial and temporal inhomogeneity through geographic variations in environmental parameters, time-dependent forcing mechanisms, and organism behavior. Fluid motions tend to amalgamate these effects in addition to introducing yet another source of variability: space-time fluctuations in the flows themselves which impact biological rates. Understanding the mechanisms responsible for observed variations in population abundance is thus a difficult task.

Coupled physical–biological models offer a framework for dissection of these manifold contributions to structure in planktonic distributions. However, their utility is predicated on an ability to construct a simulation which is representative of the natural system. One technique for doing so (the "forward" problem) is to initialize a coupled model with a set of observations, integrate forward in time and then compare with the next set of observations. A successful outcome results in minor discrepancies between observations and predictions, and the model solutions can thus be used as a basis for diagnosis of the processes controlling the observed behavior. Unfortunately, satisfactory completion of the forward problem is not always achievable due to limitations in the models, the observations, or both. Adjoint data assimilation methods provide an alternative approach which is particularly useful in such cases. These techniques can be used to determine the model inputs (e.g. parameters, forcing functions, etc.) that minimize the misfit between observations and predictions, thereby producing an optimal solution from which the underlying dynamics can be gleaned.

These various approaches to coupled physical-biological modeling are illustrated in three different applications:

1. Alexandrium spp. in a coastal plume (ECOHAB-GOM);
2. Chlorophyll-a in the Gulf of Maine (ONR-YIP);
3. Real-time nowcasting, forecasting and biological data assimilation on Georges Bank (U.S. Globec).

1. Modeling Alexandrium spp. in the Western Gulf of Maine.

Some recent coupled physical/biological modeling efforts in the ECOHAB-GOM program have focused on a retrospective analysis of the 1993-1994 data from the the Regional Marine Research Program (RMRP) on Alexandrium blooms in the western Gulf of Maine. In this study, we have attempted to use new information collected during the ECOHAB-GOM program to improve our interpretation of the 1993-1994 studies. One of the main gaps in knowledge identified in the RMRP effort was the lack of information about the source function for the input of new cells into the water column. Two new data sets relevant to this issue have emerged from early ECOHAB-GOM results:

1. new information concerning the distribution of cysts in the source region from the October 1997 cyst survey of Casco Bay, and
2. an improved understanding of the functional dependence of germination on environmental parameters such as light and temperature.

Both of these advances have been incorporated into hindcast simulations. The observed cyst distribution has been interpolated onto the model grid and is now used in the initial conditions. Input of cells into the water column from the seed bed is determined with a temperature and light dependent germination function derived from the laboratory measurements. This new approach to specification of the source term has led to an improvement in our ability to model the observed distributions of Alexandrium in 1993, as compared with earlier simulations based on a riverine input (Signell and Franks, in preparation). In particular, cell concentrations in the vicinity of Casco Bay are much more realistic. Further downstream, the differences are less pronounced.

From these simulations, it appears that the non-linear response of the river plume to wind forcing provides a mechanism for cross-isobath transport of Alexandrium cells. Under upwelling conditions, the plume thins and extends far offshore where it is inoculated by upward-swimming cells that germinated from the offshore cyst bed. When the winds shift to favor downwelling, the plume thickens and moves onshore, thereby exposing the coast to high concentrations of Alexandrium.

For more information see the ECOHAB-GOM web site

2. An adjoint data assimilation of chlorophyll-a into a spatially explicit model of the Gulf of Maine / Georges Bank region.

Our initial investigation into the large-scale seasonal variations in phytoplankton abundance in this region was based on an adjoint data assimilation technique. This approach was used by McGillicuddy et al. (1998) to study physical and biological controls on Pseudocalanus spp. distributions in this same region. The forward problem is posed as an advection-diffusion-reaction equation for organism concentration C:

where v is the velocity, K the diffusivity and H the bottom depth. The reaction term R(x,y) represents a highly idealized parameterization of population dynamics which varies in space only. Positive R implies net growth, while negative R implies net mortality. Specifying the climatological velocity and diffusivity fields, the adjoint of the advection-diffusion-reaction equation is used to invert for the population dynamics implied by changes in organism abundance and the circulation during the intervening period. This approach has proven to be successful with the climatological phytoplankton distributions mapped from the O’Reilly and Zetlin (1996) monograph. Preliminary results are described in Wang (1999).

In short, the analysis has revealed geographically specific patterns in phytoplankton source/sink terms.

These spatial patterns vary seasonally according to the phytoplankton distributions, the climatological currents, and their orientation with respect to each other. In cases when the flow is either weak or aligned with gradients in organism abundance, changes in concentration over time are dominated by local population dynamics. In situations where the currents are normal to these gradients, complex three-way balances arise between the local tendency, advective transport, and the population dynamics source term. Diffusion does not appear to play a major role in these simulations.

3. Real-time nowcasting, forecasting and biological data assimilation on Georges Bank.

As part of the third phase of the U.S. Globec Georges Bank Program, a group of investigators from six institutions (Dartmouth College, WHOI, NMFS, UNC-CH, BNL and BIO) undertook a predictive modeling effort in conjunction with field activities during several cruises from April to June 1999. Results from process studies of cross-frontal exchange on R/V Endeavor cruises EN323, EN324 and EL9905 are reported here.

The principal objective was simultaneous assessment of the transport of water and plankton in the vicinity of the tidal mixing front. The approach was to inject Rhodamine dye into specific density strata and then measure the movement of the dye patch and the associated planktonic community with respect to the neighboring front. This was accomplished through incorporation of the fluorometric dye detector into the Video Plankton Recorder system, facilitating real-time assessment of both tracer and plankton distributions (down to the species level). The adjacent waters were also seeded with radio- and satellite-tracked drifters. Real-time data assimilative modeling of the flow field (and associated transports of tracer and plankton) was carried out in concert with the observational activities, in order to (1) provide an additional interpretive framework for the measurements, and (2) provide nowcast/forecast products which could be used in planning sampling strategy.

Skill of the model predictions was evaluated against observed drifter trajectories.

In aggregate, the error growth characteristics of the ensemble of "best" model forecasts were surprisingly uniform. For the four-day time horizon over which forecast skill was evaluated in the various experiments, forecast error was a linear function of the duration of the prediction. On average, separation between simulated and observed trajectories of drifters and dye grew at a rate of 3 km/day. This error growth rate is small given the physical context of order 100 cm/sec tides and 10-30 cm/sec residual flows in this region.

While at sea, model solutions were used as a basis for data-assimilative coupled physical/biological simulations. Observed distributions of Calanus finmarchicus and hydroid predators were assimilated into the modeled flow fields in order to assess their relative transports and interactions. (See animation) Coupled simulations revealed portions of overlap in the sampling coverage due to the configuration of the survey track and phasing with the tide. Relative motion between predator and prey was apparent due to the vertical separation of the two populations in the presence of shear.

Summary

These three examples show the utility of data-driven coupled models for the study of complex physical–biological interactions in the ocean. At present, such models are used almost exclusively as research tools. However, in the future it is likely that the could mature to the point that they would become useful for naval operational needs.

References

Lynch, D.R., Ip, J.T.C., Naimie, C.E. and Werner, F.E. 1996. Comprehensive coastal circulation model with application to the Gulf of Maine. Cont. Shelf Res. 16: 875--906.

McGillicuddy, D.J., Lynch, D.R., Moore, A.M., Gentleman, W.C., Davis, C.S. and C.J. Meise, 1998. An Adjoint Data Assimilation Approach to diagnosis of physical and biological controls on Pseudocalanus spp. in the Gulf of Maine - Georges Bank Region. Fisheries Oceanography 7(3/4):205-218.

O’Reilly, J. E., and Zetlin, C. 1996. Monograph on the seasonal, horizontal, and vertical distribution of phytoplankton chlorophyll a in the northeast U. S. continental shelf ecosystem. NOAA Technical Report, NMFS.

Wang, C. 1999. Diagnosis of physical and biological controls on phytoplankton distributions in the Gulf of Maine - Georges Bank Region. Masters Thesis, MIT/WHOI Joint Program, Cambridge, MA.

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