## Modeling

The first step in any investigation is to determine what we know and do not know about the topic. We propose that the first step in the GLOBEC program should be a modeling effort to determine how well we are able to put together our present knowledge of physical oceanography with the known population biology of marine organisms that have numerous, distinct, planktonic life stages. There have been few, if any, theoretical models that have successfully addressed this question (Wroblewski and Hofmann, 1989). We see this activity as a necessary first step to uncover the limits to our present ability to utilize existing information to predict the variability in marine populations.

This use of the modeling exercise to initiate GLOBEC is a "probe" - an exploratory probe to determine where our knowledge breaks down. It should accompany any major investment in new technology and field studies, for solid progress in the coupled investigation of physical and biological processes. In this probing fashion we can uncover those crucial parameters about which we possess little empirical information; we can clarify the limits of our ability to perform a crucial measurement, suggesting where we need to develop new instrumentation. Furthermore, models can be very effective at suggesting additional variables that have greater power to discriminate among several potentially acceptable explanations for an observed phenomenon. It becomes the first step in the iterative, interactive process between theory and experimental measurement.

There are also pragmatic reasons why theory and modeling studies should appear in the earliest stages in GLOBEC. Little "start up" time is required, as opposed to the efforts required for instrumentation development and design of multi-ship, multi-investigator field programs. Moreover, the cost of theoretical and modeling investigations is substantially less than that of other efforts.

We have identified three broad categories that are critical to explore: conceptual studies of simplification and predictability; prototype investigations of biological processes in idealized flow fields; and site-specific models. We elaborate upon these three categories below. We make no claim that these are the only categories that could be profitably explored: we are confident, however, that a synthesis of efforts in these three fields can yield especially useful results. Finally, we anticipate other future GLOBEC activities, especially experimental and field measurement programs. The initiative should include, at a minimum, a requirement for participation in a yearly workshop devoted to bringing together theoreticians and empiricists. Moreover, an additional modeling/theory gathering for those working at disparate tasks is a "must".

### Simplification and Predictability

#### Simplification: Scaling, Pooling, Averaging

Researchers have put little effort into the systematic dimensional analysis of equations that contain biological parameters (but see Wroblewski et al., 1975; Hofmann et al., 1980; Lyne, 1983). This lack is especially apparent for models that incorporate the higher trophic levels beyond phytoplankton. The technique has proven to be extremely powerful in physical oceanography (and in fluid dynamics, generally); one can predict with confidence that any coupled modeling effort will have to address the issue of the "proper" non-dimensionalization, the "proper" scaling, early on.

In many population models quantities are pooled. For instance, we refer to "phytoplankton" or "zooplankton", pooling all the phyto- or zooplankton species together. Age or size classes are averaged, or pooled, and equations written for the pooled (averaged) quantities. One cannot be sure what the effects of such a simplification(s) are in various coupled physical-biological models. Arguments can be made that such averaging may miss important effects (Frost, 1980), especially when different life stages react to the physical environment in different fashion - some swimming more vigorously than others, perhaps, or seeking different depths or light environments.

Both scaling and pooling are related to the basic question of how one measures some non-dimensional group (a group that incorporates both physical and biological quantities) all age classes can be pooled, or all species of, say, phytoplankton can be pooled. Similarly, more formal investigations into these questions may tell us whether we can average over certain space and time scales.

#### Predictability in a "Chaotic" Environment

The consequences of coupling biological processes to a physical environment that has variability over a very broad range of space and time scales could be profound. There may be fundamental limits to predictability of biologically interesting quantities in such a "chaotic" environment. What such limits are, if any, is an important question with substantial ramifications. It may not be possible to predict beyond a certain point in time what the effects of changing global environments are upon marine animals, because of the fundamental limits to predictability in the coupled physical-biological systems of the sea. It may be possible to predict some quantities (e.g., biomass), but not others (e.g., abundance and distribution of individual species). Platt et al. (1977) considered this question when discussing models of phytoplankton productivity; and it seems profitable to extend their work. Perhaps there may be some guidance from more recent mathematical studies in nonlinear dynamics. Though it is not known whether the ocean as solely a physical system is chaotic (in the strict mathematical sense), one of the characteristics of chaotic (as opposed to deterministic but non-chaotic) systems is a broad spectral range. This contrasts to the narrow "line" - type spectra found in a non-chaotic, deterministic system (see Andereck et al., 1986).

The proposed approaches to both simplification and predictability are solely theoretical topics. This does not rule out applications to specific marine systems or populations of organisms, of course. Researchers should be encouraged to explore such applications of the ideas as they develop.

### Biological Processes in Idealized Flows

Biota are not mere passive tracers in the flows that characterize the sea's motions. At each life stage, an organism (planktonic or otherwise) will have behavioral responses, and will interact with the physical environment as well as with other organisms. These facts, of course, make the totality of the GLOBEC program extremely complicated (and extremely interesting). The effects of specific flow regimes might be investigated by considering the behavior of, and interaction between, organisms in simple models for these flows. A researcher might select one from a number of common flow pattems (i.e., homogeneous, three-dimensional turbulence; organized coherent structures, like Langmuir circulations; fronts and convergences; eddying structures; upwelling circulations; plumes; mixed zones and/or wakes around islands, to name several). Then, mimicking this prototype with simple, yet satisfying, physical dynamics, ask two kinds of questions. First, how do these flow regimes affect the biological properties one associates with individuals, or the properties one associates with single populations? For example, one might study the effects of small-scale turbulence on feeding success (Rothschild and Osborn, 1988). The important phenomenon of aggregation into schools or swarms (Okubo, 1986), including the effects of such processes on feeding or predator avoidance, would also be a likely candidate for investigation. Still another area for study might be how flow pattems at a variety of spatial scales affect the transport of the larval stages of benthic invertebrates (Jackson and Strathmann, 1981; Possingham and Roughgarden, 1990). How is the success of settlement of these larvae on the shore affected? How important is this settlement success relative to competitive interactions on the shore between sessile adult organisms? Second, how do these flow regimes specifically affect populations that are coupled into communities? How, for example, are competitive interactions altered (Roughgarden, 1978)? How are trophic relations modified? Perhaps the effects on size class models (or size spectra models, a la Denman et al., 1989) can be approached in investigations such as these.

It is well to note four aspects of such prototype studies at this early "proposal" stage. First, there is the well-developed field of mathematical ecology that has been little utilized in oceanographic (and only slightly more in fisheries) investigations (see Roughgarden et al. (1989) for a modern perspective). Some insights from this previous work may be useful. Second, though it may be possible to mimic a few simple flow pattems analytically, numerical simulations of the dynamics (e.g., turbulence) will certainly be very useful in these types of investigations. We should encourage investigators to consider how their "simple" models might be generalized in future studies to more complex settings that would demand numerical simulation (or, perhaps, substantially greater computer resources). Third, many of the formulations for the behavior of, and interaction between, biota are only approximate, even within quite wide confidence limits. We should encourage researchers to consider carefully what such limits mean for the predictions they calculate -- a "sensitivity analysis" for their efforts. Finally, these prototype studies are closely linked to the conceptual studies of simplification and predictability discussed above. The results of dimensional analyses of coupled physical-biological systems will surely form the bases for at least some of these prototypes studies.

### Site-specific Models

We propose a two-step process to attack the question of how the modifications we anticipate from a changing global climate will make themselves felt on specific animal populations at specific sites in the sea.

#### The Coastal Ocean and the Open Sea

The only realistic way to attack the problem of how to predict effects in the future is to understand the present. Accordingly, we focus on a specific problem at a specific site to see how well we can "put it all together". As an example, let us imagine compiling our "best" assessment of the biology of the individual life stages of a given species of, say a copepod. Let us further construct the "best" model of the transport phenomena (advection plus mixing) at a site of limited extent, perhaps a coastal site. Then, given the observed physical forcing(s) plus the observed level(s) of predators upon the copepod stages (and prey items in the copepod diet) can we make a prediction about the concentration and distribution of the copepod population as the individuals progress through their life history? Recent work of this kind in the South Atlantic Bight (Hofmann, 1988) suggests that, so long as the time horizon is not too long, we may be closer to this specific goal than ever before.

Such attempts must be generalized to other environments, longer time horizons, and a variety of populations including benthic invertebrates, widely differing groups of holoplankton, and various fish and shellfish species. We target two "sites" initially: the upper ocean, anywhere on the globe, because it is so important biologically; and coastal areas, especially questions that address cross-shelf transport. The coastal cross-shelf transport focus is important because this transport process may be crucial to a wide variety of marine animals, especially benthic invertebrates (Roughgarden et al., 1988), and larval fish and eggs (Checkley et al., 1988).

Three aspects of such models are immediately apparent. First, these studies will be dominated by numerical attempts, because only such efforts are likely to incorporate sufficient detail to be useful at specific sites. We should begin to think about ways to interact rapidly and efficiently with models that may have many tens of thousands of lines of codes and are run at remote sites. We must insist that timely and constructive protocols allow us to interact quickly in a "predictor/corrector" mode. We anticipate taking advantage of the advances occurring in modeling of the upper ocean (e.g., the Price-Weller-Pinkel model (Price et al., 1986) and modeling of coastal circulation (see particularly, E. Hofmann's (1988) coupled models in the South Atlantic Bight). These efforts give us the confidence to continue the attempt to predict. Second, the incorporation of data into models is a critical topic that needs to be addressed early by any modeling attempts. The effort must be a cooperative one between empiricists (a measurement team) and modelers. This effort might assess the usefulness of the formal techniques of data assimilation (see Haidvogel and Robinson (1989), an entire journal issue devoted to this issue for oceanic modeling). These newer approaches have not been applied in biological models, whether coupled to the physical environment or not. Third, ensure that the "fit" between theory and measurement is good. For example, the output from present acoustic sensors is often a size-frequency spectrum. Will this quantity be easily extracted from multi-level, age-structured models? Is this the quantity we desire, and why? Similar remarks apply to the "fit" with remote sensed data, like ocean color, that appears to have great biological utility. Preparation for the use of time series data, perhaps from moored instruments, in more sophisticated ways than have previously been common in biological studies, should have a high priority for both empiricists and modelers.

#### Future Predictions

We have already alluded to one straightforward way in which the model studies we propose can be used to pursue the effects of global change. That is, drive the models with differing external forcing. For example; where a freshwater source of buoyancy is an important input, ask what circulation and transport pattems, as well as derived distributions of biota, would result from the hypothesized shifts in rainfall or ice melt. Comparisons with the results of present condition models could be readily pursued. These results would be short time scale in the sense that the numerical simulations would be run only so long as the analyst believed that the flow pattems did not deviate substantially from observations -- several weeks to a month, perhaps.

There may be ways to mimic climatologists' use of atmospheric GCMs (general circulation models) in the coastal ocean for long time scale assessments; that is, run the models for very long times until they reach "equilibrium", and then compare various equilibria (Mitchell, 1989). Such calculations have been performed for the ocean general circulation, but "the jury is still out" on how much confidence one should have in the results. Generalization of the same techniques to the coastal ocean is purely speculative at this time.