CCCC -- Breakout Session 4

## Breakout Session 4 -- Modeling

### What is required to model the impact of climate change on the carrying capacity of the region?

Discussion Leaders: Al Hermann and Bernard Megrey
Participants: Lou Botsford, Mike Foreman, Sarah Hinckley, Mike Landry, Jeff Parkhurst, Tom Powell, Michiyo Shima, Gordon Swartzman, Christina Tonitto, Anne York.

The concept of "carrying capacity" is difficult to define precisely in a modeling construct. The "carrying capacity" defined in the classic logistic model is inappropriate in many situations, since limits on population levels do not simply relate to resource levels, but can vary by life stage for many species, and often vary temporally (e.g., seasonally or from year to year). Moreover, this definition does not address multi-species assemblages and multi-species population dynamics. Factors controlling abundance other than resources include advection and predation.

Irrespective of precisely how carrying capacity is expressed in mathematical models, the following specific questions motivate bio-physical modeling efforts in the North Pacific.

1. Why is there no seasonal phytoplankton bloom in oceanic regions of the Subarctic North Pacific? What controls primary production and how might that change with any climate shift?

   Programs other than the U.S. GLOBEC CCCC program are better equipped to answer these two questions. However, there is a strong need to link autotrophic production to higher trophic levels in bio-physical models of the area, a task for which a U.S. GLOBEC CCCC program is well suited.

2. What are the primary controls on fish productivity before predation occurs? Possibilities include food, offshore transport, and direct temperature effects. Responses to temperature shifts include vertical and horizontal migration of individuals.

3. How would migratory patterns change if climate alters circulation or hydrography of the environment?

4. How would the dominant species composition of the area change with any climate shift?

5. What accounts for the decline of pinnipeds in the far northern Pacific?

Both physical and biological scientists should be included in any modeling effort addressing such issues, to guide the development of the model in directions beneficial to both disciplines. A diversity of modeling approaches is more likely to be useful than any single approach.

Two reasons for this view are:

1. biological and physical questions to be explored with models are sometimes incompatible (e.g. different space and time scales);

2. ecological problems are difficult and complex, and no one modeling approach is clearly superior for all problems, or even for any single problem;

While recommendation of a single modeling approach is problematic, several characteristics may be identified as desirable attributes of modeling efforts directed at the issues above. a) Physics is best linked to biology by three-dimensional circulation models, driven by the most realistic wind and buoyancy forcing available. b) Lower trophic levels in particular should be linked to the physical forcing. c) Key species should be connected through multi-trophic level models. One reasonable approach is to choose focal species at each trophic level where good biological information is available, as a starting point for any model of the whole ecosystem. d) Models should include physiological and behavioral responses to the physical environment; this should be stage- specific, and where possible age and size specific as well. Animal behavior is especially important at higher trophic levels, but little information is currently available, especially regarding behavioral changes resulting from any climate shift.

Models could be nested: i) spatially, ii) temporally, and iii) trophically. Spatial nesting includes embedding of finer-scale regional models in coarser-scale, basin-wide or global models. This embedding allows the large-scale phenomena to impact the regional physics. Temporal nesting includes using time-averaged quantities from a short time-scale model in a long time scale model. More generally, one may use the results of a short time-scale model to aid parameterization of those processes which can not be modeled explicitly in the long time-scale model. This is akin to using fine grid circulation models to aid the development of better subgrid-scale mixing parameterizations in coarse grid circulation models. Trophic nesting refers to the use of detailed (e.g. multispecies) models within any particular trophic level of a highly aggregated, multi-trophic-level model.

Individual-based approaches are advantageous for some species; these may be coupled to hydrodynamic models for spatially explicit life histories. Advantages of the individual-based approach include its tracking of widely different life histories among individuals, which allows for a detailed analysis of successful individuals at the end of the simulation. One-dimensional Individual Based Models (IBMs) of phytoplankton have been developed, but may be difficult to implement in three dimensions. In the three-dimensional case, IBMs are more feasible (and have been developed) for species at higher trophic levels, where populations are typically smaller and more localized in space. IBMs of higher trophic levels may beneficially be coupled to more traditional, deterministic, Eulerian models of nutrients, phytoplankton, and zooplankton, especially when control of the plankton is primarily bottom-up rather than top-down. IBMs have also been combined successfully with more traditional age-structured population models.

Potentially IBMs could include a genetic component. Genetic drift may be important for species with short generation times (such as phytoplankton and zooplankton) when modeling decadal time scales. For species with longer generation times (such as fish), a presently rare genotype may become prominent following some catastrophic shift in climate; for example, rapid environmental change might confer an advantage on individuals with a particular behavioral strategy, while others suffer disastrous mortality. Genetic/behavioral tagging of individuals in an individual-based model is one way of exploring such possibilities.

Bio-physical models, like their purely physical counterparts, can ultimately benefit from the assimilation of Eulerian and Lagrangian data, especially when such models are used for hindcasts. Such bio-physical assimilation is feasible with current technology. Data which could be assimilated into bio-physical hindcasts of the northern North Pacific include moored current meter and bio-optical data, altimeter data, drogued drifter data, and fish surveys. Techniques for assimilation range from simple "nudging" of the model variables towards observed values (a primitive form of Kalman filtering), to sophisticated adjoint techniques which effectively minimize the difference between observed and modeled values by repeated adjustment of initial conditions, boundary conditions, and parameters of the governing equations. Nudging is easily implemented even in a three dimensional context (and is done currently in several primitive equation models of ocean circulation). The more sophisticated techniques are preferable in theory but computationally intensive. In practice, they have been employed mainly in one- and two-dimensional contexts, with linearized physical models. Implementations with more complex, bio-physical models are being developed by several researchers, however.

While the formulation of governing equations and choice of parameters in a bio-physical model is not trivial, reasonable choices can be made, and results of coupled bio-physical models in other areas of the world (such as the North Atlantic) have been encouraging.

A review of past, ongoing and planned physical modeling efforts is presented here for the Gulf of Alaska and Bering Sea areas. Output from eddy-resolving models with global coverage may be useful in setting boundary conditions for regional scale simulations of the Gulf of Alaska or the Bering Sea; hence both global (but eddy-resolving) and regional models are included in this summary. Many of the basin-scale and regional models are likewise eddy resolving, with horizontal grid spacing on the order of 20 km or finer.

Physical models of the Gulf of Alaska have been broadly classed here into: 1) global eddy-resolving models which include the Gulf, 2) North Pacific models which include the Gulf, and 3) coastal models of subregions of the Gulf (Table 4). The class of basin-scale models may be subdivided according to the governing equations as: 1) quasigeostrophic or 2) primitive equation. For coastal models we distinguish between 1) tidal models, which replicate tidally driven, but not wind- or buoyancy-driven currents, and 2) primitive equation and other wind and/or buoyancy driven models. Also included are hydrologic models and inverse models of currents, temperature and salinity in the Gulf.

A related classification scheme has been used to illustrate modeling efforts in the Bering Sea (Table 5). We distinguish among: 1) global eddy-resolving primitive equation models which include the Bering Sea, 2) North Pacific models which include the Bering Sea, and models which focus on the entire Bering Sea basin (though some exclude the shelf area), 3) models on the Northern Bering Sea and Bering Strait, 4) models of the Southeastern Bering Sea shelf, 5) models of sea ice in the Bering Sea, 6) inverse models of circulation and other properties in regions of the Bering Sea.