Decision Tree for Honing Attributes of Model "Detail"

Decision Tree for Honing Attributes of Model "Detail"

Interactive supplement for "Appropriate Complexity Landscape Modeling

Laurel G. Larsen, Maarten B. Eppinga, Paola Passalacqua, Wayne M. Getz, Kenneth A. Rose, and Man Liang

Earth Science Reviews

State variables

Spatial/temporal dimension

Resolution

Coupling

Extent and boundary conditions

Do state variables exhibit continuously varying attributes (e.g., age, size) that need to be tracked?

Do the processes of interest have dynamics that could be considered homogeneous or uniform?

No

Yes

No

Yes

Do the potentially coupled state variables operate at different time scales?

Do the hypothesized processes affect edges, interfaces, or transitions?

Are requirements for high spatial or temporal resolution (if applicable) likely to diminish tractability substantially?

Is the observed emergent phenomenon anisotropic?

Are the simulated processes fast for at least some of the time, relative to the size of the computational grid cells and duration of the simulated period?

Does the landscape exhibit regular patterning?

In relative terms (e.g., large, small, fast, slow), is the intended temporal extent a close match to the spatial extent?

Are there drivers that vary over an extent much larger than the phenomenon of interest?

What is the spatial scale of the dominant feedback processes?

Proceed to the next attribute

Consider using a model with low spatial dimensionality

Are the dynamics of the process heterogeneous over a smaller scale than the scale of the emergent phenomena of interest?

Consider using discrete classes or cohorts as individual state variables

No

Yes

No

Yes

No

Yes

No

Yes

No

Yes

No

Can variability along one dimension be related to a different state variable with lower dimensionality?

Proceed to the next question.

Uniform time stepping without special considerations is likely sufficient.

Grid cells should be isotropic (i.e., all faces should be the same size).

Use standard algorithms for iterating the model.

Consider spatially anisotropic computational grid cells.

Consider using a hierarchical modeling strategy.

Spatial extent should be several times larger.

Do they engage in feedback with the state variables of interest over the temporal extent of the simulation?

A uniformly sized computational grid may be appropriate.

Consider spatial averaging to reduce dimensionality.

Are distinct periods of rapid change expected, interspersed among periods of slower change?

Does the landscape have a pattern that is recurrent in space?

Use a relatively fine computational grid in the vicinity of edges, interfaces, and transitions

Strong biotic-abiotic coupling likely. May be conducive to simple representation in models. See Table 2 for suggestions relevant to conceptual model formulation.

Consider underrelaxation as a strategy to increase tractability, and/or perform spatial smoothing on a lower-resolution grid.

Does the landscape exhibit more than 2-3 types of patches or features?

Are the variables synchronous?

Is the critical time scale associated with the emergent phenomenon of interest closer to the longer of the time scales of the interacting variables

in question?

Yes

No

Yes

No

Yes

No

Yes

No

Do the drivers vary over time or space?

Consider periodic boundary conditions and a smaller spatial domain.

Impose constant or no-flux boundary conditions.

Proceed with full-dimensional model.

Consider a hierarchical modeling strategy.

Consider "quasi" N-dimensional simulations: Parameterize variability along the "quasi" (i.e., not explicitly simulated) dimension or use a lookup table or empirical relation from a separate ("offline") simulation.

Represent the shorter-timescale process through its mean.

Consider dynamic time stepping.

Model likely requires relatively high level of detail due to larger numbers of interacting state variables.

Simulate one of the variables directly, and solve for the other using the empirical relationship between variables.

Strong biotic-abiotic coupling likely. May be conducive to simple representation in models. See Table 2 for suggestions relevant to conceptual model formulation.

Small time steps are likely necessary. Choose time steps to achieve stability with the desired spatial grid size (e.g., using a stability criterion like the Courant criterion).

Do the variables consist of diverse, individual agents?

Are the dynamics (i.e., gradual changes) of the longer-timescale process likely important for the shorter timescale?

No

Yes

Represent drivers as constant boundary conditions

No

Yes

Represent drivers as specified flux boundary conditions. Is the outcome sensitive to variations in boundary conditions?

Represent feedback or forcing between variables through coupled governing equations.

Approximate the longer-timescale process with its average value.

Approximate the longer-timescale process as constant for discrete intervals in time, using distinct modules with different time steps for the long- and short-timescale processes (i.e., hierarchical modeling).

Appropriate representation may be best suited for individual- (agent-) based modeling framework.

Yes

No

Impose constant boundary conditions

Can general or idealized patterns of variability in the boundary conditions (e.g., generalized seasonality) address the central modeling

question?

No

Yes

Impose idealized patterns in boundary conditions.

Use a specified sequence for boundary conditions.