# Geospatial Considerations

Configuring Ecospace requires making choices and trade-offs to best address the research questions at hand. One will have to decide on grid cell size, the factors that drive the spatial distribution of ecosystem components, how to implement fisheries measures and fishing effort allocation, whether currents and migratory patterns are important for the question asked by the model, etc. These decisions are guided by functional group and fishing fleet structure, but are often limited by the resolution and quality of available spatial (and temporal) data. Here we provide some general guidelines to making these decisions.

The choice of the spatial domain to set the Ecospace basemap is the first step in the configuration of the model. As a rule of thumb, it should correspond to the domain used for the parameterizations of the Ecopath and the Ecosim models.

The choice of grid cell size is more challenging. Ecospace operates on a uniform raster grid of cells, where cell size directly determines the number of rows and columns that Ecospace will compute over. Higher number of cells generally mean more detail in model output but also increased demands in computational time and required memory, and do not necessarily provide better predictions. In general, the choice of cell size should be fine enough to answer research questions – but not finer. Other questions that need to be answered include: How do species relevant for the research questions utilize space, and what features affect their distributions? Are the ecological mechanisms that you want to address relevant considering the spatial extent of the modeled area? Are focal groups moving fast or slow? What are the spatial extents of fisheries management options? Are currents and/or migration patterns important? Do you have data of sufficient spatial detail to parameterize your Ecospace model? The answers to these kinds of questions may yield a range of sensible cell sizes. As an indication, most Ecospace maps fall within the 25×25 to 100×100 cell range (though an Ecospace map does not have to be square). A pragmatic approach is to use three sets of resolutions for Ecospace: one at the cell size that makes the most sense to the user, one set twice as coarse for rapidly building and testing the Ecospace scenario, and one set with cells that are twice as fine as the optimal cell size to assess whether a finer spatial scale significantly increases model predictive power. The coarse resolution offers quick runtime advantages and may help support some treatment of uncertainty. When satisfied, duplicate the entire Ecospace model, supply it with the intermediate resolution maps, and fine-tune as needed. This step is then repeated with the highest resolution maps to validate if this further improves the model.

Geospatial projection may be another consideration. If not instructed otherwise, Ecospace assumes that its grid is expressed using a World Geodetic System projection (WGS). Ecospace assumes that the Ecospace cell size is expressed in decimal degrees, and translates this to cell length in km at latitude, thus accounting for cell width tapering with latitude. Ecospace uses these cell lengths to translate species dispersal rates to actual movement (see Movement section, here below). If this default behaviour is undesired, for instance, when modeling an area using a local map projection where cell tapering is negligible (e.g., at lower latitudes) or when the coordinate system is expressed in meters, one can set Ecospace to Assume square cells, which makes Ecospace treat its grid as a uniform grid without cell tapering and where the user is responsible for entering the cell length (in km) to correctly drive species movement.

# Accounting for Effects of Latitude in Ecospace Models

Ecospace models are typically developed for grids of latitude-longitude spatial cells, with biomasses represented as densities (e.g., t km-2) within each cell. But for models of high latitude grids or grids that span a wide range of latitudes, cell widths over which biomass densities are predicted can vary considerably.

Thus, for cell i,j where i is map row (latitude) position and j is longitude position, relative width (width/height, Wi) across the top of the cell varies with map row i as:

where Lati is latitude in degrees at the cell top; thus Cos(Lati) varies from 1.0 at the equator to about 0.7 at 45 degrees north or south latitude to 0 at the poles. The Ecospace cell tapering logic assumes that the Ecospace map is projected to the World Geodetic System (WGS 1984) coordinate system with latitude and longitude are expressed in decimal degrees.

Variation in Wi requires three corrections in Ecospace calculations:

- dispersal rates across north-south cell faces need to be multiplied by Wi to account for differences in the odds of randomly moving creatures crossing those faces as opposed to east-west faces;
- fishing effort Ei,j allocated to each spatial cell using gravity models needs to be proportional to Wi, while fishing mortality rates need to vary with effort density (effort/Wi); and
- catch and discards from each cell need to be set to the model predicted catch per area times Wi.

The first and third of these corrections are trivial to implement (simply scale mixing rates m by Wi for north-south cell faces, multiply catches and discards Ci,j by Wi). The effort allocation and effort density calculations require a bit more care.

For Ecospace fishing mortality rate calculations, fishing mortality rate needs to be set proportional to the effective effort density per unit area Ei,j predicted for each spatial cell. At each time step, we make that prediction by assuming a total fishing effort Et for the step, then allocating that total over the cells using a logit choice or gravity model with the attractiveness of each cell being proportional to the profitability (revenue/cost per unit effort) of fishing in that cell, pi,j. The total effort for each cell also needs to be adjusted for relative cell area as measured by Wi. That is, the total effort ETi,j that is allocated to each cell should be calculated as,

[latex]ET_{i,j} = \frac{E_t p_{i,j}W_i }{ \sum\limits_{i,j} p_{i,j} W_i} \tag{2}\label{eq2}[/latex]

But the effort density Ei,j per unit area varies as Ei,j=ETi,jWi, implying that the gravity prediction of effort density should be,

[latex]E_{i,j} = \frac{E_t p_{i,j}}{ \sum\limits_{i,j} p_{i,j} W_i} \tag{3}\label{eq3}[/latex]

Using this model, two cells with equal profitability will be allocated the same effort density (calculated with the same denominator in the last equation, but the cell with larger Wi will then give higher total catch when catch per area is multiplied by Wi (correction factor 3 above).

Note that application of (3) requires care in setting the total effort Et so as to make total fishing mortality rates over the spatial grid have the same averages as assumed in the Ecopath/Ecosim model setup. In past Ecospace versions, we have not been careful in setting Et, assuming it to be ngEcosim where ng is the number of water spatial cells fished by gear g. This calculation of Et needs to be modified (Ecospace routine SetEffortParameters) by summing total effort over Wi times base effort per cell, so as not to generate total efforts that are unrealistically high. This is implemented via a Total efficiency multiplier for each fleet. The basic assumption for fleets in Ecospace (as described above) is that each functional target group is distributed across the map, and that the baseline effort (from Ecopath) is distributed across cells. If the effort is concentrated in a few cells only, this will result in a very high fishing effort being allocated to such a target group. In such a case the Total efficiency multiplier should be reduced from the unity level. A check for this is that with constant effort a fleet should not deplete a target species, other things being equal.

**Adaption**

The chapter is adapted, with permission, from:

De Mutsert K, Marta Coll, Jeroen Steenbeek, Cameron Ainsworth, Joe Buszowski, David Chagaris, Villy Christensen, Sheila J.J. Heymans, Kristy A. Lewis, Simone Libralato, Greig Oldford, Chiara Piroddi, Giovanni Romagnoni, Natalia Serpetti, Michael Spence, Carl Walters. 2023. Advances in spatial-temporal coastal and marine ecosystem modeling using Ecopath with Ecosim and Ecospace. Treatise on Estuarine and Coastal Science, 2nd Edition. Elsevier.