Formulation Step

• Identify conservative imports and information inputs, such as river discharge or meteorological data, which will not be calculated within the model but provided as tables of data or simple functions (such as a sine wave for solar irradiance).
• Identify any removals, losses, or exports, which will be dealt with in the same way; for examples: animal mortality due to a hunting quota (table of monthly kills); fixed rents or taxes.
• Identify inputs that are the subjects of scenarios, such as monthly number of tourists, for which there might be several sets of data.
• Identify where these inputs connect to the cause-&-effect chains in the Virtual System and decide whether they are conservative quantities, directly adding to or subtracting from model state variables, or information that acts indirectly through controls on rates.
• Identify variables that can will probably be used for testing or calibrating the sub-model or functional unit; these might be state variables (e.g., salinity, chlorophyll concentration, cash value of capital equipment), fluxes (e.g. primary production, income from sale of mussels), or indicators as agreed with stakeholders.
• Assess their relevance (i.e. the priority that should be assigned to them in acquisition of data).
• Decide whether your tests will involve simulation of specific events (e.g. for the year 2009) or of characteristic patterns (e.g. for generalized seasonal cycle); this may be decided by relevance and data availability for forcing and testing.
• Assemble information about these inputs including descriptions, units, main effects within the (virtual) system, relevance/priority, data source (details of person, institution, published work, web-page, etc.).

Instructions on how to carry out this sub task

Output:
a table of the input metadata and functions necessary for the simulation analysis.

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• Acquire the data documented above, in order of priority.
• Analyse the data statistically, in order to understand variability.
• Re-evaluate the relevance level of your inputs.
• If data unavailable, decide on a suitable (temporary or permanent) substitute, which can include proxies, results from other models, or `expert's best guess'.
• Convert the data to the units used in the model, etc, and, depending on software, insert in appropriate model-linked database (or Extend block)
• Add appropriate documentation to the metadata table and where relevant copy into the model data-base.

Instructions on how to carry out this sub task

Output:
Refined Input Table and documented sets of data in a form usable to the simulation.

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At this point you must make sure you have acquired all the necessary data to set up the ESE interpretive analysis during the Appriaisal Step, and make sure you can follow the scenario requirement. This includes planning the scope of the ecological, social and economic analyses. Note some analysis may requiring long time for acquisition of data so it is important to plan your actions carefully. In this subtask, you will try to specify and clarify what are your analysis objectives with respect to the Policy Issue and to the integration of the ESE Components.

• Clarify the specifics of the selected scenarios with the Reference Group. This will help you to clarify if you need extra data in order to run the scenarios and at the same time it will provide you the opportunity to explain to the Reference Group the probable limitations of your analysis.
• Revise the Virtual System’s definition if needed after the data acquisition and the scenarios discussion with the Reference Group. Provide the necessary scientific justifications and describe any accompanying analysis.
• Review the Impact – Response chain of the Policy Issue. Review the appropriateness of the methods for economic analysis that you choose during the Design Step. Define the relevant interactions and set-up the analysis linked to the simulation and the interpretive assessment.
• Choose the social responses linked to the Ecological and/or to the Economic Component. Define your objectives relative to the selected Policy Issue, identify the interactions between the components and set-up the analysis linked to the simulation and the interpretive analysis.

Instructions on how to carry out this sub task

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• The previous stage (System Design) resulted in a preliminary conceptual model of the Virtual System comprising from the cause-&-effect chain and the related ecosystem and socio-economic components. Review this model, revise if necessary, and identify the processes and state variables that will be simulated and the functional units that will be used to group them. Distinguish the parts of the conceptual model that will be included in the simulation models from those which will be the subject of other analyses.
• Prepare a draft table of key processes for each functional unit in the simulation model.
• Identify the state variables in each functional unit.
• Write equations for the model state variables and processes, noting the sources for these equations.
• Check the equations for correct dimensions and units in each term and for conservation of mass or energy where appropriate.
• Identify the parameters for which values will be needed, and either find sources for these or note that they will be estimated by fitting simulations to observations.

Instructions on how to carry out this sub task

Output:
A description of the model in diagrams and tables.

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• Prepare the software blocks or the program subroutines for each process equation.
• Test each process description against a range of real or “made-up” input data and ensure that results agree with those of known test-cases.
• Assemble these blocks or subroutines into functional units.
• Test each functional unit by using, if possible, several sets of realistic input data, and check that results are realistic. If the functional units generate time-series, the units must first be linked to numerical integration algorithms and the checks will include the effects of varying integration time-step and integration method.
• Choose any auxiliary models you plan to use in your analysis.

Instructions on how to carry out this sub task

Output:
Implementation of model functional units in software.

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• Assemble the functional units into sub-models of the cause-&-effect chain. One of these will be the main ecological sub-model; there may or may not be separate economic and social sub-models, or a combined socio-economic sub-model, or these two may have already be coupled to the ecological model.
• Test each sub-model to ensure that it responds realistically to realistic sets of forcing data.
• Carry out a sensitivity analysis (i.e. for each sub-model, determine how much the output changes in response to changes in parameter values).
• If necessary, calibrate some parameters (usually those to which the model is most sensitive) by adjusting their value until the sub-model simulation best fits a credible set of test data.

Instructions on how to carry out this sub task

Output:
Implementation of sub-models in the selected software.

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• Revisit and revise the tables of input and processes.
• Prepare a report describing the model and its testing.

Instructions on how to carry out this sub task

Output:
Technical report describing the model and its testing, including all the primary and secondary products of your work [e.g. initial and revised conceptual diagrams, revised input table, revised processes and functional component table, documentation of processes, approximations, validations, sensitivity tests, calibrations, linkages, hindcast calibrations, revised scenarios].

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The process of building conceptual models will be rewarding in itself, in that it is likely to bring about a greater understanding of differing conceptualizations of the Virtual System by scientists of different disciplines as well as by members of the Reference Group. But it is also part of the development of simulation models, and for this development it is useful to begin to think about the data the model will generate in later steps of the SAF application.

Identify the model variables that might be used for model testing
Identify the Virtual System variables that might be used to demonstrate reliable simulation of the coastal zone system during `System Appraisal'. Typically, these will be time series of state variables, or rates, that can be compared with observations.

Specify the system outputs for both qualitative and quantitative analyses
Ensure that the conceptual model diagram(s) contain(s) marker(s) for the information that is expected to be output from the simulation model(s), corresponding to or leading to the indicators used to evaluate the effects of various scenarios in the 'System Appraisal' and 'System Output' steps.

Instructions on how to carry out this sub task

Output
The result of this sub-task will be included in the conceptual model diagrams. Example from: Odra estuary study site;

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Check and improve the economic components
If necessary, i.e. if economic dimensions of your models are not clear from previous tasks, go through the `step-by-step' approach in Mongruel et al. (2011) to help you integrate these.

Identify economic assessment methodologies
Identify appropriate assessment methodologies to explore the future states of the Coastal Zone system, and agree these with the Reference Group.

Instructions on how to carry out this sub task

Output
The result of this sub-task will be documented decisions about approaches and methods for economic assessment. Example: human activities and associated economic information from the Søndeled Fjord study site.

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Data aquisition is often a slow process; it is best to begin it early, even when data will not be required until subsequent steps in the SAF application.

Set in motion actions to aquire data
Identify the relevant Human Activities and set in motion actions to acquire relevant `pressure' or `forcing' data. Identify existing economic data relating to these HAs and set in motion actions to acquire these data. Identify existing demographic and social attitude data relating to these HAs and set in motion actions to get them. If Coastal Zone Governance structure relative to HAs is not clear from previous tasks, set in motion actions to identify relevant laws and governance institutions. List ecological, social and economic data (for initial conditions, forcing or boundary conditions, and testing) that will be needed for simulations and tests, identify sources, and set in motion actions to acquire these data. Where possible, identify model parameter values that will be needed, identify sources, and set in motion actions to acquire these data.

Decide what to do in the absence of existing data
The options are to interpolate, simulate with auxilary models, use expert judgement, or (bearing in mind expense and time requirements) commission observations or experiments.

Instructions on how to carry out this sub task

Output
The result of this sub-task will be a set of actions initiated to obtain or substitute data. Examples: obtaining data relative to HAS: the Søndeled Fjord study site; the Thermaikos golf study site.

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