Merging models with different grids

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Scope

Often there are two models that have overlapping scopes and that are used in different assessments for describing the same variable or similar variables. It would be beneficial to be able to utilise the information in both models. However, a typical problem is that the indices used (especially spatial grids) are incompatible.

How should these different indices (or spatial grids) be operationalised in such a way that does not cause excessive workload and enables effective use of the information available?

Definition

Input

Let there be two models that describe the same variable, e.g. a pollutant concentration field over a defined area. The two models describe the concentration in different grids.

Output

The result of the variable should be usable in either assessment without technical limitations from grid systems.

Rationale

Thinking is based on intuition and practical experience.

Result

Procedure

Ideally, a variable is described in such a precise way that the value for any grid cell can be computed. Then, it does not matter which grid you use. In practice, this would require continuous descriptions, e.g. a concentration field is not described as average concentrations in each grid cell, but a continuous function (or surface) f, where the f(x) can be solved for any x. If the concentration is uncertain, then the function is described as a sample of functions f_i(x), where i=1..n and n is the number of samples.

In practice it is not at all easy to derive these functions f_i. Therefore, you need to start with something more practical. Then, I would go for a standardised index (=grid) that is used throughout the assessment. But then you have a problem, when you apply the same variable in different assessments that have non-similar grids. There are two solutions:


1) You don't care about this, but just make a new result with a new grid. Then, the version 1 (dated at time t) of variable a is only compatible with assessment A (using model A*), while the version 2 (dated at time t+1) of a is only compatible with assessment B (using model B*). The problem is that the two versions are produced using different models, and it is very difficult to estimate, whether version 2 is actually better (=closer to the truth) than version 1. Another problem is that if you want to use A*, you must use an old version of a, because of practical incompatibilities.

To overcome this, you should develop a merged model AB* that contains all knowledge from both A* and B* and both grids. In this way, a model AB* would clearly be better in theoretical (=closer to the truth) and practical (compatibility with different grids) grounds. But, the problem is that it is a lot of work and who would want to do the work, because it mostly helps the others.


2) You want to avoid the problem of changing grids. Then, you must define the grid in the scope of the variable. Then, only results given in that grid are valid answers for the research question of a, and the assessor of B will create another variable b with another grid. This makes it easier to utilise a with your model A* and your data. But the problem is that you cannot easily utilise information included in b and B*. But because information about b is valid also for a, anyone can bring that information to the Definition/Data of a, and demand that it is utilised in the development of A*.


In summary, I would start with variables where the grid is not defined in the scope. Then the first developer of a can decide the grid. If someone else starts using a with a different grid, then the original developer might want to go for 2) and create another variable c, having his original grid in the scope. If the information flow between b and c is important and useful, then the developers of b and c should start collaboration in developing a together.

See also