Scottish Shelf Model. Part 6: Wider Domain and Sub-Domains Integration

2. Methodology for developing integrated models

2.1 Introduction

A number of methods were considered for the integration of the shelf (Wolf et al. 2015) and local models (Price et al. 2015 a-d). These methods are presented and discussed in Section 2.2, and the selected method is presented in Section 2.3.

2.2 Options for integrated modelling

2.2.1 Method 1 - One way coupling

In this method, the shelf model is used to provide initial and boundary data (water level, temperature and salinity) for driving the local area models. The tools delivered will comprise Matlab scripts required for extracting initial and boundary data for any local area in the shelf model (hereafter S1 model).

The advantages of this method are: a) information flow from S1 (Stage 1 shelf model) to S2 (Stage 2 local models); b) reduced computational resources (effort and cpu times) as each model is run separately, and c) reduced data handling effort and storage space requirements.

The disadvantages are: a) no feedback from S2 to S1 model; and b) flow output data will be in separate files, and therefore inconvenient for use as an integrated set for particle model simulations.

2.2.2 Method 2 - Two way coupling

In this method, the S2 models would be incorporated into the S1 model, such that dynamic coupling occurs across the interface of the S1 and S2 models. The S1 and S2 model grids need to be designed so that the embedding occurs at logical boundaries (common nodes, elements and cross-sectional areas). This method of dynamic nesting is used in some structured grid models ( e.g. MIKE 21 Nested HD). However, this feature is not available in FVCOM. Thus, this is not considered further.

2.2.3 Method 3 - New model including S1 and S2 models

In this method, the S1 model mesh would be designed to incorporate the high resolution mesh in the areas covered by S2 models. This approach would deliver a new model, which is outside the scope of the present project.

The advantages of this method are: a) full dynamic coupling between S1 and S2 model areas; b) model results in one integrated file that can be used for particle model simulations.

The disadvantages are: a) it is practically not possible to develop such a new mesh, and at the same time preserve the properties of the already developed S1 and S2 meshes. This is because it is necessary that the S1 and S2 meshes have common cells (with identical properties) at the interface in order to preserve the properties of the S1 and S2 meshes in the combined S3 mesh. This is however practically impossible to achieve as the S1 and S2 models were developed in parallel; b) the computational time step will be constrained by smallest mesh size, hence such a model will be very expensive to run (in terms of computational times). The CPU time required is expected to be at least 1 order of magnitude more than that required for the S1 model; c) this method does not take advantage of work already done in S1 and S2. There would be a need for model re-calibration and validation and d) such a model would be difficult (impossible) to extend to other S2 areas. Each new S2 area would require complete redevelopment of integrated model.

2.2.4 Method 4 - Method 1 + Combination of S1 and S2 model results in integrated file.

This method consists of the following steps:

a) The method described in Section 2.2.1 (hereafter referred to as Method 1) is used to develop the S2 model results.

b) Next, an integrated mesh (S3 mesh) is developed including the mesh used in S1 and the mesh used in S2 in the appropriate model areas.

c) Finally, a Matlab script is used to generate the S3 model results by interpolation in the S1 and S2 results.

The tools delivered: As in method 1 + Matlab script for interpolating model results onto S3 mesh.

The advantages of this method are: a) the method makes use of development work in S1 and S2; b) it is expected to be significantly faster than the method in Section 2.2.3 (developing a new model), since S1 and S2 models can be developed separately; c) the output file will be one integrated result file; and d) the method can be adapted to incorporate more or fewer S2 areas.

The disadvantages are: a) it is practically not possible to develop such a new S3 mesh, and at the same time preserve the properties of the S1 mesh and S2 meshes as the S1 and S2 models were developed separately. In order to preserve the properties of the S1 and S2 meshes in the S3 mesh, it is necessary that the S1 and S2 meshes have common cells at the interface. However, it is expected that this will not be a problem, since the model results are to be obtained from the calibrated S1 and S2 models, rather than a new numerical solution; b) the interpolation may yield unphysical results at some locations. This will need to be checked especially at the interface of the S1 and S2 meshes; c) the integrated result file may be very large. It is expected to be slightly smaller than the sum of the file sizes for the S1 and S2 files. The large result file can be minimised by saving the results in smaller chunks ( e.g. daily).

2.2.5 Method 5 - FVCOM one-way nesting module for S2 + Combined S1 and S2 result files

This method is similar to the method described in Section 2.2.4 (Method 4). The only difference (an important difference) is that the S2 model results are obtained using boundary data obtained with the one-way nesting feature in FVCOM. Thus, for each S2 model, a nested file required as boundary data is obtained as output from the S1 model simulation using the NCNEST feature in FVCOM.

In order to use the NCNEST feature, the cells at the interface of the two models (S1 and S2) should be common. According to the FVCOM manual for v3.1.6 (see p91), two types of nesting are available for unstructured models - direct nesting and indirect nesting.

QUOTE:

For "direct nesting", the small domain FVCOM is driven directly with the nested boundary output from the large domain FVCOM. In this case, only the variables at boundary nodes and cells are required.

For "indirect nesting", the small domain FVCOM will retain its own tidal forcing at the nesting boundary and nest with the large domain FVCOM using the subtidal values of variables at boundary nodes and cells.

END QUOTE

This method requires that the cells at the interface between the S1 and S2 models are common to allow for the possibility to prepare the nesting file directly from S1 run using the NCNEST feature. However, this type of compatibility is not feasible in general. A workaround is to create the nesting file by interpolation from the S1 results file.

A key advantage of this method is in the use of native nesting module in FVCOM. This ensures compatibility of hydrodynamic conditions at the interface, and improved stability of the nested models since the combined elevation and current forcing from the S1 model are applied at the boundary of the S2 models.

The disadvantages are: a) it is practically not possible to develop such a new S3 mesh, and at the same time preserve the properties of the S1 mesh and S2 meshes at the interfaces. Special measures are required at the interface between S1 and S2; b) the integrated result file may be very large. It is expected to be slightly smaller than the sum of the file sizes for the S1 and S2 files. The large result file can be minimised by saving the results in smaller chunks ( e.g. daily).

2.3 Selected option for integrated modelling

Due to practical difficulties in combining the shelf and local model meshes while maintaining the node positions of all models and the large computational demand to run a fully integrated model, the method described in Section 2.2.5 (Method 5) was chosen. The results from the shelf and local models are combined using a Matlab script and output onto a new mesh which retains the best resolution of nodes from each of the individual model. Further details on how the results are combined are presented in Section 3. The integrated result file is used as input to the particle tracking model.

The adopted method involves one way coupling between the S1 model and the S2 models using the FVCOM nested boundary data files. Since the cells at the boundary of the S2 models and the S1 model are not common, the nested boundary files were obtained by interpolation in the S1 results file. Further details on the adopted approach for creating the nesting boundary data are presented in Section 4.