# SmoothBatimNesting

### From MohidWiki

This program creates a new sub-model bathimetry to allow a smooth transition in the boundary between the coarser model and the high resolution model. See also SmoothBatimCoefs.

## Quick start

- Create the father and son bathymetries (you may use Mohid GIS).
- Create the SmoothCoeficients griddata file (you may use SmoothBatimCoefs).
- Create and edit the options
*SmoothBatimNesting.dat*file and save it in the same path as the executable. - Run the executable.

## Options file

Here's what the options file *SmoothBatimNesting.dat* looks like:

FATHER_BATIM : ..\..\WestIberiaTide\GridData.dat SON_BATIM : ..\GridData_2.dat SMOOTH_COEF : SmoothCoef.dat NEW_SON_BATIM : SmoothData.dat

## Smoothing algorithm

Let it be , as an element of the father, the son and the interpolated bathymetries discrete fields. Let it be as the respective index mapping function. Let it be , a continuous map, so that . Let define the work domain of . In particular, verifies . The son grid is the same as the interpolated grid, meaning . However, the father field is completely independent from the other fields, meaning that . The smoothing algorithm is a simple linear interpolation of the father and son fields:

where the smoothing coefficient is given by . Thus, the smoothing coefficient gridded counterpart is defined; and its index mapping function is equal to the son's; meaning . Let us define the grid such that and . Thus the smoothing coefficient needs can be defined in . Concretely speaking, is the smoothing coefficient's Grid Data file described above, thus it leaves to the modeller the choice of the smoothing coefficient field.

### Implementation

Let us define a collection of four-vertices polygons taken from the father grid:

where is the subdomain defined by the vertices of . Let us define an auxiliary grid of the son grid given by:

- .

Let us define a new mapping into a subset of 's image:

- \.

Here's the implemented smoothing algorithm:

- .