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

Methodology for Scottish Waters Model

• Model output preparation

We have produced a set of FVCOM model results from the combined shelf and case study models to be used by the particle tracking model, using the Climatology run. The chosen approach is as follows:

1. Create a single mesh combining the shelf model and the four case study meshes using methodology developed by CH2M (Darren Price and Caroline Stuiver).
2. Run each of the case study models using nested boundaries obtained from the Shelf Model.
3. Interpolate results from each of the models (starting with Shelf model) onto this new mesh.
4. Use the new mesh result file with the particle tracking model.
5. Data must be provided as daily files of hourly data so the original SSW output files were split up into daily data, using a Linux shell script. Then the combined daily files were constructed.
6. The particle tracking code only works in Cartesian coordinates. The Climatology and other Scottish Waters model runs were done in spherical polar coordinates so a necessary step is to convert the model lat-lon grid to x-y coordinates and copy the x and y arrays back into the model output NetCDF files (the OS grid convention was used). Then the particle tracking code was run using these modified model data files.

• Particle tracking

The second step is to carry out the particle tracking, using the following experiment design:

1. Use the offline FVCOM particle tracking package (see above):
2. The particle release points were generated using a uniform 2kmx2km mesh then selecting those points which lie within the FMAs. This produced at least 1 particle release point in each FMA, except for 3 locations where a particle release point had to be generated manually. The final selection was 977 release points with between 1 and 100 particle release points per FMA ( Figure 10). Scripts which are used for FMA manipulation are in directory 'root'/output/ FVCOM_particle_tracking/ FMAs/scripts. Use plot_ FMAs.m to generate the initial set of particle release points (1093), then run the particle tracking model for the initialisation stage to identify which particles are actually not within the model grid and eliminate these (some particles are on the boundaries so will not move). The FMA names and locations are shown in Table 3.
3. Multiple particles were released at each location, using a random walk to model the diffusion, checking that the result was not sensitive to the number of particles. 100 particles per release point seemed satisfactory. A limited number of particles were used due to computational constraints. The number of particles required is discussed by Brickman et al. in North et al., (2009) which also refers to Brickman and Smith (2002). In typical releases they tested 100-2000 particles, to ensure that the final result is not sensitive to the number of particles.
4. 'Sea lice' particles are constrained to stay in the surface layer. For this it was found best to use the fixed depth option (F_DEPTH = T), with the initial depth below the surface as 3m and only horizontal diffusion. The particles do move in the vertical by advection, to some extent, but most particles stay within the surface layer (see Figure 11).
5. 'Virus' particles were released at surface, mid-depth and bottom in the water column, using 50 particles at each level, which was a compromise from the ideal (100 particles at each of 10 levels) to avoid excessively long run times of the particle tracking code.
6. The particles were tracked for appropriate PLD periods for each season (see Table 4).
7. Note that tracking cannot be done across the year end. Also the mesh changes size between April and May and between October and November as all 4 nested models were only run from May to October, with only 2 nests ( PFOW and WLLS) for the whole year. Therefore the tracking cannot be run from April to May or October to November.

Figure 10: (a) Shetland release points; (b) Orkney release points; (c); N Mainland release points; (d) S Mainland release points; (e) Western Isles release points

Table 3: FMA names and locations

Figure 11: Height above mean sea level for 1 particle from each release point over 26 hours - including 3D advection and horizontal diffusion, fixed depth, no vertical diffusion (sea lice larvae behaviour)

Table 4: Particle Tracking Runs. Total run time (estimated) = 22.5 days

• Post-processing of particle tracking output

The output from the particle tracking (in 'runname'_LAG.nc) can be processed in various ways e.g. to plot tracks. The variables in this file are shown in Table 5. The dimensions of the main arrays are nlag (or np = number of particles) and time (or nt = number of output times). In general we just use x, y and z at each time to identify the particle location (in OS grid coordinates) and metres below the surface. In order to plot the particle tracks on the model grid use the following Matlab commands:

cd 'run'\output\ FVCOM_particle_tracking\output\combined
xp=ncread('Jan01\January_LAG.nc','x');
yp=ncread('Jan01\January_LAG.nc','y');
cd ../../../FVCOM_output/Combined
x=ncread('January/Jan_01.nc','x');
y=ncread('anuary/Jan_01.nc','y');
plot(x,y,'.')
hold on
np=size(xp,1);
nt=size(xp,2);
for n=1:np
plot(xp(n,1:nt),yp(n,1:nt),'g-');
end

Table 5: Particle tracking output variables

In the next section we discuss how to calculate the particle capture and connectivity indices.

• Connectivity Indices

The final step is construction of Connectivity Indices between the FMAs. The likelihood of larval exchange between FMAs is represented using the following matrices:

• Distance matrix of the separation of individual Management Areas: this can be easily calculated as a straight line distance but will be less than the actual seaway distance that must be travelled.
• Transitional Probability Matrix P _ij (hereafter termed the Connectivity Matrix) representing the probability that an individual particle released at the source i will disperse to the destination j, over a given period of time.

The method of calculation of P _ij is as follows:

• Capture all particles which are 'infective' at each FMA downstream of original release FMA (includes self-recruitment). For sea lice this means capturing particles during the last ⅔ of the tracking period. For ISAV the capture period is the first 3 days of the virus run. For IPNV the whole of the virus tracking period is used. A 3-D array has been produced, named inxy_<mmm>_<bb> (np,nf,nh), for each month ( mmm) and both sea lice and virus runs ( bb= sl or vr). The dimensions are np (number of released particles), by nf (number of target FMAs) and nh (number of hours). From this matrix various outputs can be calculated.
• Sum over all particles starting in each origin FMA to get an 86x86 array containing numbers of particles, at each hour of the tracking period.
• Normalise by number of release points within each FMA to give a percentage of points released which are captured within any target FMA at any time.
• Finally, decide on how to plot array e.g. whole period, final destination. An alternative is to flag each FMA reached from origin FMA i.e. one or zero is recorded depending on whether a particle does or does not reach a given FMA from a specific starting FMA.

The scripts which have been used for the capture of particles and calculation of connectivity matrices are listed in Table 4. These are located in 'root'/output/ FVCOM_particle_tracking /output/combined/scripts. The inxy*.mat files are located in the same directory.

Table 4: Scripts for particle connectivity calculations