1. Using ROMS Lagrangian-float simulations to estimate exchange rates between spatial compartments in a tidal estuary Mark Hadfield NIWA

2. Outline Research strategy Setting Box modelling POL3D and Eulerian tracers ROMS and Lagrangian floats Preliminary results Conclusions

3. Strategy We want to estimate maximum carrying capacity of a selected bay for mussel aquaculture. Couple a fine-resolution hydrodynamic model with a coarse resolution transport/ecology model (a “spatially aggregated” or “box” model). Coupling achieved by having the hydrodynamic model calculate exchange rates between the boxes. Exchange rates to be estimated in the hydrodynamic model using tracers: label each box with a tracer and observing the rate of exchange with other boxes.

4. The Setting:

8. Box Model Formulation CiCi CjCj F ij = T ij C i F ji = T ji C j F ij – F ji = T ij C i – T ji C j = T D (C i – C j ) + T A (C i + C j ) / 2 where T D = (T ij + T ji ) / 2 T A = T ij + T ji

9. Evaluating coefficients: the naïve approach At a specified time, label each box with a separate tracer with concentration = 1. After a suitable interval  t measure the mass M ij of each tracer i in every other box j. Then Tij » Mij/  t.

10. 2-box example

11. Earlier Simulations — POL3D, Eulerian tracer Proudman Oceanographic Laboratory 3D model (POL3D) Grid covering Pelorus Sound, 141  140 points, 18 levels, horizontal spacing 250 m. Forced at outer boundary by M2 tide (amplitude 0.88 m). Two-day flood event beginning at 3 days –Rainfall on surface of sound, then Pelorus River flow peak. –After the flood, river flow and rainfall continue at lower rates Eulerian tracers released and followed for 5 tidal cycles

12. Current Simulations – ROMS, Lagrangian tracer ROMS Rectangular grid, 250 m horizontal spacing, 15 levels with moderate vertical stretching. Large, McWilliams, Doney (LMD) vertical mixing. Forcing as before. Float trajectories deterministic for now, i.e. no random walk.

13. Exchange calculations 500, 000 Lagrangian floats, initially distributed uniformly throughout the domain, released and tracked for 5 tidal cycles. At any instant we can mark out a region in the fluid, label the particles in that region, then follow them for the remainder of the float simulation. The results of several such pseudo-releases are averaged to eliminate: –variations with tidal phase –stochastic effects

16. Conclusions The naïve method of evaluating transfer coefficients from tracer exchange data has problems due to sharp edges in the initial fields With Lagrangian float calculations we can use the extra trajectory information to solve those problems.