As many of you know, the ROMS Lagrangian particle tracking accuracy in the vertical direction is dependent on the degree of stretching in the vertical sigma grid. The more uniform the vertical grid is, the more accurate the tracked vertical movement of the particles is and the more stretched the grid is, the more inaccurate the vertical particle movements are. This has been a known weakness associated with the ROMS particle tracking algorithm.

The alternative to this is to save history files (u, v, w velocities and zeta) regularly (e.g. 1-hourly or 1/2-hourly, etc.) and perform the particle tracking externally - outside of ROMS. This venture however is quite expensive in terms of storage requirements (for large ROMS applications) and carrying out the particle tracking within ROMS would therefore be ideal.

Could someone please let us know whether improments/corrections have been made to the ROMS particle tracking algorithms recently to rectify the above mentioned problem? For applications where the vertical motion is important (e.g. ecological applications, HABs, where the vertical movements need to be tracked accurately) what advice can you give us with regards to using ROMS or ROMS outputs?

## ROMS Particle Tracking

### Re: ROMS Particle Tracking

Lyon,

Please give users some context or justification for the statement:

Are you suggesting that the vertically stretched coordinate introduces errors than are greater in float tracking than in tracer advection algorithm (also 4th-order unless you are using MPDATA)?

John.

Please give users some context or justification for the statement:

I searched the ROMS User Forum quickly and did not see any postings along this line. Others more knowledgeable than me can comment on whether the 4th-order Runge-Kutta scheme used in LTRANS (and earlier versions of ROMS, and SPEM) is appreciably more accurate than the 4th order Milne-predictor/Hamming-corrector now implemented in ROMS.lanerolle wrote:... the ROMS Lagrangian particle tracking accuracy in the vertical direction is dependent on the degree of stretching in the vertical sigma grid. ... the more stretched the grid is, the more inaccurate the vertical particle movements are. This has been a known weakness associated with the ROMS particle tracking algorithm.

Are you suggesting that the vertically stretched coordinate introduces errors than are greater in float tracking than in tracer advection algorithm (also 4th-order unless you are using MPDATA)?

John.

John Wilkin: DMCS Rutgers University

71 Dudley Rd, New Brunswick, NJ 08901-8521, USA. ph: 609-630-0559 jwilkin@rutgers.edu

71 Dudley Rd, New Brunswick, NJ 08901-8521, USA. ph: 609-630-0559 jwilkin@rutgers.edu

### Re: ROMS Particle Tracking

The 4th order milne scheme was tested for accuracy against analytical flow (purely circular flow with oscillating vertical migration). The largest cause for error was the interpolation from the grid points to the particle location. With analytical flow fields (no interpolation) the path error was less than 1% (based on memory from long ago). With linear interpolation, the error increased to a few percent.

I did not test the scheme in a setup with variable bottom topography where the vertical spacing was variable. Perhaps someone would be interested in setting up a analytical situation to test the accuracy. Maybe it has already been done.

Given all the other errors in a numerical model, the particle tracking is about as accurate as the rest of the calculation.

By the way, it may not seem like it but circular flow (circular paths) is actually a pretty strong test of the lagrangian calculation. Set up some cases and do a few tests to convince yourself.

John

I did not test the scheme in a setup with variable bottom topography where the vertical spacing was variable. Perhaps someone would be interested in setting up a analytical situation to test the accuracy. Maybe it has already been done.

Given all the other errors in a numerical model, the particle tracking is about as accurate as the rest of the calculation.

By the way, it may not seem like it but circular flow (circular paths) is actually a pretty strong test of the lagrangian calculation. Set up some cases and do a few tests to convince yourself.

John

### Re: ROMS Particle Tracking

I believe the errors are not in the time integration scheme (which is 4th order and hence very accurate) but rather in the spatial interpolation scheme - in particular in the vertical.

As you know, in ROMS, the particle tracking is NOT done in terms of the x/lon, y/lat, z variables but rather with the corresponding I, J, K indices which are allowed to assume all real values including fractional/decimal (recurring) values.

In my (personal) communications with Mark Hadfield, it was explained to me that the vertical K coordinate index transformation/conversion (from the sigma grid z values) is only approximate - when the vertical sigma grid has no stretching, the transformation is exact (with zero error) but the more it is stretched, the greater is the error associated with this transformation. So it is the K index <--> sigma grid z depth transformation which generates the errors. In my own numerical experimentation using identical initialization and forcing fields (river, meteorological, open boundary, tides, etc.) and identical intial locations for particle ensembles, but with different sigma grid parameters (to vary the grid stretching), I have found that the resulting particle tracks (specially in the vertical) and quite different and irreconcilable.

It is also my belief that Hal Batchelder (COAS/OSU) and his group have re-written the ROMS particle tracking algorithms and I wonder whether any improvements, etc. which he has added have made their way to the ROMS trunk released by Rutgers?

As you know, in ROMS, the particle tracking is NOT done in terms of the x/lon, y/lat, z variables but rather with the corresponding I, J, K indices which are allowed to assume all real values including fractional/decimal (recurring) values.

In my (personal) communications with Mark Hadfield, it was explained to me that the vertical K coordinate index transformation/conversion (from the sigma grid z values) is only approximate - when the vertical sigma grid has no stretching, the transformation is exact (with zero error) but the more it is stretched, the greater is the error associated with this transformation. So it is the K index <--> sigma grid z depth transformation which generates the errors. In my own numerical experimentation using identical initialization and forcing fields (river, meteorological, open boundary, tides, etc.) and identical intial locations for particle ensembles, but with different sigma grid parameters (to vary the grid stretching), I have found that the resulting particle tracks (specially in the vertical) and quite different and irreconcilable.

It is also my belief that Hal Batchelder (COAS/OSU) and his group have re-written the ROMS particle tracking algorithms and I wonder whether any improvements, etc. which he has added have made their way to the ROMS trunk released by Rutgers?

- m.hadfield
**Posts:**521**Joined:**Tue Jul 01, 2003 4:12 am**Location:**NIWA

### Re: ROMS Particle Tracking

I do recall saying something like this:

Float trajectories in some circumstances can be chaotic, so small errors in the float-tracking numerics (or the initial conditions, or the flow field) will lead eventually to large differences in the trajectories.

Perhaps you could post some more information about the large trajectory differences you see with different grid stretching parameters.Re the vertical interpolation, the ROMS interpolation routines are low order (piecewise linear, I think) so I wouldn't be too surprised to see discrepancies of several centimetres when a depth is converted to a vertical grid coordinate and then back, particularly if the grid is highly stretched.

Float trajectories in some circumstances can be chaotic, so small errors in the float-tracking numerics (or the initial conditions, or the flow field) will lead eventually to large differences in the trajectories.

### Re: ROMS Particle Tracking

This is an interesting discussion, are there any news regarding the discussed inaccuracies?

thanks,

Rodrigo

thanks,

Rodrigo