Averaging in time or space (best practices)

[flq321]

I would like to know if there are any recommended best practices to average ROMS fields in space or time. ROMS has a time-varying vertical grid so strictly speaking a time-average at any location is averaging across different depths. Similarly, the vertical grid also varies in space implying a spatial average at a given vertical level at any time is also averaging across different depths. Is the solution always to average all ROMS fields to a time-invariant vertical grid before beginning any averaging operations? Or is it customary to neglect the changes in the vertical movement of a model level (in time and space)?

For reference, I am attaching a couple of plots from a 8-year ROMS solution of the Gulf of Mexico region. I have masked off regions which are shallower than 230 m in depth (along with some conditions on lat/lon) which is why you see lots of white in the plot. The color plot shows: (i) the standard deviation of the height (meters) at the shallowest model level over 8 years; and (ii) the difference (in meters) between the maximum and the minimum values of the height at the shallowest model level over 8 years. The line plot shows the vertical profile of the maximum value of these two parameters across the plotted region. The variations do not look too severe. If I include all locations without any mask, the variations are largest (naturally) towards the coast approaching 5 m (i.e., maximum -minimum). If I stick to the region with the mask, though, it appears the differences are not too large.

I am curious to hear how other ROMS users take spatial/temporal averages.

[wilkin]

In the water depths you are looking at > 250 m the vast majority of in situ ocean observations would not be referenced to a fixed vertical datum but instead as a depth below the sea surface with no regard for the changing sea surface height because depth was obtained from a pressure sensor. Most ocean applications have no problem with this.

Using the cell-based averages with depths computed from the comparably averaged sea surface height is what most ROMS users do.

Where this can become an issue is not so much with the depth value itself, but with the fluctuating layer thicknesses. When computing a vertically integrated flux from saved averaged output, the triple nonlinearity of <u><T><deltaz> might differ from <u T deltaz> if there are strong correlations in, say, <u' deltaz'> which is quite possible if sea level is correlated with flow direction.

For this reason, ROMS diagnostics include options for Huon.tracer and Hvom.tracer averages, where the fluctuating layer thickness "H" is fully included in the average.