Validating new topography dataset and smoother

[PeterHjortLauritzen]

[transferring text from issue https://github.com/NCAR/amwg_dev/issues/116 to this repo as it is relevant; the plots in this post are using GMTED2010 elevation data only (no bedmachine)]

New topography file

We have produced a new topography file where we use a Laplacian smoother (instead of the default distance weighted smoother) and turn off smoothing where the land fraction is 0 (i.e. no smoothing over ocean points; partial ocean points are still smoothed). We are curious if not smoothing over ocean points has an impact in coupled model setup since the temperatures passed to the ocean, where previously the topography was "leaking into the ocean", could be biased cold (assuming temperature decreasing with height on average).

The Figure below shows energy spectra for different topographies:

A couple of observations regarding the energy spectra:

• The energy spectra is the same when using a 3km intermediate cubed-sphere field (ncube3000, orange line) compared to using a 16km intermediate cubed-sphere grid (ncube540, red line) when computing energy spectra on 1 degree finite-volume grid. That means, we can assess smoothing using the ncube540 intermediate cubed-sphere grid which is much more computationally efficient to run the smoother on compared to the ncube3000 intermediate cubed-sphere grid.

• Below show difference between smoothing everywhere but using the ncube=3000 grid versus ncube =540 grid:

Basically this plot verifies that smoothing on ncube=3000 and ncube=540 using the same physical smoothing scale leads to almost the same result (as one would expect). For comparison distance weighted smoother minus Laplacian smoother (PHIS) below:

[very few differences!]

• Interpolation matters for computing energy spectra: bi-linear interpolation from 1 degree spectral-element grid to 1 degree finite-volume grid produces damping (compare blue and red lines). Please note that the two grid "see" the exact same smoothed topography on the intermediate cubed-sphere grid. Hence when comparing different levels of smoothing always use the same target grid.
• The energy spectra with new and old smoother are very similar (compare red and green lines).
• Not smoothing over ocean does add some energy at many scales (compared cyan and red).
• Black line is unsmoothed topography (for reference)

The next two plots show Greenland area and South America topographies (all mapped to fv 1 degree grid):

• ncube540 raw: raw topography on ~16km intermediate cubed-sphere (ncube540)
• CESM2: Current default topography
• nc540: Laplacian smoothed topography (nu=28E7) - old CESM1.5 smoothing level when the SE topography was smoothed using SE (and not in the topography software as done now; which is needed for the ridge scheme variables)
• nc540;Co11: Laplacian smoothed topography (nu=20E7) that matches C011 smoothing (default CESM2) on the ncube540 grid (for the ncube3000 grid that is equivalent to C060 smoothing radius)
• nc540; no-ocn: Laplacian smoothed topography (nu=20E7) that matches C011 smoothing (default CESM2) but no smoothing over ocean.

The cross section plots (lower right) are though 30S and 65N.

The following observations are made:

• Smoothing over peaks seems to be roughly the same for all smoothing options -> not smoothing over ocean does not seem to affect peaks a couple of grid-points inland.
• One can visually see no smoothing over ocean.

Some mathematical details on the smoothing operator:

[PeterHjortLauritzen]

Checking option to only smooth when LANDFRAC>0 (using ncube=540 intermediate cubed-sphere grid):

Laplacian smoother smoothing everywhere minus Laplacian smoother with no smoothing over LANDFRAC=0 points (PHIS):

Please note issue with ncube=3000 intermediate cubed-sphere grid:

https://github.com/NCAR/Topo/issues/41

[PeterHjortLauritzen]

After the plots above were made we decided to scale topography so that the volume remains the same. Below is PHIS using Laplacian smoother with "no leak" option with volume scaling minus the same without volume scaling:

Differences in coastal regions is due to zeroing out the smoother over ocean. The differences over land are due to “topographic volume” lost over ocean that is reintroduced through the uniform scaling.