Gert-Jan Marseille replied on 8/10/2013

First, I found that large scale mixing is indeed the default setting in cy37. Not by looking at the experiment settings but by generating energy density spectra. I was quite surprised when I saw the result.

ECMWF

First, have a look at 250hpa_ec.png (attached). It shows spectra for the u (left) and v (right) wind components as obtained from ECMWF model fields at model level 53 (around 250 hPa). For reference the curvatures of k^-3 (2-D turbulence) and k^-5/3 (3-D turbulence) are plotting in gray, k denoting wavenumber in m^-1 along the x-axis. Clearly the 3 curves, representing fc+0, fc+3 and fc+6, overlap as we normally see for ECMWF. In fact the spectrum from fc+240 will also overlap: ECMWF spectra are similar for all forecast ranges. Also clear is that ECMWF does not follow k^-5/3 for any spatial scale. For instance, spectra from AMDAR and Mode-S show a k^-3 spectrum for scales larger than 500 km (wavenumbersmaller than 2e-6) and a k^-5/3 spectrum for smaller scales.

Harmonie cold-start

Next, have a look at 250hpa_ha_cold_start.png showing a similar result for a Harmonie experiment without data assimilation (downscaling only). At FC+00 (red curve), the model spectrum is close to ECMWF (not plotted) as expected. Already after 3 hours (and probably already after one hour) Harmonie has added quite some energy on scales below 250 km (wavenumber 4e-6), not resolved by ECMWF, the curve more closely following the atmosphere k^-5/3 spectrum. Same for FC+06.

Harmonie warm-start

Next, have a look at 250hpa_ha_warm_start.png showing a similar result for a Harmonie experiment with data assimilation of conventional observing systems: TEMP/AMDAR/SYNOP. The curvature at FC+00 (red) shows a strange behaviour, following the ECMWF spectrum for scales larger than 250 km, following the Harmonie spectrum for scales below about 25 km and weird mixing in between. Indeed, the large scale mixing of Harmonie with ECMWF becomes clearly evident here, with a large spectral gap in the Harmonie field for spatial scales between 25 and 250 km.

Spectra from ICMSHANAL+0000 and MXMIN1999+0000 also show the same weird spectral behaviour.

From what I understand the reason to apply large-scale mixing with ECMWF is the superiority of the latter on the large and medium range scales. from this I conclude that you have low confidence on the added energy by Harmonie on the 25-250 km scales. In other words, apparently the added structure does not verify (with observations). But then I would also have no confidence on the smaller than 25 km scales, so why analysing these in DA?

Second, how can we expect the structure functions to be balanced (already mentioned by Ole in

hirlam.org/trac/attachment/wiki/Harmonie...entation/lsmixbc.ppt) and correct at all if they were generated without taking into account large-scale mixing?

Third, can we expect substantial positive impact from analysing spatial structures on scales that do not verify, i.e., noise?

After some discussions with colleagues at KNMI I would propose the following for Harmonie 3D-var:

1. Analyse only those scales that verify with observations. This can be tested from (o-b) statistics for a range of truncation wavenumbers applied to b. For small truncation wavenumbers (o-b) will decrease with increasing wavenumber. At a given threshold wavenumber, k_thresh, (o-b) will start to increase, meaning that the additional spatial structures added to b do not verify, i.e., noise.

2. Rather than applying large-scale mixing, truncate the first-guess at k_thresh and analyse the large scales only. I would hope that Harmonie large scales well match with ECMWF! In that case we could use the ECMWF ensemble to generate flow-dependent B structures for use in Harmonie.

With the steps above, we are at least sure to have a better founded DA implementation, including well-balanced flow-dependent B structures.

With the growing number of observations (both spatially and temporal) we can hope to better resolve the small Harmonie scales in the future.

Observation error correlation, thinning, etc. is all very important but starts after having well understood which scales to analyse in DA, rather than trying artificial mixtures.