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When downscaling meteorological data by using limited area models, many support forums recommended you to downscale incrementally in small steps. For example let's assume that your input data is on a 27x27 km resolution and you need data on 1x1 km resolution.

A suitable setup would be to downscale in three steps, incrementally increasing the resolution: 27 km -> 9 km -> 3 km -> 1 km

Why should I not simply use the following set-up? 27 km -> 1 km

The main motivations I've seen for this is that the intermediate domains (9 & 3 in the example) won't require that much computational resources compared to the final domain (1 km). But that can't be the only reason.

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  • $\begingroup$ Please read earthscience.stackexchange.com/questions/8067/… $\endgroup$
    – arkaia
    Aug 31, 2016 at 16:19
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    $\begingroup$ While that explains why an odd nesting ratio (e.g. 3:1, 5:1, etc) should be used instead of even ratios (e.g. 2:1, 4:1, etc), it does not explain why nesting should be done incrementally. edit: Using the same reasoning as suggested by the top answer, there seems to be no reason why a 5:1 or even 27:1 ratio cannot be used. I believe the answer I'm looking for is due to the different scales of dynamics, rather than the mathematical reasons in that question. $\endgroup$
    – metnix
    Sep 1, 2016 at 10:58

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The basic answer to your question is that there needs to be an overlap between the spectra of the two domains. One way to think about it is that there needs to be a connection between the Kolmogorov energy cascades (https://en.wikipedia.org/wiki/Energy_cascade) of the two domains. Kolmogorov energy cascade

Kolmogorov energy cascade (D. Newman, U. Alaska Fairbanks).

Each domain is going to be forced (have energy input) at a relatively large scale and it is going to assume that the energy that it can't resolve at sub-grid scales is going to be dissipated. If there is no (or little) overlap between the two grid resolutions, the energy from the large domain (parent) will be dissipated by viscosity at sub-grid scales that the small domain (child) cannot resolve and there is not going to be an appropriate input of energy from the parent to the child.

The reason for the odd numbers in the ratio is given in Why is WRF most often configured at 3:1 nesting ratio?

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  • $\begingroup$ Wouldn't this suggest that the child domain simply needs to be large enough to "see" the low wavenumber processes, i.e. the important part is how many parent grid cells are covered by the child domain not the nesting ratio? $\endgroup$
    – metnix
    Sep 2, 2016 at 9:26
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    $\begingroup$ It is not a question of domain size, but rather a function of spatial resolution. The spatial distribution of energy in the spectral sense is determine by dx. In the case of the child domain dx is much smaller (way smaller in your case of 27:1 ratio). The parts of the spectrum that can be resolved go from 2*dx to a number that depends on the energy input. If the energy input is not properly resolved, then the child grid can not simulate those processes. $\endgroup$
    – arkaia
    Sep 2, 2016 at 11:40
  • $\begingroup$ This is still not clear to me... From my understanding, the resolution sets the limit for how high wave numbers can be resolved by the model. The low wave-number end is limited by big the domain is. $\endgroup$
    – metnix
    Sep 2, 2016 at 12:23
  • $\begingroup$ After thinking about this some more: Is the problem that the forcing is only applied along few grid cells along the domain boundaries rather than applied over the whole grid? That would make some sense to me since there aren't that many grid cells to play with; the lowest wave number which could be retained through the nesting would then be determined by the number of grid cells __where forcing is applied__(?) $\endgroup$
    – metnix
    Sep 2, 2016 at 12:44
  • $\begingroup$ That is how I understand it, at least. $\endgroup$
    – arkaia
    Sep 2, 2016 at 12:53

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