<p>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 (<a href="https://en.wikipedia.org/wiki/Energy_cascade" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Energy_cascade</a>) of the two domains. <a href="https://i.sstatic.net/FGjXk.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/FGjXk.png" alt="Kolmogorov energy cascade"></a></p>

<p><a href="http://ffden-2.phys.uaf.edu/647fall2013_web.dir/j_stroh/tec.html" rel="nofollow noreferrer">Kolmogorov energy cascade (D. Newman, U. Alaska Fairbanks)</a>.</p>

<p>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. </p>

<p>The reason for the odd numbers in the ratio is given in <a href="https://earthscience.stackexchange.com/questions/8067/why-is-wrf-most-often-configured-at-31-nesting-ratio">Why is WRF most often configured at 3:1 nesting ratio?</a></p>

CC BY-SA 3.0
2016-09-02T09:26:17.033Z
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?
metnix
CC BY-SA 3.0
2016-09-02T11:40:15.220Z
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.
arkaia
CC BY-SA 3.0
2016-09-02T12:23:52.030Z
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.
metnix
CC BY-SA 3.0
2016-09-02T12:44:04.663Z
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__(?)
metnix
CC BY-SA 3.0
2016-09-02T12:53:11.017Z
That is how I understand it, at least.
arkaia
CC BY-SA 3.0
2016-09-01T16:27:39.003Z
2016-09-01T16:27:39.003Z
2017-04-13T12:50:30.540Z
arkaia
<p>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.</p>

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

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

<p>The main motivations I've seen for this is that the intermediate domains (9 &amp; 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. </p>

CC BY-SA 3.0
2016-08-31T16:19:40.143Z
Please read http://earthscience.stackexchange.com/questions/8067/why-is-wrf-most-often-configured-at-31-nesting-ratio
arkaia
CC BY-SA 3.0
2016-09-01T10:58:47.607Z
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.
metnix
<meteorology><atmosphere-modelling><numerical-modelling>
Why should dynamical downscaling of meteorological data be made incrementally?
metnix
# Why should dynamical downscaling of meteorological data be made incrementally?

(Asked by: username_0 on 2016-08-31)

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.

**Tags:** meteorology, atmosphere-modelling, numerical-modelling

> **Comments:**
> **username_1**: Please read http://earthscience.stackexchange.com/questions/8067/why-is-wrf-most-often-configured-at-31-nesting-ratio  
> **username_0**: 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.  

---

## 1 answers

### Answer by username_1 on 2016-09-01. Score: 2

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](https://i.sstatic.net/FGjXk.png)](https://i.sstatic.net/FGjXk.png)

[Kolmogorov energy cascade (D. Newman, U. Alaska Fairbanks)](http://ffden-2.phys.uaf.edu/647fall2013_web.dir/j_stroh/tec.html).

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?](https://earthscience.stackexchange.com/questions/8067/why-is-wrf-most-often-configured-at-31-nesting-ratio)

> **Comments:**
> **username_0**: 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?  
> **username_1**: 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.  
> **username_0**: 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.  
> **username_0**: 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__(?)  
> **username_1**: That is how I understand it, at least.  

---

