6.4 Spectral filters

There are two formulations used to smooth the fields.

The first one -- nicknamed thx because it uses the hyperbolic tangent function -- is used in ARPEGE/IFS only to smooth the fields which are horizontal derivatives, or which are build upon horizontal derivatives, espacially when the model is stretched. It looks like a smoothed step function :

$f(n) = \frac{1-\tanh({e^{-k}}(n-n_{0}))}{2}$

where n is a given wavenumber in the unstretched spectral space, k is the intensity of the filter and n₀ is the truncation threshold. : this function roughly equals 1 if n is less than n₀, and roughly equals 0 if it is bigger.

The next figure illustrates this spectral filter :

The second one is au gaussian function. In ARPEGE/IFS it writes :

$f(n)=e^{\frac{-k}{2}(n/N)^{2}}$

where n is a given wavenumber, k is the intensity of the filter and N represents the model triangular truncation.

In ALADIN it writes :

$f(n,m)=e^{\frac{-k}{2}((n/N)^{2}+(m/M)^{2})}$

where (n, m) is a given pair of wavenumbers, k is the intensity of the filter and (N,M) represent the model elliptic truncation.

In ALADIN this gaussian filter is used to filter any field ("derivative" or not).

The next figure illustrates this spectral filter :