IFS Documentation front page

I Observations
II Assimilation
III Dynamics
IV Physics
V Ensemble
VI Technical
VII Waves

2.5 Filtering in spectral space.

2.5.1 General considerations.

Three filterings are successively applied:

• 1) A "THX" filter on derivatives in ARPEGE, or a bell-shaped filter on derivatives for ALADIN.
• 2) A bell-shaped filter on all fields (derivatives and not derivatives).
• 3) A "THX" filter on all fields.

Filtering is done in routine pp_obs/SPOS (pp_obs/ESPOS for ALADIN).

2.5.2 `THX' (ARPEGE) or bell-shaped (ALADIN) filtering on derivatives.

Cases where this filtering is used:

This filtering applies in the spectral space to absolute vorticity, relative vorticity, divergence, vertical velocity, stretching and shearing deformations, and potential vorticity (and extend to all variables if the vertical coordinate of post-processing is the potential vorticity). This filter is active if:

• CFPFMT is not `MODEL' in namelist NAMFPC.
• LFPFIL=.TRUE. in namelist NAMFPF for ARPEGE, or LFPBED=.TRUE. in namelist NAMFPF for ALADIN.
• Variable NFMAX is smaller than the `equivalent unstretched sphere' truncation (in practical is between and , where is the stretching factor.

If you wish to keep these fields unfiltered, then just set LFPFIL=.FALSE. in ARPEGE/IFS, or LFPBED=.FALSE. in ALADIN (namelist NAMFPF). On the other hand, you can keep the filter active but you can tune the filtering function.

Function of filtering:

In ARPEGE/IFS, this function looks like a smoothed step function; for a given total wavenumber n in the unstretched spectral space (i.e. the spectral space of the `equivalent unstretched sphere' of truncation ), the formula is:

(2.10)

(The use of the function hyperbolic tangent is the reason of the nickname `THX' for this filter). It means that this function equals roughly 1 if is less than , and 0 if it is bigger than .

Tunable parameters in the previous function:

and are tunable parameters:

• is in the variable . If CFPFMT='GAUSS' or 'MODEL' in namelist NAMFPC, the default value is ; else, it is the truncation of the Gaussian grid which would have been defined by latitudes and longitudes with default so that (see YOMFPD and namelist NAMFPD).
• is defined as follows:

(2.11)

• where and are percentages. This means that: on times the width of the spectrum, the function will decrease quickly, and that at the boundaries of this window, the values of the function will be respectively and . Quantities and are respectively in NFPWID and RFPEPS.

Operations done in SPOS for this filtering:

One assumes that CFPFMT is not 'MODEL'.

• LFPFIL=.T. and : the previous function is computed in the `equivalent unstretched sphere' of truncation , so reading dilatation and contraction matrixes respectively denoted by and (computed by the configuration 911 of ARPEGE/IFS, see the corresponding documentation) is necessary. The operator applied to spectral fields in the computational sphere is a matrical operator pre-computed in the routine pp_obs/FPFILTER (called by setup/SU3FPOS) and stored in the array RFPMAT. In SPOS the initially unfiltered fields are in SPDFP and the filtered fields are put in SPBFP. Filtering is done only if NFMAX < \Nc , elsewhere there is a simple copy of SPDFP in SPBFP without filtering.
• LFPFIL=.T. and \Ns = \Nc : identity \Ns = \Nc is satisfied if the model resolution has no stretching. fTHX(n) is stored in the array RFPFIL. This function is directly applied in SPOS to SPDFP and the filtered fields are put in SPBFP. Filtering is done only if , elsewhere there is a simple copy of SPDFP in SPBFP without filtering.
• LFPFIL=.F.: no filtering, simple copy of SPDFP in SPBFP.

ALADIN:

In ALADIN, this filter is a `bell-shaped' function and is done in the computational geometry. For a given pair of wavenumbers , the formula is:

(2.12)

where is the model truncation (NSMAX) and a tunable variable. is in variable RFPBED of namelist NAMFPF.

2.5.3 `Bell-shaped' filtering on non-derivative fields.

Way of filtering:

It is also possible to filter the non-derivative post-processed fields through "bell-shaped" filters. Separate `bell-shaped' filters are available for geopotential, temperature, mean sea level pressure, relative humidity and all other non-derivatives. By default, these filters are active for geopotential, temperature, mean sea level pressure and relative humidity. In ALADIN, the formula is the same as above (formula (2.12)). In ARPEGE/IFS, for a given wavenumber n in the stretched spectral space, the formula is:

(2.13)

where is the model truncation (NSMAX) and a tunable variable. In SPOS, the bell-shaped filtering is done by multiplying the array SPAFP by , the result is still in SPAFP.

Variables controlling bell-shaped filtering:

• Switches LFPBEG for geopotential, LFPBET for temperature, LFPBEH for relative humidity, LFPBEP for mean sea level pressure, LFPBEL for other non-derivatives, LFPBED for derivatives (LFPBED is used only in ALADIN): .TRUE. if filtering, .FALSE. if no filtering.
• Variables RFPBEG for geopotential, RFPBET for temperature, RFPBEH for relative humidity, RFPBEP for mean sea level pressure, RFPBEL for other non-derivatives, RFPBED for derivatives (RFPBED is used only in ALADIN): to control the intensity of the filtering (variable of formula (2.13)).

2.5.4 Additional `THX' filtering on all fields.

Way of filtering:

Filtering is still made according the formula (2.10): the threshold is now the variable NPMAX and filtering is always made in the computational space. There is filtering only for between NPMAX and . If there is no filtering.