Examining regional model output Examining regional model output on different spatial scales using an on different spatial scales using an isotropic digital 2d filterisotropic digital 2d filter

Frauke Feser Frauke Feser and Hans von Storchand Hans von Storch

Institute for Coastal ResearchInstitute for Coastal Research GKSS Research Center, GKSS Research Center,

Geesthacht, GermanyGeesthacht, Germany

Spatial Scales

Vari

an

ce

Global Model

Well resolved

Insufficiently

resolved

Added Value

Well resolved

Insufficiently resolved

Regional Model

The construction of a 2d digital filter :

The filter array should be isotropic, i.e., the response function should be the same for the same wavelength, independent of the direction.

The filter should suppress most of the variance on certain frequency bands, while retaining almost all variance on others.

We have constructed an algorithm which determines an optimal set of filter weights so that the response approximates for wavenumbers k

- with 0≤k≤k1 and k2≤k≤kmax: (k) 0- with k1≤k≤k2: (k) 1

Feser, F., and H. von Storch, 2005: Spatial two-dimensional discrete filters for limited area model evaluation purposes. Mon. Wea Rev. (accepted)

Response functions for fitted optimal low pass, medium pass and high pass filters

Example: Filters for a limited area of 81 grid points in zonal and meridional direction.

The symmetrical filter base is made up of 2*8+1 filter weights in zonal and meridional direction. Here, the response functions is shown only for the „waves“ with directions in the E/N quadrant.

Application of filters

• Analysis of 43 year simulation of REMO-SN (spectrally nudged REMO) with NCEP large scale control. 50 km grid

• The case of a snapshot, showing an example of filtered fields

• Statistics of filtered fields: long term mean (stationary components) and long term standard deviation (time variable components)

• Comparison of time variable components with a) high quality analysis prepared by German Weather Service DWDb) with driving NCEP analyses after suitable fine grid interpolation

Zonal wind component at 10 m height

A case of a field subject to the three filters

Full fieldLow pass

Medium band pass

High pass

Time mean distribution (stationary component) of filtered 10m wind speed in DJF 1992-1999

Full fields

Medium band pass

Low pass

High pass

Full fields

Medium band pass

Low pass

Distribution of standard deviation (time variable component) of filtered 10m wind speed in DJF 1992-1999

High pass

Validation of medium scale variability –comparison of standard deviations simulated by REMO-SN

with high quality DWD analysis

DJF

Ratios of standard deviations REMO-SN/DWD, in %

2m air temperature

JJA

Ratios of standard deviations REMO-SN/NCEP, in %

Added value provided by RCM: Increased medium-scale variability

2m air temperature

JJA

DJF

Summary and outlook:

A two-dimensional almost isotropic digital filter was created for low, medium and small scales; the algorithm is applicable for model grids of miscellaneous resolution and size.

Pre-processing by subtracting a fitted polynomial is often required (not shown).

Results show effective scale separation.

Medium scale variability greatly increased in downscaled (REMO-SN) reconstruction 1959-2002 compared to driving NCEP analysis – ADDED VALUE

Feser, F., and H. von Storch, 2005: Spatial two-dimensional discrete filters for limited area model evaluation purposes. Mon. Wea Rev. (accepted)

End

Top: K=1,2-polynomials Pu1

and Pu2 fitted to the wind speed

field [m/s] at a height of 10 m on December 3rd, 1999, 6 p.m. (storm 'Anatol').Bottom: Full wind speed field for the same date, and after subtraction ofthe K=1,2-polynomials i.e., u - Pu

1 and u - Pu2.

Filter weights (N=8)

for :

Low pass filter

High pass filter

Medium pass filter

Filtering of a finite, non-periodic field.

Digital filtering

With certain constants αk. Δ represents the grid distance.

Note that the filtering calculates a weighted average of the „base point“ f(x) and its K neighbors to the right and to the left. At the interval ends this causes problems.

However, in case of regional modelling at the interval ends are irrelevant because of the „sponge zones“. The width of the sponge zone is typically 10, so that K = 10 is a useful choice.

When the digital filter is applied to a spectrally represented function

])()([)()(1

0*

K

kk kxfkxfxfxf

)2cos()2sin()(2/

10 kxbkxaaxf k

n

kk

with the „filter characteristic“, or „response function“

The filtered function f* may be written as

)]2cos()2sin([)(2/

100

* kxbkxaaxf k

n

kkk

K

llk lk

10 )2cos(2