Fuzzy Parameters Optimized for C-Band

The new features imply reprocessing of the algorithm parameters in the new class basis, in a variety of climates, and in the hybrid polarimetric processing mode. Adding these customizations, the understanding of data and phenomena at S-band was extended to C-band.

The existing CSU parameter optimization procedure was applied to multi- season data samples obtained at the Vaisala polarimetric weather radar prototype at University of Helsinki.1

The data samples represented a variety of weather cases (see the following 3 figures) as follows:

  • Summer convection
  • Winter storm
  • Stratiform frontal precipitation

As result, new membership functions and rule strength coefficients were obtained that are used as default settings for C-band weather radars operating in the 'hybrid' mode. The distributions of the membership functions are visualized in the following figures.

For numerical values and more details of the membership function parameters, see Parametrized Fuzzy Parameters.

Figure 1. Selected Observables in the RHI Data Sample of a Summer Convection used for Optimizing the Fuzzy Parameters
1
Reflectivity Z (dB)
2
Differential reflectivity Zdr (dB)
3
Cross-correlation coefficient RhoHV(0)
4
Classification result ('D.S': dry snow, 'W.S': wet snow, 'G/S.H' graupel, small hail)
Figure 2. Selected Observables in the RHI Data Sample of a Stratiform Precipitation (Warm Front) used for Optimizing the Fuzzy Parameters
1
Reflectivity Z (dB)
2
Differential reflectivity Zdr (dB)
3
Cross-correlation coefficient RhoHV(0)
4
Classification result ('D.S': dry snow, 'W.S': wet snow)
Figure 3. Selected Observables in the RHI Data Sample of a Winter Precipitation Event used for Optimizing the Fuzzy Parameters
1
Reflectivity ZH (dB)
2
Differential reflectivity Zdr (dB)
3
Cross-correlation coefficient RhoHV(0)
4
Classification result ('D.S': dry snow, 'W.S': wet snow)
Figure 4. C-band Default Settings of the Membership Functions for Reflectivity (ZH)
Figure 5. 2D Membership Functions for Differential Reflectivity (Zdr) (Expressed as 0.5 Compatibility Contours as Function of Reflectivity)
Class compatibilities are greater than 0.5 when Zdr values fall between the regions depicted by the contours.
Figure 6. 2D Membership Functions for Specific Differential Phase (Kdp) (Expressed as 0.5 Compatibility Contours as Function of Reflectivity)
Figure 7. Membership Functions of the Cross-Correlation Coefficient (RhoHV)
Figure 8. Membership Functions for Altitude (h) (Depicted for Melting Layer Height at 2.5 km)
The contours shift linearly as function of the melting layer height. All heights are expressed with respect to mean sea level.

The optimized expressions for rule strengths (RS) are analogous to the literature reference with the following new default coefficients:

R S i ( M L > 0 ) = M B F i ( Z H ) × M B F i ( h ) × M B F i ( Z d r ) + 0.5 × M B F i ( K d p ) + 0.5 × M B F i ( R h o H V ) 2
R S i ( M L < 0 ) = M B F i ( Z H ) × 0.7 × M B F i ( h ) × M B F i ( Z d r ) + 0.3 × M B F i ( K d p ) + 0.5 × M B F i ( R h o H V ) 3

In these expressions RSi(ML>0) and RSi(ML<0) refer to rule strengths of a class i for warm and cold season cases, respectively. MBFi(x) refers to membership functions of variable x for the class i.

1 Puhakka, T. et al., 2006: University of Helsinki Research Radar Setup. 4th European Conference on Radar Meteorology and Hydrology, Barcelona, Spain.