1. AQUARADAR -D The effects of inhomogeneous rain drop size distributions (DSDs) in a radar volume Vertical structure of DSD profiles Spectral modes of DSDs The effects of inhomogeneous rain drop size distributions (DSDs) in a radar volume Vertical structure of DSD profiles (Kowalewski & Peters, 2009) Spectral modes of DSDs (S. Melchionna, Met. Z. 2008) 1AQUARADAR - D, Bonn 2009

2. The effects of inhomogeneous rain drop size distributions (DSDs) in a radar volume Impact on Attenuation Correction Algorithms Non-linear Z-R-relation 2AQUARADAR - D, Bonn 2009

3. Non-linear Z-R-relation 3AQUARADAR - D, Bonn 2009

4. Non-linear Z-R-relation 4AQUARADAR - D, Bonn 2009 Peters G., B. Fischer, Rain estimation from partially filled scattering volumes, ERAD 2006: Transition from small pixels (60 m ×160 m) to large pixels (960 m × 960 m) causes relative overestimation of rain rate up to 1.3 according to observations of convective and stratiform rain events. Attempts to infer sub-scale variability from standard weather radar data were not successful.

5. Impact on Attenuation Correction Algorithms 5AQUARADAR - D, Bonn 2009 1.Iterative „robust“ algorithm by Hildebrand, 1978 2.Analytic „unstable“ algorithm by Hitschfeld and Bordan, 1954 Definitions: Path Integrated Attenuation Transmission

6. Iterative “robust” algorithm 6 AQUARADAR - D, Bonn 2009 Hildebrand, 1978

7. 7AQUARADAR - D, Bonn 2009 Transmit Signal Scattered Signals http://mathworld.wolfram.com/PowerTower.html

8. 8AQUARADAR - D, Bonn 2009 Good News: It can be shown that the iteration T (i) actually converges to Bad News: is defined only for corresponding to -1.6 dB

9. 9AQUARADAR - D, Bonn 2009 The inverse retrieval function

10. 10AQUARADAR - D, Bonn 2009 Retrieved transmission after various iteration steps

11. 11AQUARADAR - D, Bonn 2009 PIA SIBO and PIA HL at K-band as function of simulated Marshall-Palmer rain rate for Δ r = 100 m and 3 ranges.

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13. 13AQUARADAR - D, Bonn 2009 Analytic „unstable“ algorithm by Hitschfeld and Bordan, 1954 If can be observed, the solution assumes a particularly simple form:

14. 14AQUARADAR - D, Bonn 2009 by Due to the finite range resolution we have to replace Problem: If we assume homogeneity for κ in the scattering volume, it will be inhomogeneous for κ a Solve this equation for κ:

15. 1.Set, set 2.Calculate 3.Calculate 4.Calculate 5.Calculate 6.Calculate 7.Set 8.Go to step 2 15AQUARADAR - D, Bonn 2009 Modification of the original retrieval New!

16. 16AQUARADAR - D, Bonn 2009 Finite Range Gate

17. 17AQUARADAR - D, Bonn 2009 R-k-Relation

18. 18AQUARADAR - D, Bonn 2009 Z-k-relation

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