## 1. Algorithm name

Rain attenuation correction of reflectivity an differential reflectivity: PolRainAttCorr?

## 2. Basic description

A number of methods have been proposed in the literature for correcting ZHH for rain attenuation (Bringi el. al., 1990, Carey et al., 2000, Tesud et. al., 2000, Bringi et al., 2001). Describing each one of these is beyond the scope of this report. However, it is suffice to state that from an operational point of view, the so-called “Linear ФDP with a fixed linear α”, by Bringi et. al., (1990) is preferred as it is easy to implement in real-time and is not too demanding computationally. However, its main dis-advantage is that it can over or under-estimate attenuation. In the current version of the software, this method has been implemented to correct for the attenuation suffered by ZHH and ZDR in rain.

## 3. Computational procedure

Similar to computing KDP, correcting ZHH and ZDR for rain attenuation is rather challenging as the underlying ФDP(r) are very “noisy” i.e., generally contain many outliers. The current method used at DMI was inspired by Bringi et. al. (2005) and involve the following steps:

1. Compute the texture of ФDP, Tex( ФDP(x,y)), using equation (2).
2. Generate range mask based on thresholds for Tex(ФDP(x,y)threshold), Signal-to-Noise Ratio (SNRthreshold) and ρHVthreshold to remove bad ФDP values.
3. Interpolate ФDP across “bad” data segments.
4. Compute the ФDP(0) i.e., offset at the “origin” by averaging the first N range gates FDP containing precipitation.
5. ФDP(r) is then smoothed using a median filter with a window size of ~ 5.0 km - 6.5 km.
6. Correct both ZHH and ZDR for rain attenuation using equations (13) and (16), respectively.

## 4. Theoretical background

For an inhomogeneous path, i.e. Ah varies along the path, the corrected ZHH (units of dB) is related to the measured measured ZHH at range r from the radar by the following expression

Substituting equation (10) into the above expression and assuming a is constant we get

Now substituting for KDP from equation (1), the following expression is obtained for the corrected ZHH

Thus knowing by how much ФDP increases from its value at the origin ФDP(0) it is possible to correct the radar reflectivity, ZHH,

### Radar differential reflectivity rain attenuation correction

Just like the above radar horizontal reflectivity, ZHH , the differential reflectivity also suffer from rain attenuation, especially at C- and X-bands. To estimate the rain attenuation of ZDR, we repeat the above procedure for ZHH. We get in this case the following expression

where ADP is the difference between the specific attenuations between the horizontally and vertically polarized waves, i.e., ADP = AH - AV , and is normally referred to as the specific differential attenuation. By analogy to equation (10) a linear relationship between ADP and KDP has been proposed (Bringi et. al., 1990) i.e.,

Substituting equation (15) into (14) we get the following expression for the corrected ZDR

The coefficient β is typically 0.01-0.003 at C-band (Bringi et. al., 2005).

### References

Bringi V. N., Chandrasekar N., Balakrishnan and Zrnic D. S., 1990, ”Anexamination of propagationeffects in rainfall on radar measurements at microwave frequencies”, J. Atmos. Oceanic Tech.,vol., 7, 829 – 840.

Bringi, V. N., Chandrasekar, V.: 2001, ”Polarimetric Doppler Weather Radar”, Cambridge Univ.press, Cambridge, UK.

Bringi V. N., Thurai R., and Hannesen R., 2005, “Dual-Polarization Weather Radar Handbook”,AMS-Gematronik GmbH.

Carey L. D., Rutledge S. A., Ahijevych D. A., and Keenan T. D., 2000, “ Correcting propagationeffects in C-band polarimetric radar observations of tropical convection using differential propagationphase”, J. Appl. Meteor., vol. 39, 1405 – 1433.