BALTRAD

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 Z_HH 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 Ф_DP 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 Z_HH and Z_DR in rain.

3. Computational procedure

Similar to computing K_DP, correcting Z_HH and Z_DR for rain attenuation is rather challenging as the underlying Ф_DP(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:

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

4. Theoretical background

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

$\begin{equation*} Z_{HH}(r) = Z^{measured}_{HH}(r) + 2\int_{0}^{r} A_h(r) dr \tag{1}\end{equation*}$

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

$\begin{equation*} Z_{HH}(r) = Z^{measured}_{HH}(r) + 2\alpha\int_{0}^{r} K_{DP}(r) dr \tag{2}\end{equation*}$

Now substituting for K_DP from equation (1), the following expression is obtained for the corrected Z_HH

$\begin{equation*} Z_{HH}^{corrected}(r) = Z^{measured}_{HH}(r) + \alpha[\phi_{DP}(r) - \phi_{DP}(0)] \tag{3}\end{equation*}$

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

Radar differential reflectivity rain attenuation correction

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

$\begin{equation*} Z_{DR}^{corrected}(r) = Z^{measured}_{DR}(r) + 2\int_{0}^{r} A_{DP}(r)dr (4) \tag{4}\end{equation*}$

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

$\begin{equation*} A_{DP} = \beta\cdot K_{DP} \tag{5}\end{equation*}$

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

$\begin{equation*} Z_{DR}^{corrected}(r) = Z^{measured}_{DR}(r) + \beta[\phi_{DP}(r) - \phi_{DP}(0)] \tag{6}\end{equation*}$

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.[[BR]]

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

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

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.