A Bayesian approach for precipitation attenuation correction with a Ku-band Broad Band Radar network

A meteorological Broad Band Radar (BBR) at Ku-band has been developed by Osaka University. In recent years, small scale phenomena has caused serious damage in Japan. In May of 2012, for instance, a tornado gave a terrible damage on Tsukuba City in North-Kanto region. Meteorological radars are one of the most useful devices to observe weather phenomena. However, it is difficult for conventional long range radar systems (range resolution of about 100m and temporal resolution of about 5 min) at S-, C-, and X-band to detect small scale phenomena such as tornadoes and downbursts, whose horizontal scale is several hundred meters, and whose duration is several minutes. Therefore, there is a growing need for a weather radar system with high spatial and temporal resolution. The BBR transmits and receives wide-band (80MHz (max)) signals at Ku-band (a center frequency of 15.75GHz) to use pulse compression, which gives us high resolution (range resolution of several meters) and high signal-to-noise ratio (SNR). This radar has no need to integrate coherent or incoherent pulses as many as conventional radars do because of the high SNR achieved by pulse compression with a long pulse, and this allows us to scan over the entire sky (a volume scan with 30 elevations) in the short time of roughly 1 minute. A bistatic antenna system is applied to reduce a direct coupling level (-70dB) and to observe at a little distance (within a few hundred meter radius) from the BBR (Yoshikawa et al. 2010 [1]). With this radar system, we reported good observation results and analysis of some tornadoes near Shonai Airport in the North part of Japan in winter.

With one BBR, however, observable area is only a 20-kilometer radius at most, spatial resolution at the distant from the radar becomes worse, and in a severe convective rain, it is seriously affected by precipitation attenuation. Precipitation attenuation at Ku-band is more serious than at S-, C-, and X-band. Therefore, a conventional method for attenuation retrieval such as Hitschfeld-Bordan (HB) method (Hitschfeld and Bordan, 1954 [2]) does not work well at Ku-band because of the instability of attenuation coefficients which basically depend on the transmitted frequency. In order to solve these problems, we have developed a weather radar network consisting of three BBRs covering a wide observation area. In addition, a weather phenomenon in the overlapped area is observed simultaneously and multilaterally by multiple BBRs, and even if one BBR is affected seriously by precipitation attenuation and measured reflectivity with this BBR is underestimated, another can observe the same precipitation event from different view with low attenuation. We can integrate measured values from each BBR and calculate more accurate values. And precipitation attenuation correction at Ku-band can be accomplished accurately and stably.

Now, we have developed the radar network system consisting of three BBRs in North Osaka area in Japan, and we also have been developing a new retrieval method for precipitation attenuation at Ku-band under the condition of network observation with several BBRs. This method adds Bayesian theory to the HB method, and optimizes the attenuation coefficient. A cost function of the optimization is determined as the squared error between intrinsic values of reflectivity and measured values with each radar. The prior distribution of intrinsic reflectivity is assumed as non-informative. And the adaptively-optimized value of the coefficient can be derived by minimizing the cost function. This means the maximization of the product of likelihood functions of each radar. We apply the proposed method to observation data, and compare with the conventional HB method. As a result, with our method, we can retrieve precipitation attenuation stably, and with the HB method, on the other hand, in area far from BBRs, the value of radar reflectivity is overestimated. Moreover, we have a comparison between observation result of the BBR network and that of other weather radars, including a C-band radar operated by Japan Meteorological Agency, and a Phased Array Radar (PAR) developed by Toshiba Corporation and Osaka University under a grant of NICT. These two radar systems cover almost all the observable area of the BBR network. The error between our network system and each other radar is within a few dB, and we conclude that our proposed method for precipitation attenuation retrieved accurately and stably, and the BBR network worked well under heavy precipitation.

Reference [1] E. Yoshikawa et al., Development and initial observation of high-resolution and volume-scanning radar for meteorological application, IEEE Trans. Geosci. Remoto Sens., vol. 48. no. 5, 2010. [2] Hitschfeld, W. and J. Bordan, 1954: Errors inherent in the radar measurement of rainfall at attenuating wavelengths. J. Meteor.