Simulations of space-borne radar data using ground-based radar observations: Non-uniform beam filling and attenuation correction

Space-borne precipitation radars (PRs) operate at short wavelengths (< 3 cm), due to trade-offs among numerous factors including desired spatial resolution, antenna size, cost, weight, and power (Meneghini and Kozu 1990). Attenuation is a limiting factor in these radars when observing long path-lengths through rain, causing the apparent measured radar reflectivity factor (Zm) to be an underestimate of the true radar reflectivity factor (Ze). The underestimate can cause negatively biased estimates of rain rate (Iguchi and Meneghini 1994), a first-order product from PR observations. However, a PR's top-down view of precipitating clouds provides an opportunity to mitigate effects of attenuation by measurement of the path integrated attenuation (PIA). The PIA is obtained when the radar return from the underlying surface can be accurately determined using the surface reference technique (SRT; Iguchi and Meneghini 1994). Under ideal conditions the PIASRT attenuation is used directly to correct Zm for attenuation and obtain Ze. In the case of non-uniformity within the PR (FOV) there is a need for an additional correction factor (Iguchi et al. 2009). This non-uniform beam-filling (NUBF) correction factor is especially important for correcting attenuation due to the combined effects of high rain rates and high spatial variability associated with convective rain cells (Kozu and Iguchi 1999). An exact analytical expression for a NUBF correction factor has been derived (Iguchi et al. 2009), assuming the sub-FOV variability of specific attenuation (k) is represented by an ensemble of Gamma random variables. The correction is applied as follows;

dBZe = dBZm + (PIASRT)*{1+[(sigman)squared]/beta} (1)

where sigman is the coefficient of variation of k and beta is the exponent of a power-law relation between k and Ze. Radar reflectivity factors and PIASRT in (1) are expressed in decibels (dB(.) = 10*Log10(.)). For uniform rain sigman is zero and PIASRT needs no correction. In practice, the value of sigman must be assumed or estimated from PR measured quantities.

In this paper we explore the NUBF correction problem in a simulation study utilizing ground-based radar (GV radar) data with high horizontal resolution to represent the spatial variability of precipitation systems. A number of simplifying assumptions were made to isolate first-order effects of the NUBF problem. The GV radar reflectivity data were transformed to rain rate and specific attenuation via convective Z – R and k – Z relations appropriate for a Ku-band radar. The two-way illumination function of the space-borne PR was represented by a bivariate Gaussian function (Heymsfield et al. 2000) with a nominal FOV diameter of 5 km, mimicking the TRMM PR. Simulated PR observations were obtained by convolving the GV radar data over the PR FOV and assuming a depth of 3 km for the attenuation calculation. Validation rain rates were averaged over the nominal PR FOV at the lowest altitude (1 km). The PIASRT values were assumed to be retrieved with no error.

Surface based radar observations from a C-band bistatic polarimetric Doppler radar in Okinawa were used in this simulation study. Six days of data from a field campaign in early June 2004 were used, including the seasonal Baiu frontal system and Typhoon CONSON. The radar data was interpolated to ½ km and 1 km horizontal resolution at 3 altitudes, 1 km, 2 km, and 3 km. Two modes of data were used: uncorrected for C-band attenuation, and corrected for C-band attenuation using a polarimetric based algorithm. For each mode the vertical structure was represented in two different ways. First, as a simple extension of the field at 1 km altitude with a depth of 3 km, and second, by integrating attenuation over the crude vertical structure represented at altitudes 1, 2 , and 3 km. Simulations were confined to data with 60 km of the radar.

Attenuation correction errors and rain rate retrieval errors were assessed for numerous schemes, including those used in TRMM PR algorithms. The results indicate that future progress in minimizing the NUBF problem will be possible.