3.1 Introduction

Weather radars are essential tools in providing high-quality information about precipitation with high spatial and temporal resolution in three dimensions. However, several uncertainties deteriorate the accuracy of rainfall products, with calibration contributing the most amount (Houze et al. 2004), while also varying in time (J. Wang and Wolff 2009). While adjusting ground radars (GR) by comparison with a network of rain gauges (also know as gauge adjustment) is a widely used method, it suffers from representativeness issues. Furthermore, gauge adjustment accumulates uncertainties along the entire rainfall estimation chain (e.g. including the uncertain transformation from reflectivity to rainfall rate), and thus does not provide a direct reference for the measurement of reflectivity. Relative calibration (defined as the assessment of bias between the reflectivity of two radars) has been steadily gaining popularity, in particular the comparison with spaceborne precipitation radars (SR) (such as the precipitation radar onboard the Tropical Rainfall Measuring Mission (TRMM; 1997–2014; Kummerow et al. (1998)) and the dual-frequency precipitation radar on the subsequent Global Precipitation Measurement mission (GPM; 2014–present; Hou et al. (2013)). Several studies have shown that surface precipitation estimates from GRs can be reliably compared to precipitation estimates from SRs for both TRMM (Amitai, Llort, and Sempere-Torres 2009; Joss et al. 2006; Kirstetter et al. 2012) and GPM (Gabella et al. 2017; Petracca et al. 2018; Speirs, Gabella, and Berne 2017). In addition, a major advantage of relative calibration and gauge adjustment in contrast to the absolute calibration (i.e. minimizing the bias in measured power between an external or internal reference noise source and the radar at hand) is that they can be carried out a posteriori, and thus be applied to historical data.

Since both ground radars and spaceborne precipitation radars provide a volume-integrated measurement of reflectivity, a direct comparison of the observations can be done in three dimensions (Anagnostou, Morales, and Dinku 2001; Gabella et al. 2006, @gabella_using_2011; Keenan et al. 2003; Warren et al. 2018). Moreover, as the spaceborne radars are and have been constantly monitored and validated (with their calibration accuracy proven to be consistently within 1 dB) (TRMM: Kawanishi et al. (2000),Takahashi, Kuroiwa, and Kawanishi (2003); GPM: Furukawa et al. (2015),Kubota et al. (2014),Toyoshima, Masunaga, and Furuzawa (2015)), they have been suggested as a suitable reference relative calibration of ground radars (Anagnostou, Morales, and Dinku 2001; Islam et al. 2012; Liao, Meneghini, and Iguchi 2001; Schumacher and Houze Jr 2003).

Relative calibration between SRs and GRs was originally suggested by Schumacher and Houze (2000), but the first method to match SR and GR reflectivity measurements was developed by Anagnostou, Morales, and Dinku (2001). In their method, SR and GR measurements are resampled to a common 3-D grid. Liao, Meneghini, and Iguchi (2001) developed a similar resampling method. Such 3-D resampling methods have been used in comparing SR and GR for both SR validation and GR bias determination (Bringi et al. 2012; Gabella et al. 2006; Gabella, Morin, and Notarpietro 2011; Park, Jung, and Lee 2015; J. Wang and Wolff 2009; Zhang et al. 2018; Zhong et al. 2017). Another method was suggested by Bolen and Chandrasekar (2003) and later on further developed by Schwaller and Morris (2011), where the SR–GR matching is based on the geometric intersection of SR and GR beams. This geometry matching algorithm confines the comparison to those locations where both instruments have actual observations, without interpolation or extrapolation. The method has also been used in a number of studies comparing SR and GR reflectivities (Chandrasekar, Bolen, and Gorgucci 2003; Chen and Chandrasekar 2016; Islam et al. 2012; Kim et al. 2014; Wen et al. 2011). A sensitivity study by Morris and Schwaller (2011) found that method to give more precise estimates of relative calibration bias as compared to grid-based methods.

Due to different viewing geometries, ground radars and spaceborne radars are affected by different sources of uncertainty and error. Observational errors with regard to atmospheric properties such as reflectivity are, for example, caused by ground clutter or partial beam blocking. Persistent systematic errors in the observation of reflectivity by ground radars are particularly problematic: the intrinsic assumption of the bias estimation is that the only systematic source of error is radar calibration. It is therefore particularly important to address such systematic observation errors.

In this study, we demonstrate that requirement with the example of partial beam blocking. The analysis is entirely based on algorithms implemented in the open-source software library wradlib (M. Heistermann, Jacobi, and Pfaff 2013), including a technique to infer partial beam blocking by simulating the interference of the radar beam with terrain surface based on a digital elevation model. Together, that approach might become a reference for weather services around the world who are struggling to create unbiased radar observations from many years of archived single-polarized radar data, or to consistently monitor the bias of their radar observations. We demonstrate the approach in a case study with 5 years of data from the single-polarized S-band radar near the city of Subic, Philippines, which had been shown in previous studies to suffer from substantial miscalibration (Abon et al. 2016; M. Heistermann et al. 2013).

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