4.1 Introduction

Weather radar observations are the key to quantitative precipitation estimation (QPE) with large spatial coverage and at high resolution in space and time (in the order of \(10^2-10^3\) meters, and \(10^0-10^1\) minutes). Yet, the indirect nature of the precipitation retrieval paves the way for a multitude of systematic estimation and measurement errors. The estimation errors (in the retrieval of the precipitation rate R from the radar’s prime observational target variable, the radar reflectivity factor Z) is caused mainly by the unknown microphysical properties of the target—let it be meteorological or non-meteorological. Before that, measurement errors affect the observation of Z through a multitude of mechanisms that can accumulate as the beam propagates through the atmosphere (such as beam blockage, or path-integrated attenuation). On top, the prominence of these measurement errors heavily depends on scenario-specific interaction of factors such as radar bandwidth, beam width, obstacles in the direct and wider vicinity, topography in the radar coverage, atmospheric refractivity, or the microphysical properties of precipitation along the beam’s propagation path. Much has been written about these sources of uncertainty, and much has been done to address them adequately (see Villarini and Krajewski (2010) for an extensive review).

Yet, the single-most contribution of uncertainty to radar-based QPE often comes, maybe surprising to some, from the (mis)calibration or (in)stability of the radar instrument itself (Houze et al. 2004) which can also vary in time (J. Wang and Wolff 2009). Apart from the simple fact that miscalibration can easily deteriorate the accuracy of precipitation estimates by an order of magnitude, calibration issues become particularly annoying if weather radars are operated in a network where the consistency of calibration between radars is a prerequisite for high-quality radar mosaics (see e.g. Seo, Krajewski, and Smith (2014)).

There are various options to carry out and monitor the calibration of a radar instrument in an operational context through absolute calibration techniques (based on a well-defined reference noise source, see Doviak and Zrnić (2006) for an overview). Yet, to the reflectivity that is already measured and recorded, any changes to the instrument’s calibration are irrelevant. In such a case, relative calibration techniques can be used to correct the measurements a posteriori. Many institutions have archived massive radar reflectivity records over the years, but they struggle to tap the potential of these data due to unknown and temporally volatile calibration biases. And while radar polarimetry offers new opportunities to address calibration issues, many archived data still originate from single-polarization radars.

As to relative calibration, the usage of rain gauge observations is typically not recommended, not only due to issues of representativeness in space and time, but also due to the fact that a comparison between R, as observed by rain gauges, and R, as retrieved from radar reflectivities, lumps over measurement and estimation uncertainties. As an alternative, the usage of spaceborne reflectivity observations from the Tropical Rainfall Measuring Mission (TRMM) and Global Precipitation Measurement (GPM) platforms has become increasingly popular over the recent years. Measurement accuracies of both TRMM and GPM are reported to have excellent calibration (within < 1dB) (Kawanishi et al. 2000; Hou et al. 2013), and thus can be used as a reference to calibrate reflectivity. Moreover, a major benefit of relative calibration is that it allows for a posteriori correction of historical data.

In a recent study for an S-band radar in the Philippines, Crisologo et al. (2018) adopted a technique to match ground radar (GR) and spaceborne radar (SR) observations. That technique was originally suggested by Bolen and Chandrasekar (2003), then further developed by Schumacher and Houze Jr (2003), and finally by Warren et al. (2018). The underlying idea of that technique is to match observations based on the geometric intersection of SR and GR beams. That way, the algorithm confines the comparison to locations where both instruments have valid observations, and avoids artefacts from interpolation or extrapolation. In that context, Crisologo et al. (2018) demonstrated that explicitly taking into account the quality of the GR observations is vital to enhance the consistency between SR and GR reflectivity measurements, and thus to estimate the calibration bias more reliably. The relevance of quality was exemplified by considering partial beam blockage: for each GR bin, a quality index between 0 and 1 was inferred from the beam blockage fraction. These quality indices were then used to compute a quality-weighted average of volume matched GR reflectivities.

The present study aims to extend the approach of Crisologo et al. (2018) in several respects:

  1. We extend the framework to account for the quality of GR observations by introducing path integrated attenuation (PIA) as a quality variable, in addition to partial beam blockage. Instead of attempting to correct GR reflectivities for PIA, we explicitly acknowledge the uncertainty of any PIA estimate by assigning a low weight to any GR bins that are substantially affected by PIA. In order to investigate the role of PIA, we include a C-band weather radar in the present study, in addition to the S-band radar included by Crisologo et al. (2018).

  2. We verify the ability to estimate the GR calibration bias from SR overpass data by evaluating the consistency of GR reflectivity measurements in a region of overlap, before and after bias correction.

  3. We investigate whether estimates of GR calibration bias, as obtained from SR overpass data, can be interpolated in time in order to correct GR reflectivity observations for miscalibration, even for those times in which no suitable SR overpasses were available.

The latter item—the interpolation of bias estimates in time—would be a key requirement towards actually tapping the potential of the fundamental concept in research and applications: if we aim to use SR overpass data for monitoring GR calibration bias, and for a homogeneous correction of archived GR reflectivities, we have to assume that those bias estimates are, to some extent, representative in time. Crisologo et al. (2018) found that the bias estimates for the Subic S-band radar exhibited a substantial short-term temporal variability, and stated that they “would not expect changes in calibration bias to occur at the observed frequency, amplitude, and apparent randomness.” By investigating whether such bias estimates can be interpolated in time, the present paper will investigate whether the apparently “volatile” behaviour of calibration bias is not a mere artefact of the estimation procedure, but a real property of the investigated radar systems.

Section @ref(sec:data_studyarea) of the present paper will describe the study area and the underlying radar data sets; section 4.3 will outline the methodologies of matching GR and SR as well as GR and GR observations, the quantification of beam blockage and PIA, and the quality-based framework for bias estimation; in section 4.5, we will show and discuss the various inter-comparison results; and section ?? will conclude.

References

Bolen, Steven M., and V. Chandrasekar. 2003. “Methodology for Aligning and Comparing Spaceborne Radar and Ground-Based Radar Observations.” Journal of Atmospheric and Oceanic Technology 20 (5): 647–59. http://journals.ametsoc.org/doi/abs/10.1175/1520-0426(2003)20%3C647%3AMFAACS%3E2.0.CO%3B2.

Crisologo, Irene, Robert A. Warren, Kai Mühlbauer, and Maik Heistermann. 2018. “Enhancing the Consistency of Spaceborne and Ground-Based Radar Comparisons by Using Beam Blockage Fraction as a Quality Filter.” Atmospheric Measurement Techniques 11 (9): 5223–36. https://doi.org/https://doi.org/10.5194/amt-11-5223-2018.

Doviak, Richard J., and Dušan S. Zrnić. 2006. Doppler Radar and Weather Observations. 2nd ed., Dover ed. Mineola, N.Y.: Academic Press.

Hou, Arthur Y., Ramesh K. Kakar, Steven Neeck, Ardeshir A. Azarbarzin, Christian D. Kummerow, Masahiro Kojima, Riko Oki, Kenji Nakamura, and Toshio Iguchi. 2013. “The Global Precipitation Measurement Mission.” Bulletin of the American Meteorological Society 95 (5): 701–22. https://doi.org/10.1175/BAMS-D-13-00164.1.

Houze, Robert A., Jr., Stacy Brodzik, Courtney Schumacher, Sandra E. Yuter, and Christopher R. Williams. 2004. “Uncertainties in Oceanic Radar Rain Maps at Kwajalein and Implications for Satellite Validation.” Journal of Applied Meteorology 43 (8): 1114–32. http://journals.ametsoc.org/doi/abs/10.1175/1520-0450(2004)043%3C1114:UIORRM%3E2.0.CO%3B2.

Kawanishi, Toneo, Hiroshi Kuroiwa, Masahiro Kojima, Koki Oikawa, Toshiaki Kozu, Hiroshi Kumagai, Ken’ichi Okamoto, Minoru Okumura, Hirotaka Nakatsuka, and Katsuhiko Nishikawa. 2000. “TRMM Precipitation Radar.” Advances in Space Research, Remote Sensing and Applications: Earth, Atmosphere and Oceans, 25 (5): 969–72. https://doi.org/10.1016/S0273-1177(99)00932-1.

Schumacher, Courtney, and Robert A. Houze Jr. 2003. “Stratiform Rain in the Tropics as Seen by the TRMM Precipitation Radar.” Journal of Climate 16 (11): 1739–56. http://journals.ametsoc.org/doi/full/10.1175/1520-0442(2003)016%3C1739:SRITTA%3E2.0.CO%3B2.

Seo, Bong-Chul, Witold F. Krajewski, and James A. Smith. 2014. “Four-Dimensional Reflectivity Data Comparison Between Two Ground-Based Radars: Methodology and Statistical Analysis.” Hydrological Sciences Journal 59 (7): 1320–34. https://doi.org/10.1080/02626667.2013.839872.

Villarini, Gabriele, and Witold F. Krajewski. 2010. “Review of the Different Sources of Uncertainty in Single Polarization Radar-Based Estimates of Rainfall.” Surveys in Geophysics 31 (1): 107–29. https://doi.org/10.1007/s10712-009-9079-x.

Wang, Jianxin, and David B. Wolff. 2009. “Comparisons of Reflectivities from the TRMM Precipitation Radar and Ground-Based Radars.” Journal of Atmospheric and Oceanic Technology 26 (5): 857–75. https://doi.org/10.1175/2008JTECHA1175.1.

Warren, Robert A., Alain Protat, Steven T. Siems, Hamish A. Ramsay, Valentin Louf, Michael J. Manton, and Thomas A. Kane. 2018. “Calibrating Ground-Based Radars Against TRMM and GPM.” Journal of Atmospheric and Oceanic Technology, February. https://doi.org/10.1175/JTECH-D-17-0128.1.