Numerical weather prediction (NWP) models generally struggle with limitations of existing parameterisation schemes to adequately capture the complexity of microphysical processes . Since polarimetric radars enable us to distinguish between hydrometeors with different microphysical properties and/or habits (e.g. shape and number concentration) and to identify so-called polarimetric fingerprints indicating ongoing dominating microphysical processes like e.g. aggregation, size sorting or dendritic growth among others, they can serve as a powerful tool for improving NWP parameterisation schemes and cloud models . The fusion of radar polarimetry and atmospheric modelling is a promising pathway to improve the representation of clouds and precipitation in NWP . Using observation- (forward) operators , such as the Efficient Modular VOlume scan RADar Operator EMVORADO;, synthetic polarimetric variables can be calculated from simulated hydrometeor mass fractions and number concentrations of NWP models and directly compared with observed polarimetric variables e.g. on the radar grid;. E.g., with a detailed model evaluation in radar observation space, identified excessive graupel production in the COnsortium for Small scale MOdeling (COSMO) model with the Seifert-Beheng two-moment microphysical parameterisation (SB2MP) scheme . To date, extensive graupel formation is still an ongoing challenge in many microphysical paramerisation schemes. Furthermore, model evaluation studies in radar observation space as well as polarimetric microphysical retrievals and in-situ observations show that existing NWP models coupled with various microphysical schemes tend to overestimate the size of aggregates and underestimate the number concentration of ice particles in general e.g.among others. Besides case studies, climatologies of polarimetric variables and microphysical retrievals are particularly important and serve as a statistically significant reference to understand and finally improve precipitation processes in atmospheric models.

In order to provide the required reliable information to NWP modelers, but also for most other radar applications in the scientific community and operational services, like quantitative precipitation estimation (QPE), nowcasting, hydrometeor classification and microphysical retrievals, precise calibration is a mandatory prerequisite e.g.. Although the use of novel gradient approaches e.g. and phase-based measurements are gaining increased attention and popularity, it is unlikely that absolute values of the reflectivity factor ZH and differential reflectivity ZDR will ever become superfluous and instead will always remain a part of hybrid QPE and microphysical retrieval derivations. Calibration is also (even maybe to a lesser extent) relevant for climatologies in order to represent reality with sufficient accuracy and statistical significance by minimizing calibration induced uncertainties as much as possible. In principle, calibration induced uncertainties can be attributed to the characteristics of the receiver, transmitter, and, above all, the antenna, with the latter controlling the link between transmitted and received pulse power e.g..

Over the years, many techniques for calibrating ZH and ZDR have been developed and applied. Examples are the use of disdrometer data e.g., corner reflectors or metal spheres attached on e.g. drones and balloons; e.g., virtually generated radar targets , solar signals e.g., stable ground clutter signals e.g. or dominant point targets located close to the radar site , self-consistency relations of polarimetric variables e.g., ZH-ZDR dependencies in light rain e.g., satellite (spaceborn) radar information , quasi-vertical profiles QVPs; in light rain , dry aggregated snow e.g., clear air Bragg scattering e.g., or the so-called birdbath scan method e.g..

The latter exploits vertical scans, where raindrops appear nearly spherical to the radar, and is one of the most frequently used methods for accurate ZDR calibration. Similarly, ZDR is expected to be 0 dB when the radar is pointing towards the sun, due to the unpolarized nature of solar radiation in this direction. Monitoring the sun allows the detection potential receiver malfunctions or radar antenna misalignment . To determine more precisely which components of the radar system are responsible for any system biases, the latter two techniques can be combined, as demonstrated in . In particular, the difference between the ZDR derived from solar signals and that obtained from birdbath scans can be used to identify transmitter biases.

The first part of the paper series focuses on the prior, as noted above, very important calibration of ZDR and ZH, while the second part deals with the description and the statistical analysis of the climatology of QVPs of polarimetric variables and ice-microphysical retrievals obtained from 10 years of X-band radar data measured in stratiform rain.

Most of the calibration methods briefly presented above are either not retrospectively applicable because e.g. the required scanning strategy is missing, the radar system is simply not capable of setting it up, the required measurements are not saved, or it is not possible to cover the whole time period. Although the birdbath method is widely used to calibrate ZDR, the results were not reliable throughout the entire climatological period; In particular, the offset values obtained for 2014 appeared unrealistically small, limiting the usefulness of the calibrated ZDR. Instead applying the birdbath scan, a modified method adapted from using QVPs in light rain is exploited for ZDR calibration and a ZH calibration technique applicable to the entire time series from 2013–2023 is presented. It uses the known ZH-ZDR dependency , but with ZDR as a predictor for ZH measured on PPI scans at 18° elevation angle. This calibration method of ZH is validated and compared to ZH offset values obtained from satellite measurements, provided for a 5.5 year subset by and self-consistency relations as described in e.g. .

The paper is structured as follows: Section 2 shortly introduces most important technical information and scanning strategies of the used radar and describes the steps of phase processing in more detail. The following Sect. 3 explains the problems encountered when using the birdbath scan method to correct ZDR and presents the above mentioned alternative ZDR calibration method used in this study, followed by the novel ZH calibration method, its validation and the comparison with the self-consistency relation. Section 4 summarizes the results, highlights deficiencies and identifies potential improvements for future studies.

The radar data used in this study have been obtained with the polarimetric X-band radar in Bonn, Germany (BoXPol), located at 50.7305° N and 7.0717° E and 99.5 m above mean sea level (a.m.s.l). BoXPol measures within a radius of 100 km since 2009 (Fig. ). The hardware includes an EEC DWSR-2001-X-SDP weather radar without a radome, operating in the simultaneous transmit and receive of horizontally and vertically polarized electromagnetic (EM)-waves (STAR or SHV) mode using an Enigma signal processor. Plan position indicator (PPI) scans are generated at 10 different elevation angles, ranging from 1–28° and a (90°) birdbath scan in 5 min temporal and 1° azimuthal resolution. The range resolution depends on the chosen configuration of the elevation scan and ranges from 25–200 m. For the 18° elevation angle (used in this two paper series) it is 100 m until the third of April 2017 and afterwards 125 m, where Enigma 3 was updated to Enigma 4. BoXPol operates in dual pulse repetition frequency (PRF) unfolding (staggering) mode 3, with alternating low PRF and high PRF values in the azimuth dimension with values ranging from 400–1150 Hz (1600 Hz for the birdbath scan) and from 320–920 Hz, respectively, for various range resolutions personal communication with Kai Mühlbauer

Further information is available in the GAMIC Enigma 3 manual.

Assuming no specific attenuation AH; e.g., wet radome effects e.g. or noise influences e.g., a simple representation of the measured ZH e.g. based on the well-known radar equation e.g. , can be used to characterize possible calibration errors with the following equation:

1ZH=-10log⁡10×π3Kw2λ2×1024⋅ln⁡2×1018PtH(GHθH)2cτAtHArH︸CrH+20log⁡10r+10log⁡10PrH. PrH is the received and PtH the transmitted power of the horizontal polarization channel in W, Kw is the dielectric factor of water, θH is the half power antenna beam width of the horizontal polarization channel in rad, c is the speed of light in ms-1, GH is the antenna gain of the horizontal polarization channel with the assumption that the antenna is for both transmitting and receiving, AtH and ArH are the transmitter and the receiver gains of the horizontal polarization channel, τ is the pulse duration of transmitted signals in s and r is the radial distance of the target in m.

The underbraced term in Eq. () is the so-called radar constant of the horizontal channel CrH e.g., which can vary over time and due to degradation of radar hardware e.g. and represents the main source of potential calibration errors.

Similarly, Eq. () is valid for the reflectivity factor of the vertically polarized EM wave (ZV) in the STAR mode, i.e. superscripts and subscripts “H” can be replaced by “V” e.g.. As a result, any difference in the radar constants for both polarization channels may also result in a ZDR miscalibration, as illustrated by the following equation: 2ZDR=10log⁡10PrH⋅CrVPrV⋅CrH. In the case of a perfectly calibrated (fictitious) radar e.g. for the transmitter channel, for the receiver channel and for the antenna;, CrH=CrV and thus, ZDR depends on PrV and PrH only e.g.. Since a perfect internal calibration for the estimation of Cr is almost impossible, external sources/methods are mandatory for a sufficient calibration of ZH and/or ZDR

Some of these techniques are briefly mentioned above.

The birdbath method, broadly used for ZDR calibration, provided only for a limited time period (April 2014–April 2017) of the BoXPol data set reliable results. Otherwise, inaccuracies of more than 0.2 dB have been detected. Instead, the approach by has been modified and applied successfully to ensure sufficient accuracy of ZDR for the entire period (2013–2023).

This study aims to raise awareness of the need to critically use the birdbath method (or any other method based on one elevation scan only) and not apply the resulting offsets to the entire volume scan without further verification. Elevation dependent offsets have been identified already for other radars as well e.g.. It may be necessary to calculate an individual ZDR offset value for each of the elevations of interest, which can be time consuming and computationally expensive.

Since accurately calibrated ZDR values are key for applications such as QPE, HMC, or ZH calibration exploiting the reverse ZH-ZDR method, further research is required to ensure reliable quantitative use of ZDR in radar meteorology.

The reverse ZH-ZDR method has been validated and compared with satellite-based measurements and self-consistency relations. ZH offsets derived with the reverse ZH-ZDR methodology agree well with the averaged ZH offsets derived from GPM overpasses in stable RCA periods between 2014 and 2019 . Even a direct point-to-point comparison of daily ZH offsets, which is critical due to the large difference in sample sizes, shows similar trends and acceptable RMSE and MAE values. To gain additional insights, expected ZH values using self-consistency relations (ZHself) based on QVPs have been calculated as well. A stratiform filtering technique (see and Appendix ) guarantees a sufficient degree of homogeneity for QVP generation. The comparison of ZHself and ZH calibrated with the reverse ZH-ZDR method are consistent with results shown in , with acceptable values for the RMSE, MAE and MB. In addition, the general overestimation of ZHself values is in agreement with the more negative daily derived ZH offset values using self-consistency relations compared to the ones using the reverse ZH-ZDR method. The small number of outliers in ZHself can most likely be explained by uncertainties in KDP derivations, DSD variability, temperature dependencies, assumptions on the canting angle distribution and the raindrop shape model used in the T-matrix simulations.

The comparison between ZHself and the offset corrected ZH using the reverse ZH-ZDR method gives confidence in the use of the 30 d rolling mean gap-filling procedure to adequately fill missing ZH offset values.

In summary, we conclude on the overall reliability of the reverse ZH-ZDR method for ZH calibration assuming a sufficiently accurate prior calibration of ZDR. It may serve as a powerful alternative to standard ZH calibration techniques like self-consistency relationships, and/or can be used, if satellite-based information for most accurate calibration of ZH is missing. We do not intend to suggest that the self-consistency method is generally inferior. Rather, we wish to emphasize that BoXPols ZH is calibrated with the method introduced with sufficient accuracy and, compared with an already established method, with even greater precision. Regarding satellite-based calibration, seasonal variations and their impact on RCA stable time periods could be addressed in the future by applying a dynamic clutter map to reduce potential uncertainties in the GPM derived ZH offset values.

Even though diurnal variations have been partially observed in the ZDR offsets, this study aimed at daily ZDR and ZH offsets, deleting days with higher variability in the offset values (ZDR offset standard deviation>0.2dB; ZH offset standard deviation>4dB). However, calculations of temporally higher resolved offsets could potentially lead to more accurate estimates of offsets and especially reduce potential errors associated with the gap-filling method based on a 30 d rolling mean. To enable also the inclusion of e.g. sequences not fulfilling the filtering criteria for light rain, or even more intense convective events in the offset calculations, other ZH-calibration methods, e.g. the one proposed by using AH, or methods in the integrated Satellite and Clutter Absolute Radar calibration SCAR; scheme like solar calibration could be combined with the introduced reverse ZH-ZDR method. Further validation of the reverse ZH-ZDR method in different climate regimes, at different radar wavelengths, and with an increased number of GPM overflights, should be carried out in the future.