In the initial phase of the ESPOIRS project, a doppler dual-polarization X-band radar was deployed in Reunion Island ahead of the campaigns in Seychelles and Madagascar. Quality control of radar data was conducted in Reunion, where Météo France has set up an extensive network of rain gauges with a high temporal resolution of 6 min and 1 h. As the project focuses mainly on heavy precipitation, this study was carried out with data collected during the intense cyclone Batsirai, which spanned from 1 to 4 February 2022, a period when continuous radar and rain gauges data were available. The total number of volume scans is 576.

Figure 1a shows the track of Tropical Cyclone Batsirai, while Fig. 1d illustrates an example of a PPI of raw reflectivity at 11° elevation during Batsirai's passage close to Réunion Island. Additional examples of PPIs with filtered reflectivity data are provided in Appendix A.

The radar was located in Saint-Joseph in the south of Reunion Island (Fig. 1b and c), at 20 m above sea level, with a maximum range set at 75 km. The radar performed 360-degree azimuthal scans along 12 constant elevation angles at 1.0, 2.2, 3.3, 4.4, 7, 9, 11, 15, 19, 21, 25, and 29°, with a range gate resolution of 125 m. The complete set of scans was repeated at 10 min intervals. Table 1 lists the main characteristics of the radar.

Six rain gauges were chosen to validate the radar data (Fig. 1b and c), because they were located within the radar's field of view and provided continuous data recordings. The closest (i.e., lowest elevation) unobstructed radar beam to each rain gauge was selected to compare the rain gauge measurements with the corresponding radar estimate (Fig. 2).

Figure 2 below presents the characteristics of the selected rain gauges based on their location with respect to the radar location and the selected radar beams, revealing two distinct groups of rain gauges:

Group 1: rain gauges located within 15 km of the radar with a vertical distance between the radar beam and rain gauge of less than or equal to 600 m, including Crete, Grand-Coude, and Grand-Galet.

The processing applied to radar data is detailed in this section and summarized in Fig. 3.

In the first processing step, all non-meteorological signals were removed using two filters. The first filter consists of keeping signals with copolar correlation coefficient ρHV values greater than 0.85. This simple but efficient tool for data quality control is an easy way to remove non-meteorological echoes, since in most precipitation regions, ρHV values typically exceed 0.8 (Rauber and Nesbitt, 2018). The second filter involves using a horizontal signal-to-noise ratio (SNRH) greater than 3, a threshold value recommended by our radar manufacturer “Gamic” to suppress noisy data; higher values indicate better data quality.

In the second processing step, the attenuation of reflectivity Z was corrected by employing one of two algorithms: (1) an algorithm based on single polarization proposed by Hitschfeld and Bordan (1954), with the advantage of its ease of implementation as detailed in Sect. 2.2.1; and (2) an algorithm based on dual polarization, known as the philinear method, which uses the differential phase ϕdp and requires pre-processing, as detailed in Sect. 2.2.2 below. The respective performances of these two algorithms were compared with rain gauge measurements using the Z–R relationship, (Koffi et al., 2014) used by Météo France Z=300R1,35 for Réunion Island. This relation is derived from tropical cyclones observations (Jorgenses and Wills, 1981), with Z corrected for attenuation. An additional estimator was used to derive the radar QPE: R=8.06kdp0.49, calculated from our radar observations and detailed in Sect. 2.2.3 below.

In addition to R(Z) and R(kdp), many studies have demonstrated the effectiveness of multi-parameter polarimetric rain rate estimators, such as R(KDP,ZDR) or R(ZH,ZDR,KDP) (e.g., Matrosov et al., 2002; Illingworth, 2005; Figueras I Ventura et al., 2012; Koffi et al., 2014; Li et al., 2023). However, estimators involving ZDR require accurate calibration of the radar system. Two main sources of bias can significantly affect ZDR: i.

the transmission and reception chains, especially uncertainties in the relative attenuation or gain between the two polarimetric channels, and

Calibration methods exist in the literature, including approach based on the intrinsic properties of meteorological targets observed at high elevation angles (near 90° in PPI mode), where ZDR values close to 0 dB are expected (Gorgucci et al., 1999). However, such high-elevation PPI scans were not available during the first campaign in La Réunion, as the system was still in a testbed phase.

Given these constraints and to avoid potential errors associated with poorly calibrated ZDR. This study relied exclusively on R(Z) and R(kdp) estimators. Nevertheless, this choice is further supported by previous studies showing that R(Z) performs better in light to moderate rainfall, while R(kdp) is more robust in heavy rainfall conditions (Koffi et al., 2014).

In this study, we also explored the influence of precipitation type on the radar QPE. Two classes of precipitation were therefore defined: the first relates specifically to stratiform precipitation, while the second includes all precipitation occurring during the study period by combining convective and stratiform precipitation.

According to the literature (Fabry and Zawadzki, 1995; Matrosov, 2021), stratiform rain is associated with the bright band. In tropical regions, stratiform rain often originates from old convective cells (Houze, 1997). The turbulence and vertical motion of convective rain inhibit the formation of a bright band (Ghada et al., 2022), which thus becomes a marker of stratiform rain. In our precipitation classification methodology, the identification of stratiform rain is based on the detection of the bright band in the maxdisplay plots. Maxdisplay shows the maximum value of the radar reflectivity along the vertical column.

The bright band can be recognized by a circular region with elevated reflectivity values, observed prominently in both the maximum reflectivity values around the radar and the maximum vertical cross-sections of the maxdisplay plots. Its presence signifies the occurrence of stratiform precipitation during the corresponding time step. As the bright band occurs only during the early morning of 3 February, the identification of stratiform precipitation was performed manually.

The agreement between radar-based QPE and rain gauge measurements was evaluated using the normalized bias (NB) and correlation coefficient (corr).

1NB=R‾G‾-12corr=∑∀iGi-G‾Ri-R‾∑∀iGi-G‾2∑∀iRi-R‾2 where R and G represent hourly rainfall observed by the radar and rain gauge, respectively, while R‾ and G‾ denote the average.

In this section, the interpretation focuses solely on the “all precipitation” types mentioned in Table 3, as the sample “n” is sufficiently large.

According to Table 3, for all stations, the HB method showed a lower correlation coefficient than the philinear method, particularly for stations located more than 19 km from the radar, such as Bellecombe and Commerson (group 2). At these distant stations, the HB method exhibited correlation coefficient close to zero, suggesting the absence of link between the radar rainfall estimates and rain gauge measurements.

The NB reveals that for the rain gauges located less than 15 km from the radar (group 1) such as Crete, Grand-Coude and Grand-Galet, both methods (HB and philinear) exhibit a positive NB, indicating a slight overestimation by the radar. Conversely, for stations located further from the radar (group 2) such as Tampon, Bellecombe, and Commerson, the NB is negative, indicating the radar's underestimation of precipitation. This underestimation is more pronounced for the HB method compared to the philinear method. For instance, for Commerson, the NB is -0.6 with the HB method and becomes -0.2 with the philinear method.

To summarize, the results show that the philinear method improves attenuation correction compared to the HB method. This improvement is due to the fact that the HB method relies solely on reflectivity as the algorithm input. Reflectivity is sensitive to attenuation, radar calibration errors, and the presence of non-rain scatter. Hitschfeld and Bordan (1954) emphasized that even a minor error in the radar calibration could result in significant inaccuracy in the rain rate measurements, particularly at 3 cm wavelength. These limitations negatively impact the rainfall estimation (Jacobi and Heistermann, 2016). However, the use of the differential propagation phase shift directly related to path-integrated attenuation (PIA) as in the method helps to overcome these uncertainties (Zrnić and Ryzhkov, 1996), as ϕdp is immune to partial beam blockage, radar calibration, and ground clutter.

However, attenuation is not the only factor influencing rainfall estimates derived from the Z–R relationship. The Z–R relation used in this study, adopted from Jorgenses and Wills (1981), was originally derived from hurricane observations and is implicitly representative of both stratiform and convective rainfall regimes, typical of tropical cyclones rain (Houze, 1977). Nevertheless, under tropical cyclone conditions ( in the outer rainbands in this case), rainfall is often characterized by high concentrations of small-to-medium drops and relatively fewer large drops (Wu et al., 2021; Radhakrishna, 2022). Deviations from the drop size distributions (DSDs) underlying the Z–R relationship of Jorgenses and Wills (1981) can therefore lead to biased rainfall estimates.

Jorgensen and Willis (1982) themselves highlighted limitations of this relationship, noting that it exhibits less scatter near the surface than at higher altitudes (around 1500 m). At higher altitudes, their measurements are above the cloud base, where a larger number of small droplets get transported through updrafts. This process introduces larger variability in the Z–R relationship.

Our results are in line with their findings. At low-altitude stations (Group 1), the Z–R relationship performs better, as the observed DSDs are closer to the climatological assumptions embedded in the Z=300R1.35 formulation. In contrast, performance degrades at high-altitude stations (Group 2; Bellecombe and Commerson), where two main mechanisms may explain this discrepancy:

First, these stations are located on mountain peaks and are therefore strongly influenced by orographic precipitation processes. Singh et al. (2024) have demonstrated that in both orographic and convective rainfall, microphysical processes such as collisional drop breakup are frequent due to enhanced turbulence, strong vertical motions, and frequent drop–drop interactions. These processes reshape the DSD and lead to significant deviations from standard Z–R relationships. Notably, Singh et al. (2024) also show that the occurrence of equilibrium DSDs decreases with increasing rain rate, meaning that at high rain rates, the DSD is least likely to match the assumptions embedded in climatological Z–R relationship.

In this section, the interpretation focuses exclusively on the class “all types of precipitation” due to the sufficient number of samples.

For stations close to the radar (Group 1), the correlation coefficient ranges from 0.73 to 0.86, indicating good agreement between radar QPE and rain gauge measurements. However, the positive NB values (0.51 to 0.64) show that the radar tends to overestimate rainfall at short distances.

For stations located further from the radar (Group 2), the correlation increases (0.56 to 0.78) compared to R(Z) estimation. However, the correlation remains significant. In this case, the negative NB values (-0.27 to -0.11) but close to zero indicate a slight underestimation of rainfall by the radar at larger ranges.

Overall, the results show a better performance of R(kdp) compared to R(Z) for stations located more than 15 km from the radar (group 2), particularly during heavy rainfall (median value > 20 mm h⁻¹, where the radar beam is located far from the ground station, at approximately 1 km above the ground) (Fig. 9). The results are consistent with those of previous studies showing that kdp-based estimators are more reliable for intense precipitation, as they are less affected by attenuation (e.g., Figueras i Ventura et al., 2012; Koffi et al., 2014; Schneebeli et al., 2014).

In addition, unlike reflectivity, which is proportional to the sixth moment of the drop size distribution (∝D6) and is therefore highly sensitive to large drops, kdp scales approximately with the fourth moment (∝D4). As a result, kdp is less dominated by a few large drops and is more closely related to drop concentration and liquid water content.

Under tropical-cyclone conditions, particularly at the outer rain bands where very high concentrations of small-to-medium drops are often observed, so kdp can become large even when Z remains only moderate. This provides a physical explanation for why the derived R(kdp) relationship performs better for heavy rain (Bellecombe and Commerson) than the borrowed Z–R relation in this event. Furthermore, warm-rain processes below the freezing level, including coalescence and breakup, play an important role in shaping these DSD characteristics (Thurai et al., 2020; Yang et al., 2025). The present R(kdp) relation should therefore be viewed as event-specific, reflecting the microphysical conditions sampled during this tropical cyclone rather than a universally transferable X-band relation.

According to Table 3, “stratiform precipitation” has a better correlation with raingauge than “all types of precipitation” regardless of the distance between the rain gauges and the radar or estimator used. One hypothesis is that stratiform precipitation is associated with horizontally homogeneous rain (Sánchez-Diezma et al., 2000) and low turbulence, which explains the presence of the bright band. Thus, despite the vertical separation between the radar beam and the rain gauges on the ground, and without considering microphysical processes like evaporation, the precipitation measured within the radar beam at altitude has similar characteristics as the rain drop reaching the rain gauges. The drop size distribution at this altitude will be similar as on the ground.

As illustrated in Fig. 10, a bright band may sometimes appear in certain regions (Fig. 10a) or be disrupted above others (Fig. 10b), especially at higher altitudes. Ding et al. (2014) revealed that precipitation types are significantly influenced by altitude. Terrain and intense wind associated to the tropical cyclone cause air to flow over the mountains (Yu and Cheng, 2008), which leads to produce more liquid water cloud (Lee et al., 2018) enhancing precipitation in higher elevation. Hence, the intensification of precipitation at higher altitudes, together with high winds near the mountain summit, may explain why at Commerson, located at 2310 m above sea level, the correlation coefficient is lower, even during stratiform rain. Nevertheless, we should bear in mind that the limited number of stratiform precipitation samples limits the conclusions that can be drawn from the latter analysis.

To summarize, the comparison between the rain gauge measurements and the radar QPE can be classified as follows:

Group 1 (including Crete, Grand-Coude, and Grand-Galet), vertically close to the radar beam (less than 600 m) and horizontally close to the radar (less than 10 km). As these stations are located close to the coast and at a middle altitude, rainfall intensity is relatively lower, with a median value of around 10 mm h⁻¹. At these stations, all estimators (i.e., R(Z) and R(kdp) show higher correlation coefficients, but an overestimation for R(kdp) (greater than 0.5 NB). The impact of attenuation is less significant due to their location. Furthermore, the estimation of kdp is particularly difficult at low rain rates. As kdp is the range derivative of the differential phase, small phase shifts associated with weak precipitation result in a noisy kdp signal.

Overall, various processes contribute to the disparity between the radar QPE and the rain gauge measurements, mainly due to the different sampling approaches of the two observations. The radar QPE provides real coverage over large volumes, while rain gauges measure precipitation at specific points on the ground. However, this difference in sampling can introduce inconsistencies. Radar, for instance, samples a broader area but is affected by various factors like beam height and attenuation, while gauges give precise readings at ground level.

Furthermore, the drop size distribution may exhibit significant differences on the ground and at higher altitudes due to microphysical processes linked to the precipitation system dynamics and orography. Two factors may contribute to this disparity. First, under the influence of horizontal wind, the drops detected by the radar just above the rain gauges may not reach the ground where the rain gauges are situated and may instead fall far away, due to high wind. Second, several microphysical phenomena can alter the drop size distribution, including coalescence, evaporation, and bursting of drops before they hit the ground. This discrepancy between the drop size distribution at altitudes and at ground level can impact the accuracy of precipitation estimates. Drop size distribution is one source of uncertainty in the radar QPE (Rosenfeld and Ulbrich, 2003). The values of the a and b coefficients in the R(Z) relationship are based on different factors such as the type of precipitation (convective or stratiform) and the physical processes that influence the drop size distribution (Zeng et al., 2021).

Although rain gauge measurements are considered to be the “ground truth” for precipitation, they may also have associated errors (Dhiram and Wang, 2016), notably in high wind conditions.