Radar reflectivity from the nationwide HSR composite was converted to rainfall intensity using the operational Z–R relationship adopted by KMA: 1Z=148R1.59, as reported by Ro et al. (2022). Radar–gauge temporal matching followed the procedure described in Ryu et al. (2025). For each 10 min radar time step, gauge rainfall was accumulated over the corresponding 10 min period ending 8 min after the radar observation time and then converted to rainfall intensity (mmh-1). A minimum rainfall threshold of 0.1 mmh-1 was applied uniformly to both radar and gauge data across all temporal aggregations, and values below this threshold were treated as no-rain. This value corresponds to the finest resolvable rainfall rate achievable with ASOS gauges (0.1 mm) when accumulated over 60 min window. For 10 min accumulation, the same nominal threshold was retained for consistency; in this case the minimum non-zero rainfall rate that any gauge in the network can physically report is higher (0.6 mmh-1 for ASOS and 3.0 mmh-1 for AWS, owing to their respective tipping/weighing resolutions), so that the 0.1 mmh-1 threshold functions equivalently to a strictly non-zero criterion at this timescale.

Radar rainfall at each gauge location was extracted from the nearest grid cell. To reduce representativeness differences between point-scale gauge measurements and gridded radar data, radar rainfall was averaged over a 3 pixels × 3 pixels window (1.5 km × 1.5 km) centered on each station.

Bias correction factors were estimated only when both radar and gauge rainfall exceeded 0.5 mmh-1 and when at least 20 valid gauge–radar pairs were available. Individual ratios were calculated as 2qi(t)=Gi(t)Ri(t), where Gi(t) and Ri(t) denote gauge and radar rainfall at station i and time t, respectively. Ratios outside the 5th–95th percentile range were excluded to limit the influence of outliers. The raw bias correction factor was defined as 3C(t)=∑i=1NGi(t)∑i=1NRi(t), where N is the number of valid pairs. To reduce abrupt temporal variability, changes in C(t) relative to the previous time step were limited to ± 30 %. The final correction factor was obtained using an exponentially weighted moving average (EWMA; Hunter, 1986): 4CEWMA(t)=αC(t)+(1-α)CEWMA(t-1),α=0.5.

If fewer than 20 valid pairs were available, the correction factor from the previous time step was retained.

After bias correction, residuals between gauge observations and corrected radar rainfall were computed as 5ϵi(t)=Gi(t)-CEWMA(t)Ri(t).

Residual interpolation was performed only when at least five stations satisfied the rainfall threshold (≥ 0.5 mmh-1 for both radar and gauge observations). The residuals were interpolated at an arbitrary location z using a radial basis function (RBF) approach (Buhmann, 2003; Fasshauer, 2007; Ryu et al., 2025): 6ϵ^RBF(z,t)=∑i=1Nwi(t)ϕ(|z-zi|).

Here, an exponential RBF kernel was adopted, defined as ϕ(|⋅|)=exp(-|⋅|/s), with a shape parameter of s = 16 km (Ryu et al., 2024). When fewer than five stations satisfied the threshold, residual interpolation was omitted, and only the bias-corrected radar rainfall was retained. The final merged precipitation field was defined as 7P^(z,t)=CEWMAR(z,t)+ϵ^RBF(z,t).

Figure 3 presents scatter density plots comparing estimated rainfall with rain gauge observations for summer 2022 events. Figure 3a–d show 10 min accumulated rainfall (mm). Figure 3e–h show non-overlapping 60 min accumulated rainfall obtained by summing six consecutive 10 min accumulations from the 10 min time series; these windows are not necessarily aligned to the top of the clock hour. For reference (Fig. 3a and e), gauge-only rainfall fields were obtained by interpolating gauge observations using the RBF method. Radar-only estimates based on the operational Z–R relationship and mean field bias (MFB) adjustment are shown in Fig. 3b, c and f, g, respectively. The RRBF results (Fig. 3d and h) correspond to LOOCV estimates, ensuring independence between validation observations and interpolation inputs.

For rainfall intensities derived from 10 min accumulations (Fig. 3a–d), the Z–R estimates exhibit a negative bias (NBE = -35.15 %) and relatively large dispersion (COR = 0.7854; MAE = 0.62 mm). The MFB adjustment reduces the bias (NBE = -6.65 %) but still shows considerable scatter around the 1:1 line. The RRBF method demonstrates higher correlation (COR = 0.8318) and lower MAE (0.50 mm), with near-zero bias (NBE = 1.06 %). The discrete banding patterns visible in the scatter plots, particularly along the x-axis, arise from the finite resolution of tipping-bucket rain gauges. Rainfall is recorded in discrete increments (e.g., 0.5 mm), resulting in quantized 10 min accumulations that produce distinct linear patterns in the scatter distribution.

For the 60 min accumulated rainfall (Fig. 3e–h), all methods show improved agreement due to temporal aggregation. The RRBF method achieves the highest correlation (COR = 0.9386) and lowest MAE (0.93 mmh-1), compared to the Z–R (COR = 0.8762; MAE = 1.53 mmh-1) and MFB (COR = 0.8949; MAE = 1.41 mmh-1) estimates.

Across both temporal aggregation approaches, the RRBF-based merging approach shows reduced bias and improved agreement with rain gauge observations relative to radar-only estimates. These results indicate that the RRBF framework provides consistent performance across different temporal scales.

Figure 4 presents the spatial distribution of accumulated precipitation from June to August 2022 derived using different estimation methods. Figure 4a shows the gauge-based precipitation field obtained by applying radial basis function (RBF) interpolation to rain gauge observations, while Fig. 4b–d show the corresponding accumulations from the radar-only Z–R product, the mean field bias (MFB) – corrected field, and the RRBF-based merged field, respectively.

The gauge-based RBF interpolation (Fig. 4a) reproduces localized rainfall maxima associated with summer precipitation but exhibits spatial smoothing and pronounced gradients in regions with sparse station coverage. The dashed contours indicate areas where the 3-month accumulated precipitation exceeds 100 mm based on the gauge-only RBF field. This threshold is used as a practical criterion to identify regions with substantial seasonal rainfall and strong gauge influence and does not represent a physical boundary. Outside these regions, spatial uncertainty increases due to limited station density.

The radar-only Z–R product (Fig. 4b) captures the large-scale precipitation patterns over the Korean Peninsula but shows lower accumulated amounts in regions influenced by intense convective rainfall compared to the gauge-based field. The MFB-corrected field (Fig. 4c) reduces the overall differences in accumulated precipitation relative to the Z–R product; however, its spatially uniform adjustment results in residual spatial discrepancies.

The RRBF-based merged field (Fig. 4d) preserves the large-scale spatial structure of radar-derived precipitation while incorporating gauge-based adjustments. The resulting accumulation patterns show closer agreement with the gauge-based field in regions with dense gauge coverage. When precipitation is accumulated over the full 3-month period, azimuthal spatial features associated with radar beam geometry and scanning characteristics remain evident (Fig. 4b and c). These artifacts originate from the HSR compositing process and therefore should be addressed within the radar processing stage. Although residual interpolation partially reduces these features, they are not fully eliminated.

Annual accumulated precipitation was calculated for each year from 2016 to 2024 using the RRBF-based merged dataset. Annual totals were spatially averaged within the dashed region shown in Fig. 4, which represents an area with sufficiently dense gauge observations to ensure a consistent influence on the merged field and defines the analysis domain for interannual comparison.

Figure 5 presents the time series of annual mean precipitation over this domain. Pronounced interannual variability is evident throughout the 9-year period. Among the analyzed years, 2017 exhibits the lowest annual precipitation, whereas 2020 records the highest total, reflecting year-to-year differences in precipitation conditions. Despite these variations, the dataset exhibits temporally consistent behavior without abrupt discontinuities. The time series indicates that interannual variability is robustly preserved across the full record from 2016 to 2024.

Figure 6 shows the spatial distribution of annual accumulated precipitation for the driest year (2017), the wettest year (2020), and the 9-year mean over the period 2016–2024. The dashed boundary denotes the analysis domain used for the statistical evaluation presented in Fig. 5. 2020 exhibits substantially higher annual precipitation over widespread areas, together with pronounced spatial variability, particularly over the southern and eastern parts of the peninsula. This spatial structure is likely associated with a combination of the exceptionally prolonged summer rainy season, orographic and coastal effects, and heavy rainfall from successive typhoons in late August and early September. In particular, Typhoons Maysak and Haishen produced substantial rainfall over southern and eastern Korea, including the mountainous regions of Gangwon Province (KMA National Typhoon Center, 2021), which may have contributed to the enhanced spatial structure observed in the 2020 annual accumulation field. The 9-year mean field represents the average spatial distribution of precipitation during the study period and shows relatively persistent localized maxima associated with orographic and coastal influences.

Compared to event-scale precipitation fields derived from short-term summer events, annual and multi-year accumulations exhibit substantially smoother spatial patterns. This smoothing reduces the apparent impact of short-term variability and radar observation artifacts. However, weak spatial signatures related to radar beam geometry are still detectable in some areas, indicating that residual structural artifacts of radar observations persist even in long-term accumulations. It should be noted that Fig. 6 presents only the sub-domain used for statistical analysis. The full dataset is available over the complete radar composite domain (2305 × 2881 grid points) shown in Fig. 1a. Annual accumulation maps for all individual years over the full domain are provided in Appendix A.

The long-term statistical performance of the merged precipitation dataset was evaluated against KMA rain gauge observations over the period 2016–2024 at an hourly time scale, using non-overlapping 60 min accumulated rainfall derived by summing six consecutive 10 min observations, with windows not necessarily aligned to the top of the clock hour. Radar-only Z–R precipitation and RRBF-based merged precipitation were compared across multiple rainfall intensity thresholds. Figure 7 presents scatter density plots for cases with gauge-observed rainfall ≥ 0.1 mmh-1. Radar-only values were obtained from the nearest radar grid cell at each gauge location, whereas RRBF values correspond to LOOCV estimates, ensuring independence between validation observations and interpolation inputs.

Consistent with the event-based analysis, the Z–R estimates exhibit a systematic negative bias across the full range of observed intensities, with increasing dispersion at higher rainfall rates. Moreover, the long-term evaluation demonstrates that these error characteristics persist across the entire analysis period. In contrast, the RRBF estimates show a sustained reduction in bias and improved agreement with gauge observations over all intensity ranges. For rainfall ≥ 0.1 mmh-1, the normalized mean absolute error (NMAE) decreases from 53.38 % (Z–R) to 28.85 % (RRBF), while the correlation coefficient increases from 0.7703 to 0.9251 (Table 2). The bias is also markedly reduced, from -13.13 % to 0.58 %.

Table 2 summarizes performance metrics for rainfall thresholds of 0.1, 0.5, 1.0, and 5.0 mmh-1. Across all thresholds, the RRBF-based estimates consistently demonstrate improved performance relative to radar-only Z–R estimates, indicating that the benefits observed in event-scale analysis are robust across long-term conditions. As the threshold increases, the negative bias of the Z–R estimates becomes progressively larger (NBE from -13.13 % to -30.73 %) and their correlation with gauge observations decreases (COR from 0.7703 to 0.6852), reflecting the tendency of radar-only estimates to underestimate more heavily during higher-intensity rainfall. In contrast, the RRBF estimates maintain a bias close to zero across all thresholds (NBE within ± 3.3 %) and show only a modest decline in correlation (COR from 0.9251 to 0.8699), indicating that the gauge-based bias correction remains effective even for higher rainfall intensities.

Seasonal variations in the performance of the RRBF-based precipitation estimates are presented in Fig. 8 for winter (December–February, DJF), spring (March–May, MAM), summer (June–August, JJA), and autumn (September–November, SON). The correlation coefficient ranges from approximately 0.86 in DJF to values exceeding 0.92 in JJA and SON. A relatively larger dispersion is evident during winter, whereas warm-season estimates show tighter clustering around the 1:1 reference line.

To assess the spatial characteristics of estimation performance, station-based COR and NBE were computed for each rain gauge over the period 2016–2024 using non-overlapping 60 min accumulated rainfall derived from 10 min data. Only hours with gauge-observed rainfall ≥ 0.5 mmh-1 were included in the analysis. Figure 9 presents the spatial distribution of these metrics for radar-only Z–R estimates and RRBF-based precipitation. For the RRBF product, station-level statistics were derived from LOOCV estimates to ensure independence from the gauge observations used in the merging process.

For the radar-only Z–R estimates (Fig. 9a), correlation coefficients exhibit moderate to high values across South Korea, with pronounced spatial variability. Lower correlations are evident in some coastal regions and areas of complex terrain. In contrast, the RRBF-based estimates (Fig. 9b) show generally higher correlations at many stations and reduced spatial variability compared to the Z–R product.

The spatial distribution of normalized bias error further highlights differences between the two approaches. Radar-only Z–R estimates (Fig. 9c) are characterized by widespread negative bias across much of the domain, with spatially coherent underestimation in several regions, including coastal and mountainous areas. In the RRBF results (Fig. 9d), bias magnitudes are substantially reduced at many stations, and NBE values are more frequently centered near zero. Localized differences are apparent in regions such as the Seoul metropolitan area and Jeju Island, where bias patterns differ between the Z–R and RRBF estimates. On Jeju Island, this likely reflects beam blockage near Hallasan (1947 m, the highest mountain in South Korea), which requires the HSR algorithm to use higher-elevation scans and can lead to underestimation in the Z–R estimates; the RRBF estimates are less affected, as gauge observations are directly incorporated into the bias correction. Although some stations still exhibit relatively large positive or negative bias in the RRBF results, these are spatially isolated rather than regionally coherent. Overall, the station-based spatial analysis indicates that the RRBF-based precipitation estimates exhibit reduced bias magnitude and more spatially uniform correlation patterns compared to the radar-only Z–R estimates over the 2016–2024 period.

To investigate the temporal characteristics of the radar–gauge adjustment, the distribution of CEWMA was analyzed by month and season for the period 2016–2024 (Fig. 10). The correction factor CEWMA represents the multiplicative bias adjustment factor applied to radar-derived precipitation; values greater than 1 indicate that radar estimates are, on average, lower than gauge observations. Figure 10a presents monthly boxplots of CEWMA aggregated over the 9-year period. Median values exceed 1 in all months. Slightly higher medians are observed from late spring to summer (May–August), whereas winter months exhibit comparatively lower values. The interquartile range varies seasonally, with broader distributions during the warm season and narrower distributions in winter. Monthly sample counts (Fig. 10b) show a pronounced seasonal cycle, with substantially higher counts in July and August and lower counts during winter months. Months with larger sample sizes also tend to exhibit wider distributions of CEWMA.

Seasonal boxplots (Fig. 10c) indicate that median values are lowest in DJF and higher in the other seasons. Variability also differs by season, with broader interquartile ranges in MAM and JJA and narrower distributions in DJF. These seasonal patterns reflect differences in both the magnitude and variability of the radar–gauge adjustment factor across seasons during 2016–2024.