A total of 2155 sub-daily rain gauge stations (with observations aggregated to hourly resolution; Fig. 1a) and 3659 independent daily rain gauge stations (Fig. 1b) (Bureau of Meteorology, 2025) were used in this study. The hourly gauges, sourced from both automatic weather stations and flood warning stations, were recorded at sub-hourly intervals and served as the primary input for the blending process. The daily gauges, obtained primarily from human-recorded observations, provided an independent evaluation dataset for the final blended product. To prevent redundancy, any gauge present in both datasets was retained only in the hourly dataset. The network density varies significantly for hourly gauges (Fig. 1a), with some areas – particularly along the populated and flood-prone Great Dividing Range in eastern Australia – having dense coverage, while others have little to no data. In contrast, daily gauges (Fig. 1b) are more evenly distributed, though substantial data voids remain, particularly in the arid and sparsely populated western interior.

Both the hourly and daily datasets were subjected to rigorous quality control procedures, including checks for anomalously high values based on historical rainfall distributions and gridded Intensity-Frequency-Duration (IFD) statistics. Additional procedures included spatial intercomparisons to detect anomalously high values or prolonged periods of zero values indicative of instrument failure or gauge blockage, intercomparisons between sub-daily and daily observations where both were available, and checks for long sequences of identical non-zero values. Specifically, potential rainfall spikes were identified using thresholds of two and four times the historical 99.9th percentile. Extreme rainfall observations were also checked against local IFD statistics, including the 1 % Annual Exceedance Probability (AEP) and 1-in-1000-year rainfall thresholds. Spatial consistency checks further compared unusually high observations with neighbouring gauges within 50 km. These complementary checks used historical, climatological, and spatial information to identify potentially erroneous high rainfall values while retaining plausible extreme rainfall observations.

Although the quality control procedures remove many identifiable erroneous observations, residual measurement and sampling uncertainties may remain in the gauge data used in this study. The hourly observations are aggregated from sub-hourly measurements, primarily from tipping-bucket gauges, and may therefore retain uncertainties associated with the original sub-hourly measurements and their aggregation into hourly totals. In addition, some isolated gauges have few nearby reference stations available for spatial consistency checks, while random or less readily identifiable errors may not be detected by the quality control procedures. It is also worth noting that rainfall measured by an individual gauge may differ from the corresponding 2 km grid-cell average because of sub-grid precipitation variability, introducing spatial representativeness uncertainty when point observations are used to represent gridded precipitation.

An additional independent hourly dataset (approximately 2000 stations) was obtained from third-party providers, including local councils, water utilities, and other water management organisations through ongoing data-sharing arrangements. As this dataset continued to expand throughout the project, these observations became available only after completion of the bias correction and blending analyses and were therefore used for supplementary independent validation. These observations were subjected to the same quality control procedures as the primary hourly gauge dataset. The spatial distribution of these hourly gauge stations is shown in Fig. S15 in the Supplement.

Radar rainfall estimates (Bureau of Meteorology, 2022) were obtained from the Bureau's operational Rainfields system, which provides real-time data at a spatial resolution of 1 km and a temporal resolution of 5 min. Weather radar observations have been available in Australia since the late 1990s, with the network progressively expanding from coverage concentrated around major population centres to its current broader coverage. The radar network during 2022–2023 used in this study covered approximately 72 % of the Australian land area. Further information on Australian weather radar data availability and archiving is provided by the Australian Unified Radar Archive (https://opus.nci.org.au/spaces/NDP/pages/399803502/ Australian+Unified+Radar+Archive, last access: 9 October 2026).

The Rainfields system offers both raw and calibrated radar rainfall rates. Raw rainfall rates are derived using reflectivity–rainfall rate (Z–R) relationships, which are established for each radar based on long-term historical data. Calibrated rainfall rates are then generated by applying dynamic bias correction to the raw estimates using nearby gauge observations within a 150 km radius and a 15 min time window, employing a Kalman filtering approach (Chumchean et al., 2006). By incorporating real-time gauge data, calibrated radar rainfall rates provide an additional refinement to the Z–R-based estimates, allowing adjustments to reflect current conditions that may deviate from those during the historical period used to derive the Z–R relationships.

In this study, we used hourly radar accumulations derived from 5 min calibrated radar rainfall rates as a blending input at the target hourly resolution. However, we recalibrated the radar data using gauges within a 300 km radius and a 1 h window to increase the availability of co-located radar-gauge pairs for estimating local radar errors. The larger spatial radius allows more co-located radar-gauge pairs to be included, particularly in gauge-sparse regions, while the longer temporal window increases gauge availability by accommodating their reporting latency. These two modifications therefore address the spatial and temporal availability of gauge information, respectively. We refer to the operational calibrated product as R0 and the recalibrated version as R1. In addition, to match the spatial resolution of the satellite data, the original 1 km radar grids were aggregated to 2 km. Figure 1c shows an example of the recalibrated hourly radar rainfall accumulation (R1) across Australia at 08:00 UTC on 1 March 2022.

The R1 radar estimates used for blending benefit from both the operational Rainfields calibration and the additional hourly gauge-based recalibration applied in this study. Nevertheless, residual errors and artefacts present in the underlying radar observations may remain after these corrections. For example, local effects associated with beam blockage, anomalous echoes, and other retrieval or sampling issues may not always be fully identified or removed during operational quality control and processing.

In addition, the gauge-based bias correction estimates local radar biases from available gauge observations and interpolates these estimates to construct spatially continuous bias fields. However, this correction does not necessarily remove biases across all precipitation intensities, and residual biases may remain within specific rainfall intensity ranges. Its effectiveness also depends on the availability and representativeness of nearby gauges and on how well the interpolated bias field represents the spatial variability of the actual radar bias. The correction may therefore be less effective in areas far from available gauges or with sparse gauge coverage. Details of the bias-correction procedure are provided in Sect. 3.3.

The Himawari-based CRRPH v2.1 product (Bureau of Meteorology, 2024) was selected as the background field for this study because it provides continental coverage at a spatial resolution of 2 km and a temporal resolution of 10 min, helping to compensate for gaps in the ground-based observation network. The product is derived from observations collected by the Japanese Himawari-8/9 geostationary satellites, which carry the Advanced Himawari Imager (AHI) and provide multi-spectral observations of cloud and atmospheric properties over the Australian region. CRRPH exploits the high-frequency, multi-channel infrared observations from AHI to infer convective rainfall rates based on cloud physical properties, including cloud optical depth and effective radius.

The CRRPH product is available from 2015 onwards and is updated operationally with a latency of approximately 15 min, making it suitable for near-real-time applications. In this study, the native 2 km spatial resolution of CRRPH was adopted as the target grid for blending, thereby defining a common spatial grid across all input datasets. This choice avoids additional spatial resampling of the satellite field and reduces potential interpolation-induced errors. Temporally, the 10 min CRRPH rainfall rates were aggregated to hourly accumulations prior to blending to ensure consistency with other data sources and downstream hydrological applications. Figure 1d illustrates an example of the CRRPH hourly rainfall accumulation across Australia at 08:00 UTC on 1 March 2022, highlighting its ability to represent large-scale precipitation patterns with fine spatial detail. As with other satellite-based precipitation products, CRRPH rainfall estimates are subject to systematic biases.

As an infrared satellite precipitation product, CRRPH infers surface rainfall indirectly from cloud properties observed by the Himawari AHI. Retrieval errors may therefore occur when the observed cloud characteristics do not adequately represent the occurrence or intensity of surface precipitation (Karagiannidis et al., 2023; So and Shin, 2018). In addition, the calibrated lookup tables used to convert retrieved cloud properties into rainfall rates represent empirical relationships and may not fully capture variations in the cloud–rainfall relationship under different precipitation conditions.

To reduce systematic discrepancies with gauge observations, a spatially varying local bias correction was applied, as described in Sect. 3.3. S0 denotes the original CRRPH product without bias correction, while S1 denotes the bias-corrected product used as the background field for blending. The correction is designed to reduce the overall systematic bias of CRRPH relative to gauge observations towards zero, but does not necessarily remove biases across all precipitation intensities. Residual biases may therefore remain within specific rainfall intensity ranges. Moreover, the correction cannot fully address errors in rainfall occurrence or spatial structure inherent in the satellite retrieval. As the estimated bias field is derived from available gauges and spatially interpolated, its effectiveness depends on the availability and representativeness of nearby gauges and may be reduced in areas far from available gauges or with sparse gauge coverage.

The multi-source blending workflow (Fig. 2) integrates satellite, radar, and gauge data through a multi-step process to produce a high-resolution blended rainfall product. After temporal and spatial aggregation, quality control, and bias correction, satellite data serve as the background field, radar data as the first-layer observations, and gauge data as the second-layer observations. These inputs are then combined using the multi-source statistical interpolation framework to generate the final blended rainfall (BRAIN) product. The key processing steps are described in the following subsections.

A range of approaches have been developed for producing blended gridded datasets (e.g., Yin et al., 2021; Gavahi et al., 2023; Khedhaouiria et al., 2022; Chappell et al., 2013; Shen et al., 2014; Yu et al., 2020; Zhang et al., 2025). Statistical interpolation, also commonly referred to as optimal interpolation (OI), was originally developed within the framework of objective meteorological analysis (Gandin, 1965) and has been widely used as an interpolation method by many meteorological organisations (e.g., Mitchell et al., 1990; Huang et al., 1997; De Mey, 1994; Lorenc et al., 1991) for blending or assimilating observations with weather models, particularly before the development of more advanced variational methods (e.g., Gauthier et al., 2007; Rawlins et al., 2007; Rabier et al., 2000; Rabier, 2005). More recently, OI and related statistical interpolation approaches have been widely applied to precipitation interpolation and blending (e.g., Bergman, 1978; Chua et al., 2023; Mahfouf et al., 2007; Xia and Wang, 2025; Xie and Xiong, 2011; Yu et al., 2020).

Statistical interpolation enables the integration of multi-source precipitation data by updating a background estimate – in this case, the satellite-derived first guess – based on observations (gauge and radar data) to generate an analysis, with adjustments weighted according to the estimated error characteristics of each data source. The formulation adopted in this study follows the established OI framework (Gandin, 1965; Xie and Xiong, 2011; Yu et al., 2020; Mahfouf et al., 2007; Zhang et al., 2026), as described by Eqs. (1)–(5) below. A detailed derivation of the formulation is provided in our recent study (Zhang et al., 2026). The method assumes Gaussian error distributions, which may not strictly hold for precipitation but are commonly used as an approximation to avoid the additional complexity associated with data transformation, while bias correction is applied to both satellite and radar data to help satisfy the assumption of unbiased errors. Statistical interpolation operates as an iterative, grid-based analysis, adjusting each target grid cell using observations within a predefined search radius (e.g., 200 km in this study).

For a given target grid cell k, the analysis value is computed as: 1Ak=Bk+∑i=1nwi⋅Oi-Bi where Ak is the analysis value, Bk is the background value, Oi is the observation value at a nearby location i, Bi is the corresponding background value, and n is the total number of nearby observations. The term Oi-Bi represents the observation increment, and wi are the weights assigned to each observation.

The analysis error at the target grid cell k, denoted by Ek, is then determined as the difference between the theoretical “true value” Tk and the analysis value Ak: 2Ek2=Tk-Ak2=Tk-Bk-∑i=1nwi⋅Oi-Bi2

Here, Tk denotes the unknown theoretical true value at the target grid cell k, which cannot be directly observed in practice and is introduced for error definition and derivation purposes.

By defining the background error fi=Ti-Bi and observation error ϵi=Oi-Ti, the analysis error equation can be rewritten as: 3Ek2=fk-∑i=1nwi⋅fi+ϵi2

Minimising this error allows us to optimally assign weights to nearby observations, yielding the most statistically accurate estimate for each target grid cell. To solve this optimisation problem, we take the partial derivative of Ek2 with respect to each wi and set it to zero, which leads to the following equation: 4∑j=1nfi+ϵifj+ϵjwi=fkfi+ϵi,i=1,2,…,n

By expanding and expressing Eq. (4) in standardised form: 5∑j=1nμij+τijσj+τjiσi+ρijσiσjwi′=μki+τkiσi,i=1,2,…,n where:

μij=fifj/fi2fj212,μij∈Rn×n is the background (satellite) error correlation between the ith and jth observation locations. Similarly, μki∈R1×n is the background error correlation between the target grid cell k and the ith observation location.

This system of linear equations is solved to determine the optimal weights wi, which are used to obtain the optimal precipitation estimate at each target grid cell by combining information from the background field and available observations (e.g., radar and gauge data). The treatment of different observation sources is described below, while the corresponding source-specific error characteristics are introduced in Sect. 3.4.

These equations require knowledge of the background error correlations (μij,μki), background-to-observation error correlations (τij,τki), observation error correlations (ρij), the ratios of observation to background error variances (σi), and the spatial variation in background errors (fi2/fk2).

The background error correlation is typically derived from an analytical function (e.g., Bergman, 1978; Xie and Xiong, 2011; Yu et al., 2020), while background-to-observation error correlations are assumed to be zero, as errors from different sensor systems are considered independent. Similarly, the observation-to-background error variance ratio is estimated separately for satellite, radar, and gauge data using analytical functions (e.g., Bergman, 1978; Xie and Xiong, 2011; Yu et al., 2020), with the corresponding ratios computed between different data sources. The most challenging part of statistical interpolation is determining the observation error correlations (ρij), as this requires accounting for the number of observations in different cases and their respective sensor systems, particularly as the number of data sources increases.

In this study, both gauge and radar data are incorporated as observations. Radar–gauge observation error cross-correlations are assumed to be zero. Explicit estimation of these cross-correlations requires independent characterisation of both radar and gauge errors. In particular, robust estimation of gauge representativeness errors generally requires a sufficiently dense gauge network to provide an independent estimate of areal rainfall, which is difficult to achieve consistently across Australia. Seo and Krajewski (2011), using high-density gauge networks, showed that radar–gauge error correlations can vary across individual samples and scales, but their mean correlations remained close to zero across the spatial and temporal scales examined. We therefore adopt zero radar–gauge error cross-correlation as a practical simplifying assumption for the national-scale implementation. Furthermore, errors from gauges at different locations are also assumed to be independent. Accordingly, radar–gauge and gauge–gauge observation error correlations are set to zero. However, a full representation of radar-to-radar error correlations would require retaining potentially hundreds of radar grid cells within the influence radius (e.g., 200 km in this study) for each target grid cell, substantially increasing the size of the observation-error covariance matrix (i.e., in Eq. 5), computational cost, and risk of matrix rank deficiency.

To address this issue, an error-informed localisation strategy is adopted within the statistical interpolation framework. Specifically, a highly efficient implementation is introduced in which only the nearest radar grid cell within a 200 km search radius, identified as the grid cell with the minimum Euclidean distance to the target grid cell, is retained as a supplementary observation. If no valid radar grid cell is available within this radius, no radar observation is included for that target grid cell. The 200 km radius defines the maximum search range, while the effective influence of the selected radar observation is further controlled by the distance-dependent error correlation function. In cases where multiple grid cells have the same minimum distance, the grid cell with the lowest error variance is retained. This nearest-point approximation reflects a deliberate selection strategy that prioritises the most locally relevant radar information while avoiding dilution by redundant contributions. Consequently, each local analysis contains at most one radar observation, and no radar–radar error covariance terms arise in the resulting observation-error covariance matrix. The suitability of this nearest-point approximation has been evaluated in our previous study (Zhang et al., 2026). As a result, this approach enables scalable, grid-cell-wise blending suitable for continental-scale precipitation analysis at kilometre-scale spatial and hourly temporal resolutions under practical computational constraints.

The design offers several advantages. First, it substantially reduces computational complexity by limiting the number of radar observations included in the statistical interpolation linear system, which is particularly important for continental-scale applications in Australia involving more than five million grid cells. Second, because each local analysis contains at most one radar observation, it avoids the need to explicitly represent radar-to-radar error correlations, thereby simplifying the modelling chain and reducing the number of processing steps. Third, by constraining the spatial influence of radar observations, the approach limits error extrapolation, an important consideration given the directional and range-dependent nature of radar errors. Finally, despite its simplicity, the strategy allows radar observations to contribute effectively both within and outside radar coverage, ensuring consistency and spatial continuity across data sources in the blended rainfall fields.

Following the above strategy and design, we solve the simplified system of linear equations given by Eq. (5): 6∑j=1nμij+ρijσiσjwi′=μki,i=1,2,…,n where n represents the number of available observations within the search radius, which is set to 200 km in the trial implementation. A sensitivity test using an alternative search radius of 100 km showed only minor differences compared with the 200 km configuration (Fig. S23). We therefore retained the 200 km radius as a conservative choice to avoid excluding potentially useful observations, although this incurs a slightly higher computational cost than using a 100 km radius.

The number of observations varies depending on data availability and includes five possible cases: (1) a single radar grid cell, (2) a single gauge, (3) multiple gauges, (4) one or more gauges combined with one radar grid cell, and (5) no available gauge or radar observations. For cases involving multiple gauges, up to the 20 nearest gauges within the 200 km search radius are used. When a radar observation is also present, the total number of observations does not exceed 21. This system size remains computationally manageable.

In Eq. (5), the background-to-observation error correlation terms, including τij, τji and τki, are assumed to be zero. This assumption reflects the negligible correlations between background and observation errors and leads directly to the simplified formulation in Eq. (6). And then gauge-to-gauge error correlations are assumed to be zero between different locations and equal to one at the same location. Under the nearest-point approximation, only a single radar observation is included. Gauge–radar error correlations are also assumed to be negligible. Under these assumptions, the observation error correlation matrix ρ reduces to the identity matrix (ρ=I). The radar observation contributes only through its self-correlation, which is represented by the final diagonal element and set to one.

With these simplifications, the linear system remains computationally efficient in all cases. This efficiency is essential for continental-scale applications and is particularly important for real-time monitoring and nowcasting. It also supports the efficient production and iterative refinement of long-term historical products at high spatial and temporal resolution. Once the weights are determined, the analysis value at the target grid cell is computed using Eq. (1), yielding the optimal precipitation estimate.

Using the scaled weights wi′ from Eq. (6), the uncertainty information in the blended field can be expressed either as the estimated error variance of the final analysis (Ek2‾) or as its normalised form (Ek2‾fk2‾), as below: 7Ek2‾fk2‾=1-∑i=1nwi′⋅μki+τkiσi

This formulation shows how the analysis error is reduced according to the correlation between each observation and the background error at the target location, together with the associated observation error. Observations with stronger correlations and smaller errors contribute more to reducing the analysis uncertainty.

Bias correction for satellite and radar data followed a Kalman filtering approach similar to that of Chumchean et al. (2006), but was adapted from the original mean-field framework to estimate spatially varying local bias fields at the target hourly timescale. Bias estimation was based on co-located satellite/radar–gauge pairs, obtained by extracting satellite or radar estimates at gauge locations and pairing them with the corresponding gauge observations. All available gauges were included in the satellite bias correction, whereas only gauges within radar coverage were included in the radar bias correction because radar estimates are unavailable outside the radar coverage area. Bias at each gauge location was estimated using a Kalman filter with an autoregressive model of order one (AR(1)) to capture temporal dependence, and the resulting point-based bias estimates were interpolated using ordinary kriging to generate a continuous spatially varying bias field. The corrected precipitation estimates were then obtained by applying the bias field multiplicatively to the raw precipitation estimates.

The calibrated radar estimates (R1) used in this study differ from the operational Rainfields product (R0) in both temporal and spatial configurations. R0 applies bias correction using gauges within a 150 km radius and a 15 min window. The spatial radius limits the number of nearby co-located radar–gauge pairs available for local bias estimation, while the temporal window is constrained by gauge reporting latency and the short operational update interval. In contrast, R1 uses gauges within a 300 km radius and a 1 h window, increasing the number of radar–gauge pairs available for estimating the local radar bias. No predefined limit is imposed on the number of pairs within this radius. All available pairs are considered, with their point-scale bias estimates subsequently interpolated using ordinary kriging to construct a spatially continuous bias field. The larger spatial radius allows more spatially distributed gauge observations to be included, while the longer temporal window accommodates additional observations that become available after accounting for gauge reporting latency. This approach also uses the same set of available gauge observations for satellite and radar bias correction, subject to the availability of radar observations at each gauge location. However, this configuration is tailored to the Australian radar system and can be adjusted for other radar systems according to their operational configurations and production objectives.

Error characterisation is essential for determining observation weights. It involves estimating the error variances and correlations of each data source for both gauged and ungauged locations. Ideally, this error analysis should be conducted at each target grid cell to obtain accurate error estimates.

For gauged locations, this task is relatively straightforward, as gauge observations can be used as a reference for estimating the error characteristics of the background and observation inputs. Although gridded satellite and radar products represent areal averages while gauges provide point measurements, the gauge network is generally too sparse to derive reliable areal-average estimates at the 2 km grid scale. Therefore, point gauge observations were used directly as the reference. At the 2 km spatial resolution adopted in this study, point-to-area representativeness differences were assumed to be sufficiently small and were not explicitly considered. Consequently, the estimated error characteristics should be interpreted as relative measures of uncertainty among different data sources rather than absolute estimates of their true errors.

For ungauged grid cells (99.9 % of the national 2 km land grid cells), however, error characterisation becomes considerably more challenging. A common approach is to incorporate spatial and temporal windows to gather sufficient samples. For example, for a target grid cell, one might analyse data from preceding month to capture recent performance and include all available hourly gauges within a 10° × 10° longitude–latitude window to account for spatial variability. However, implementing such a strategy is impractical for the kilometre-scale national framework considered in this study. A 2 km resolution product over Australia comprises more than 5 million grid cells (including ocean areas of interest, see Fig. 1d). Furthermore, the sparse and highly uneven distribution of hourly gauges means that fixed spatial and temporal windows are generally unsuitable. Instead, the search windows would need to be adaptively adjusted for each grid cell and time step according to local gauge availability to ensure sufficient samples, resulting in substantial computational costs, implementation complexity, and extensive parameter tuning.

To simplify the process, regional error characteristics were estimated by dividing the analysis domain into three subregions. Satellite errors showed a clear latitudinal dependence, with larger errors generally occurring in tropical northern Australia. In contrast, radar error characteristics are more radar-specific, with errors differing depending on local topography around the radar range, differences in the radar type and hardware configuration, and site-specific Z–R parameters. In addition, the bias correction of radar data helped reduce range-dependent error to some extent. Nevertheless, for simplicity and consistency in this first instance, the same regional divisions were applied to both satellite and radar error characterisation. Specifically, the Australian domain was divided into tropical, subtropical, and temperate subregions. Within each subregion, analytical functions describing error variances and error correlations were fitted using data from gauged locations, and the resulting error characteristics were subsequently applied to ungauged locations within the same subregion.

For error variance estimation, we calculated the squared differences between satellite (or radar) estimates and gauge observations. The error variance increases with precipitation intensity, making this relationship suitable for fitting error variance curves. To capture this, precipitation intensities were divided into bins, and within each bin, the mean squared error between satellite (or radar) estimates and gauge observations was calculated as an estimate of the error variance. This analysis showed that error variance is a function of precipitation intensity. Various analytical models were tested to represent the scatter, and the optimised parameters for the best-fitting curves were obtained.

For error correlation estimation, pairs of satellite (or radar) estimates and gauge observations were collected, and the error correlation was calculated for each pair along with their corresponding distance. Distances were similarly divided into bins, and within each bin, the mean error correlation was calculated. This revealed that error correlation is a function of distance. As with error variances, different analytical models were applied to the scatter, and the optimised parameters for the best-fitting curves were determined.

The evaluation was designed primarily to assess the added value of integrating satellite, radar, and gauge observations within the BRAIN framework. The three-source satellite–radar–gauge analysis was therefore evaluated against individual-source fields and reduced-source blending configurations (i.e., satellite–gauge blending) to determine how the incorporation of additional observation sources affects analysis performance.

BRAIN was also compared with rainfall products and methods currently used operationally by the Bureau to provide additional operational context. Gauge-based IDW interpolation was included as a simple gauge-only reference because it is currently used in the Bureau's operational flood forecasting system to estimate catchment- and/or sub-catchment-scale rainfall from sub-daily gauge observations for hydrological modelling (Malone, 1999; Malone and Carroll, 2022), rather than to generate a national sub-daily gridded rainfall product. AGCD was included as an existing national operational daily gridded rainfall product (Jones et al., 2009).

Figure 3 demonstrates the spatial patterns and statistical improvements in mean bias for satellite and radar precipitation estimates after bias correction, evaluated against hourly gauge observations across Australia over 2022–2023 period.

Before correction, satellite data exhibit a clear latitude-dependent bias pattern, with notable overestimation in tropical regions, which decreases progressively towards subtropical and temperate regions (Fig. 3a; see also Fig. S1a in the Supplement). The corresponding histogram (Fig. 3e) reveals a highly positive-skewed distribution, indicating substantial overestimation across most hourly gauges. After correction, biases (Fig. 3b) are significantly reduced where initial errors were large, and the bias distribution (Figs. 3f and S1c) becomes narrower and more symmetric.

For radar data, the operational Rainfields product shows no clear latitude-dependent bias but exhibits localised errors, particularly along the east coast (R0, Fig. 3c; see also Fig. S1b). The histogram (Fig. 3g) indicates a general tendency toward overestimation. After applying the bias correction used in this study (R1, Fig. 3d), the spatial distribution of biases becomes more consistent, and large biases are reduced. The error distributions (Figs. 3h and S1d) become more symmetric and centred around zero.

These results highlight the importance of bias correction as a critical pre-processing step to reduce systematic errors and improve the quality of inputs for blending.

Figure 4 presents a subregion-dependent analysis of error variance and error correlation for satellite and radar products. Figure 4a shows that error variance increases approximately quadratically with precipitation intensity for both products. Satellite data have higher error variance than radar data across all intensities, especially in tropical regions, where the fitted curve is steepest. Radar consistently shows lower error variance, reflecting its generally higher accuracy and supporting the assignment of greater weights to radar observations in blending. The constant term of the quadratic fit was fixed to ensure an approximate 2:1 error variance ratio between satellite and radar. To account for gauge errors, the error variance of each gauge was defined as the precipitation intensity plus one. This parameterisation was based on empirical estimates from Xie and Xiong (2011), given the limited availability of sub-daily gauge data in Australia.

Figure 4b shows that satellite error correlation declines exponentially with distance, with a similar pattern observed across all subregions. Tropical areas exhibit the highest short-range correlations, followed by subtropical and temperate regions. Only satellite error correlations are shown, as radar–radar and radar–gauge correlations were not considered in the blending framework. These results highlight region-specific error characteristics. The quadratic relationship with intensity underscores the need for intensity-dependent error variance estimation, while the exponential decay in correlation reflects the spatially localised nature of precipitation errors.

Figure 9 shows the spatial performance of the blended product (BR-SRG) in terms of correlation and RMSE metrics evaluated against hourly gauge observations using the 20-fold cross-validation. High correlations were observed across most regions, particularly where gauge density is higher (Fig. 9a–c). RMSE was generally lower in coastal and well-observed areas, with higher values in regions with sparse gauges or greater rainfall variability (Fig. 9d–f). Some outliers may be attributed to imperfect gauge quality control or residual errors in satellite and radar inputs (e.g., Fig. S6; see also Figs. S9 and S18). Performance estimates may also be affected by limited gauge records, such as those from gauges operating during wet seasons.

Additional spatial performance maps based on independent daily-gauge (Fig. S11) and hourly-gauge (Fig. S22) evaluations are presented in the Supplement. Monthly variations in performance at both hourly and daily scales are also presented in Fig. S12 in the Supplement. Overall, BR-SRG demonstrated good performance across Australia, with room for improvement in sparsely gauged regions.

Figure 10 demonstrates the spatial characteristics of the hourly blended product (BR-SRG) for two selected extreme precipitation events, alongside the AGCD daily product and hourly gauge-based IDW interpolation: a 24 h accumulation during Cyclone Ellie from 22:00 UTC on 22 December to 22:00 UTC on 23 December 2022, and a 24 h accumulation during Cyclone Jasper from 22:00 UTC on 12 December to 22:00 UTC on 13 December 2023. The corresponding satellite and radar estimates are shown in Fig. S13. Hourly and daily gauge observations are shown in Fig. S14. The highest daily rainfall accumulations recorded by sub-daily and daily gauges during Cyclone Ellie and Cyclone Jasper are summarised in Tables S1 and S2, respectively.

Both satellite and radar captured the major rainfall systems associated with the two events, with satellite providing spatially continuous information across Australia and radar providing additional high-resolution information within its coverage. By integrating these spatially distributed estimates with gauge observations, BR-SRG captured the broad-scale rainfall patterns while retaining finer-scale spatial structures and variations in precipitation intensity that were less evident in AGCD and IDW.

The representation of the most intense rainfall, however, depended on how well the different observations captured the rainfall maxima. During Cyclone Ellie, satellite (Fig. S13a) and radar (Fig. S13b) both identified substantial rainfall over northern Australia, but the highest rainfall occurred in an area with relatively sparse hourly gauge observations (Fig. S14a). Only one hourly gauge recorded a 24 h accumulation exceeding 100 mm (168.2 mm), while the next highest accumulation was 51.4 mm (Table S1). In comparison, the denser daily gauge network (Fig. S14b) provided multiple observations of high rainfall, including accumulations of 208.0, 184.6, and 141.4 mm (Table S1). The limited sampling of the rainfall maximum by hourly gauges therefore constrained the observational information available to BR-SRG (Fig. 10a) for representing the highest rainfall centre, whereas the additional daily observations provided stronger constraints for AGCD (Fig.  10b).

During Cyclone Jasper, satellite (Fig. S13c) and radar (Fig. S13d) clearly captured the intense rainfall system, with several hourly gauges located within the heavy rainfall centre and recording high rainfall accumulations (Fig. S14c). The highest hourly-gauge-derived 24 h accumulations reached 479.2, 456.5, and 378.4 mm (Table S2). The combination of spatially distributed satellite and radar estimates with these high-rainfall gauge observations enabled BR-SRG (Fig. 10d) to better represent the extreme rainfall than in the Cyclone Ellie case (Fig. 10a).

Multi-source blending of satellite, radar, and gauge precipitation observations using bias correction and statistical interpolation is not a new concept (e.g., Gandin, 1965; Xie and Xiong, 2011; Yu et al., 2020; Xia and Wang, 2025), but the BRAIN framework differs from previous approaches in several aspects of its implementation. First, BRAIN was designed for computationally efficient application over a continental-scale domain such as Australia at high spatial and temporal resolution. The nearest-radar-point approximation within the localisation strategy substantially reduces the dimensionality of the statistical interpolation problem while retaining the source-specific error characterisation (Zhang et al., 2026), differing from the more computationally intensive formulation used in UKGrsHP (Yu et al., 2020).

BRAIN also uses a single satellite product as the spatially continuous background, with radar incorporated as an additional observation together with gauge observations. This differs from approaches that first combine satellite and radar to construct a blended background field for subsequent statistical interpolation with gauge observations (e.g., Xia and Wang, 2025). Because statistical interpolation requires characterisation of the spatial error structure of the background field, such pre-blending produces a new background whose error characteristics may differ from those of the original satellite and/or radar products. By retaining satellite and radar as separate sources, BRAIN allows their respective error characteristics and contributions to be explicitly represented within the statistical interpolation framework.

A further distinctive feature is that radar information is not restricted by a hard coverage mask. For each target location, BRAIN searches for the nearest available radar observation within a predefined maximum distance (200 km in this study). Consequently, radar information can still contribute to the blended estimate when the target location lies outside radar coverage, provided that a sufficiently close and reliable radar observation is available. Its effective contribution is determined by both the distance-dependent error correlation (Fig. 4b) and the estimated error variance, with greater weight generally assigned to observations that are closer to the target location and have lower estimated errors. Even when the nearby radar estimate is not more accurate than the local satellite estimate on its own, it can provide complementary information that can improve the resulting estimate after blending.

This formulation allows radar information to contribute both within and near radar-covered regions, providing a gradual transition across radar-coverage boundaries while retaining the satellite estimate as the spatially continuous background. This differs from simple radar extrapolation, in which rainfall information within the radar domain is spatially extended into areas without radar observations. In BRAIN, the radar field itself is not extrapolated. The satellite estimate remains the background at every target location, while available radar and gauge observations contribute through the statistical interpolation according to their estimated error characteristics and spatial correlations.

The evaluation revealed two notable behaviours of IDW: its mean error (ME, or mean bias) remained consistently close to zero despite relatively large RMSE and lower correlation (Figs. 5 and S16), while its relative performance improved from hourly to daily evaluation, achieving a lower RMSE than BR-SRG at the daily timescale (Fig. 6), a pattern consistently observed across different subregions outside radar coverage (Fig. S2). To examine these behaviours, we compared the station-level contributions of positive and negative errors (Figs. 11, S24, and S25). The median positive-error contribution of IDW remained close to 0.5 across all three evaluations despite relatively large MAE (mean absolute error), indicating nearly equal contributions from positive and negative errors. At the hourly scale, this balance results in a near-zero ME despite relatively large individual errors, as reflected by the MAE and RMSE. The near-zero ME of IDW therefore primarily reflects error cancellation rather than uniformly small estimation errors. When hourly precipitation is accumulated to daily totals, these opposing errors can further offset over time, reducing the accumulated daily errors and contributing to the improved relative performance of IDW at the daily timescale (Figs. 6 and S24).

The sensitivity of IDW (Fig. 12) to its interpolation configuration was further examined using the same rainfall cases (Fig. 10). IDW-K5 provides a continuous field but can extend gauge influence over long distances in gauge-sparse regions. Applying a maximum search distance (IDW-K5-L) avoids such long-range interpolation but produces isolated rainfall patterns and areas without estimates, while increasing the number of gauges (IDW-K20-L) provides only limited improvement. Despite these differences, all configurations strongly smooth the rainfall field and poorly represent its spatial structure, particularly in gauge-sparse regions. These limitations are more evident in the spatial case studies than in the point-based validation above, which evaluates performance only at gauge locations.

More sophisticated gauge-based interpolation methods, such as thin-plate spline (TPS; Nguyen et al., 2026) (Fig. 13), can improve spatial continuity but remain constrained by sparse gauge observations, with local rainfall features being overly smoothed and estimates becoming increasingly unreliable far from available gauges.

One limitation of the current framework is the propagation of residual errors from input observations into the blended analysis. Residual errors that are not identified through quality control, particularly for gauge observations, or are not fully removed by bias correction, particularly for satellite and radar estimates, can propagate into the blended analysis. Although the statistical interpolation weighting accounts for the intensity-dependent error characteristics of each source, an individual source generally does not receive complete weight, as this would require the error of the other sources to become overwhelmingly large in comparison. Consequently, residual biases in sources retaining non-zero weights can propagate into the final analysis.

For example, during Cyclone Jasper, underestimation in the satellite estimates contributed to underestimation in BR-SRG even when radar closely represented the observed accumulation (Fig. 14b). Conversely, during Cyclone Ellie, radar substantially underestimated the observed accumulation, while the satellite estimates were higher and partly compensated for the radar underestimation in the blended analysis (Fig. 14a). These contrasting cases demonstrate the value of retaining complementary information from multiple data sources, rather than simply increasing the contribution of a single source.

Together with the relative differences among S1, R1, BR-SG, and BR-SRG in the rainfall-intensity analysis (Fig. 7), these cases suggest that residual underestimation in the satellite estimates may contribute to the negative bias observed in BR-SRG, although the intensity-stratified bias is also affected by observation-based stratification. Further improvements should therefore focus on bias correction, particularly in better accounting for systematic biases across different rainfall intensities.

A second limitation concerns the spatial continuity of the blended precipitation field, particularly across radar coverage boundaries. Outside radar coverage, the analysis is primarily constrained by the satellite background and gauge observations, whereas within radar coverage, radar observations provide an additional constraint and can strongly influence the analysis when their estimated errors are smaller. When satellite and radar estimates are broadly consistent, the transition is generally smooth. However, large discrepancies between the two sources can produce visible spatial transitions near radar coverage boundaries. This occurs because the analysis within radar coverage is adjusted towards radar when its estimated errors are much smaller than those of the satellite, while areas outside radar coverage remain primarily constrained by the satellite background (Fig. 10). Importantly, radar information in the present framework is not restricted by a hard coverage boundary. Through error-informed localisation, surrounding radar observations can influence nearby areas beyond the nominal radar coverage, with their influence gradually decreasing with distance. This provides a smoother transition between radar-dominated and satellite-dominated regions than approaches relying solely on co-located observations, substantially reducing abrupt discontinuities at radar coverage boundaries. However, it cannot fully eliminate discontinuities when the input precipitation fields differ substantially. Improving consistency among input sources through better retrieval algorithm, quality control, and bias correction, together with incorporating additional independent data sources, could further improve spatial continuity.

A further consideration is the scale mismatch between point-based gauge observations and gridded precipitation estimates. Gauge measurements represent precipitation at individual locations, whereas satellite, radar, and blended estimates represent precipitation over grid cells. This representativeness difference affects not only the evaluation but also gauge-based bias correction and the estimation of error characteristics used in the blending framework. The effect can be particularly evident for localised and spatially variable hourly rainfall, where a point gauge may record substantially higher or lower rainfall than the corresponding grid-cell estimate (e.g., Fig. 10), particularly when local rainfall maxima occur within only a small fraction of the grid cell. Previous studies have attempted to quantify this uncertainty using dense gauge networks and point-to-area approaches (Bohnenstengel et al., 2011; Li et al., 2026; Tang et al., 2018), but it remains difficult to eliminate where gauge observations are sparse. Future work could explicitly characterise point-to-grid representativeness uncertainty as a function of gauge density, rainfall intensity, and spatial scale.