Description:
FIELD OF THE INVENTION
The present invention relates to the field of meteorology and atmospheric sciences, and more particularly to methods and systems for quantitative precipitation estimation (QPE) using polarimetric Doppler weather radar (PDWR) data. Specifically, the invention pertains to the generation of pseudo reflectivity profiles and the estimation of surface rainfall intensity (SRI) and precipitation accumulation (PAC) by leveraging Vertically Integrated Liquid (VIL) as a seeding parameter for improved accuracy in radar-based rainfall measurements.

Application of the Invention

The invention is applicable to a wide range of meteorological and hydrological applications, including but not limited to:
• Real-time and near real-time weather monitoring and forecasting, particularly for severe weather events such as storms, cyclones, and monsoons.
• Generation of high-resolution rainfall maps for use by meteorological agencies, disaster management authorities, and governmental organizations.
• Hydrological modeling and flood forecasting, where accurate surface rainfall intensity and precipitation accumulation data are critical inputs.
• Validation and calibration of radar-based precipitation estimates against ground-based in-situ observations, such as disdrometers and rain gauges.
• Support for emergency response planning, water resource management, and agricultural decision-making by providing improved spatial and temporal resolution of precipitation data.
• Enhancement of existing weather radar networks and data processing systems to deliver more reliable and comprehensive precipitation products.

BACKGROUND OF THE INVENTION
Accurate measurement and estimation of precipitation are fundamental requirements in meteorology, hydrology, and disaster management. Surface rainfall intensity (SRI) and precipitation accumulation (PAC) are critical parameters for weather forecasting, flood prediction, and water resource management.

Traditionally, ground-based rain gauges and disdrometers have been used to measure rainfall. While these instruments provide direct and reliable measurements, their spatial coverage is limited due to the high cost and logistical challenges of deploying dense networks, especially over large or inaccessible regions.

Doppler Weather Radars (DWRs) have emerged as essential tools for remote sensing of precipitation. DWRs provide high-resolution, wide-area coverage and enable continuous monitoring of atmospheric phenomena, including storms, cyclones, and monsoons.

Conventional DWRs primarily utilize reflectivity (Z) measurements to estimate rainfall rates using empirical relationships such as the R(Z) relation. However, these estimates are often affected by uncertainties arising from drop size distribution (DSD) variability, radar miscalibration, and signal attenuation, particularly in heavy rain.

The introduction of polarimetric capabilities in weather radars has significantly advanced precipitation estimation. Polarimetric Doppler Weather Radars (PDWRs) provide additional parameters such as differential reflectivity (ZDR) and specific differential phase (KDP), which offer insights into the size, shape, and phase of hydrometeors.
Dual-polarization radar products enable the use of advanced quantitative precipitation estimation (QPE) algorithms that combine Z, ZDR, and KDP to improve the accuracy of rainfall rate estimation. These algorithms can mitigate some of the limitations of single-parameter approaches.

Despite these advancements, current radar-based QPE methods still face several challenges. One common approach is to use a Constant Altitude Plan Position Indicator (CAPPI) layer, typically at 1 km altitude, to extract Z, ZDR, and KDP values for SRI estimation.

The CAPPI-based method, while effective in many scenarios, is limited by the radar’s scanning strategy. Since the radar does not scan all azimuths simultaneously, significant precipitation echoes may be missed, leading to gaps or underestimation in the derived SRI and PAC products.

Lower altitude radar data are often contaminated by ground clutter, while higher altitude data may not accurately represent surface precipitation due to evaporation or phase changes as hydrometeors descend.

The R(Z) relation, widely used for rainfall estimation, is particularly sensitive to DSD variability and radar calibration errors. While the use of ZDR and KDP can reduce some of these uncertainties, each parameter has its own limitations. For example, KDP-based estimates are robust at high rain rates but become noisy and unreliable at lower rain rates.

The need for a more comprehensive and robust approach to radar-based precipitation estimation is evident, especially in regions prone to severe weather events where timely and accurate rainfall data are crucial for public safety and resource management.

Prior art methods have attempted to address these issues by developing blended or composite QPE algorithms that dynamically select among R(Z), R(Z, ZDR), and R(KDP) relations based on reflectivity thresholds. However, these methods still rely on CAPPI layers and are subject to the same limitations regarding spatial coverage and data gaps.

Another challenge in the prior art is the inability to fully utilize all the volumetric information captured by the radar during a scan. Valuable data from different elevation angles and altitudes are often underutilized or discarded in the process of generating CAPPI layers.

The technical solution provided by the present invention addresses these shortcomings by introducing a novel method for generating pseudo reflectivity profiles based on Vertically Integrated Liquid (VIL) as a seeding parameter.

VIL is a radar-derived product that represents the total liquid water content integrated vertically through the atmosphere at a given location. High VIL values are indicative of strong updrafts and heavy precipitation, making VIL a valuable indicator for severe weather.

In the present invention, the radar data are first converted into a three-dimensional grid with fine horizontal and vertical resolution. VIL is then calculated for multiple altitude layers below a predetermined altitude, typically below 4 km, where hydrometeors are predominantly in the liquid phase.

For each grid point, the altitude layer with the maximum VIL value is identified. The radar data corresponding to this layer are then used to generate pseudo profiles of reflectivity (Z), differential reflectivity (ZDR), and specific differential phase (KDP).

These pseudo profiles serve as enhanced inputs to a composite QPE algorithm, which dynamically selects the most appropriate rainfall estimation relation (R(KDP), R(Z, ZDR), or R(Z)) based on reflectivity thresholds and radar frequency band.

By leveraging the maximum VIL layer, the invention ensures that the most representative and information-rich data are used for SRI and PAC estimation, thereby reducing the likelihood of missing significant precipitation echoes.

The technical effect of this approach is a substantial improvement in the spatial completeness and accuracy of radar-based precipitation products. The pseudo profile method captures more precipitation features and provides a more meaningful representation of rainbands and convective structures.

Validation studies using in-situ observations from disdrometers and rain gauges demonstrate that the SRI and PAC estimates derived from the pseudo profile method exhibit higher correlation with ground truth data compared to conventional CAPPI-based methods.

The invention is particularly advantageous in tropical and subtropical regions, where rapid development of convective systems and complex precipitation structures pose significant challenges for traditional radar QPE techniques.

The technical advancement of the present invention lies in its ability to fully exploit the volumetric radar data, integrate VIL as a physically meaningful seeding parameter, and dynamically adapt the QPE algorithm to local precipitation characteristics.

The method is adaptable to different radar frequency bands (e.g., C-band, X-band) and can be calibrated for local conditions using ground truth data, further enhancing its versatility and accuracy.

The invention also incorporates robust data quality control measures, including masking of invalid pixels and synchronization of radar and in-situ observation data, to ensure the reliability of the final precipitation products.

The need for the invention is underscored by the increasing frequency and intensity of extreme weather events, which demand more accurate and timely precipitation data for effective disaster response and mitigation.

Existing radar networks and data processing systems can be readily upgraded to implement the invention, providing immediate benefits in terms of improved rainfall estimation and operational forecasting capabilities.

The invention supports a wide range of applications, including real-time weather monitoring, hydrological modeling, flood forecasting, agricultural planning, and water resource management.

By providing high-resolution, spatially complete, and validated precipitation products, the invention enables meteorological agencies, governmental organizations, and emergency responders to make more informed decisions and take proactive measures to protect life and property.

In summary, the present invention overcomes the limitations of prior art radar-based QPE methods by introducing a novel, VIL-based pseudo profile approach that enhances the accuracy, reliability, and utility of surface rainfall intensity and precipitation accumulation estimates.

The invention represents a significant step forward in the field of radar meteorology, offering a technically advanced, practical, and scalable solution to the longstanding challenges of quantitative precipitation estimation. The approach is validated with real-world data from multiple radar sites and weather events, demonstrating its robustness and generalizability across different meteorological contexts.

The invention is compatible with existing radar infrastructure and can be implemented as a software upgrade, minimizing the need for additional hardware investment.

The technical solution provided by the invention is expected to set a new standard for radar-based precipitation estimation, with broad implications for weather forecasting, climate research, and disaster management.

The present invention fulfills a critical need in the meteorological community for more accurate, comprehensive, and actionable precipitation data, ultimately contributing to improved public safety, resource management, and scientific understanding of atmospheric processes.

OBJECT OF THE INVENTION
The primary object of the present invention is to provide an improved method and system for estimating surface rainfall intensity (SRI) and precipitation accumulation (PAC) from polarimetric Doppler weather radar (PDWR) data, which overcomes the limitations of conventional CAPPI-based approaches.

Another object of the invention is to utilize Vertically Integrated Liquid (VIL) as a seeding parameter to generate pseudo reflectivity, differential reflectivity, and specific differential phase profiles, thereby enabling more accurate and spatially complete precipitation estimation.

A further object of the invention is to enhance the quantitative precipitation estimation (QPE) process by dynamically selecting among multiple rainfall estimation relations (R(KDP), R(Z, ZDR), and R(Z)) based on reflectivity thresholds and radar frequency bands, thus improving the reliability of SRI and PAC products under varying meteorological conditions.

It is also an object of the invention to provide a method and system that fully exploit the volumetric data captured by PDWR, reducing data gaps and minimizing the impact of radar scanning limitations and ground clutter.

Another object is to enable real-time or near real-time generation of high-resolution rainfall maps and accumulation products for use in meteorological forecasting, hydrological modeling, disaster management, and water resource planning.

A further object is to facilitate the validation and calibration of radar-based precipitation estimates against in-situ observations, such as disdrometers and rain gauges, to ensure the accuracy and reliability of the derived products.

Yet another object of the invention is to provide a solution that is adaptable to different radar frequency bands and operational environments, and that can be integrated with existing radar infrastructure with minimal hardware modifications.

Ultimately, the invention aims to deliver a technically advanced, robust, and scalable approach to radar-based precipitation estimation, thereby supporting improved public safety, resource management, and scientific understanding of atmospheric processes.

SUMMARY OF THE INVENTION
The present invention provides a novel method and system for estimating surface rainfall intensity (SRI) and precipitation accumulation (PAC) using polarimetric Doppler weather radar (PDWR) data. Unlike conventional approaches that rely on constant altitude plan position indicator (CAPPI) layers, the invention leverages Vertically Integrated Liquid (VIL) as a seeding parameter to generate pseudo reflectivity profiles, resulting in more accurate and spatially complete precipitation estimates.

The method begins by receiving and processing polarimetric radar data, including reflectivity (Z), differential reflectivity (ZDR), and specific differential phase (KDP), from a PDWR. The radar data are converted into a three-dimensional (3D) grid with fine horizontal and vertical resolution, enabling detailed spatial analysis of atmospheric conditions.

For each grid point, the invention calculates VIL across multiple altitude layers below a predetermined threshold, typically below 4 kilometers, where hydrometeors are predominantly in the liquid phase. The VIL is computed by vertically integrating the liquid water content derived from radar reflectivity measurements over each layer.

The altitude layer with the maximum VIL value is identified for each grid point. The radar data corresponding to this layer are then used to generate pseudo profiles of Z, ZDR, and KDP, which serve as enhanced inputs for quantitative precipitation estimation (QPE).

A composite QPE algorithm is applied to the pseudo profiles, dynamically selecting among R(KDP), R(Z, ZDR), and R(Z) rainfall estimation relations based on reflectivity thresholds and radar frequency band. This adaptive approach ensures that the most suitable estimation method is used for each meteorological scenario, improving the reliability of SRI and PAC products.

The invention further includes robust data quality control measures, such as masking invalid pixels and synchronizing radar data with in-situ observations from disdrometers or rain gauges. This validation step ensures that the radar-based estimates closely match ground truth measurements, enhancing confidence in the results.

The system is implemented using dedicated hardware components, including a radar receiver, data acquisition module, processing unit (CPU and/or GPU), memory, and display interface. The architecture supports real-time or near real-time processing, making the invention suitable for operational weather forecasting and emergency response.

The method and system are adaptable to different radar frequency bands, such as C-band and X-band, and can be calibrated for local conditions using ground truth data. This flexibility allows the invention to be deployed across diverse meteorological environments and radar networks.

By fully exploiting the volumetric data captured by PDWR and integrating VIL as a physically meaningful parameter, the invention overcomes the limitations of prior art CAPPI-based methods. It reduces data gaps, captures more precipitation features, and provides a more accurate representation of rainbands and convective structures.

The invention has been validated with real-world data from multiple radar sites and weather events, demonstrating higher correlation with in-situ observations compared to conventional methods. The improved accuracy and spatial completeness of the SRI and PAC products make the invention highly valuable for meteorological agencies, hydrological modeling, disaster management, and water resource planning.

In summary, the present invention delivers a technically advanced, robust, and scalable solution for radar-based precipitation estimation, supporting improved public safety, resource management, and scientific understanding of atmospheric processes.

BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS
The accompanying drawings are provided solely for the purpose of illustrating exemplary embodiments of the present invention and are not intended to limit the scope of the invention in any way. The features shown in the drawings are for illustrative purposes only and may not be to scale. Variations, modifications, and alternative configurations may be made by those skilled in the art without departing from the spirit and scope of the invention as defined in the appended claims. The drawings should be interpreted in conjunction with the detailed description and are not intended to represent every possible embodiment or arrangement of the invention.

FIGURE 1: Architecture of Radar Data Product Generation
A block diagram illustrating the main hardware and software components of the radar-based rainfall estimation system. It shows the data flow from the radar receiver through data acquisition, signal processing, database storage, SRI/PAC generation, and visualization modules.

FIGURE 2: SRI/PAC Algorithm Data Processing Flowchart
A detailed flowchart outlining the step-by-step process from radar data acquisition, preprocessing, 3D grid generation, VIL calculation, pseudo profile generation, QPE algorithm application, validation, and output.

FIGURE 3: 3D Grid Generation Schematic
A schematic diagram showing how radar data in polar coordinates is transformed into a 3D Cartesian grid, including grid resolution and altitude layers, and the steps involved in this transformation.

FIGURE 4: VIL Calculation Illustration
A side-view diagram depicting the vertical integration of liquid water content (LW) across multiple altitude layers at a single grid point, illustrating how VIL is calculated from reflectivity values.

FIGURE 5: Pseudo Profile Generation Diagram
A diagram showing the process of selecting the altitude layer with maximum VIL at each grid point and extracting the corresponding Z, ZDR, and KDP values to form the pseudo profile.

FIGURE 6: Composite QPE Algorithm Decision Tree
A flowchart or decision tree illustrating the logic for selecting among R(KDP), R(Z, ZDR), and R(Z) relations for rainfall estimation, including threshold values and frequency band considerations.

FIGURE 7: Validation and Comparison Plots
Graphs or scatter plots comparing SRI and PAC estimates from the invention with in-situ observations (e.g., disdrometers, rain gauges) and with conventional CAPPI-based methods, including correlation plots and error histograms.

FIGURE 8: Output Visualization Examples
Example output maps or visualizations of SRI and PAC generated by the system, showing spatial coverage and resolution, with side-by-side comparisons to conventional methods.

FIGURE 9: Real-Time Operation Workflow
A workflow diagram illustrating the real-time or near real-time operation of the system, from data acquisition to output and alert generation.

FIGURE 10: Additional Supporting Diagram or Visualization
An additional figure supporting the invention, such as a specialized plot, schematic, or visualization relevant to the described methodology or results (e.g., a detailed comparison for a specific event or a system performance summary).

DETAILED DESCRIPTION OF THE INVENTION
The detailed description of the invention set forth herein is provided to enable any person skilled in the art to make and use the invention and is presented for purposes of illustration and explanation only. It is not intended to be exhaustive or to limit the invention to the precise forms, configurations, or embodiments disclosed. Various modifications, adaptations, and alternatives will be apparent to those skilled in the art in view of this description, and such modifications and variations are intended to be within the scope of the invention as defined by the appended claims.

The invention is not limited to the specific examples, materials, or methods described, and the use of specific terminology herein is for the purpose of description and not of limitation. No limitation with respect to the scope of the invention is intended or should be inferred from the detailed description, and all such modifications and equivalents are intended to be included within the scope of the invention.

The present invention relates to a method and system for estimating surface rainfall intensity (SRI) and precipitation accumulation (PAC) using polarimetric Doppler weather radar (PDWR) data. The invention introduces a novel approach that leverages Vertically Integrated Liquid (VIL) as a seeding parameter to generate pseudo reflectivity profiles, thereby overcoming the limitations of conventional CAPPI-based methods.

In a typical embodiment, the system comprises a radar receiver configured to acquire polarimetric radar data, including reflectivity (Z), differential reflectivity (ZDR), and specific differential phase (KDP), from a PDWR. The radar receiver is connected to a data acquisition module that digitizes and preprocesses the incoming signals.

The preprocessed radar data are transmitted to a central processing unit (CPU) and/or graphics processing unit (GPU), which is operatively coupled to a memory storing executable instructions for implementing the inventive method. The system may further include a database server for storing estimated SRI and PAC products, and a display interface for outputting results.

The method of the invention begins with the reception and processing of polarimetric radar data. The data are typically received in polar coordinates, corresponding to the radar’s scanning geometry. The data acquisition module performs initial quality checks, filtering out noise and ground clutter.

The processed radar data are then converted into a three-dimensional (3D) Cartesian grid. In a preferred embodiment, the grid is generated with a horizontal resolution of 500 meters and a vertical resolution of 250 meters, although these parameters can be adjusted based on radar capabilities and application requirements.

The 3D grid enables detailed spatial analysis of atmospheric conditions and serves as the foundation for subsequent VIL calculation and pseudo profile generation. Each grid point represents a specific location in space, with associated radar measurements at various altitudes.

For each grid point, the system calculates VIL across multiple altitude layers below a predetermined threshold, typically below 4 kilometers. This altitude range is selected because hydrometeors are predominantly in the liquid phase below this level, which is most relevant for surface precipitation estimation.

Each altitude layer may have a depth of 1 kilometer, and the layers may be defined as follows: 250–1250 m, 500–1500 m, 750–1750 m, 1000–2000 m, 1250–2250 m, 1500–2500 m, 1750–2750 m, and 2000–3000 m. The system iterates through these layers for each grid point.

Conventionally, CAPPI layers of a constant height are used for SRI estimation, this may fail to capture many significant echoes, as the radar is not scanning the whole 360 deg azimuth simultaneously. By using the method of the present invention, the maximum possible information captured by the radar can be used during a volumetric scan. The usage of VIL reduces the probability of erroneous estimates as it directly represents the liquid water content. But this method may not have the upper hand in situations where sub-cloud evaporation exists that modify reflectivity as precipitation descends. However, in most of the events VIL based SRI approach can outperforms conventional method as it incorporates the missing information.

R(KDP) relation is used to estimate SRI for pixels with CAPPI ZVIL > 40 dBZ. Further the algorithm checks the reflectivity value exceeds 35 dBZ for those pixels where the reflectivity value is below 40 dBZ. If this condition is satisfied R (Z, ZDR) relation is used. For the grid points which doesn’t come under the above two categories R(Z) relation is used to estimate the rainfall rate. The coefficients of this relations differ for different frequency bands of operations. The relations used in this study are listed below. Z is converted into linear units where as unit remain unchanged for the other two variables. For CDWR, R(KDP) relation is tuned for CDWR observations and R (Z, ZDR) and R(Z) relations are adpated from Sasidharan et al. 2024.
R(KDP) = 59.5202 KDP 0.8451
R(Z,ZDR) = 0.0067 Z 0.945 ZDR -0.019
R(Z)= 0.017 Z 0.714
For XDWR , the QPE relations specified for X-band adapted from Thompson et al. (2018). The rainfall estimation relations applied to XDWR observations are listed below.
R(KDP) = 21.9729 KDP 0.7221
R(Z, ZDR) = 0.0085 Z 0.9294 ZDR -0.0445
R(Z)= 0.029 Z 0.719

The SRI is derived using the Pseudo profiles and the conventional CAPPI layers to compare the outcomes from these two different inputs. To validate the accuracy of the new SRI approach, in-situ observations from disdrometers and rain gauges are used. The results obtained from CDWR is compared with a Joss–Waldvogel Disdrometer (JWD RD80, Joss and Waldvogel 1967). The JWD used in this study is installed at the Indian Institute of Space Science and Technology (IIST, 8.62650N, 77.03380E) (refer to Fig. 1) IIST is situated at a distance of about 21 km from the CDWR site. The JWD recorded observations at 1-minute intervals for a duration of three days (29th November–2nd December 2017) have been used in this analysis.

Rainfall observations with fine resolution were not available in the XDWR scanning area, hence 24-hour precipitation accumulation values obtained from rain gauges have been used. The rain gauge data sets were published in Tamil Nadu System for Multi-hazard potential impact assessment, Alert, emergency Response planning & Tracking (TNSMART) website. The data sets from December 02, 2023 for Tropical Cyclone (TC) Michaung rainfall comparison have been used.

The CDWR has captured by TC Ockhi during its transition from depression (D) stage to severe cyclonic storm (SCS) stage. Once the quality checks are over CDWR data is converted into 3D grid, for generating pseudo CAPPI layer. Once the pseudo CAPPI layers are created SRI is estimated. Figure 4 shows the radar imageries of SRI generated from conventional CAPPI and the Pseudo profiles.

From the Figure 2, it is clearly visible that SRI estimated from Pseudo profiles captures more data and provides more meaningful representation of the rainbands of Ockhi. Now, the correlation of CDWR SRI with in-situ observations need to be checked. For that, average R value obtained from 4 nearest data points to JWD location is calculated both the sensors record the data at same time. A one-minute tolerance is allowed in order to reduce the data gaps. Thus, the SRI over JWD location is computed from the new method and the conventional method, the estimates are compared with rainfall rate measured by JWD.

Figure 3.a shows the rainfall rate measured by of the JWD and CDWR using conventional method at the same time over IIST, whereas Figure 3.b represents rainfall rate (R) from JWD and CDWR derived rainfall using new method.

Figure 3 demonstrates the R obtained from new SRI approach is highly correlated with JWD observations. The correlation between R obtained from new SRI approach and the R recorded by JWD is found to be 93% where as that of conventional SRI method observed to be 89%. Thus, conventional SRI exhibits a weaker correlation to JWD rain rate than the new method, which may be a resulted from the significant gaps in data.

The new SRI approach is also tested with XDWR observations. Figure 4 shows the XDWR SRI generated from conventional CAPPI and the Pseudo profiles. The gaps in conventional layers are filled and a significant increase in intensity also visible in pseudo profile-based SRI.

To check the validity of new SRI approach with XDWR observations rain gauge recorded data downloaded from TNSMART website have been used. The details rain gauges used in this study are included in Table 2. The location of is depicted in Figure 2.

Station Lat Lon ABR
Sholinganallur 12.8773 80.2277 SNGR
Perambur 13.0965 80.2922 PMBR
Nungambakkam 13.0667 80.25 NGBK
DGP Office 13.05 80.2333 DGPO
CD Hospital Tondaripet 13.1093 80.2427 TNDR
Chennai Collectorate 13.1282 80.292 COLL
Cheyyur 12.3525 80 CHEY
Table 2. List of Rain Gauges used for PAC comparison.

TC Michaung brought significant rainfall to the XDWR coverage area and we have analysed data from 2nd to 4th December 2023. The 24-hour precipitation accumulation (PAC) at 08:30 IST is estimated from XDWR and the same is compared with accumulation obtained from rain gauges. Presently we have included recordings from SNGR, DGPO and TNDR for comparing TC Michaung PAC. Figure 5 represents a comparison between precipitation accumulation obtained from rain gauges, the new method and the conventional method.

For the three stations VIL based PAC closely matches with rain gauge measured accumulation compared to conventional PAC on 3rd December 2024 (Figure 5.a). In case of SNGR there is a difference of 10 mm between VIL based PAC and Rain gauge PAC estimate, but still, it is more than conventional PAC method. The comparison plot in Figure 5.b shows much higher rainfall for DGPO and TNDR stations, but XDWR couldn’t produce any nearby estimate both in new and conventional method. But it is visible that the proposed method still out performs the conventional method. The disparity in PAC measurements may arose due to the fact that the coefficients in rainfall relations is not tuned for this heavy downpour.

This process is repeated for all defined layers at each grid point, resulting in a set of VIL values corresponding to different altitude layers. For each grid point, the system identifies the altitude layer at which the maximum VIL value occurs. This layer is considered to contain the most significant liquid water content and is likely to be most representative of the actual precipitating cloud at that location. The radar data corresponding to the altitude layer with the maximum VIL value are then used to generate pseudo profiles of reflectivity (Z), differential reflectivity (ZDR), and specific differential phase (KDP) for each grid point. These pseudo profiles serve as enhanced inputs for quantitative precipitation estimation (QPE). Unlike conventional pseudo CAPPI methods, which fill gaps in CAPPI layers using data from other scan elevations, the present invention leverages VIL as a physically meaningful seeding parameter.

The system applies a composite QPE algorithm to the pseudo profiles to estimate SRI and PAC. The algorithm dynamically selects among R(KDP), R(Z, ZDR), and R(Z) rainfall estimation relations based on reflectivity thresholds and radar frequency band.

In one embodiment, the composite QPE algorithm operates as follows: if the pseudo reflectivity ZZ exceeds 40 dBZ, the R(KDP) relation is used; if ZZ is between 35 dBZ and 40 dBZ, the R(Z, ZDR) relation is used; and if ZZ is below 35 dBZ, the R(Z) relation is used. The specific coefficients for these relations are selected based on the radar’s operating frequency (e.g., C-band or X-band) and may be further tuned for local conditions using ground truth data.

The SRI is estimated for each grid point using the selected QPE relation. PAC is then calculated by integrating the SRI over time for each location. The resulting SRI and PAC products are spatially resolved and can be output as maps, tables, or other visualizations. The system incorporates robust data quality control measures, including masking of invalid pixels based on radar signal integrity and data quality checks. Invalid or unreliable data points are excluded from the final SRI and PAC products. The estimated SRI and PAC products are validated against in-situ observations from disdrometers and rain gauges. The system includes an interface module for receiving ground truth data, and time synchronization is performed to ensure that radar and in-situ data are compared within a predetermined tolerance interval.

In one embodiment, the system is configured for real-time or near real-time operation, enabling timely generation of high-resolution rainfall maps and accumulation products. This capability is particularly valuable for operational weather forecasting, emergency response, and disaster management.

The method and system are adaptable to different radar frequency bands, such as C-band and X-band, and can be calibrated for local meteorological conditions using ground truth data. The coefficients of the rainfall estimation relations may be adjusted based on local calibration to further improve estimation accuracy.

The system includes a visualization module, which may be implemented on a dedicated GPU or visualization hardware, for generating and displaying maps or graphical representations of the estimated SRI and PAC. The output can be tailored for meteorological analysts, governmental agencies, or public dissemination.

In another embodiment, the invention is implemented at a meteorological radar site equipped with a PDWR, providing continuous, high-resolution rainfall monitoring for a metropolitan area. The system can be deployed across a network of radar sites, with centralized processing and data fusion to generate regional or national precipitation products.

The invention is applicable to a wide range of meteorological and hydrological applications, including real-time weather monitoring, flood forecasting, hydrological modeling, agricultural planning, and water resource management.

The present invention offers several advantages over prior art methods, including enhanced spatial completeness and accuracy of SRI and PAC estimates by leveraging VIL as a seeding parameter, reduction of data gaps, and improved representation of precipitation features compared to CAPPI-based approaches.

The dynamic adaptation of QPE algorithms to local meteorological conditions and radar frequency bands ensures that the most appropriate estimation method is used for each scenario, further improving the reliability of the results.

The robust validation against in-situ observations ensures high reliability of the derived products, making the invention suitable for operational use in critical applications such as disaster management and emergency response.

The invention is compatible with existing radar infrastructure and can be implemented as a software upgrade, minimizing the need for additional hardware investment and facilitating rapid deployment.

In a further embodiment, the system may include automated alert generation for severe weather events based on threshold exceedances in SRI or PAC, integration with hydrological models for flood risk assessment, or cloud-based data storage and dissemination for collaborative meteorological analysis.

The system may also support historical data analysis, enabling retrospective studies of precipitation events and long-term climate monitoring.

The invention can be integrated with other meteorological data sources, such as satellite observations or numerical weather prediction models, to provide a comprehensive view of atmospheric conditions.

The method is scalable and can be adapted for use with different radar network configurations, from single-site installations to nationwide or continental-scale systems.

In one embodiment, the system supports user-defined customization of grid resolution, altitude layer configuration, and QPE algorithm parameters, allowing adaptation to specific operational requirements or research objectives.

The invention may further include a user interface for manual review and adjustment of estimated SRI and PAC products, supporting quality assurance and expert oversight.

The system can be configured to generate automated reports and alerts for end users, including meteorological agencies, emergency responders, and the general public.

The invention supports data export in standard formats for integration with external systems, such as hydrological models, GIS platforms, or decision support tools.

The present invention represents a significant advancement in radar-based precipitation estimation, providing a technically advanced, robust, and scalable solution that delivers more accurate, reliable, and actionable precipitation products.

By fully exploiting volumetric radar data and integrating VIL as a physically meaningful parameter, the invention addresses longstanding challenges in quantitative precipitation estimation and supports improved public safety, resource management, and scientific understanding of atmospheric processes.

In summary, the invention provides a comprehensive framework for radar-based precipitation estimation, encompassing data acquisition, processing, quality control, validation, visualization, and application, and is adaptable to a wide range of operational and research contexts.

DESCRIPTION OF THE FIGURES:
FIGURE 1: Architecture of Radar Data Product Generation
This figure is a block diagram illustrating the overall system architecture for radar-based rainfall estimation. It depicts the main hardware and software components and their interconnections. The diagram starts with the Radar Receiver, which captures atmospheric signals. The data flows to the Data Acquisition Module, responsible for digitizing and formatting the incoming radar signals. Next, the data is sent to the Signal Processing Unit (SPU), which performs pulse compression and extracts base radar products (such as reflectivity and phase information). The processed data is stored in a Database/Archival System. The Data Product Generation Application (DPGA) retrieves data from the database to compute SRI/PAC using both conventional and VIL-based algorithms. The results are compared with In-situ Data (from disdrometers and rain gauges) also stored in the database. The final products are sent to a Visualization Module for display and user interaction. Arrows in the diagram indicate the direction of data flow between each component, emphasizing the modular and sequential nature of the system.

FIGURE 2: SRI/PAC Algorithm Data Processing Flowchart
This figure presents a detailed flowchart outlining the end-to-end data processing pipeline for generating Surface Rainfall Intensity (SRI) and Precipitation Accumulation Content (PAC). The process begins with Radar Data Acquisition, followed by Preprocessing steps such as clutter removal and KDP estimation. The data is then transformed from polar to Cartesian coordinates to create a 3D Grid. The flowchart splits into two branches:
• The Conventional Method branch generates a 1 km CAPPI layer and applies the composite QPE algorithm to estimate SRI/PAC.
• The VIL-Based Method branch calculates VIL for each vertical layer, identifies the layer with maximum VIL at each grid point, and generates pseudo profiles (Z, ZDR, KDP) for QPE.
Both branches converge at the Validation step, where radar-derived estimates are compared with in-situ measurements. The final step is Output Generation, where results are formatted for visualization and further analysis. The flowchart uses decision diamonds, process rectangles, and data storage symbols to clearly delineate each step and decision point.

FIGURE 3: 3D Grid Generation Schematic
This schematic illustrates the transformation of radar data from polar coordinates (azimuth, range, elevation) into a 3D Cartesian grid suitable for volumetric analysis. The figure shows the radar at the origin, emitting beams at various elevation angles. Each beam is sampled at discrete range intervals, forming a set of polar coordinate points. These points are mapped onto a 3D grid with defined horizontal (e.g., 500 m) and vertical (e.g., 250 m) resolutions. The schematic details the steps: reading radar data, extracting necessary fields, defining grid parameters (max range, elevation limits, grid resolution), and using interpolation functions (e.g., wradlib.vpr.make_3d_grid) to populate the 3D grid. The output is a volumetric dataset where each voxel contains radar-derived values, ready for further processing.

FIGURE 4: VIL Calculation Illustration
This figure provides a side-view diagram of the vertical integration process used to calculate Vertically Integrated Liquid (VIL) at a single grid point. The atmosphere is divided into horizontal layers (e.g., every 250 m in altitude). For each layer, the radar reflectivity (Z) is used to estimate the liquid water content (LW) using a power-law relationship. The VIL for a given column is computed by integrating LW across all layers up to a specified altitude (e.g., 4 km). The diagram uses color-coded layers to show the integration path and includes mathematical annotations to illustrate the calculation, such as the summation of LW values across layers and the use of the reflectivity-to-LW conversion formula.

FIGURE 5: Pseudo Profile Generation Diagram
This diagram demonstrates the process of generating pseudo profiles for Z, ZDR, and KDP at each grid point. For each horizontal grid location, the VIL is calculated for multiple vertical layers. The layer with the maximum VIL is identified (highlighted in the diagram). The corresponding Z, ZDR, and KDP values from this layer are extracted and assigned to the pseudo profile for that grid point. The figure uses a matrix or table format to show VIL values across layers and grid points, with arrows indicating the selection of maximum values and the extraction of associated radar parameters. This process is repeated for all grid points to form complete pseudo profiles for input to the QPE algorithm.

FIGURE 6: Composite QPE Algorithm Decision Tree
This figure is a flowchart or decision tree that visualizes the logic used to select the appropriate rainfall estimation relation (R(KDP), R(Z, ZDR), or R(Z)) for each grid point. The tree starts with a decision node checking if the reflectivity (Z) exceeds 40 dBZ; if true, the R(KDP) relation is used. If not, the next node checks if Z exceeds 35 dBZ; if so, the R(Z, ZDR) relation is applied. Otherwise, the R(Z) relation is used. The tree also includes branches for different radar frequency bands (C-band, X-band), with each branch specifying the appropriate coefficients for the QPE relations. The diagram uses labeled arrows and boxes to clearly indicate the decision criteria and resulting actions.

FIGURE 7: Validation and Comparison Plots
This figure comprises a set of graphs and scatter plots comparing the SRI and PAC estimates from the radar-based methods (both conventional and VIL-based) with ground truth measurements from in-situ instruments (disdrometers and rain gauges). The plots may include:
• Time series comparisons of rainfall rates at specific locations
• Scatter plots showing correlation between radar-derived and observed values
• Error histograms illustrating the distribution of estimation errors
• Bar charts comparing precipitation accumulation across multiple stations
The figure highlights the improved correlation and reduced error of the VIL-based method compared to the conventional approach.

FIGURE 8 : Output Visualization Examples
This figure presents example output maps generated by the system, displaying spatial distributions of SRI and PAC over the radar coverage area. The maps use color scales to represent rainfall intensity or accumulation. The figure includes side-by-side comparisons: one map generated using the conventional CAPPI-based method and another using the VIL-based pseudo profile method. The improved spatial coverage, resolution, and accuracy of the VIL-based outputs are visually evident, with fewer gaps and better alignment with observed rainfall patterns.

FIGURE 9: Real-Time Operation Workflow
This workflow diagram illustrates the real-time or near real-time operation of the radar data product generation system. The process begins with the radar performing a volumetric scan, followed by immediate data acquisition and transfer to the SPU for base product generation. The SPU saves the data in cfradial format in an archival folder. The DPGA monitors the folder for new files, processes incoming data to generate SRI/PAC and alert products, and saves the results for access by the visualization application. The diagram uses arrows to show the continuous, automated flow of data and processing, emphasizing the system’s capability for timely rainfall estimation and alert generation.

FIGURE 10: Additional Supporting Diagram or Visualization
This figure provides an additional schematic, plot, or visualization that supports the invention’s methodology or results. Possible examples include:
• A detailed comparison plot for a specific rainfall event, showing how the VIL-based method captures features missed by the conventional method
• A system performance summary, such as a bar chart of processing times or a map of system coverage
• A schematic of the integration between radar data, in-situ observations, and external data sources
The figure is designed to reinforce the advantages and robustness of the proposed approach, providing further evidence of its novelty and effectiveness.

ADVANTAGES OF THE INVENTION:

1. Enhanced Accuracy in Precipitation Estimation:
By leveraging Vertically Integrated Liquid (VIL) as a seeding parameter, the invention provides more accurate estimates of surface rainfall intensity (SRI) and precipitation accumulation (PAC) compared to conventional CAPPI-based methods.

2. Improved Spatial Completeness:
The pseudo profile approach captures more precipitation features and reduces data gaps that commonly occur in traditional radar products, resulting in spatially complete rainfall maps.

3. Dynamic Algorithm Adaptation:
The composite QPE algorithm dynamically selects among R(KDP), R(Z, ZDR), and R(Z) relations based on reflectivity thresholds and radar frequency, ensuring optimal estimation under varying meteorological conditions.

4. Utilization of Full Volumetric Radar Data:
The invention fully exploits the volumetric data captured during a radar scan, rather than relying solely on a single CAPPI layer, thereby maximizing the information used for precipitation estimation.

5. Robust Validation with Ground Truth:
The method includes validation against in-situ observations from disdrometers and rain gauges, ensuring that radar-based estimates closely match actual ground measurements.

6. Reduction of Calibration and Attenuation Errors:
By incorporating polarimetric parameters and VIL, the invention mitigates errors due to drop size distribution variability, radar miscalibration, and signal attenuation, especially in heavy rain.

7. Real-Time and Near Real-Time Capability:
The system supports real-time or near real-time processing, making it suitable for operational weather forecasting, disaster management, and emergency response.

8. Adaptability to Multiple Radar Bands:
The method is compatible with different radar frequency bands (e.g., C-band, X-band) and can be calibrated for local conditions, enhancing its versatility and applicability.

9. Scalability and Integration:
The invention can be implemented as a software upgrade to existing radar infrastructure, allowing for rapid deployment and integration with current meteorological systems.

10. Support for Advanced Applications:
The high-resolution, validated precipitation products generated by the invention are valuable for hydrological modeling, flood forecasting, agricultural planning, and water resource management.

11. Automated Quality Control:
The system incorporates automated data quality checks and masking of invalid pixels, ensuring the reliability and integrity of the output products.

12. User-Friendly Visualization:
The invention provides intuitive visualizations and spatially resolved outputs, facilitating interpretation by meteorologists, governmental agencies, and decision-makers.

13. Facilitation of Research and Retrospective Analysis:
The method supports historical data analysis and can be used for retrospective studies of precipitation events and long-term climate monitoring.

14. Contribution to Public Safety and Resource Management:
By delivering more reliable and actionable precipitation data, the invention supports improved public safety, disaster preparedness, and efficient management of water resources.

15. Scientific Advancement:
The invention advances the state of the art in radar meteorology by introducing a physically meaningful, VIL-based approach to quantitative precipitation estimation, setting a new standard for accuracy and reliability.

The embodiments, examples, and descriptions provided herein are intended solely for the purpose of illustrating the principles and operation of the present invention. While specific implementations and configurations have been described, these are not intended to limit the scope of the invention. Modifications, variations, and equivalents may be made by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.

The present invention may be subject to further refinement, optimization, or adaptation to suit particular applications or technological advancements. The inventors and assignees make no representation or warranty, express or implied, regarding the accuracy, completeness, or suitability of the disclosed embodiments for any particular purpose. The invention is not limited to the specific details, arrangements, or methods described, and all such modifications and variations are intended to be included within the scope of the invention.

Nothing in this disclosure should be construed as an admission of prior art or as limiting the invention to any specific combination of features or steps. The inclusion of references to publications, patents, or other documents is for informational purposes only and does not constitute an acknowledgment that such references are prior art to the present invention.
, Claims:
1. A method for estimating surface rainfall intensity (SRI) and precipitation accumulation (PAC) from polarimetric Doppler weather radar (PDWR) data in a Doppler radar, the method comprising:
i) receiving and processing polarimetric radar data comprising reflectivity (Z), differential reflectivity (ZDR), and specific differential phase (KDP) from a PDWR;
ii) converting the polarimetric radar data into a three-dimensional (3D) grid having defined horizontal and vertical resolutions;
iii) calculating, for each of a plurality of altitude layers below a predetermined altitude, a Vertically Integrated Liquid (VIL) value at each grid point by vertically integrating liquid water content derived from radar reflectivity measurements;
iv) identifying, for each grid point, the altitude layer at which the maximum VIL value occurs;
v) generating, for each grid point, pseudo profiles of reflectivity (Z), differential reflectivity (ZDR), and specific differential phase (KDP) based on the radar data corresponding to the altitude layer with the maximum VIL value;
vi) applying a composite quantitative precipitation estimation (QPE) algorithm to the pseudo profiles to estimate the SRI and PAC, wherein the QPE algorithm selects among R(KDP), R(Z, ZDR), and R(Z) relations based on reflectivity thresholds; and
vii) comparing or validating the estimated SRI and PAC with in-situ observations obtained from disdrometers or rain gauges.

2. The method of claim 1, wherein the step of calculating VIL comprises, for each altitude layer, integrating the liquid water content over the vertical extent of the layer using the relation
LW=3.44×10−6×Z4/7LW=3.44×10−6×Z4/7
and summing the contributions from all relevant radar tilts.

3. The method of claim 1, wherein the composite QPE algorithm comprises:
a) applying an R(KDP) relation when the pseudo reflectivity Z exceeds a first threshold;
b) applying an R(Z, ZDR) relation when the pseudo reflectivity Z is between the first and a second threshold; and
c) applying an R(Z) relation when the pseudo reflectivity Z is below the second threshold.

4. The method of claim 1, wherein the in-situ observations comprise time-synchronized measurements from a disdrometer or precipitation accumulation data from a rain gauge network.

5. The method of claim 1, further comprising outputting or displaying the estimated SRI and PAC as spatially resolved products for meteorological analysis or forecasting.

6. The method of claim 1, wherein the three-dimensional grid is generated with a horizontal resolution of approximately 500 meters and a vertical resolution of approximately 250 meters.

7. The method of claim 1, wherein the plurality of altitude layers for VIL calculation each have a depth of approximately 1 kilometer and are confined to altitudes below approximately 4 kilometers.

8. The method of claim 1, wherein the step of generating pseudo profiles further comprises selecting, for each grid point, the reflectivity (Z), differential reflectivity (ZDR), and specific differential phase (KDP) values from the radar data corresponding to the altitude layer with the maximum VIL value.

9. The method of claim 1, wherein the composite QPE algorithm applies different rainfall estimation relations depending on the operating frequency band of the radar, including C-band and X-band specific coefficients.

10. The method of claim 1, wherein the method further comprises masking invalid pixels in the estimated SRI and PAC products based on data quality checks or radar signal integrity.

11. The method of claim 1, wherein the in-situ observations used for validation are time-synchronized with the radar data within a predetermined tolerance interval.

12. The method of claim 1, wherein the method further comprises storing the estimated SRI and PAC in a database for subsequent meteorological analysis or historical recordkeeping.

13. The method of claim 1, wherein the method further comprises generating visualizations or maps of the estimated SRI and PAC for display to end users or meteorological analysts.

14. The method of claim 1, wherein the method is performed in real-time or near real-time to support operational weather forecasting and emergency response.

15. The method of claim 1, wherein the method further comprises adjusting the coefficients of the rainfall estimation relations based on local calibration with ground truth data to improve estimation accuracy.

16. A system for estimating surface rainfall intensity (SRI) and precipitation accumulation (PAC) from polarimetric Doppler weather radar (PDWR) data, the system comprising:
i) a radar receiver configured to receive polarimetric radar data comprising reflectivity (Z), differential reflectivity (ZDR), and specific differential phase (KDP) from a PDWR;
ii) a data acquisition module operatively coupled to the radar receiver for digitizing and preprocessing the received radar data;
iii) a processing unit comprising a central processing unit (CPU) and/or a graphics processing unit (GPU);
iv) a memory operatively coupled to the processing unit and storing instructions that, when executed by the processing unit, cause the system to:
o generate a three-dimensional (3D) grid representation of the radar data with defined horizontal and vertical resolutions;
o calculate, for each of a plurality of altitude layers below a predetermined altitude, a Vertically Integrated Liquid (VIL) value at each grid point by vertically integrating liquid water content derived from radar reflectivity measurements;
o identify, for each grid point, the altitude layer at which the maximum VIL value occurs;
o generate, for each grid point, pseudo profiles of reflectivity (Z), differential reflectivity (ZDR), and specific differential phase (KDP) based on the radar data corresponding to the altitude layer with the maximum VIL value;
o apply a composite quantitative precipitation estimation (QPE) algorithm to the pseudo profiles to estimate the SRI and PAC, wherein the QPE algorithm selects among R(KDP), R(Z, ZDR), and R(Z) relations based on reflectivity thresholds;
o and output or display the estimated SRI and PAC as spatially resolved products via a display interface.

17. The system of claim 16, further comprising an interface module for receiving in-situ observation data from disdrometers or rain gauges, wherein the processing unit is further configured to compare or validate the estimated SRI and PAC with the in-situ observation data.

18. The system of claim 16, wherein the processing unit is configured to calculate the VIL for each altitude layer by integrating the liquid water content over the vertical extent of the layer using the relation
LW=3.44×10−6×Z4/7LW=3.44×10−6×Z4/7
and summing the contributions from all relevant radar tilts.

19. The system of claim 16, wherein the processing unit is configured to apply the composite QPE algorithm by:
i) applying an R(KDP) relation when the pseudo reflectivity Z exceeds a first threshold;
ii) applying an R(Z, ZDR) relation when the pseudo reflectivity Z is between the first and a second threshold;
iii) and applying an R(Z) relation when the pseudo reflectivity Z is below the second threshold.

20. The system of claim 16, wherein the display interface comprises a graphical user interface (GUI) for outputting or displaying the estimated SRI and PAC in a format suitable for meteorological analysis, forecasting, or hydrological modeling.

21. The system of claim 16, wherein the memory further stores instructions that cause the processing unit to generate the three-dimensional grid with a horizontal resolution of 500 meters and a vertical resolution of 250 meters.

22. The system of claim 16, wherein the processing unit is configured to calculate VIL for a plurality of altitude layers, each having a depth of approximately 1 kilometer and confined to altitudes below approximately 4 kilometers.

23. The system of claim 16, wherein the processing unit is further configured to select, for each grid point, the reflectivity (Z), differential reflectivity (ZDR), and specific differential phase (KDP) values from the radar data corresponding to the altitude layer with the maximum VIL value to generate the pseudo profiles.

24. The system of claim 16, wherein the processing unit is configured to apply different rainfall estimation relations in the composite QPE algorithm based on the operating frequency band of the radar, including C-band and X-band specific coefficients.

25. The system of claim 16, wherein the processing unit is further configured to mask invalid pixels in the estimated SRI and PAC products based on data quality checks or radar signal integrity.

26. The system of claim 16, further comprising a database server operatively coupled to the processing unit for storing the estimated SRI and PAC for subsequent meteorological analysis or historical recordkeeping.

27. The system of claim 16, further comprising a visualization module implemented on a dedicated graphics processing unit (GPU) or visualization hardware, configured to generate and display maps or graphical representations of the estimated SRI and PAC.

28. The system of claim 16, wherein the processing unit is configured to perform the estimation and output of SRI and PAC in real-time or near real-time to support operational weather forecasting and emergency response.

29. The system of claim 16, wherein the processing unit is further configured to synchronize the in-situ observation data with the radar data within a predetermined time interval for validation purposes.

30. The system of claim 16, wherein the processing unit is further configured to adjust the coefficients of the rainfall estimation relations based on local calibration with ground truth data to improve estimation accuracy.

31. A non-transitory computer-readable storage medium storing instructions that, when executed by a processor, cause the processor to perform a method for estimating surface rainfall intensity (SRI) and precipitation accumulation (PAC) from polarimetric Doppler weather radar (PDWR) data, the method comprising:
i) receiving and processing polarimetric radar data comprising reflectivity (Z), differential reflectivity (ZDR), and specific differential phase (KDP) from a PDWR;
ii) converting the polarimetric radar data into a three-dimensional (3D) grid having defined horizontal and vertical resolutions;
iii) calculating, for each of a plurality of altitude layers below a predetermined altitude, a Vertically Integrated Liquid (VIL) value at each grid point by vertically integrating liquid water content derived from radar reflectivity measurements;
iv) identifying, for each grid point, the altitude layer at which the maximum VIL value occurs;
v) generating, for each grid point, pseudo profiles of reflectivity (Z), differential reflectivity (ZDR), and specific differential phase (KDP) based on the radar data corresponding to the altitude layer with the maximum VIL value;
vi) applying a composite quantitative precipitation estimation (QPE) algorithm to the pseudo profiles to estimate the SRI and PAC, wherein the QPE algorithm selects among R(KDP), R(Z, ZDR), and R(Z) relations based on reflectivity thresholds;
vii) and outputting or displaying the estimated SRI and PAC as spatially resolved products.

32. The non-transitory computer-readable storage medium of claim 31, wherein the instructions further cause the processor to compare or validate the estimated SRI and PAC with in-situ observations obtained from disdrometers or rain gauges.

33. A computer program product comprising a non-transitory computer-readable medium having stored thereon instructions that, when executed by a processor, cause the processor to perform a method for estimating surface rainfall intensity (SRI) and precipitation accumulation (PAC) from polarimetric Doppler weather radar (PDWR) data, the method comprising:
i) receiving and processing polarimetric radar data comprising reflectivity (Z), differential reflectivity (ZDR), and specific differential phase (KDP) from a PDWR;
ii) converting the polarimetric radar data into a three-dimensional (3D) grid with defined horizontal and vertical resolutions;
iii) calculating, for each of a plurality of altitude layers below a predetermined altitude, a Vertically Integrated Liquid (VIL) value at each grid point by vertically integrating liquid water content derived from radar reflectivity measurements;
iv) identifying, for each grid point, the altitude layer at which the maximum VIL value occurs;
v) generating, for each grid point, pseudo profiles of reflectivity (Z), differential reflectivity (ZDR), and specific differential phase (KDP) based on the radar data corresponding to the altitude layer with the maximum VIL value;
vi) applying a composite quantitative precipitation estimation (QPE) algorithm to the pseudo profiles to estimate the SRI and PAC, wherein the QPE algorithm selects among R(KDP), R(Z, ZDR), and R(Z) relations based on reflectivity thresholds;
vii) and outputting or displaying the estimated SRI and PAC as spatially resolved products.

34. The computer program product of claim 35, wherein the instructions further cause the processor to compare or validate the estimated SRI and PAC with in-situ observations obtained from disdrometers or rain gauges.