Collaborative Station Learning for Rainfall Forecasting

Abstract

Cloudbursts and other extreme rainfall events are becoming more frequent and intense, making precise forecasts and disaster preparedness more challenging. Despite advances in meteorological monitoring, current models often lack the precision needed for hyperlocal extreme rainfall forecasts. This study addresses the research gap in spatial configuration-aware modeling by proposing a novel framework that combines geometry-based weather station selection with advanced deep learning architectures. The primary goal is to utilize real-time data from well-placed Automatic Weather Stations to enhance the precision and reliability of extreme rainfall predictions. Twelve unique datasets were generated using four different geometric topologies—linear, triangular, quadrilateral, and circular—centered around the target station Chinchwad in Pune, India, a site that has recorded diverse rainfall intensities, including a cloudburst event. Using common performance criteria, six deep learning models were trained and assessed across these topologies. The proposed Bi-GRU model under linear topology achieved the highest predictive accuracy (R² = 0.9548, RMSE = 2.2120), outperforming other configurations. These findings underscore the significance of geometric topology in rainfall prediction and provide practical guidance for refining AWS network design in data-sparse regions. In contrast, the Transformer model showed poor generalization with high MAPE values. These results highlight the critical role of spatial station configuration and model architecture in improving prediction accuracy. The proposed framework enables real-time, location-specific early warning systems capable of issuing alerts 2 h before extreme rainfall events. Timely and reliable predictions support disaster risk reduction, infrastructure resilience, and community preparedness, which are essential for safeguarding lives and property in vulnerable regions.

1. Introduction

Extreme rainfall events have become more frequent and severe in recent decades, posing risks to infrastructure, ecosystems, agriculture, and human lives worldwide. Particularly in regions with complex topography and high population density, these short-duration events can trigger flash floods, landslides, and other cascading hazards [1,2]. For disaster risk reduction and climate resilience planning, it is consequently essential to accurately and promptly predict such downpour events. However, severe rainfall continues to be one of the most difficult meteorological occurrences to accurately anticipate because of its confined and sudden nature. Due to resolution, parameterization, and computing cost constraints, traditional methods frequently fail to represent spatiotemporal variability towards extreme occurrences at smaller resolutions, despite their strength at large scales [3]. The phenomenon of cloudbursts (CB) and mini-cloudbursts (MCB) is one of the most harmful effects of such heavy rainfall. The India Meteorological Department (IMD) defines a cloudburst as an abrupt and severe weather phenomenon that is characterized by exceptionally high rainfall rates, frequently reaching 100 mm within an hour over a small geographical area (usually less than 30 km²). Similarly, recent climatological research has introduced the term ‘mini-cloudburst’ to describe similar but moderately less extreme events, characterized by 50 mm or more of rainfall over two consecutive hours. These occurrences are closely linked to cumulonimbus clouds, which develop in the presence of high levels of moisture, severe atmospheric instability, and substantial orographic lifting, particularly in mountainous areas [4,5,6,7]. In India, both the 2021 Nainital cloudburst in Uttarakhand and the 2013 Kedarnath tragedy are notable instances where the combination of high terrain, delicate soils, and insufficient drainage infrastructure exacerbated the damage [8,9].

Historically, two fundamental approaches have been employed: dynamical models, based on physical equations simulating atmospheric behavior, and empirical models, which derive relationships from historical data using regression and fuzzy logic [10,11]. Among empirical methods, ML algorithms like SVM, RF, and Bayesian Networks have been widely used for classification and regression tasks [12,13]. Traditional models often fail to capture complex spatiotemporal dependencies and the complexity of extreme weather events. To overcome these limitations, neural network-based models have emerged as promising alternatives [14]. Artificial Neural Networks (ANNs), including Backpropagation Neural Networks (BPNN) and Multilayer Perceptrons, have been used for monthly and regional rainfall forecasts. However, their inability to handle sequential dependencies limits their performance in time-series prediction [15,16]. In contrast, RNNs and variants such as LSTM and GRU excel at learning from time series weather data, which is more useful for predicting rainfall patterns over time [17]. Recent developments have also introduced the adoption of spatial data processing and Transformer models for capturing long-range dependencies in both time and space [18]. Recent studies have applied diverse machine-learning-based rainfall prediction using datasets with varying temporal resolution and geographic scope. For example, models such as Decision Tree, KNN, SVM, ANN, LSTM, and ensemble techniques have been employed on historical weather data, incorporating temperature, humidity, rainfall, and large-scale climatic indices. These studies span various regions, including Malaysia, Pakistan, China, Iran, and Spain, and report performance metrics such as R² from 0.532 to 0.8593, depending on models and dataset characteristics [19,20,21,22,23]. According to the literature surveyed in Atmosphere, previous rainfall prediction studies have reported accuracies of 88% [24], 85.71% [25], and 87.15% [26] across various regions. Despite significant progress in deep learning-based rainfall prediction, most existing studies treat meteorological stations as isolated feature vectors and focus primarily on refining temporal sequence modeling using RNNs, LSTMs, GRUs, and Transformers. While these approaches have improved short-term forecasting, they generally overlook the geometric spatial configuration of Automatic Weather Stations (AWSs), which strongly influences convective triggers, orographic lifting, and wind–moisture channeling factors critical to rainfall capture and prediction accuracy. The systematic role of geometry-based spatial arrangement thus remains underexplored, creating a critical research gap. Addressing this research gap, the present study reconceptualizes rainfall prediction as a spatial–temporal learning problem by explicitly integrating station topology into the modeling framework, with the aim of advancing extreme rainfall and cloudburst forecasting. The integration of spatial reasoning, such as geometry-based station selection, is expected to enhance model performance by optimizing input structure, especially relevant in data-rich environments with dense Automatic Weather Station (AWS) networks like India. This study proposes a novel geometry-based collaborative station learning framework for extreme rainfall prediction, systematically assessing how different spatial configurations influence forecasting accuracy through integration with deep learning models.

The main contributions of this study are as follows:

• A systematic analysis of four geometric station topologies: linear, triangular, quadrilateral, and circular, to evaluate their impact on prediction accuracy.
• Integration of these topologies with six state-of-the-art deep learning models (LSTM, Bi-LSTM, Stacked-LSTM, GRU, Bi-GRU, and Transformer) for comprehensive benchmarking.
• Demonstration that the linear topology with Bi-GRU configuration achieves the highest predictive performance (R² = 0.9548, RMSE = 2.2120), surpassing both prior studies and all other tested topologies.

Establishment of geometric topology as a critical yet previously overlooked determinant of rainfall forecasting skill, with direct implications for AWS network design, early warning systems, and disaster preparedness.

2. Study Area

For this study, Pune City in the Indian state of Maharashtra was selected as the rainfall study region. Pune is situated in western India on the Deccan Plateau, experiences hot summers, heavy monsoon rains, and mild winters. During the southwest monsoon season, Pune typically receives moderate to heavy rainfall; however, the distribution of rainfall across time and space can vary greatly. In the past decade, the frequency of extreme rain, including cloudbursts and mini-cloudbursts, has increased [13,23].

Pune city has a dense network that effectively records these events across all rainfall intensities, making the data suitable for ML-based studies on extreme rainfall. The city is a major hub for education, research, and information technology, and is considered one of the fastest-growing urban centers in India. Automatic Rain Gauge (ARG) Chinchwad station, chosen as the target for prediction, has documented rainfall across all intensity classes, including a significant cloudburst event, making it ideal for evaluating model performance. The locations of IMD-installed and maintained automatic weather stations in and around Pune are depicted in Figure 1, along with the city’s geographic position.

3. Data and Methods

3.1. Data Sources and Processing

In and around Pune, IMD has strategically installed 20 ARG and 13 AWSs; metadata are presented in

Table 1. Station Metadata for IMD AWS and ARG sites in Pune districts, Maharashtra, India.

Station Name	Latitude	Longitude	Elevation	Type
NIMGIRI	19.2092	73.8725	619.0	AWS
SHIVAJINAGAR1	18.5386	73.8420	559.0	AWS
LAVASA	18.4144	73.5069	687.3	AWS
DAPODI	18.6032	73.8541	563.2	AWS
HADAPSAR	18.4659	73.9244	618.7	AWS
DAUND	18.5056	74.3304	554.0	AWS
LONAVALA	18.7240	73.3697	620.8	AWS
HAVELI	18.4697	74.0013	563.0	AWS
NARAYANGOAN	19.1003	73.9655	694.5	AWS
BARAMATI	18.1530	74.5003	569.7	AWS
PASHAN1	18.5167	73.8500	577.0	AWS
RAJGURUNAGAR	18.8410	73.8840	598.1	AWS
TALEGAON	18.7220	73.6632	635.8	AWS
BALLALWADI	19.2396	73.9155	719.8	ARG
KOREGOANPARK	18.5400	73.8886	546.2	ARG
CHINCHWAD	18.6595	73.7987	588.3	ARG
GIRIVAN	18.5607	73.5211	750.0	ARG
BHOR	18.0728	73.6706	773.0	ARG
JUNNAR	19.2070	73.8679	619.0	ARG
KHADAKWADI	18.9052	74.0938	585.0	ARG
LAVALE	18.5363	73.7325	577.0	ARG
MAGARPATTA	18.5115	73.9285	618.7	ARG
AMBEGAON	19.1574	73.6811	778.7	ARG
PASHAN2	18.5383	73.8045	586.4	ARG
SHIVANE	18.4700	73.7800	586.4	ARG
INDAPUR	18.1748	74.6890	386.2	ARG
SHIRUR	18.8344	74.0536	667.3	ARG
DUDULGAON	18.6751	73.8772	574.7	ARG
SHIVAJINAGAR2	18.5286	73.8493	559.0	ARG
DHAMDHERE	18.6710	74.1480	562.4	ARG
KHED	18.9390	73.7744	742.7	ARG
WADGAONSHERI	18.5482	73.9278	618.7	ARG
WPURANDAR	18.1748	74.1498	585.0	ARG

. ARG stations measure temperature, humidity, and rainfall, while AWSs record temperature, humidity, wind speed, direction, pressure, and rainfall. Data from these sites from 2020 to 2024 were considered for this investigation. Four distinct topologies, linear, triangular, quadrilateral, and circular, were used to construct 12 datasets with a target station for rainfall prediction, with ARG Chinchwad as the target station, with a wide range of rainfall classes, including extreme rainfall events, recorded. A total of 175,392 records were collected at 15 min intervals. Outliers and missing values are present at certain stations; the percentage of missing data ranges from 6% to 36%. Short-term gaps were treated using mean substitution and forward/backfill methods, while long-term gaps were filled using data from the nearest neighboring stations. Data validation followed WMO QA/QC protocols (range, step, internal consistency, and persistence checks), and 80% of the preprocessed dataset was used for training, and 20% was used for testing [23,26,27,28,29,30].

The Automatic Weather Station (AWS) and Automatic Rain gauge (ARG) networks employed in this study were installed and are currently maintained by the India Meteorological Department (IMD) through its Surface Instruments Division (SID), Climate Research and Services, Pune. Both networks adhere to World Meteorological Organization (WMO) guidelines for calibration, exposure, and maintenance, and follow IMD’s standard operating procedure for weather forecasting and warning services to ensure high data quality. A standard AWS is equipped with Pt100 RTD air temperature sensors and capacitive relative humidity sensors at approximately 2 m, a tipping bucket rain gauge (TBRG) at 0.5 m above ground level, ultrasonic wind sensors at 10 m, and a barometric pressure sensor at around 2 m. ARG stations primarily consist of TBRGs and ATRH sensors. Data are recorded at 15 min intervals under routine operations. Routine calibration, quarterly field inspections, and real-time quality control checks (range, step, persistence, and spatial consistency checks) are applied to ensure data reliability. All station data (CSV format), archived at the National Data Center (NDC), IMD Pune, were used in this study. The computing facilities at COEP Technological University, Pune, were employed for Python (v3) and TensorFlow (v2) based deep learning model development on Intel Xeon CPU-based workstations [23,26,27,28,29,30].

3.2. The Proposed Conceptual Framework

As shown in Figure 2, the methodology used in this study adheres to a defined conceptual framework for machine learning based on the prediction of excessive rainfall. The first step in the approach is gathering quality long-term surface weather data from every AWS and ARG in the study area. Following that, the data goes through pre-processing and feature engineering, which includes feature selection, handling missing values and outliers, cleaning, scaling, and normalization. Subsequently, a geometric data selection strategy is applied, where data is integrated based on the geometrical configuration of station locations using patterns such as linear, triangular, quadrilateral, and circular arrangements. Based on station positions, 12 datasets were formed using the four geometry types described above, keeping ARG Chinchwad as the target station for rainfall prediction. After refining, the 12 datasets are fed into machine learning models. Finally, standard criteria are used to assess the models’ performance and determine the optimal geometrical configurations and model setup for accurate forecasting of excessive rainfall.

3.3. Experiments

Out of 33 stations, in and around Pune district, twelve datasets, comprising linear, triangular, quadrilateral, and circular topologies, were produced using various geometries based on station location alignments and arrangements. The target station, ARG Chinchwad, is at the center of these topologies, with the other stations acting as input stations. The entire spectrum of rainfall, from mild to heavy, is recorded in the ARG Chinchwad station, which also depicts the cloudburst event on 23 June 2024. Because cloudburst and mini-cloudburst events are usually brief and localized over small geographical ranges, all AWS/ARG stations taken into consideration are located within a 50 km radius only for this investigation.

Figure 3a presents linear geometrical topology consisting of heterogeneous AWS/ARG stations within a 5 km band, utilizing available stations positioned with an NNE-SSW orientation, and other stations’ location at approximately 22 km and 15 km from the central ARG Chinchwad station. ARG Chinchwad (590 m a.s.l.), where 590 m represents the station elevation above sea level. Similarly, the north direction and station elevations are indicated for all AWS/ARG topologies. Whereas Figure 3b presents the linear geometrical topology, which utilizes available stations positioned with an NNW-SSE orientation consisting of homogeneous AWSs, approximately opposite the previous one, and the ARG Chinchwad target station at one corner. These other stations are located at approximate distances of 15 km and 18 km from the target station.

Figure 3c presents a triangular geometrical topology, utilizing available stations positioned in a triangular orientation, with ARG Chinchwad as the target center station. Figure 3d presents another triangular geometrical topology, which utilizes available stations positioned with an orientation opposite that of the corner stations shown in Figure 3c.

Figure 3e presents quadrilateral geometry, utilizing available stations positioned in a quadrilateral orientation, with ARG Chinchwad as the target center station. Figure 3f presents another quadrilateral geometrical topology, which utilizes available stations positioned with an orientation opposite that of the corner stations shown in Figure 3e. Figure 3g–l present circular geometrical topologies with the combination of homogeneous and heterogeneous AWS/ARG networks, utilizing available stations positioned at various radii and orientations, with ARG Chinchwad as the target center station. Figure 3g covers stations within a radius of 15 km, showing only about 40% area coverage, with no stations in the remaining area. Figure 3h presents another circular topology with a heterogeneous network, offering full station coverage in all directions within a radius of 20 km. Figure 3i displays full area coverage with a heterogeneous network, extending to a radius of 35 km. Figure 3j shows a circular topology with a radius of 15 km, where only 25% of the area is covered by the network, and the rest has no stations. Figure 3k presents a circular topology that has a radius of 30 km, featuring a heterogeneous network combination covering 50% of the area. Figure 3l consists of stations within a 35 km radius, forming a heterogeneous combination network. More details on the screening and selection of stations are described in Section 3.5.

As shown in Figure 3, AWS/ARG station geometrical arrangements for 12 Datasets, showing Linear, Triangular, Quadrilateral, and Circular Geometry. A total of 12 datasets were methodically created by merging AWS and ARG stations based on different geometric topologies, to aid in the machine learning based prediction of extreme rainfall.

Table 2. Datasets Formed Based on Geometric Topologies of AWS and ARG Station Combinations for Extreme Rainfall Prediction.

DATASETS	GEOMETRY	AWS/ARG	STATION
1	LINEAR	ARG	CHINCHWAD
		ARG	LAVALE
		AWS	RAJGURUNAGAR
2	LINEAR	ARG	CHINCHWAD
		AWS	SHIVAJINAGAR1
		AWS	PASHAN1
3	TRIANGULAR	ARG	CHINCHWAD
		AWS	TALEGAN
		ARG	LAVALE
		ARG	DHAMDHERE
4	TRIANGULAR	ARG	CHINCHWAD
		AWS	SHIVAJINAGAR1
		AWS	TALEGAON
		AWS	RAJGURUNAGAR
5	QUADRILATERAL	ARG	CHINCHWAD
		ARG	LAVALE
		ARG	WADGAONSHERI
		AWS	TALEGAON
		AWS	RAJGURUNAGAR
6	QUADRILATERAL	ARG	CHINCHWAD
		AWS	TALEGAON
		ARG	GIRIVAN
		AWS	PASHAN1
		AWS	DHAMDHERE
7	CIRCULAR	ARG	CHINCHWAD
		ARG	TALEGAON
		ARG	LAVALE
		AWS	SHIVAJINAGAR1
8	CIRCULAR	ARG	CHINCHWAD
		AWS	TALEGAON
		ARG	LAVALE
		AWS	SHIVAJINAGAR1
		ARG	MAGARPATTA
		ARG	SHIVANE
		AWS	RAJGURUNAGAR
9	CIRCULAR	ARG	CHINCHWAD
		AWS	TALEGAON
		ARG	LAVALE
		AWS	SHIVAJINAGAR1
		ARG	MAGARPATTA
		ARG	SHIVANE
		AWS	RAJGURUNAGAR
		ARG	GIRIVAN
		ARG	DHAMDHERE
10	CIRCULAR	ARG	CHINCHWAD
		AWS	TALEGAON
		ARG	LAVALE
11	CIRCULAR	ARG	CHINCHWAD
		AWS	TALEGAON
		ARG	LAVALE
		ARG	GIRIVAN
		ARG	SHIVANE
		AWS	PASHAN1
		ARG	MAGARPATTA
12	CIRCULAR	ARG	CHINCHWAD
		AWS	TALEGAON
		ARG	LAVALE
		ARG	GIRIVAN
		ARG	SHIVANE
		ARG	MAGARPATTA
		AWS	RAJGURUNAGAR
		AWS	PASHAN1
		AWS	DHAMDHERE

provides specifics on each dataset’s topology and the AWS/ARG stations that were chosen for this study.

In configurations where Chinchwad was located outside the linear geometry and others, the surrounding stations were excluded if they were not aligned with the geometry, failed to meet the acceptable limits of linear topology, or risked introducing redundancy and noise. Stations beyond 50 km were also avoided, as such arrangements extend beyond the effective spatial scale of cloudbursts and thus fail to adequately capture their localized signatures. The IMD prediction manuals’ classification of rainfall categories based on 24 h’ rainfall amount, including hourly defined CB and MCB events, is shown in

Table 3. Categorization of 24 h rainfall accumulation, including hourly defined Cloudburst and Mini-Cloudburst events [3,4].

Sr. No.	Terminology	Rainfall Ranges in mm	Number of Events
1	Very Light Rainfall	Trace—2.4	256
2	Light Rainfall	2.5–15.5	166
3	Moderate Rainfall	15.6–64.4	147
4	Heavy Rainfall	64.5–115.5	11
5	Very Heavy Rainfall	115.6–204.4	6
6	Extremely Heavy Rainfall	≥204.5	1
7	Cloudburst (CB)	≥100 mm in one hour	1
8	Mini-Cloudburst (MCB)	≥50 mm in two consecutive hours.	7

. The table also provides a summary of the incidents that were recorded at the ARG Chinchwad station [3,4].

3.4. Cloudburst Event Recorded at ARG Chinchwad Station

The cloudburst event shown in Figure 4 was well captured at IMD-installed ARG Chinchwad station at Pune, Maharashtra, from 10:15 UTC to 11:15 UTC on 23 June 2024. The hourly rainfall increased dramatically in this one hour, driving the cumulative rainfall over 100 mm to the day’s total of 121 mm. The wet, cooling environment characteristic of such intense precipitation is highlighted by simultaneous temperature reductions and saturation-level increases in relative humidity. Modern machine-learning–based approaches can more easily identify this signature, which is notoriously hard for older deterministic models to capture. These sudden, tightly coupled movements across all four variables confirm a short-duration, high-impact cloudburst. These occurrences frequently destabilize cities, resulting in flooding, gridlock, and aircraft delays. Predicting these intense rainfall events in advance is crucial for preventing fatalities and minimizing property damage.

3.5. Geometric Station Screening and Topology Design

The design of station topologies is central to ensuring that rainfall prediction frameworks capture the localized nature of cloudbursts. To achieve this, a systematic screening and geometry-based selection process was adopted, integrating quality assurance checks, temporal completeness filters, and geometric alignment criteria. This framework ensures that only reliable and spatially representative stations contribute to rainfall prediction. The following section outlines the pipeline used to construct reproducible linear, triangular, quadrilateral, and circular topologies from AWS and ARG networks.

3.5.1. Selection of Geometrical Configurations

In this study, four geometries: linear, triangular, quadrilateral, and circular were adopted, as they were feasible with the actual AWS/ARG distribution, compatible with existing networks, and deployable even in hilly terrain. These geometries provide a practical balance between minimal and robust configurations that are easily planned and implemented. More complex topologies, such as hexagonal, star, grid, or hybrid, were not considered, since they require evenly spaced or uniformly distributed stations. Nevertheless, the proposed framework remains extendable to such geometries in future applications where station density permits.

3.5.2. Station Screening Criteria for Cloudburst-Scale Analysis

Cloudburst and mini-cloudburst events occur over very short durations (≤1–2 h) and small spatial footprints (20–30 km²), making spatiotemporal resolution a critical factor in station selection. To capture these localized extremes, only AWS and ARG stations with 15 min temporal resolution and located within 50 km of the target site were retained. This ensured that the constructed geometrical configurations were both spatially representative of the typical cloudburst footprint and temporally capable of recording rapid rainfall intensities.

3.5.3. Screening of AWS/ARG Based on Sensor Type

AWS and ARG were both included in this study, and stations were screened based on sensor type. Rainfall measurement with a tipping-bucket rain gauge was set as the common and essential requirement for inclusion, as it is available in both AWS and ARG stations. Preference was given to stations equipped with validated tipping-bucket sensors and simultaneous relative humidity (RH) and atmospheric temperature (AT) sensors. In addition, only stations that recorded at least three overlapping meteorological parameters were considered. This criterion ensures comparability between AWS and ARG stations, with rainfall as the common sensor, while additional temperature and humidity measurements further enhance the robustness of the dataset. Cloudburst and mini-cloudburst events demand high temporal resolution. Therefore, only AWS and ARG stations with 15 min rainfall data were included, ensuring accurate event timing and validation. The IMD-installed stations were arranged into linear, triangular, quadrilateral and circular topologies, based on their availability and spatial suitability for this study.

3.5.4. Data-Quality (QA/QC) Filters

To ensure reliability and precision of geometrical input data, rigorous Quality Assurance and Quality Control procedures were applied before model training. Data from each ARG and AWSs underwent automated validation based on WMO and IMD guidelines. Basic QC was implemented at the data logger level at remote sites, while advanced QA/QC was performed at the IMD server level to flag and validate data. The QA/QC workflow included range checks, temporal consistency checks, step-change detection, persistence tests, and spatial consistency assessments. Range checks verified that each variable (rainfall, temperature, relative humidity, wind speed, and surface pressure) remained within climatologically realistic bounds (e.g., temperature −40 °C to 60 °C; RH 0–100%; SLP 600–1100 hPa). Consistency checks ensured inter-parameter coherence—such as verifying dew point ≤ air temperature and rainfall events coinciding with temperature decreases and humidity increases, while step and spike tests detected abrupt, non-physical variations using dynamic thresholds (|Vi − Vi − 1| + |Vi − Vi + 1| ≤ 4σ). Where Vi − 1, Vi, and Vi + 1 represent the previous, current, and next observations, and σ denotes the standard deviation of the variable over a rolling window [30]. Persistence checks flagged unrealistically static readings across 60 min windows, and spatial checks compared neighboring stations to detect outliers and transmission errors.

Quality assurance procedures included pre- and post-monsoon preventive maintenance, calibration with traveling standards, and periodic field validation to minimize sensor drift. Only stations with at least 70% temporal completeness and ≥90% overlapping with the target station record were retained. Redundant or low-quality stations were excluded to avoid multicollinearity and ensure robustness of the predictive framework.

3.5.5. Topology Design for Cloudburst-Scale Prediction

To enhance prediction accuracy, four geometrical configurations were designed from 33 AWS/ARG stations in the study domain. This approach introduces novelty by linking network geometry with machine learning performance, offering insights into optimal designs for complex terrains. The station selection criteria applied for these configurations are described as follows.

(i)

Linear topology: Two configurations were developed (Figure 3a,b) with reversed orientations, but both aligned with the target station (ARG Chinchwad). In Figure 3a, the target lies at the center, with partner stations aligned NNE–SSW within a ±2.5 km band. In Figure 3b, the target is placed at the edge, resulting in distinct partner combinations. Stations beyond a 5 km lateral offset were excluded, as they introduced zigzag rather than linear alignments. Partner stations were required to lie within 3–50 km of the target. Minimum station count: ≥2 partners (3 including target). Linear layouts are well suited for tracking rainfall along orographic channels, valleys, ridges, transport corridors, and river basins where precipitation propagates linearly.

(ii)

Triangular topology: Stations were arranged at azimuth separations of ~120° ± 15°. Two designs (Figure 3c,d) with reversed orientations tested variable lengths of 20 km and 35 km. This ensured balanced sampling of inflow variability and convective initiation. Minimum station count: ≥3 partners (4 including target). Triangular configurations are particularly suited for capturing directional inflows from three azimuthal sectors, such as hillslopes and ridge environments.

(iii)

Quadrilateral topology: Four stations were positioned at ~90° ± 15° azimuth separations (Figure 3e,f), with reversed orientations tested. This design is effective for resolving rainfall fields across mesoscale domains. Minimum station count: ≥4 partners (5 including target). Quadrilateral arrangements are therefore suited for systems with moderate spatial extent, requiring balanced four-way sampling.

(iv)

Circular topology: Circular layouts ensure full 360° sampling of radial precipitation gradients. Six designs were tested (Figure 3g–l), with radii distributed between 15–35 km from the target. Minimum station count: ≥4 partners (5 including target). Circular topologies help capture convergent and centripetal rainfall patterns. Base stations were selected within 15, 20, 30, and 35 km radii around the target ARG Chinchwad. Additionally, extended layouts (Figure 3g–l) were tested with broader coverage (~20%, 30%, 45%, 75%, and up to 100% of the network area). Circular topology is the only configuration that provides flexibility to accommodate the maximum number of stations within the defined radius from the central target station. With this intention, six cases with variations in the number of stations, including the central target station (3, 4, 7, 7, 9, and 9), were considered to examine whether incorporating more spatial information could enhance the model’s ability to learn rainfall trends and patterns. This approach enabled us to investigate how various spatial arrangements affect the model’s performance and its ability to capture underlying rainfall patterns accurately.

Certain stations were excluded from topology construction if they exceeded the effective CB/MCB spatial boundary, exhibited frequent data gaps, contained poor-quality or noisy records, did not align with defined topology boundaries, or introduced redundancy and multicollinearity.

3.6. Algorithm Selection

To assess the interaction between model and spatial station topology, we benchmark six representative sequence-modeling architectures: LSTM, Stacked-LSTM, Bi-LSTM, GRU, Bi-GRU, and Transformer. These models were selected to represent standard temporal sequence learners (LSTM, GRU), directional-context enhancement (bidirectional variants), depth-based temporal hierarchies (stacked LSTM), and attention-based long-range dependency modeling (Transformer). Brief justifications are provided in-line below, while full mathematical definitions, layer diagrams, and derivations are presented in Appendix A to conserve space and maintain focus on the geometry-based methodology.

• LSTM—standard memory-cell architecture to capture long short-term dependencies; widely used for meteorological time series [25].
• Stacked-LSTM—deeper LSTM layers to capture hierarchical temporal scales [25].
• Bi-LSTM—processes the sequence forward and backward to exploit context from both directions [25].
• GRU—a simplified recurrent cell with fewer parameters, offering computational efficiency [18].
• Bi-GRU—bidirectional GRU, combining speed with contextual richness (empirically best performer in our experiments) [18].
• Transformer—self-attention architecture for long-range interactions and non-sequential dependency modeling [19].

All models were trained using the hyperparameters and architectures summarized in

Table 4. Deep Learning Models, Architectures, and Hyperparameters for Rainfall Prediction.

Model	Layers and Units	Activation Function
LSTM	LSTM (64, 32)	(tanh/relu)
STACKED-LSTM	LSTM (128, 64, 32)	relu
Bi-LSTM	Bi-LSTM (64, 32)	relu
GRU	GRU (64, 64, 32)	relu
Bi-GRU	Bi-GRU (64, 64, 32)	relu
TRANSFORMER	MultiHeadAttention (4 heads), FFN (128)	relu (FFN), linear (output)

.

3.6.1. Model Evaluation and Evaluation Metrics

The study uses performance evaluation metrics to determine how accurate the models’ predictions are. Metrics such as $R^2$, MSE, RMSE, MAE, and MAPE are used to quantify and analyze the forecasting model’s performance [5,6,31,32,33].

$$\mathit{RMSE}=\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{(y_i-\widehat{y_i})}^2}$$

(1)

$$\mathit{MAE}={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n|y_i-\widehat{y_i}|$$

(2)

$$\mathit{MSE}={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{(y_i-\widehat{y_i})}^2$$

(3)

$$\mathit{MAPE}={\displaystyle \frac{100}{n}}{\sum }_{i=1}^n\left|{\displaystyle \frac{(y_i-\widehat{y_i})}{y_i}}\right|$$

(4)

$$R^2=1-{\displaystyle \frac{\sum _{i=1}^n{(y_i-\widehat{y_i})}^2}{\sum _{i=1}^n{(y_i-\overline{y})}^2}}$$

(5)

where $\widehat{y}$—predicted value of y, $\overline{y}$—mean value of y, and $n$—number of data points.

To quantitatively assess the prediction performance of the model, this study employs RMSE, MAE, MSE, MAPE, and R² as the primary evaluation metrics. Each of these metrics provides unique insights into model accuracy and reliability. Equation (2), MAE intuitively reflects the average magnitude of errors in predictions by calculating the arithmetic means of the absolute differences between predicted and actual values [13]. It is less influenced by outliers and maintains the same unit as the original data, making it easily interpretable. In Equation (3), MSE emphasizes larger errors by squaring the deviations. This amplifies the impact of large prediction errors and effectively captures the dispersion of the prediction results. Together, MAE and MSE form a complementary evaluation system, MAE focusing on robust estimation of overall deviation, and MSE on sensitivity to extreme errors, offering a multidimensional quantitative basis for model optimization. Equation (1) for RMSE, derived from MSE, is analogous to the standard deviation but applied to residuals, measuring the average magnitude of prediction errors relative to actual values. It is more sensitive to outliers than MAE and is expressed in the same unit as the predicted variable, helping in direct comparison. Whereas Equation (4), MAPE expresses the prediction error as a percentage, which makes it useful for understanding relative performance [33]. However, MAPE can be disproportionately high when actual values are very small, making it sensitive in such cases. Equation (5), R² indicates how well the predicted values explain the variability of the actual values. A higher R² value implies better model fit. Although a higher R² and lower RMSE, MAE, and MSE generally indicate better model performance, experiments in this study showed that MAPE may still be high due to its sensitivity to low actual values of the target variable. Therefore, in selecting the best-performing model, this study prioritizes those with the highest R² and lowest RMSE, MAE, and MSE, acknowledging that MAPE must be interpreted cautiously, especially when actual values approach zero.

3.6.2. Model Configuration and Training Setup

After extensive iteration and experimentation, the following combinations of models demonstrated superior performance. The following common hyperparameters were used to train all models: MSE as the loss function, Adam-Optimizer, 64 batch size, Learning Rate of 0.001, and 100 Epochs. Model architecture and hyperparameters utilized for rainfall prediction are compiled in Table 4. In the LSTM model, “tanh/relu” denotes tanh for the internal cell state and ReLU for the output layer. Other models primarily use ReLU for hidden layers and a linear activation at the output.

Detailed model definitions are provided in Appendix A. Detailed descriptions of the deep learning models and architectures, along with model equations, training logs, and loss curves, are presented in Figure A8, while curves comparing actual and predicted rainfall are presented in Figure A9.

4. Results and Discussion

This section presents the experimental outcomes of the proposed framework. The discussion is organized into three parts: (i) the performance of deep learning (DL) models across various geometrical topologies, (ii) a comparative assessment with results reported in the literature, and (iii) an analysis of the dependence of prediction accuracy on lead time, highlighting the model’s capability for Early Warning.

4.1. Performance Evaluation of the DL Models

The results highlight two key findings: (i) geometric topology plays a decisive role in rainfall prediction accuracy, and (ii) the Bi-GRU model with linear topology offers the most robust and operationally valuable solution. As summarized in

Table 5. Best-performing model for each topology.

Topology	Best Model	R2	RMSE
Linear	Bi-GRU	0.9548	2.2120
Triangular	Bi-GRU	0.9445	2.4719
Quadrilateral	Bi-GRU	0.9409	2.5305
Circular	Bi-LSTM	0.9497	2.3337

and illustrated in Figure 5, this configuration consistently outperformed all other model–topology combinations, achieving the highest R² (0.9548) and lowest RMSE (2.2120). Notably, it not only surpasses benchmarks reported in the literature but also provides reliable early warnings of cloudburst and mini-cloudburst events up to two hours in advance, highlighting its practical utility for disaster preparedness. For clarity and focus, Table 5 summarizes only the best-performing model under each topology, while Figure 5 provides a concise performance comparison (R² and RMSE) across all deep learning architectures and geometrical configurations. Complete result tables and detailed model statistics are available in Appendix B and Appendix C.

Table A2. Performance Summary of Deep Learning Models across Topologies and Datasets.

S. No.	Geometry	Model	RMSE	MAE	MSE	MAPE%	R2
1	Linear	LSTM	2.3624	0.3503	5.5808	14.27	0.9485
		STACKED-LSTM	2.4852	0.3995	6.1761	25.98	0.9430
		Bi-LSTM	2.3045	0.3324	5.3108	17.94	0.9510
		GRU	2.2762	0.3135	5.1812	24.60	0.9522
		Bi-GRU	2.2120	0.3300	4.8932	33.38	0.9548
		TRANSFORMER	2.5322	0.7164	6.4121	44.28	0.9408
2	Linear	LSTM	2.5401	0.4758	6.4520	23.82	0.9404
		STACKED-LSTM	2.6564	0.4632	7.0565	52.02	0.9349
		Bi-LSTM	2.4649	0.6026	6.0759	27.88	0.9439
		GRU	2.4635	0.5016	6.0688	29.24	0.9440
		Bi-GRU	2.4103	0.3403	5.8096	27.26	0.9464
		TRANSFORMER	2.9407	0.7782	8.6478	33.20	0.9202
3	Triangular	LSTM	2.8059	0.5586	7.8729	25.30	0.9273
		STACKED-LSTM	2.8131	0.4926	7.9133	40.85	0.9269
		Bi-LSTM	2.7727	0.5528	7.6881	35.67	0.9290
		GRU	2.5708	0.4644	6.6088	42.26	0.9390
		Bi-GRU	2.5666	0.4195	6.5876	31.83	0.9392
		TRANSFORMER	3.6062	0.8816	13.005	58.80	0.8799
4	Triangular	LSTM	2.4805	0.4067	6.1527	18.54	0.9441
		STACKED-LSTM	2.5922	0.3643	6.7195	35.78	0.9390
		Bi-LSTM	2.5579	0.3748	6.5426	29.38	0.9406
		GRU	2.4957	0.5252	6.2285	29.73	0.9434
		Bi-GRU	2.4719	0.4344	6.1102	37.11	0.9445
		TRANSFORMER	2.4522	0.5343	6.0131	42.10	0.9454
5	Quadrilateral	LSTM	2.5216	0.4382	6.3587	19.19	0.9413
		STACKED-LSTM	2.5895	0.4065	6.7053	25.91	0.9381
		Bi-LSTM	2.5614	0.4193	6.5606	24.07	0.9394
		GRU	2.4889	0.5227	6.1945	30.43	0.9428
		Bi-GRU	2.5367	0.4201	6.4346	32.78	0.9406
		TRANSFORMER	2.4884	0.5884	6.1919	34.37	0.9428
6	Quadrilateral	LSTM	3.3339	0.4991	11.115	19.69	0.8974
		STACKED-LSTM	3.0963	0.4267	9.5868	33.52	0.9115
		Bi-LSTM	3.1238	0.5341	9.7583	33.46	0.9099
		GRU	2.6731	0.4620	7.1453	41.67	0.9340
		Bi-GRU	2.5305	0.5479	6.4034	24.44	0.9409
		TRANSFORMER	2.8931	0.8883	8.3702	88.55	0.9227
7	Circular	LSTM	2.4360	0.5438	5.9339	22.08	0.9452
		STACKED-LSTM	3.1797	0.4989	10.110	34.16	0.9067
		Bi-LSTM	2.3337	0.4390	5.4463	30.28	0.9497
		GRU	2.6579	0.4835	7.0642	50.14	0.9348
		Bi-GRU	2.3738	0.3412	5.6349	28.62	0.9480
		TRANSFORMER	3.9518	0.7899	15.617	29.39	0.8558
8	Circular	LSTM	2.7107	0.4333	7.3482	17.37	0.9322
		STACKED-LSTM	3.2281	0.5484	10.420	34.69	0.9038
		Bi-LSTM	2.6706	0.5816	7.1321	32.74	0.9342
		GRU	2.6742	0.4857	7.1513	32.24	0.9340
		Bi-GRU	2.7343	0.5497	7.4764	34.98	0.9310
		TRANSFORMER	2.7447	0.4518	7.5335	28.06	0.9305
9	Circular	LSTM	2.7794	0.4562	7.7253	23.63	0.9287
		STACKED-LSTM	3.1237	0.6906	9.7573	57.03	0.9099
		Bi-LSTM	3.3988	0.6445	11.551	25.84	0.8934
		GRU	2.9888	0.6755	8.9331	34.47	0.9175
		Bi-GRU	2.7356	0.5185	7.4836	35.33	0.9309
		TRANSFORMER	2.4166	0.5821	5.8401	35.34	0.9461
10	Circular	LSTM	2.4798	0.5006	6.1492	23.28	0.9432
		STACKED-LSTM	2.5361	0.3883	6.4318	45.34	0.9406
		Bi-LSTM	2.3905	0.3566	5.7143	29.99	0.9472
		GRU	2.5084	0.4362	6.2923	27.75	0.9419
		Bi-GRU	2.4359	0.3423	5.9334	42.73	0.9452
		TRANSFORMER	2.4932	0.5385	6.2161	24.70	0.9426
11	Circular	LSTM	2.9640	0.5287	8.7854	29.94	0.9189
		STACKED-LSTM	2.9042	0.3911	8.4343	26.45	0.9221
		Bi-LSTM	2.6139	0.3651	6.8325	26.44	0.9369
		GRU	2.5842	0.4671	6.6783	52.13	0.9383
		Bi-GRU	2.6316	0.3934	6.9252	30.54	0.9361
		TRANSFORMER	2.6790	0.4525	7.1772	30.92	0.9337
12	Circular	LSTM	2.9764	0.6382	8.8592	39.91	0.9182
		STACKED-LSTM	3.9451	0.6159	15.563	35.68	0.8563
		Bi-LSTM	3.0196	0.4275	9.1182	26.74	0.9158
		GRU	3.0586	0.5747	9.3549	47.31	0.9136
		Bi-GRU	3.1390	0.6020	9.8534	34.96	0.9090
		TRANSFORMER	2.9312	0.5595	8.5919	53.18	0.9207

presents a detailed performance summary of six deep learning models across twelve topologies and datasets.

While the linear topology consistently delivered superior predictive accuracy, performance varied across other geometrical configurations. Circular arrangements showed inconsistent results despite involving a greater number of stations. This suggests that simply increasing network density does not guarantee improved model accuracy. Instead, excessive spatial redundancy and heterogeneous data inputs may introduce noise, diminishing the predictive skill of deep learning models. By contrast, triangular and quadrilateral configurations yielded moderate performance (average R² ≈ 0.94), reflecting a balance between spatial diversity and information redundancy. These findings reinforce that strategic alignment of observation points rather than uniform or arbitrary densifications crucial for optimizing predictive performance in data-driven rainfall forecasting frameworks.

Overall, the analysis demonstrates that Bi-GRU consistently achieved the best performance, confirming that station topology is as important as model architecture for extreme rainfall prediction.

4.2. Comparison with Literature Results

The performance of the proposed models was benchmarked against results reported in earlier studies to contextualize their effectiveness. As illustrated in Figure 6, the Bi-GRU with linear topology consistently outperforms previous published approaches, thereby confirming its superiority in predictive accuracy.

4.3. Dependence on Lead Time

This section emphasizes the powerful capability of the proposed model for Early Warning. As the operational relevance of rainfall prediction critically depends on the forecast horizon, the influence of varying lead times on model accuracy was assessed. Figure 7, Figure 8 and Figure 9 present the validation results, indicating that the Bi-GRU model with linear topology achieved the best performance, providing reliable early prediction of extreme cloudburst rainfall events with a lead time of up to two hours. As lead times increase from 15 min (T + 1) to 120 min (T + 8) with T = 0 at 11:15 UTC, the rainfall prediction validation accuracy (R² Score) is depicted in Figure 7. The accuracy steadily declines as the forecast horizon lengthens, reaching 0.7048 at 120 min, but peaks at shorter lead times, with an R² of 0.9624 at 15 min. When compared to lengthier lead times, the model performs better for short-term predictions, as evidenced by the downward trend.

Actual cumulative rainfall over various lead times (T + 1 to T + 8) is contrasted with model forecast validation in Figure 8, at shorter lead times, predictions closely match observed rainfall, with strong agreement between T + 1 and T + 2 (R² > 0.93). But variations get bigger as the predicted horizon lengthens, with rainfall totals being overestimated or underestimated, especially beyond T + 5. This suggests that predictions with longer lead times are less reliable.

A comparison of actual and expected rainfall values at 15 min intervals for various lead durations (T + 1 to T + 8) is shown in Figure 9. The model has great validation accuracy at shorter lead times, where predicted rainfall closely resembles observed values, as illustrated in Figure 7 and Figure 8. However, disparities become more noticeable as lead times increase, and there is a propensity to overestimate the severity of rainfall. The steady decrease in forecast accuracy over longer time horizons is shown in all three Figure 7, Figure 8 and Figure 9.

Quantitatively, the linear Bi-GRU model consistently outperformed the other (Table A2, Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9), indicating that high accuracy was obtained even with a limited number of strategically positioned stations, whereas circular topologies, despite having more nodes, performed worse, likely due to redundancy and noise. The model reliably forecasted extreme rainfall events up to two hours in advance, providing critical lead time for early warning. This improved performance of the Bi-GRU model with linear topology, supported by geographically and meteorologically, the linearly aligned stations around Chinchwad, Pune, Maharashtra. The region is on the western Deccan Plateau at ~590 m elevation, featuring a relatively flat urban landscape on Deccan trap basalt with minor undulations. The Pavana River basin creates linear topographic features that influence near-surface wind patterns. The Arabian Sea’s moisture-laden winds, which are channeled by the local terrain and affect rainfall distribution and wind flow alignment, boost cloud formation and excessive rainfall during the active southwest monsoon (June–September) by orographically lifting over the Sahyadri Mountains [4,13].

Furthermore, these findings provide actionable guidance for observation network construction in resource-limited regions. Instead of pursuing uniform spatial coverage, results suggest prioritizing linear densification along dominant moisture transport or topographic corridors, which enhances predictive performance while optimizing cost. High-quality, well-calibrated stations spaced at 15–25 km intervals along key advection pathways are more valuable than dense, redundant networks. Ensuring regular maintenance and sensor calibration before and after monsoon seasons is also crucial, as forecast accuracy depends strongly on AWS data quality.

Nevertheless, this study acknowledges certain limitations. The analysis is geographically focused on a single region (Pune) and based on a moderate temporal dataset (2020–2024) with a limited number of extreme-event samples, which may constrain model generalization across diverse climatic regimes and terrains. Model performance may also vary with changes in network density, data quality, or prevailing synoptic conditions. Future research should therefore validate the proposed framework across different topographic and climatic settings, incorporate additional hydro-meteorological predictors such as soil moisture and convective indices, explore graph-based architectures with explicit spatial encoding, and conduct cost–benefit assessments to optimize operational deployment and resource allocation.

Additionally, this study is constrained by the dependence of forecasting accuracy on the quality of AWS data. Forecasting extreme weather events remains challenging due to their inherent rarity. A major limitation is the scarcity of training data, as extreme rainfall events such as cloudbursts and mini-cloudbursts are infrequent. Consequently, most predictive models tend to either underestimate or overestimate these events. Despite these challenges, the present study demonstrates the applicability of advanced deep learning algorithms, which show potential to improve the reliability of extreme rainfall predictions.

5. Conclusions and Future Work

One of the most important problems in the environmental sector is rainfall estimation, and this method attempted to predict rainfall using a geometry-based approach. The key findings of this study are as follows:

• This study evaluated the performance of six machine learning models for extreme rainfall prediction using different Automatic Weather Station network topologies. The proposed linear geometry-based approach using the Bi-GRU model emerged as the most consistently accurate model, achieving a greater value of training R² of 0.9548, validation R² of 0.9426, and a small RMSE of 2.2120. Comparison shows significant improvements over earlier studies. These enhanced prediction skills can help disaster managers in making timely and informed decisions by providing more accurate forecasting of extreme rainfall events with two hours of lead time.
• The Bi-GRU model with a linear topology achieved the highest predictive performance, surpassing triangular, quadrilateral, and circular station layouts. This result indicates that strategically aligned but fewer stations can outperform larger yet suboptimal placed networks, even at the (15–25 km) spacing required to capture cloudburst signatures. The linear configuration, particularly along the Pavana River basin, effectively represented orographic lifting and wind-channeling effects of the western Deccan Plateau, thereby enhancing precipitation forecasting accuracy.
• Though state-of-the-art in time series modeling, the Transformer model showed inconsistent performance in localized rainfall prediction, with high R² but elevated MAPE, likely due to redundancy or noise from dense station networks with much additional information. Further investigations are needed to unlock the full capability that requires tailored adaptation to meteorological datasets and data quality and redundancy handling.

Future research is required to evaluate model performance and geometric responses using datasets from river basins, coastal stations, and hilly terrains, enabling more generalized modeling and comparative analysis. There is also scope for extending this work by integrating high-resolution quality Automatic Weather Station (AWS) data with weather radar and satellite imagery, in conjunction with topographical studies, to enhance the accuracy of short-term extreme rainfall forecasts and early warning.