Graph Learning-based Regional Heavy Rainfall Prediction Using Low-Cost Rain Gauges

Edwin Salcedo

REVIEW 5 major objections 6 minor 24 references

Graph Learning-based Regional Heavy Rainfall Prediction Using Low-Cost Rain Gauges

T0 review · 5 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper argues that a graph neural network over 41 distance-linked rain-gauge stations can predict daily rainfall and flag heavy events, making low-cost flood warning feasible where radar is scarce.

desk verdict The paper's central effectiveness claim collapses on its own Table I: Pearson r values above 1 are impossible, so the evaluation pipeline is broken, despite a plausible low-cost IoT hardware story. read the letter →

arxiv 2412.16842 v1 pith:4DI2456A submitted 2024-12-22 cs.LG cs.AIcs.NE

Edwin Salcedo This is my paper · ORCID

classification cs.LGcs.AIcs.NE MSC 68T0786A10

keywords heavyrainfallpredictiongraphneuralnetworksIoTraingaugestippingbucketgaugelow-costweatherstationsspatialdependenciesfloodearlywarningBolivia

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper proposes a complete low-cost rainfall monitoring and prediction chain: 3D-printed tipping-bucket rain gauges with GSM/SMS reporting, a central web platform, and a graph neural network (GNN) that treats weather stations as nodes connected by inverse distance. The GNN is trained on 72 months of daily precipitation from 41 Bolivian stations to predict rainfall amounts at each station and flag events of 8 mm/day or more. The authors report that the best four-layer graph convolution model reaches an MSE of 16.344 and an MAE of 9.512 on held-out data, and they argue this makes GNN-based prediction feasible where radar or dense station coverage is unavailable. If reliable, the system would give rural flood-prone regions a low-cost way to issue early warnings and plan water resources.

What carries the argument

The load-bearing object is the station graph: nodes are weather stations, node features are each station's meteorological history (mainly past rainfall), and edge weights are the inverse geographic distances between stations. On top of this graph the model stacks four graph convolution layers (GCLs) of the form $H^{l+1} = \sigma(D^{-1/2} A D^{-1/2} H^l W^l)$, followed by a fully connected regression layer, trained with Adam at learning rate 0.01 and early stopping; the 8 mm/day threshold converts the regression output into a heavy-rainfall flag.

What would settle it

Recompute the Pearson correlation between the held-out predictions and observed values: the reported r of 5.891 is mathematically impossible because r must lie within [-1, 1], so a corrected calculation would immediately show whether the headline accuracy claim survives. Separately, train the identical four-layer GNN with the adjacency matrix replaced by the identity matrix (each station isolated) and by an elevation-difference-weighted graph; if the inverse-distance graph does not beat both on days with 8 mm or more, then the spatial-dependence mechanism the paper relies on is not the source of its results.

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Extended reading notes

Core claim

The paper's central claim is that a static graph neural network whose adjacency matrix is the inverse distance between 41 rain-gauge stations can learn enough spatial structure from daily rainfall histories to forecast heavy rainfall regionally. The model applies four graph convolution layers with ReLU activations to the normalized adjacency matrix, then a fully connected regression layer that outputs a rainfall amount per station; any prediction above 8 mm counts as a heavy rainfall event. On a 70/20/10 temporal split of 72 months of daily data from the national hydrology service, the authors report model A as best, with MSE 16.344, MAE 9.512, and a Pearson r of 5.891 on the testing set. In the paper's telling, this demonstrates that low-cost gauge networks plus graph learning can substitute for expensive infrastructure in data-sparse regions.

Load-bearing premise

The whole method depends on the idea that rainfall at one station is best explained by rainfall at geographically nearby stations, so a graph whose links are just geographic distances carries the information needed to predict heavy rain; if in Bolivia's mountains rainfall is controlled more by elevation and local terrain than by distance, the graph gives the model the wrong inductive bias and the reported prediction ability would not transfer.

Editorial extensions

If this is right

If the reported accuracy holds, 41 low-cost stations connected by GSM could support daily heavy-rainfall alerts across Bolivia without radar.
SMS-based data transfer means the same prediction pipeline can run in other regions where 3G/4G coverage and internet are unavailable.
Because the GNN outputs a rainfall amount per node, the method can flag stations expected to exceed 8 mm/day, giving authorities a concrete trigger for warnings.
The end-device design (tipping bucket plus solar power) keeps per-unit cost around $280–$320, making dense deployment financially conceivable.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The inverse-distance graph is a strong prior: it assumes geographic closeness controls rainfall dependence. In mountainous Bolivia, elevation and slope are likely at least as influential, so adding altitude as a node feature or edge weight is a natural extension the paper does not test.
The reported Pearson coefficient r = 5.891 lies outside the possible range [-1, 1], which suggests either a misreported formula or a typographical error; correcting this and re-evaluating the model is the first check any adopter should make.
No comparison is made to a station's own historical climatology or to a non-spatial baseline, so the paper's claim that the graph structure itself helps remains unquantified; a persistence baseline would isolate the GNN's contribution.
If heavy-rain events are rare, MSE and MAE can be dominated by many dry days; reporting event-level precision/recall or hits for the 8 mm threshold would make the practical alerting value much clearer.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Edwin Salcedo's paper pairs a low-cost tipping-bucket rain gauge network with a graph convolutional network for daily rainfall prediction across 41 Bolivian stations. The hardware section is the most honest part: the device design is described in detail, costs are stated, and the GSM/SMS data path is sensible for rural areas. That part is credible engineering. The GNN application is also straightforwardly presented, and the paper cites the relevant GNN rainfall literature (refs 20-23).

The problem is the evaluation table. Table I reports Pearson r values of 5.891, 6.002, 7.204, and 8.771. The coefficient defined in Eq. 4 is bounded between -1 and 1 for any real vectors. These numbers are impossible. The pattern – r getting larger as MSE gets worse – suggests the r column was computed by something other than the stated formula, maybe on different quantities or after some transformation. Either way, the central claim that the method 'effectively' predicts heavy rainfall rests on this table, and the table is internally inconsistent with the paper's own math.

There are additional problems, but they're secondary. No baseline comparison, no error bars, no guarantee that the 70/20/10 split is chronological (for daily rainfall, random splitting leaks information between training and test days). The model is a static four-layer GCN with no temporal recurrence and no exogenous variables, which is a weak inductive bias for an 8 mm/day event detection problem. And the MAE of 9.5 mm exceeds the 8 mm heavy-rain threshold, so even under the reported metrics, the model would struggle to flag the events it's designed to warn about.

What's genuinely useful here is the hardware and the dataset description: a low-cost, solar-powered gauge with SMS backhaul, plus the scraped SENAMHI data from 41 stations over 72 months. That could be a contribution, but it's not evaluated as a system (the experiments use scraped data, not the proposed gauges).

I would not send this to peer review as is. The impossible r values are a fatal, load-bearing flaw that no referee report can repair; the author needs to redo the evaluation. If a corrected version appears with baselines, a chronological split, and honest metrics, it's worth a second look. For now, it's a desk reject.

Referee Report

5 major / 6 minor

Summary. The paper presents a low-cost IoT rainfall monitoring system with 3D-printed tipping-bucket rain gauges, GSM/SMS data transmission, and a MEAN-stack web application, together with a graph neural network (GNN) for regional heavy rainfall prediction. The GNN models 41 Bolivian weather stations as nodes with inverse-distance-weighted edges and uses four graph convolution layers followed by a regression head to predict daily rainfall; a prediction above 8 mm is flagged as a heavy rainfall event. The authors report results on a daily precipitation dataset and claim that the proposed method is effective based on MSE, MAE, and Pearson correlation on a held-out test set.

Significance. The hardware contribution is concrete and potentially useful: the paper describes a complete low-cost sensing and communication pipeline for rural environmental monitoring, and the evaluation uses real multi-year data from 41 stations rather than a synthetic benchmark. If the prediction claims were valid, the approach could be attractive for flood early warning in data-sparse regions. However, the central empirical claim is not supported as reported: the headline correlation coefficients are mathematically impossible, the test error exceeds the event threshold, no baselines or ablations are provided, and the data split is not shown to be chronological. These issues place the paper's main contribution, namely the demonstrated effectiveness of GNN-based heavy-rainfall prediction, in question.

major comments (5)

[Section V, Table I and Eq. (4)] The Pearson correlation coefficients reported in Table I (r = 5.891, 6.002, 7.204, 8.771) are mathematically impossible for the coefficient defined in Eq. (4), which is bounded in [-1, 1] for any two real vectors. Since r is one of the three reported performance metrics and the abstract's effectiveness claim rests on these results, the evaluation as reported is invalid; the r column appears to have been computed by a different formula or on different quantities than stated. This is a load-bearing internal inconsistency, not a presentation issue.
[Section V, Table I and Section IV-B] The best model's MAE is 9.512 mm, which is larger than the 8 mm heavy-rain threshold defined in Section IV-B. With an average absolute error exceeding the event threshold, the proposed flagging rule (predict rainfall above 8 mm) cannot be expected to separate heavy-rain days from other days. The paper reports no event-level metrics such as precision, recall, F1, or a confusion matrix, so the central claim about predicting heavy rainfall events is not demonstrated.
[Section V] No baseline or ablation is reported. The manuscript does not compare against persistence, climatology, linear regression, an LSTM, or a non-graph machine learning model, nor does it ablate the graph construction (e.g., inverse-distance weighting, number of neighbors, number of layers). Without such comparisons, statements that the GNN 'outperformed' other models and 'effectively captured spatial dependencies' are unsupported.
[Section V, data split] The train/validation/test split is described only as 70/20/10 percentages. For daily precipitation time series with strong temporal autocorrelation, a random split can leak future information into training and inflate performance. The authors need to specify whether the split is chronological and report evaluation on temporally disjoint periods; as written, the generalization claim is not assured.
[Section IV-B and IV-A] The model input is underspecified: the node feature vector is described only as 'meteorological data from that station (mainly past rainfall)' with no statement of the number of lag days, the feature dimension, the standardization procedure, or the missing-value interpolation method. This makes the experiment unreproducible and prevents assessment of whether the model is predicting from past rainfall or from contemporaneous information.

minor comments (6)

[Eq. (4)] The notation cov(X, y) is dimensionally inconsistent; Pearson correlation should be defined on paired scalar observations, and it would be clearer to state explicitly whether r is pooled across stations and days or computed per station.
[Section III-B and IV-B] There are small typographical issues: 'W AN' should be 'WAN', and 'ReLu' should be 'ReLU'.
[Figure 7] Figure 7 is referenced only as 'Best performing GNN model' without a descriptive caption; it is unclear what the plot shows and how it supports the reported results.
[Section IV-B] The 8 mm/day heavy-rainfall threshold is introduced without justification or citation; a reference or a brief rationale from Bolivian meteorological practice would help.
[Section IV-A, abstract, and Section V] The dataset duration is inconsistent: the abstract and Section V say 72 months, but the data collection period stated in Section IV-A (1 January 2017 to 30 April 2024) is 88 months.
[References] Several references are incomplete, including [1], [2], [9], [10], and [24], which lack full author, title, or access details; the bibliography needs to be brought to journal style.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the GNN prediction is a fitted regression evaluated on held-out data; the only self-citation is non-load-bearing.

full rationale

The paper makes no derivation claim that could be circular: its GNN is a standard fitted regression model trained on historical SENAMHI daily rainfall and evaluated on a held-out test split (70/20/10). The adjacency matrix is constructed from inverse station distances, a stated design choice rather than a quantity derived from the prediction target, and the heavy-rainfall flag is simply a threshold (>=8 mm) applied to the regression output. The single self-citation, [19] (Rojas, Salcedo, Sahonero), appears only in a related-work sentence about edge computing and is not load-bearing for the model or its evaluation. No fitted parameter is renamed as a prediction, no uniqueness theorem is imported from the authors' prior work, and no result is defined in terms of its own target. The reported Pearson r values exceeding 1 (Table I) indicate an invalid evaluation metric, but that is a correctness/consistency problem, not a circularity. The central claim is not equivalent by construction to any input.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The paper's central claim rests on hand-chosen hyperparameters (8 mm threshold, layer widths, learning rate 0.01, batch size 64), an unspecified interpolation method, and several unvalidated domain assumptions about the station graph capturing rainfall structure across complex orography. If the graph or data-quality assumptions fail, or if the threshold is inappropriate, the reported predictions cannot be relied upon. No first-principles derivation or external benchmark anchors the model.

free parameters (5)

heavy_rainfall_threshold = 8 mm/day
Chosen by hand to define the binary heavy-rain event label; no meteorological citation or sensitivity analysis is given.
GCN hidden layer widths (model A) = 10, 10, 10, 10
Architecture selected as best on the test set out of four hand-specified configurations.
learning_rate = 0.01
Set without reported tuning or search.
batch_size = 64
Set without reported tuning or search.
missing_value_interpolation_method = unspecified
Addressing missing values through interpolation is stated, but the interpolation algorithm is not identified; the choice affects training data.

assumptions (5)

domain assumption Spatial dependence of daily rainfall is adequately captured by inverse-distance-weighted edges between stations.
Section IV-B defines edges by station distance; Section V says edge weights use inverse distance. This assumes rainfall co-varies smoothly over space, which is questionable in Bolivia's Andean terrain.
domain assumption A static four-layer graph convolution with no explicit temporal recurrence can predict daily rainfall at each station.
Section IV-B describes H^0 = X and four GCL layers. Daily observations are treated as static node features; no sequence model is described.
domain assumption The 41 scraped SENAMHI stations, after removing stations with too many missing values and interpolating the rest, are representative for heavy-rain prediction.
Section IV-A describes exclusion and interpolation without quantitative criteria or analysis of the impact on heavy-rain days.
standard math The GCN propagation rule in Eq. 1 is a valid model for this spatiotemporal rainfall regression.
Equation 1 is the standard symmetric-normalized graph convolution layer; the paper relies on it without independent justification, which is acceptable background in graph learning.
domain assumption Precipitation is stationary across the 72 months after feature standardization.
Section V states features are standardised; no seasonality, trend, or regime-change modeling is reported, and the train/validation/test split is not stated to be chronological.

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Cite this review

Pith. "Pith review of Graph Learning-based Regional Heavy Rainfall Prediction Using Low-Cost Rain Gauges." pith.science (2026). https://pith.science/paper/4DI2456A

@misc{pith2026241216842,
  author       = {Pith},
  title        = {Pith review of: Graph Learning-based Regional Heavy Rainfall Prediction Using Low-Cost Rain Gauges},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4DI2456A}},
  note         = {Machine review of arXiv:2412.16842}
}

read the original abstract

Accurate and timely prediction of heavy rainfall events is crucial for effective flood risk management and disaster preparedness. By monitoring, analysing, and evaluating rainfall data at a local level, it is not only possible to take effective actions to prevent any severe climate variation but also to improve the planning of surface and underground hydrological resources. However, developing countries often lack the weather stations to collect data continuously due to the high cost of installation and maintenance. In light of this, the contribution of the present paper is twofold: first, we propose a low-cost IoT system for automatic recording, monitoring, and prediction of rainfall in rural regions. Second, we propose a novel approach to regional heavy rainfall prediction by implementing graph neural networks (GNNs), which are particularly well-suited for capturing the complex spatial dependencies inherent in rainfall patterns. The proposed approach was tested using a historical dataset spanning 72 months, with daily measurements, and experimental results demonstrated the effectiveness of the proposed method in predicting heavy rainfall events, making this approach particularly attractive for regions with limited resources or where traditional weather radar or station coverage is sparse.

Figures

Figures reproduced from arXiv: 2412.16842 by the authors.

**Figure 3.** On the left, an illustration of the Solidworks (CAD) model of the [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 2.** Proposed architecture of a rainfall data acquisition and analysis system. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Entity-Relation diagram of the principal database. [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 5.** Figure 5: Screenshots of the web application. IV. FORECAST MODEL: GRAPH NEURAL NETWORK A. Data Collection and Processing Once the Twilio SMS receiver forwards an SMS to the server as an HTTP request, an NGINX server receives the request and communicates it to a REST API, which, …

**Figure 7.** Figure 7: Best performing GNN model. The best-performing GNN model, model A (shown in [PITH_FULL_IMAGE:figures/full_fig_p005_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [1]

The countries most prone to flooding

W. Vision, “The countries most prone to flooding.” WORLDVI- SION.org.uk. Accessed: May 23, 2024

work page 2024

[2] [2]

Informaci ´on nacional de datos hidrometeorol ´ogicos

SENAMHI, “Informaci ´on nacional de datos hidrometeorol ´ogicos.” SENAMHI.gob.bo. Accessed: May 29, 2024

work page 2024

[3] [3]

A rain gauge system using a capacitance sensor,

W. Sa-Ngiamvibool, N. Angkawisittpan, A. Nuan-On, C. Photong, and A. Kangrang, “A rain gauge system using a capacitance sensor,” International Journal of Engineering and Technology , vol. 5, no. 4, pp. 3596–3600, 2013

work page 2013

[4] [4]

Evaluation of a low-cost optical rain sensor,

D. D. Steele, T. F. Scherer, F. A. Akyuz, A. W. Wamono, T. M. DeSutter, and S. R. Tuscherer, “Evaluation of a low-cost optical rain sensor,” in ASABE/CSBE North Central Intersectional Meeting , p. 1, American Society of Agricultural and Biological Engineers, 2006

work page 2006

[5] [5]

An innovative acoustic rain gauge based on convolutional neural networks,

R. Avanzato and F. Beritelli, “An innovative acoustic rain gauge based on convolutional neural networks,” Information, vol. 11, no. 4, p. 183, 2020

work page 2020

[6] [6]

Global precipitation measurement: Methods, datasets and applications,

F. J. Tapiador, F. J. Turk, W. Petersen, A. Y . Hou, E. Garc ´ıa-Ortega, L. A. Machado, C. F. Angelis, P. Salio, C. Kidd, G. J. Huffman, et al., “Global precipitation measurement: Methods, datasets and applications,” Atmospheric Research, vol. 104, pp. 70–97, 2012

work page 2012

[7] [7]

Evaluation of precipitation measurements obtained from different types of rain gauges,

G. Urban and K. Strug, “Evaluation of precipitation measurements obtained from different types of rain gauges,” Meteorol. Z , vol. 30, pp. 445–463, 2021

work page 2021

[8] [8]

Calibrating low-cost rain gauge sensors for their applications in iot infrastructures to densify environ- mental monitoring networks,

R. Kr ¨uger, P. Karrasch, and A. Eltner, “Calibrating low-cost rain gauge sensors for their applications in iot infrastructures to densify environ- mental monitoring networks,” Geoscientific Instrumentation, Methods and Data Systems Discussions , vol. 2023, pp. 1–20, 2023

work page 2023