Rio de Janeiro is a city that lives with rain on a knife’s edge. Steep granite massifs plunge into dense coastal neighborhoods, and when moderate storms roll in off the Atlantic, the combination of unplanned urban expansion and rugged terrain can turn an ordinary downpour into a deadly flood or landslide. Forecasting these events has long been a challenge for machine intelligence as much as for meteorologists: the most powerful machine learning models often behave like black boxes, delivering predictions without explaining which atmospheric factors actually drive them. Now, a team of Brazilian researchers has shown that a decades-old, transparent statistical technique — the Bayesian Network — can learn the physics of rainfall directly from data, revealing exactly how humidity, solar radiation and wind combine to produce rain over the city, all while consuming almost no energy in the process.
The study, led by Lucas Dirk Gomes Ferreira of the Institute of Computing at Fluminense Federal University, together with Mariza Ferro and meteorologist Fernanda Cerqueira Vasconcellos of the Federal University of Rio de Janeiro, was published in the International Journal of Data Science and Analytics. The researchers mined 22 years of hourly weather-station records from Brazil’s National Institute of Meteorology (INMET), spanning four telemetric stations across the municipality from 2002 through late 2024, and used them to build Bayesian Networks that model the probabilistic web of relationships linking atmospheric conditions to precipitation.
A Bayesian Network is a probabilistic graphical model in which random variables are represented as nodes in a directed acyclic graph, with arrows indicating conditional dependencies. Instead of asking a neural network to produce an opaque probability of rain, a Bayesian Network explicitly factorizes the joint probability distribution of all variables into a product of local conditional probabilities, each variable depending only on its parent nodes. The result is a map of who influences whom — something a forecaster, a civil defense official, or a city planner can actually inspect and debate.
Building such a network, however, is only half the battle; the harder question is how to learn its structure from data. The Brazilian team systematically compared fourteen structure-learning algorithms drawn from the three main families in the literature. Score-based methods, such as Hill Climbing and TABU Search guided by scoring functions like the Bayesian Information Criterion (BIC), the Akaike Information Criterion (AIC), the K2 score and the Bayesian Dirichlet equivalent (BDe) score, treat structure discovery as a global optimization problem, searching for the graph that best explains the data. Constraint-based methods, including the Peter-Clark and Grow-Shrink algorithms, instead rely on chains of conditional independence tests to decide where arrows belong. Hybrid approaches, such as Max-Min Hill Climbing, combine the two strategies.
The comparison produced a striking and methodologically important result. The constraint-based and hybrid algorithms failed to connect any meteorological variable directly to precipitation. Their reliance on local conditional independence tests made them vulnerable to the weak, noisy correlations and severe class imbalance inherent in rainfall data, leaving the rain node isolated in the graph. Only the score-based algorithms, which evaluate the overall fit of the entire network, succeeded in capturing meaningful links between the atmosphere and the rain gauge.
To learn robust structures, the researchers wrapped the entire procedure in a bootstrap-consensus protocol: for every algorithm, they ran 300 bootstrap resamples of the dataset, learned a network from each, and retained only those arcs that appeared in at least 85 percent of the resulting graphs. Domain knowledge entered the process as hard constraints. Precipitation was forbidden from acting as a parent of any other variable, since it is the response being predicted; future measurements could never influence past observations; and seasonal variables such as time of day and season of the year were locked in as root nodes, immune to incoming arrows because they are causes, not effects, in the atmospheric system. Any structure violating these physical rules was rejected, the constraint blacklist was updated, and learning restarted.
The raw data itself demanded careful engineering. For each of six meteorological variables — including temperature, humidity, pressure, wind speed, solar radiation and dew point — the team generated features representing values measured one, two and three hours before each target hour. Principal component analysis then revealed that the derived variation features were largely redundant with the lagged values, so they were pruned. All continuous variables were discretized with k-means clustering into a small number of categories to keep the conditional probability tables tractable, and precipitation itself was binned into three classes: no rain, rain, and extreme rain at 25 millimeters per hour or more. The final dataset contained 468,811 instances across 20 features — and, notably, roughly 92 percent of hours had no rain at all, a stark imbalance that any rain model must confront.
When it came to raw predictive power, the Hill Climbing algorithm scored with the K2 criterion came out on top, achieving a cross-validated accuracy of 0.742, a specificity of 0.748 and an area under the ROC curve of 0.79, with undersampling of the dominant no-rain class used within training folds to temper the imbalance. But for interpretation, the team deliberately selected the more parsimonious network learned by Hill Climbing under the BIC criterion, which penalizes complexity and distilled the atmosphere’s influence on rain into a handful of essential connections. “The two goals — squeezing out the best possible classification metrics and producing a graph that a meteorologist can read like a sentence — are not always the same,” the underlying logic of the study suggests, and the authors chose transparency for their physical analysis.
What that transparency revealed is a textbook picture of tropical coastal rainfall, learned by the machine rather than dictated by humans. In the BIC-learned network, the rain node’s parents are precisely three variables, all lagged by a single hour: global radiation, relative humidity and wind speed. In other words, the model concluded that whether it rains in the next hour depends almost entirely on the atmosphere’s state right now, not on conditions two or three hours old. Probabilistic inference on the fitted network quantified the pattern with numbers a decision-maker can use. When wind speed was held at moderate levels and humidity was high, the probability of rain within the hour rose to 26.24 percent; under low humidity, it collapsed to below 1 percent. Similarly, when solar radiation was low and humidity high — conditions indicating that cloud decks were already thickening overhead — the probability of rain reached 19.25 percent, whereas low radiation combined with low humidity left the chance of rain under 2 percent.
The physics embedded in these numbers is coherent with how forecasters understand convective storms in humid coastal environments. High relative humidity signals an atmosphere rich in the water vapor needed for cloud formation. Reduced solar radiation reaching the surface is a telltale sign that clouds are already intercepting sunlight, and an hour is typically enough time for those clouds to mature and deliver rain. Moderate wind facilitates the transport of moisture into the region without suppressing convection, whereas very strong winds can shear developing storms apart. The Bayesian Network also correctly reproduced other physical expectations, modeling tight dependencies among temperature, humidity and dew point across time lags, and leaving seasonal and diurnal variables as root causes. Calibration analysis showed the models tended to slightly underestimate the highest rainfall probabilities — a known and stubborn challenge in probabilistic forecast verification — but performance was broadly consistent across all four scoring criteria.
Perhaps the most unexpected contribution of the study is its environmental accounting. The authors framed their work under the emerging “Green AI” paradigm, which calls on researchers to report the energy cost of machine learning alongside its accuracy. Using a tool called wAIter, developed by two of the same research group’s members, they estimated that the full set of structure-learning experiments ran for about three hours on a modest AMD Ryzen 5 desktop processor with 16 gigabytes of RAM, consumed a total of 0.20 kilowatt-hours of electricity, and generated approximately 0.02 kilograms of carbon-dioxide equivalent emissions and a water footprint of 3.65 liters — figures that contrast sharply with the data-center-scale appetites of large neural networks. For operational meteorology in developing regions, where computing budgets and grid emissions are real constraints, that efficiency is not a footnote; it is a feature.
The researchers are candid about the limits of their model. It is built on point observations at four stations, so it does not track the spatial movement of rain systems the way radar-based nowcasting does, and it should be read as a municipal-scale probabilistic framework rather than a station-by-station forecast product. The extreme-rain class, at just 0.03 percent of instances, is too rare for robust validation, and the network’s inferences about extreme events must be treated as exploratory. In many respects, the study confirms what meteorologists already knew — that saturated, dim, moderately windy hours are the ones that bring rain — but the authors argue this is precisely the point: the network formalizes, quantifies and renders transparent the reasoning that experts previously held only as intuition.
Future work, the team says, will push toward physics-informed probability estimation, spatio-temporal network structures spanning multiple stations and lead times, and validation metrics designed specifically for rare, high-impact events. For now, the study stands as a demonstration that in the age of billion-parameter weather models, a graph of a few dozen arrows, learned honestly from two decades of rain gauges and sensors, can still earn its place in the forecast conversation — explaining itself as it goes, and barely costing the planet a drop of water to train.
Subject of Research: Probabilistic modeling of rainfall occurrence in Rio de Janeiro, Brazil, using data-driven Bayesian Network structure learning applied to 22 years of hourly meteorological station observations.
Subject of Research: Technology and Engineering
Article Title: Data-driven Bayesian Network structure learning for probabilistic inference of rainfall in Rio de Janeiro
Article References: Ferreira, L. D. G., Ferro, M., & Vasconcellos, F. C. (2026). Data-driven Bayesian Network structure learning for probabilistic inference of rainfall in Rio de Janeiro. International Journal of Data Science and Analytics, 22(1), Article 269. https://doi.org/10.1007/s41060-026-01247-x
Image Credits: AI Generated
DOI: 10.1007/s41060-026-01247-x
Keywords: Bayesian networks, rainfall prediction, probabilistic graphical models, structure learning, meteorological data, Rio de Janeiro, interpretability, Green AI, probabilistic inference, hill climbing, BIC criterion, flood risk
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Denise Maddox. (September 10, 2026). Bayesian networks improve probabilistic rainfall inference in Rio de Janeiro. Scienmag. https://scienmag.com/bayesian-networks-improve-probabilistic-rainfall-inference-in-rio-de-janeiro/
Denise Maddox. “Bayesian networks improve probabilistic rainfall inference in Rio de Janeiro.” Scienmag, 10 September 2026, https://scienmag.com/bayesian-networks-improve-probabilistic-rainfall-inference-in-rio-de-janeiro/. Accessed 10 September 2026.
Denise Maddox. “Bayesian networks improve probabilistic rainfall inference in Rio de Janeiro.” Scienmag. September 10, 2026. https://scienmag.com/bayesian-networks-improve-probabilistic-rainfall-inference-in-rio-de-janeiro/
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