Hidden Maps of Thirst: Bayesian Model Reveals Bogotá’s Water Use Defies Simple Explanation

Water is the most local of all urban resources. It arrives through pipes that snake beneath specific streets, fills tanks on particular rooftops, and drains from taps in individual kitchens. Yet when city officials and researchers model how much water a metropolis consumes, they often reach for city-wide averages: how much rain fell this month, what the temperature was, how incomes and tariffs shifted across the whole urban fabric. A new study of Bogotá, Colombia, argues that this habit of averaging may be quietly blinding water managers to the true structure of demand. By applying fully Bayesian spatio-temporal models to locality-level consumption data from 2019 through 2024, researchers Danna Lesley Cruz-Reyes and Daniel Leonardo Ramírez Orozco have shown that the city’s sixteen or so localities do not simply rise and fall together in response to shared forces. Each one carries its own temporal signature, and that heterogeneity is strong enough to transform the statistical picture entirely.

The study, published in PLOS Water, set out with a deceptively simple question. If you adjust water consumption in every locality for the same city-wide drivers—climate swings, socioeconomic trends, the shared shocks of a period that included a global pandemic and severe drought stress—do the localities then behave as statistical clones of one another, differing only by a fixed offset? The additive model the authors built first assumes exactly that. It allows each locality to sit higher or lower than the city average, capturing a static spatial ranking, but it forces every locality to follow the same temporal trajectory once common covariates are accounted for. In a city as geographically and socially layered as Bogotá, where highland neighborhoods, dense commercial cores, and sprawling southern districts experience water very differently, that assumption was always going to be under strain.

To test it rigorously, the researchers turned to the machinery of modern Bayesian inference. Rather than producing a single best-fit line, Bayesian models express uncertainty as full posterior distributions over every parameter, which makes them well suited to the noisy, short, and irregularly structured data that characterize municipal water records. The authors fitted models to monthly consumption at the locality level across six years, a period long enough to span dramatic climatic and social disruption but short enough that data-hungry methods must be handled with care. The additive specification adjusted for common temporal dynamics and city-wide climatic and socioeconomic time series, then asked how much spatial structure remained in the residuals.

The answer came from a formal sensitivity analysis, and it was unambiguous. When the researchers added a structured space–time interaction—a term that lets each locality’s deviation from the common trajectory evolve over time, borrowing strength from neighboring localities through spatially correlated priors—the improvement in model fit was enormous. The Widely Applicable Information Criterion, a standard Bayesian measure of predictive fit that penalizes complexity, dropped from 2502.7 in the additive model to 604.0 in the interaction model. The Deviance Information Criterion fell in parallel, from 2500.5 to 333.9. In the vocabulary of statistical modeling, gaps of this magnitude are not marginal refinements; they signal that the simpler model is missing something fundamental about how the data are generated. Locality deviations, the authors conclude, are not adequately represented as constant throughout the study period.

What does that mean in practical terms? Imagine two neighborhoods that consumed similar volumes of water in 2019. Under the additive model, they would be expected to track each other through the pandemic lockdowns, the rationing anxieties, and the shifting rainfall patterns of the following years, differing only by a fixed amount. The interaction model says otherwise: the same shared events landed differently in different places, and those differential responses are themselves spatially organized. Neighborhoods that are geographically close tend to deviate from the city-wide pattern in similar ways, a signature consistent with localized infrastructure, microclimates, settlement histories, and social composition shaping how water demand responds to stress. The spatial structure is not a static backdrop but an active, evolving dimension of consumption.

The study also confronted a subtler statistical hazard: heavy tails. Water consumption data, like many environmental and socioeconomic series, occasionally produce extreme observations—a billing anomaly, a meter failure, a localized crisis—that a normal distribution treats as vanishingly rare. The researchers therefore compared their Gaussian models against versions using a Student-t likelihood, which has heavier tails and down-weights extreme observations. The posterior mean degrees of freedom told the story: around 3.02 in the additive model and 2.60 in the interaction model. Values this low, well below the roughly 30 of a Gaussian distribution, indicate genuinely heavy residual tails—outliers are a real feature of these data, not a modeling artifact. The Student-t likelihood was not a paranoid precaution; it was describing something true about Bogotá’s water records.

Yet here the study delivers one of its most interesting and technically consequential findings. Despite the evidence for heavy tails, the Gaussian interaction model retained substantially better information criteria than its Student-t counterpart. That apparent paradox—acknowledging fat-tailed errors yet preferring the thinner-tailed model—reflects the way information criteria balance fit against effective complexity. The Student-t likelihood, with its additional flexibility, appears to absorb structure that the interaction term would otherwise capture, blurring the space–time signal the researchers most wanted to isolate. When the authors compared the principal spatial main effects estimated under the two likelihoods, they found a correlation of 0.975. In other words, the overall spatial ordering of localities—which places consume more, which consume less—is remarkably robust to the choice of error distribution, even as the finer temporal dynamics are sensitive to it.

That robustness matters for anyone hoping to act on these results. A water utility deciding where to target conservation campaigns, where to prioritize leak detection, or how to design tariff structures needs to trust the spatial ranking of demand. The near-perfect correlation across likelihoods suggests that ranking is solid ground. But a utility trying to forecast how a specific district will respond to the next drought, or to evaluate whether an intervention changed behavior in one locality but not its neighbors, needs the space–time interaction. The additive model, however convenient, would systematically misattribute those differential dynamics, potentially crediting or blaming city-wide policies for changes that were in fact deeply local.

The methodological lesson radiates well beyond Bogotá. Cities across Latin America and the wider global South face similar conditions: administratively defined zones of uneven size and character, consumption records of moderate length, and climatic pressures—like the multi-year rainfall deficits that have strained Andean reservoirs in recent years—that do not fall uniformly across the urban landscape. The Bayesian framework used here offers a template because it handles short series gracefully, quantifies uncertainty honestly, and makes its assumptions explicit and testable. The sensitivity analysis is the crucial move. Rather than asserting a single model, the authors demonstrated that their central conclusion—spatially heterogeneous temporal dynamics—survives a deliberate stress test of its core assumptions, from the error distribution to the structure of the interaction term.

There is also a quieter, more civic implication. When consumption is modeled as a single city-wide curve, the localities that deviate most—those that conserve aggressively under stress, or those that cannot—become statistical noise. The space–time interaction model makes those deviations visible and locatable, turning them into evidence. In a period when Bogotá and many other cities are confronting the reality that water infrastructure, climate, and inequality intersect block by block, that visibility is not an academic luxury. It is the difference between managing a city as an abstraction and managing it as the mosaic of places it actually is. The maps hidden inside Bogotá’s water bills, this study shows, were always there; it took a model willing to let space and time talk to each other to reveal them.

Subject of Research: Bayesian spatio-temporal modeling of locality-level urban water consumption in Bogotá, Colombia

Article Title: Spatial structure in urban water consumption: A Bayesian space-time analysis of Bogotá (2019–2024)

Article References: Cruz-Reyes, D. L., & Ramírez Orozco, D. L. (2026). Spatial structure in urban water consumption: A Bayesian space-time analysis of Bogotá (2019–2024). PLOS Water, 5(9), e0000512. https://doi.org/10.1371/journal.pwat.0000512

Image Credits: AI Generated

DOI: 10.1371/journal.pwat.0000512

Keywords: urban water consumption, Bogotá, Bayesian modeling, spatio-temporal analysis, PLOS Water, space-time interaction, Student-t likelihood, WAIC, water management, spatial heterogeneity, climate, sensitivity analysis