Evolution, applications, and emerging challenges in probable maximum precipitation estimation: A bibliometric and systematic review

Imagine standing on the edge of a massive dam, a structure built to hold back a river that could one day swell to a size no one has ever seen. Engineers do not design these critical barriers based on what has happened in the past, but on what could possibly happen in the worst-case scenario. They need to know the absolute limit of how much rain a specific region could produce in a single storm, a theoretical ceiling known as the "Probable Maximum Precipitation." This number is not a prediction of what will fall tomorrow, but a safety calculation for the next century. If this estimate is too low, the dam might fail, releasing a catastrophic flood. If it is too high, the structure becomes unnecessarily expensive and wasteful. For decades, scientists have tried to pin down this limit, treating it as a fixed number derived from historical records. However, as the planet warms and the atmosphere holds more moisture, the question has shifted: is that limit still the same, or is it moving?

A comprehensive review of global research, published by a team from the Federal University of Espírito Santo in Brazil, reveals that the science behind these estimates is undergoing a profound transformation. The researchers analyzed nearly 400 scientific articles published over the last seventy years, tracking how the field has evolved from a reliance on simple historical records to a complex integration of climate models and physical simulations. Their work shows that while the old methods are still in use, the scientific community is increasingly recognizing that the rules of extreme weather are changing. The study finds that the field is moving away from the idea of a single, unchangeable number and toward a more flexible approach that accounts for a warming world, though significant gaps in data and understanding remain.

The history of this research tells a story of slow beginnings followed by a rapid explosion of interest. For the first few decades, from the 1950s through the 1990s, only a handful of papers were published on the subject each year. The field was quiet, dominated by a few countries like the United States, where the foundational methods were developed. However, starting around 2011, the volume of research surged dramatically. By the mid-2020s, more than 70 percent of all the studies ever written on this topic had been published. This boom coincides with a growing global awareness of climate change and the urgent need to ensure that dams, bridges, and drainage systems can withstand storms that are becoming more intense. The research has also spread geographically; while the United States, India, and China remain the primary contributors, scientists from across Asia, Europe, and the Americas are now actively participating, bringing diverse local climates into the conversation.

When the researchers looked at how scientists actually calculate these maximum rainfall limits, they found that the field is still heavily anchored in two traditional approaches. The most common method, used in over a third of the studies, is a statistical technique that looks at the largest rainfalls recorded in history and applies a mathematical factor to estimate the extreme. The second most popular approach is a hydrometeorological method, which involves taking a real, severe storm that has occurred and mathematically "maximizing" its features—such as how much moisture the air held or how fast the wind blew—to see how much rain it could have produced under perfect, worst-case conditions. Together, these two traditional methods account for nearly two-thirds of all the new estimates produced in recent years. They remain popular because they are relatively simple to apply and do not require massive amounts of complex data.

However, the review highlights a clear and steady shift toward more sophisticated techniques. A growing number of researchers are now using computer models that simulate the physics of the atmosphere, treating storms as dynamic systems rather than just statistical outliers. These models can account for how mountains influence rain, how heat drives storms, and how moisture moves through the air. While these physical models are still less common than the traditional methods, their presence signals a move toward a deeper understanding of the mechanisms that create extreme rain. The authors note that this diversification is not about discarding the old ways, but rather about testing their assumptions and filling in the gaps where simple statistics fall short.

One of the most critical findings of the review concerns the impact of climate change. For a long time, the standard assumption was that the maximum possible rain for a location was a fixed value, determined by the climate of the past. The review shows that this view is being challenged. About 35 studies in the analyzed group explicitly tried to calculate what the maximum rain might be in the future, using climate models to project how a warmer atmosphere would alter storm potential. The results are not uniform; in some regions, the projected maximum rainfall increases significantly, while in others, the changes are smaller or even decrease. This variability proves that there is no single "climate adjustment factor" that can be applied everywhere. The change depends on local geography, the type of storm, and the specific future scenario being modeled.

Despite these advances, the review identifies a significant hesitation in the scientific community regarding the concept of "nonstationarity"—the idea that the statistical rules of weather are changing over time. Only a tiny fraction of the studies, fewer than three percent, formally tested whether the historical data actually showed a trend of changing extremes. Most researchers still rely on the assumption that the past is a reliable guide to the future, even as evidence mounts that the atmosphere is holding more moisture and storms are becoming more intense. The authors suggest that this gap is a major limitation, as it means many safety calculations for critical infrastructure might be based on outdated assumptions.

The study also points out where the science is struggling. In many parts of the world, especially in mountainous regions or areas with few weather stations, the data is too sparse to make accurate estimates. Scientists are beginning to use satellite data and radar to fill these gaps, but these tools come with their own uncertainties. Furthermore, the review emphasizes that estimating the maximum rain is only the first step; the real danger lies in how that rain translates into flooding, which depends on soil conditions, snowmelt, and river flow. The authors argue that the future of this field lies in combining the best of the old statistical methods with new physical models, while constantly updating the data to reflect a changing climate.

Ultimately, this review serves as a map of a field in transition. It shows that while the core goal remains the same—ensuring the safety of human infrastructure against the worst possible storms—the tools and assumptions used to reach that goal are evolving. The science is moving from a static view of the world, where the past dictates the future, to a dynamic one that acknowledges the shifting nature of our climate. The researchers conclude that the path forward requires a blend of statistical rigor, physical understanding, and a willingness to update our estimates as new evidence emerges, ensuring that the structures we build today can survive the storms of tomorrow.