Hidden in the Rain: Serbia’s Shifting Rainfall Predictability Reveals Climate Fingerprints

Climate change is often measured in averages: a degree or two of warming here, a few extra millimeters of rain there. But a new study of six decades of rainfall data from Serbia suggests that some of the most profound fingerprints of a changing climate may be invisible to the statistics we rely on most. By applying a sophisticated entropy-based technique to daily precipitation records from 14 weather stations spanning 1961 to 2020, researchers found that the predictability of rainfall has shifted dramatically in many locations, even where annual rainfall totals barely moved. The findings, published in the journal Nonlinear Processes in Geophysics, hint that climate change is rewriting the hidden temporal structure of rain in ways that conventional averages simply cannot see.

The research team, led by Tatijana Stosic of the Federal Rural University of Pernambuco in Brazil together with Ivana Tošić and Vladimir Djurdjević of the University of Belgrade, set out to answer a deceptively simple question: has the complexity of precipitation dynamics in Serbia changed between two consecutive 30-year periods, 1961–1990 and 1991–2020? Their tool of choice was the Generalized Weighted Permutation Entropy, or GWPE, a recently introduced method that extends the classical permutation entropy framework developed by Christoph Bandt and Bernd Pompe in 2002. That original method encodes a time series into symbolic patterns by sorting short overlapping segments of data and counting how often each ordering appears. A highly regular, predictable series produces a skewed pattern distribution and low entropy; a chaotic, unpredictable one spreads probability evenly across all possible patterns, yielding high entropy.

The innovation of GWPE lies in a continuous scaling parameter, q, which acts like a mathematical magnifying glass. Negative values of q emphasize small fluctuations in the data, while positive values amplify the influence of large swings. At q=0 the method reduces to classical permutation entropy, and at q=2 it becomes the weighted variant that accounts for the amplitude of values within each segment. This scale-sensitive lens allowed the team to separately probe the predictability of light drizzles and heavy downpours, something no single entropy measure had done before. Combined with a statistical complexity measure in the so-called complexity-entropy causality plane, the approach can even distinguish between random noise and deterministic chaos in real-world data.

The dataset comprised daily precipitation amounts from 14 synoptic stations across Serbia, a continental Balkan country whose climate ranges from moderate continental in the northern lowlands to a modified Mediterranean character in the south and southwest. Annual precipitation across the stations varies between roughly 550 and 1050 millimeters, with the driest conditions in the northern plains around Sombor, Zrenjanin, Novi Sad, and Sremska Mitrovica, and the wettest in the western mountains near Loznica and Zlatibor. The Serbian Meteorological Service, which performed technical and critical quality controls on the measurements, provided the data. The researchers deseasonalized the series by converting each day’s rainfall into an anomaly relative to the long-term mean and standard deviation for that calendar day, ensuring that the analysis captured irregularity rather than the regular seasonal cycle.

The first striking result concerns what did not change. Entropy values at q=0 and q=2, corresponding to the classical permutation entropy and weighted permutation entropy, remained remarkably stable across stations and between the two 30-year subperiods. Had the team stopped there, they would have concluded that rainfall dynamics in Serbia were essentially unchanged. But when they turned the magnifying glass to the extremes, setting q to -10 to isolate small fluctuations and q to +10 to isolate large ones, a very different picture emerged. Entropy values at these settings exhibited significant spatial and temporal variation between the two periods, revealing changes in predictability that the standard measures had completely masked.

Across both periods and all locations, entropy at q=-10 was consistently lower than at q=+10, meaning that small precipitation fluctuations are systematically more predictable than large ones. This makes intuitive sense: light rain often arises from persistent, large-scale atmospheric conditions, whereas heavy rainfall events are driven by more volatile processes. But the spatial pattern of change was anything but uniform. In the first subperiod, small fluctuations were most predictable in Sombor, Zaječar, Loznica, and Kragujevac, and least predictable in Smederevska Palanka and Niš. Between the two periods, predictability of small fluctuations declined at Kragujevac, Negotin, Niš, Sremska Mitrovica, Veliko Gradište, and Zrenjanin, while it improved at Belgrade, Kraljevo, Smederevska Palanka, and Zlatibor. Novi Sad, Sombor, Zaječar, and Loznica showed no change at all.

Two stations tell the story most vividly. Belgrade recorded the largest gain in predictability, with entropy for small fluctuations falling from 0.360 to 0.138, while Negotin suffered the greatest loss, with entropy rising from 0.138 to 0.360, a near-perfect mirror image. Remarkably, at both locations the average annual precipitation remained essentially stable between the two subperiods. The underlying temporal structure of the rain, however, had transformed almost completely. Conversely, Novi Sad experienced the most pronounced increase in mean annual precipitation of any station, a jump of 151 millimeters, yet the predictability of its small fluctuations did not budge. This decoupling between how much rain falls and how predictably it falls is perhaps the study’s most consequential finding, suggesting that rainfall volume and rainfall dynamics respond to climate change through partly independent pathways.

Large fluctuations showed their own pattern of change. Entropy values at q=10 were consistently higher than at q=-10, confirming that heavy rainfall events are harder to anticipate everywhere in the country. Temporal changes were evident nonetheless: seven stations, predominantly in the eastern and northern regions such as Negotin, Veliko Gradište, Zaječar, Novi Sad, and Zrenjanin, saw slight increases in entropy, indicating declining predictability of large events. But two stations bucked the trend dramatically. At Kraljevo in central Serbia, entropy for large fluctuations decreased from 0.765 to 0.636, and at Sremska Mitrovica in the north it plunged from 0.780 to 0.428, both signaling improved predictability despite stable annual totals. Meanwhile, at Zlatibor and Sombor, where precipitation increased over the same period, the predictability of large fluctuations remained unchanged, once again underscoring the volume-versus-structure decoupling.

Why do these shifts matter beyond the mathematics? The predictability of small rainfall fluctuations has direct consequences for hydrology and agriculture. Light, frequent rains govern surface moisture retention and evapotranspiration dynamics, and predictable light rainfall helps farmers optimize irrigation schedules and planting times. Prolonged low-intensity rainfall can also trigger urban landslides and contribute significantly to soil erosion. The spatial patterns identified in the study, with increasing predictability of small fluctuations across northern and eastern Serbia, potentially reflecting growing local atmospheric order, and declining predictability in the central and western regions, could therefore translate into regionally divergent pressures on farming, water management, and landslide risk. Meanwhile, the reduced predictability of large fluctuations everywhere poses persistent challenges for flood and drought mitigation strategies.

The researchers note that precipitation variability in Serbia is largely steered by large-scale atmospheric circulation patterns, including the Arctic Oscillation, the East Atlantic/Western Russia Oscillation, and the North Atlantic Oscillation, all modulated by the country’s complex topography and its position at the crossroads of Mediterranean and continental climate systems. Disentangling how these drivers interact with a warming climate to reshape rainfall predictability is a task for future work. The authors propose comparing their entropy results with outputs from climate models under various emission scenarios, and applying the GWPE analysis in sliding windows over longer records to detect long-term trends and crossovers in predictability. For now, the message is clear: the climate is changing not only how much it rains, but how knowable the rain is, and a full accounting of climate impacts will require looking past the averages and into the hidden structure of the storm.

Subject of Research: Climate change effects on the predictability and complexity of precipitation dynamics in Serbia

Article Title: Spatiotemporal variation in rainfall predictability in Serbia under a changing climate

Article References: Stosic, T., Tošić, I., da Silva, A. S. A., Djurdjević, V., & Stosic, B. (2026). Spatiotemporal variation in rainfall predictability in Serbia under a changing climate. Nonlinear Processes in Geophysics, 33(1), 157-172. https://doi.org/10.5194/npg-33-157-2026

Image Credits: AI Generated

DOI: 10.5194/npg-33-157-2026

Keywords: rainfall predictability, climate change, Serbia, permutation entropy, GWPE, precipitation dynamics, complexity, hydrology, time series analysis, nonlinear processes, Balkan climate, entropy