Why Hydrology's "Farewell to Stationarity" Was Just the Beginning
When hydrologist Z.W. Kundzewicz penned his poignant "Farewell, HSJ!" editorial, he mourned the demise of a foundational concept: stationarity—the idea that natural systems fluctuate within a stable, predictable range. For decades, this principle guided flood prediction, dam design, and water management. But in our era of climate change and land-use upheaval, Kundzewicz declared stationarity dead, urging hydrologists to navigate an uncertain future. Yet, was this farewell premature—or even misunderstood? Emerging research reveals a more nuanced truth: Hydrology hasn't abandoned predictability; it has transformed it. By embracing intrinsic change and multi-scale uncertainty, scientists are forging tools that honor the past while navigating complexity. This article explores how the "death" of stationarity birthed a renaissance in water science.
Stationarity assumed that statistical properties (like average rainfall or flood frequency) remained constant over time. Engineers relied on historical data to build infrastructure for "100-year floods." But as climate change accelerated, this assumption crumbled. Kundzewicz's lament reflected real anxiety: How do we plan when the past no longer predicts the future? 2 .
In the 1950s, hydrologist H.E. Hurst uncovered a paradox while studying the Nile River. Long-term hydrological records revealed persistent cycles and abrupt shifts—"Hurst-Kolmogorov dynamics"—where change wasn't noise but fundamental behavior. This aligned with Heraclitus' ancient dictum: "Panta Rhei" (everything flows). Modern hydrology now frames water systems as inherently dynamic, driven by feedback loops across time scales—from raindrops to millennia 2 4 .
Uncertainty isn't a flaw to fix; it's a feature to quantify. As Koutsoyiannis argues, "Modeling and mitigating natural hazards: Stationarity is immortal!"—not as a static rule, but as a scaffold for stochastic (probability-driven) tools that incorporate change 4 .
To test Kundzewicz's concern that "non-stationarity" cripples flood prediction, a landmark 2023 study led by Günter Blöschl investigated regional flood anomalies across Europe.
| Region | % Change in Flood Frequency | Dominant Mechanism Shift | Climate Driver |
|---|---|---|---|
| Northwestern | +40% | Rainfall → Intense Convection | ↑ Extreme Precipitation |
| Southern | -25% | Mixed → Reduced Soil Moisture | ↑ Aridity |
| Eastern | No change | Snowmelt → Rainfall Variability | ↑ Winter Temperatures |
Kundzewicz's fear of unpredictability is countered by spatial heterogeneity. Flood risks haven't become chaotic; they've reorganized along process lines, allowing targeted adaptation. As Blöschl notes, "Megafloods can be anticipated from observations in hydrologically similar catchments" 3 .
Modern hydrology replaces stationarity with a versatile arsenal:
Quantify long-term persistence in data
Example: Predicting multi-decadal flood cycles 4
Estimates uncertainty for "impossible" events
Example: Po River drought risk assessment 4
Groups floods by mechanism for regional transfer
Example: Identifying similar basins 1
Merges data-driven and mechanistic approaches
Example: Urban flash floods 3
A 2024 study by Montanari, Merz, and Blöschl tackled Kundzewicz's dread of "unknown unknowns" head-on. Using the "Sword of Damocles" metaphor, they modeled floods beyond historical records:
| Scenario | Probability of 100-yr Flood | Probability of 500-yr Flood |
|---|---|---|
| Stationary (1980s) | 1% | 0.2% |
| Non-Stationary (2024) | 1.5% (±0.3%) | 0.5% (±0.1%) |
| RCP 8.5 (2100) | 4% (±1.1%) | 1.7% (±0.4%) |
Impossible floods are inevitable but manageable. Uncertainty bounds let planners design "adaptable infrastructure" (e.g., floodplains with adjustable levees) 3 .
Kundzewicz's farewell to stationarity was not an epitaph but a passing of the torch. Hydrology today thrives on dynamic predictability—where change is modeled, uncertainty quantified, and regional wisdom shared. As Koutsoyiannis reminds us, "Change occurs on all time scales [...] our modeling practices must reflect this intrinsic flux" 2 . In this light, Kundzewicz's editorial is less a lament and more a call to evolution: an invitation to build resilient systems that bend, like rivers, through an ever-changing world.