In alpine regions, the design flood of a given return period (such as the 100-year flood used for sizing protection structures) can be estimated either by flood frequency statistics of gauge records or by rainfall–runoff modelling, and the two routes often disagree strongly. The HOWATI project (Tyrol, Austria, 2011) traced this divergence mainly to two mechanisms: the choice of design precipitation driving event-based models, and storage-threshold behaviour in high-storage catchments, which introduces a step change (S-shaped bend) into the flood frequency curve so that rare floods far exceed what gauge statistics suggest. The open problem is to turn this diagnosis into predictive capability: to determine how widespread threshold-induced step changes are across regions and catchment sizes, to develop criteria based on readily observable catchment characteristics that predict where such step changes occur and at which return period, to bound the uncertainty that design-precipitation selection contributes to event-based estimates, and to quantify how sensitive extreme flood quantiles are to continuous-simulation model structure, parameters, and stationarity assumptions. Follow-up literature through 2025 provides idealized mechanistic quantification, automated detection tools, and synthetic-catchment experiments, but no validated, regionally applicable prediction, so the problem remains open.

Background

Flood protection structures are dimensioned against a design flood, the peak discharge of a stated return period TT (for example the 100-year flood, HQ100HQ_{100}, whose exceedance probability in any year is 1%). Two estimation traditions coexist. In river engineering, flood frequency statistics fits a probability distribution (commonly the generalized extreme value distribution) to the annual maxima recorded at a gauging station and reads off the TT-year quantile; it assumes a homogeneous, stationary flood-generating process and is limited by record length, typically a few decades. In torrent and avalanche control (Wildbachverbauung), event-based rainfall–runoff models are standard: a design storm of given duration and return period, taken from intensity–duration–frequency (IDF) curves or from stochastic or convection-resolving atmospheric models, is routed through a catchment model of interception, infiltration, soil moisture, and runoff concentration to produce a flood hydrograph. In addition, continuous simulation approaches couple a stochastic weather generator (a statistical model producing long synthetic precipitation series with realistic statistics) with a rainfall–runoff model, so that thousands of years of synthetic annual maxima yield flood frequency curves without choosing a design storm. Because these routes rest on different assumptions, they frequently return very different design values for the same catchment, which matters directly for the safety and cost of hydraulic infrastructure.

The HOWATI project (Hydrographischer Dienst Tirol and the Forest Technical Service for Torrent and Avalanche Control, Tyrol) studied ten lead catchments in Tyrol with detailed field mapping of runoff processes and hydrogeology, comparing flood frequency statistics, an event-based model, and Monte Carlo based long-term simulation. Its central findings were that a plausible choice of design precipitation input is decisive for not overestimating floods with the event-based model, and that in catchments with large subsurface storage the statistical distribution of floods can exhibit a kink (an S-shaped curve): once a storage threshold is exceeded, a much faster runoff component activates, so that beyond some return period floods jump to substantially higher magnitudes than gauge statistics extrapolate. Such threshold behaviour was documented in some of the ten lead catchments, and it remained unclear how common it is across larger regions and in larger catchments, where spatially compensating runoff processes may mask the threshold signal. A step change located at a return period longer than the gauge record is essentially invisible in the data, which makes purely statistical estimation unreliable precisely in the catchments at risk.

Subsequent work sharpened the mechanistic picture. Idealized experiments with a stochastic rainfall model and a simple rainfall–runoff model showed that the magnitude of the step change decreases with increasing temporal variability of antecedent soil storage and increases with the area of the variably saturated region, and that the step change occurs near the return period of the rainfall volume needed to fill the storage deficit. A 2022 review formalized the broader phenomenon as heavy-tailed flood peak distributions — distributions whose upper tail decays more slowly than an exponential, so that extreme floods occur far more often than conventional frequency analysis suggests — and proposed nine process hypotheses; the same review concluded that predicting tail heaviness from process knowledge and data remains a key unsolved difficulty. Automated statistical tools now exist for detecting such discontinuities (termed flood divides) in observed and simulated frequency curves, and process-mixture statistics can reproduce curves in the few documented real catchments exhibiting them. Synthetic large-sample experiments indicate that threshold processes in runoff generation produce heavier tails and step changes, that the return period beyond which the rainfall tail dominates depends on catchment storage relative to mean annual precipitation, and that spatial rainfall variability attenuates tails in large catchments. What is still missing is the step from mechanism to prediction: criteria computable from catchment descriptors (geology, soil, storage indicators, land form, catchment size, climate indices) that predict, before any flood record is consulted, whether a catchment's frequency curve will step up, at which return period, and how much design precipitation selection and model structure can move the resulting extreme quantiles.

Problem Statement

Determine why and when flood frequency statistics and rainfall–runoff-model-based estimates of design floods diverge, and make the divergence predictable, by answering three linked questions for catchments in general (not only the ten Tyrolean lead catchments of HOWATI):

  1. How widespread is storage-threshold behaviour — step changes (S-shaped bends) in flood frequency curves caused by activation of fast runoff once subsurface storage fills — across hydrological regions and catchment sizes, including larger catchments where spatially heterogeneous storage and compensating runoff processes may mask the threshold signal? Develop systematic criteria, computable from readily available catchment descriptors (geology and storage indicators, soil and landform properties, catchment size and morphology, hydroclimatic characteristics), that predict whether a catchment's flood frequency curve exhibits such a step change and at which return period it occurs.

  2. How can the selection of design precipitation for event-based rainfall–runoff models be standardized and its uncertainty bounded, so that the choice is no longer substantially expert-based — including the error bounds of design storms from stochastic precipitation generators, atmospheric models, and gauge-based intensity–duration–frequency (IDF) statistics relative to each other?

  3. How sensitive are extreme flood quantiles (e.g. HQ100HQ_{100}, the 100-year flood peak, and rarer) to the structure and parameterization of continuous-simulation model chains (rainfall–runoff model structure, deep-storage parameterization, stochastic weather generator) and to the stationarity assumptions implicit in long synthetic runs?

The aim is to quantify these effects so that statistical and model-based design flood estimates can be reconciled within stated error bounds.

The three linked questions are jointly required, and a partial result on any one of them does not resolve the task. Question 1 is resolved only when a criterion computable from the listed catchment descriptors predicts both whether a given catchment's flood frequency curve exhibits such a step change and the return period at which it occurs, and thereby indicates how widespread the behaviour is across hydrological regions and catchment sizes; question 2 only when design-precipitation selection for event-based models is standardized, no longer substantially expert-based, and accompanied by quantified error bounds among the precipitation sources it names; and question 3 only when the sensitivity of extreme flood quantiles to the named continuous-simulation model structures, parameters, and stationarity assumptions has been quantified.

References

  1. Rogger, M., Kohl, B., Pirkl, H., Hofer, M., Kirnbauer, R., Merz, R., Komma, J., Viglione, A., Blöschl, G. (2011). HOWATI – HochWasser Tirol – Ein Beitrag zur Harmonisierung von Bemessungshochwässern in Österreich. Österreichische Wasser- und Abfallwirtschaft 63(7–8), 153–161. DOI 10.1007/s00506-011-0325-3, https://doi.org/10.1007/s00506-011-0325-3
  2. Rogger, M., Kohl, B., Pirkl, H., Viglione, A., Komma, J., Kirnbauer, R., Merz, R., Blöschl, G. (2012). Runoff models and flood frequency statistics for design flood estimation in Austria – Do they tell a consistent story? Journal of Hydrology 456–457, 30–43. DOI 10.1016/j.jhydrol.2012.05.068, https://doi.org/10.1016/j.jhydrol.2012.05.068 (English companion of HOWATI)
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