Hydrometeorologic stochastics for hydrologic applications: extremes, scales, probabilities

Over the last decades, a significant body of empirical and theoretical work has revealed the departure of statistical properties of hydrometeorological processes from the classical statistical prototype, as well as the scaling behaviour of their variables in general, and extremes in particular, in either state, space and/or time. In the meantime, extremes and more generally the statistics of hydrometeorologic processes are the key input for hydrological applications. As a classic example the estimation of design rainfall should be mentioned. Beside the estimation of the absolute rainfall amount related to a certain return period, the intra-event rainfall distribution, its spatial extension and the rainfall intensities at neighbouring stations can be required, depending on the intended application and thus the analysed scale. But design rainfall is only one among numerous hydrologic applications, which shape the framework for this session.

The estimation of the hydrometeorological extremes and probability distribution, the identification and involvement of supporting information and the hydrologic application over wide range of scales are open challenges, especially under non-stationary conditions. On the other side, hydrometeorologists had never access to so much computer power and data to face these open challenges.

This session welcomes, but is not limited to submissions on:
- Coupling stochastic approaches with deterministic hydrometeorological predictions, in order to better represent predictive uncertainty
- Development of robust statistics under non-stationary conditions for dimensioning purposes
- Development of parsimonious representations of probability distributions of hydrometeorological extremes over a wide range of scales in risk analysis applications and hazard prediction
- Improvements for reliable estimation of extremes with high return periods under consideration of upper or lower limits due to physical constraints
- Linking underlying physics and stochastics of hydrometeorologic extremes
- Exploration of supporting data sets for additional stochastic information (e.g. unintended use of other measurements, citizen scientist data, soft data, …)

An overall aim of the session is to bridge the gap between the theoretical stochastic analysis of hydrometeorological processes and its practical hydrological application.

Co-organized by NH1, co-sponsored by IAHS-ICSH
Convener: Hannes Müller-Thomy | Co-conveners: Marco Borga, Auguste Gires, Jose Luis Salinas Illarena, Alberto Viglione
vPICO presentations
| Thu, 29 Apr, 13:30–14:15 (CEST)

vPICO presentations: Thu, 29 Apr

Chairpersons: Hannes Müller-Thomy, Alberto Viglione, Auguste Gires
Ilaria Prosdocimi and Thomas Kjeldsen

The potential for changes in hydrometeorological extremes is routinely investigated by fitting change-permitting extreme value models to long-term observations, allowing one or more distribution parameters to change as a function of time or some physically-motivated covariate. In most practical extreme value analyses, the main quantity of interest though is the upper quantiles of the distribution, rather than the parameters' values. This study focuses on the changes in quantile estimates under different change-permitting models. First, metrics which measure the impact of changes in parameters on changes in quantiles are introduced. The mathematical structure of these change metrics is investigated for several models based on the Generalised Extreme Value (GEV) distribution. It is shown that for the most commonly used models, the predicted changes in the quantiles are a non-intuitive function of the distribution parameters, leading to results which are difficult to interpret. Next, it is posited that commonly used change-permitting GEV models do not preserve a constant coefficient of variation, a property that is typically assumed to hold and that is related to the scaling properties of extremes. To address these shortcomings a new (parsimonious) model is proposed: the model assumes a constant coefficient of variation, allowing the location and scale parameters to change simultaneously. The proposed model results in more interpretable changes in the quantile function. The consequences of the different modelling choices on quantile estimates are exemplified using a dataset of extreme peak river flow measurements.

How to cite: Prosdocimi, I. and Kjeldsen, T.: Understanding change in hydrometeorological extremes with statistical models - the importance of model parametrization, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1071, https://doi.org/10.5194/egusphere-egu21-1071, 2021.

Meghana Nagaraj, Srinivasan Kasturirengan, Jency Maria Sojan, and Roshan Srivastav

Extreme precipitation events are increasing due to climate change and leading to frequent flooding and severe droughts. These events vary in both space and time and are positively correlated with the climate teleconnections representing the oscillations of the ocean-atmospheric system. However, large numbers of climate signals and the precipitation response may vary at certain time lags with each climate indices. This study identifies time lags for climate indices using cross-correlation analysis between extreme precipitation and climate indices. These time-lagged climate indices are used as a covariate to fit a non-stationary generalized extreme value (NS-GEV) model over Monsoon Asia. The best NS-GEV model among non-stationary models is selected based on Akaike information criteria (AICc). Results show that the correlation between precipitation and different climate indices is spatially non-uniform. Incorporating time lag climate indices as covariate improves the performance of the non-stationary models. This study helps in understanding the teleconnections influencing the variation of extreme precipitation in a non-stationary framework and to revise the infrastructure designs and flood risk assessment.

How to cite: Nagaraj, M., Kasturirengan, S., Maria Sojan, J., and Srivastav, R.: Non-stationary Modeling of Extreme Precipitation over Monsoon Asia – Role of Teleconnection Time Lags , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3650, https://doi.org/10.5194/egusphere-egu21-3650, 2021.

Theano Iliopoulou and Demetris Koutsoyiannis

Curves of rainfall intensity at various scales and for various return periods, else known as ombrian (or IDF) curves, are central design tools in hydrology and engineering. Construction of such curves often relies heavily on empirical or semi-empirical approaches, which hinder their applicability over large scales, and preclude simulation. Recent work by Koutsoyiannis (2020) has advanced these curves to theoretically-consistent stochastic models of rainfall intensity (ombrian models) extending their applicability to the full range of available scales, e.g. from minutes to decades. We present an open-source python toolbox implementing these advances in a straightforward and user-friendly manner and prove its applicability. The toolbox also employs advanced statistical fitting methods for extremes (K-moments), accounts for bias induced by temporal dependence, and allows optional blending of daily-scale data to reduce uncertainty of sub-daily records. The end result is the parameterization of the ombrian model and the graphical representation of rainfall intensity for any range of scales (supported by the data) and return periods.

Reference: Koutsoyiannis, D. 2020. ‘Rainfall extremes and Ombrian modelling’ in Stochastics of Hydroclimatic Extremes - A Cool Look at Risk (ed 0), National Technical University of Athens, Athens, pp 243-273, http://www.itia.ntua.gr/en/docinfo/2000/.

How to cite: Iliopoulou, T. and Koutsoyiannis, D.: PythOm: A python toolbox implementing recent advances in rainfall intensity (ombrian) curves, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-389, https://doi.org/10.5194/egusphere-egu21-389, 2021.

Felix Fauer, Jana Ulrich, Oscar E. Jurado, Uwe Ulbrich, and Henning W. Rust

Intensity-Duration-Frequency (IDF) curves describe the main statistical characteristics of extreme precipitation events. Providing information on the exceedance probability or return period of certain precipitation intensities for a range of durations, IDF curves are an important tool for the design of hydrological structures.

Although the Generalized-Extreme-Value (GEV) distribution is an adequate model for annual precipitation maxima of a certain duration, the core problem of extreme value statistics remains: the limited data availability. Hence, it is reasonable to use a model that can describe all durations simultaneously. This reduces the total number of parameters and a more efficient usage of data is achieved. The idea of implementing a duration dependence directly into the parameters of the extreme value distribution and therefore obtaining a single distribution for a range of durations was proposed by Koutsoyiannis et al. (1998). However, while the use of the GEV is justified by a strong theoretical basis, only empirical models exist for the dependence of the parameters on duration.

In this study, we compare different models regarding the dependence of the GEV parameters on duration with the aim of finding a model for a wide duration range (1 min - 5 days). We use a combination of existing model features, especially curvature for small durations and multi-scaling for all durations, and extend them by a new feature that allows flattening of the IDF curves for long durations. Using the quantile score in a cross-validation setting, we provide detailed information on the duration and probability ranges for which specific features or a systematic combination of features lead to improved modeling skill.

Our results show that allowing curvature or multi-scaling improves the model only for very short or long durations, respectively, but leads to disadvantages in modeling the other duration ranges. In contrast, allowing flattening of the IDF curves leads to an improvement for medium durations between 1 hour and 1 day without affecting other duration regimes.

How to cite: Fauer, F., Ulrich, J., Jurado, O. E., Ulbrich, U., and Rust, H. W.: An Extended Model in Estimating Consistent Quantiles for Intensity-Duration-Frequency Curves, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7562, https://doi.org/10.5194/egusphere-egu21-7562, 2021.

Roberto Quaglia, Ross Woods, and Dawei Han

Determination of peak flow or flow hydrograph in ungauged basins can be affected by considerable degree of uncertainty. Despite the considerable efforts to overcome this challenge, current methods provide design flood estimates that are still highly uncertain in ungauged catchments, even in the UK where the gauged network is relatively dense. A possible solution may be found in stochastic approaches and more specifically in the Derived Flood Frequency method, which gives the possibility to decompose runoff response effects dictated by the dominant hydrological processes for a catchment under study. Data scarcity can be then circumvented by application of UK-specific stochastic models, from which rainfall events and their relevant features are sampled. In this work, the latter rainfall model will be presented as a joint distribution function of spatial and temporal moments of catchment rainfall, along with their Intensity and Total Depth. The marginal distributions for each rainfall characteristic are studied through the L-moment method, which was previously developed for regional frequency analysis. The multivariate distribution of these rainfall characteristics will be described through the Vine Copula method, which can account for dependence very flexibly among several variables. Parameterisation procedures still require more development to allow application over ungauged case of studies.

How to cite: Quaglia, R., Woods, R., and Han, D.: Joint Distribution of Rainfall Characteristics: Intensity, Total Depth, Spatial and Temporal Moments, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8961, https://doi.org/10.5194/egusphere-egu21-8961, 2021.

Jeremy Rohmer, Rodrigo Pedreros, and Yann Krien

To estimate return levels of wave heights (Hs) induced by tropical cyclones at the coast, a commonly-used approach is to (1) randomly generate a large number of synthetic cyclone events (typically >1,000); (2) numerically simulate the corresponding Hs over the whole domain of interest; (3) extract the Hs values at the desired location at the coast and (4) perform the local extreme value analysis (EVA) to derive the corresponding return level. Step 2 is however very constraining because it often involves a numerical hydrodynamic simulator that can be prohibitive to run: this might limit the number of results to perform the local EVA (typically to several hundreds). In this communication, we propose a spatial stochastic simulation procedure to increase the database size of numerical results with synthetic maps of Hs that are stochastically generated. To do so, we propose to rely on a data-driven dimensionality-reduction method, either unsupervised (Principal Component Analysis) or supervised (Partial Least Squares Regression), that is trained with a limited number of pre-existing numerically simulated Hs maps. The procedure is applied to the Guadeloupe island and results are compared to the commonly-used approach applied to a large database of Hs values computed for nearly 2,000 synthetic cyclones (representative of 3,200 years – Krien et al., NHESS, 2015). When using only a hundred of cyclones, we show that the estimates of the 100-year return levels can be achieved with a mean absolute percentage error (derived from a bootstrap-based procedure) ranging between 5 and 15% around the coasts while keeping the width of the 95% confidence interval of the same order of magnitude than the one using the full database. Without synthetic Hs maps augmentation, the error and confidence interval width are both increased by nearly 100%. A careful attention is paid to the tuning of the approach by testing the sensitivity to the spatial domain size, the information loss due to data compression, and the number of cyclones. This study has been carried within the Carib-Coast INTERREG project (https://www.interreg-caraibes.fr/carib-coast).

How to cite: Rohmer, J., Pedreros, R., and Krien, Y.: Spatial stochastic simulation to aid local extreme value analysis of cyclone-induced wave heights when numerical hydrodynamic simulations are scarce, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2081, https://doi.org/10.5194/egusphere-egu21-2081, 2021.

Faizan Anwar, András Bárdossy, and Jochen Seidel

We demonstrate that in data sparse environments, model parameter uncertainty is not the only cause of concern. To get a meaningful outcome, input data uncertainty has to be taken into account as well. The procedure involved calibration of a hydrological model using recent daily data rich time period along with validation. A historical flood was simulated (after warmup) for which the input data were relatively sparse in space, namely precipitation and temperature, using the calibrated model parameters. Precipitation was assumed to be the main driver of this event. Results showed that by only using interpolated precipitation (e.g. IDW or Kriging), the magnitude and timing of the peak were incorrect, even after using very many different parameter vectors that performed equally well for the recent times. Subsequently, the model was inverted for precipitation i.e. input fields that produced the correct timing, magnitude, dependence in space and distributions were searched for. This was done using a previously developed simulation algorithm. The new fields showed that the same hydrograph could have been produced by two main types of conditions, namely, early snow cover that melted and heavy rain. The plausibility of the simulated fields was also assessed by comparing their structure in space to events in recent times.

How to cite: Anwar, F., Bárdossy, A., and Seidel, J.: Hydrological modeling in data sparse environments, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-5040, https://doi.org/10.5194/egusphere-egu21-5040, 2021.

Hsing-Jui Wang, Soohyun Yang, Ralf Merz, and Stefano Basso

Heavy-tailed probability distributions of streamflow are frequently observed in river basins. They indicate sizable odds of extreme events in these catchments and thus signal the existence of enhanced hydrological perils. Notwithstanding their relevance for characterizing the hydrological hazard of river basins, identifying specific mechanisms which promote the emergence of heavy-tailed flow distributions has proved challenging due to the complex hydrological response of such dynamical systems exposed to highly variable rainfall inputs.

In this study we combine a continuous hydrological model grounded on the geomorphological theory of the hydrologic response with archetypical descriptions of the spatial and temporal distributions of rainfall inputs and catchment attributes to investigate physical mechanisms and stochastic features leading to the emergence of heavy tails.

In the model, soil moisture dynamics driven by the water balance in the root zone trigger superficial and subsurface runoff contributions, which are routed to the catchment outlet by means of a representation of transport by travel time distributions. The framework enables a parsimonious distributed description of hydrological processes, suitably considered with their stochastic character, and is thus fit for the goal of investigating manifold mechanisms promoting heavy-tailed streamflow distributions.

A set of archetypical spatial and temporal variabilities of rainfall inputs and catchment attributes (e.g., localized versus uniform rainfall in the catchment, lumped versus distributed catchment attributes, mainly upstream versus downstream source areas, high versus low rainfall frequency) are finally imposed in the model and their capability (or not) to affect the tail of the streamflow distribution is investigated.

The proposed framework provides a way to disentangle physical attributes of river catchments and stochastic properties of hydroclimatic variables which control the emergence of heavy-tailed streamflow distributions and thus identify the key drivers of the inherent hydrological hazard of river basins.

How to cite: Wang, H.-J., Yang, S., Merz, R., and Basso, S.: Investigating rainfall and catchment attributes promoting heavy-tailed distributions of river flows, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2682, https://doi.org/10.5194/egusphere-egu21-2682, 2021.

Luis Mediero, Enrique Soriano, Peio Oria, Stefano Bagli, Attilio Castellarin, Luis Garrote, Paolo Mazzoli, Jaroslav Mysiak, Stefania Pasetti, Simone Persiano, David Santillán, and Kai Schröter

High-intensity and short-duration storms can generate pluvial floods in urban areas. Currently, 2D hydrodynamic models are recognised to be the best tool to simulate pluvial floods. The T-year synthetic design storm is usually assumed to generate the T-year pluvial flood. However, synthetic design storms cannot represent the variability in duration, precipitation and intensity temporal distribution of real storms that should be considered to account for their influence on water depths in pluvial floods. A more sound approach consists in estimating the T-year water depth in a given location from the frequency curve of water depths generated by a long series of possible rainfall events similar to the real storms.

However, 2D hydrodynamic models require high computation times that are not well suited with stochastic simulations. The Safer_RAIN tool is a rapid hydrostatic flood model based on a filling-and-spilling technique that has been developed within the SAFERPLACES project funded by the EIT Climate-KIC (Samela et al., 2020). Depressions and links between them are identified from a digital terrain model. The continuity equation is used to simulate how depressions are filled and spill to downstream depressions. Infiltration is simulated by using a distributed implementation of the Green and Ampt model that accounts for ponding time.

In this study, a stochastic methodology to delineate pluvial flood hazards is proposed in the Pamplona metropolitan area in Spain. First, the Safer_RAIN tool has been benchmarked by using spatially distributed high-resolution quantitative precipitation estimates (QPE) at time steps of 10 minutes for three real pluvial flood events. QPEs were obtained merging the data recorded at a set of automatic weather stations from the Spanish State Meteorological Agency (AEMET), the Regional Government of Navarre and crowdsourced networks, with continuous fields of radar observations. The Safer_RAIN tool has been benchmarked with the 2D hydrodynamic IBER model. In Barañáin, the results show a bias of -0.17–0.18 m and a RMSE of 0.22–0.49 m between water depths, as well as an accuracy correlation coefficient (ACC) of 0.87–0.99. In Zizur Mayor, the bias is -0.19–0.20 m, the RMSE is 0.29–0.55 m and the ACC is between 0.88 and 0.98.

Second, a long set of 10 000 synthetic storms has been generated by using a stochastic rainfall generator based on a bivariate copula approach fitted to data recorded at four rainfall-gauging stations located close to the case study. The 10 000 synthetic storms generated with a Gumbel copula fitted to the real rainfall events have been used as input data of the Safer_RAIN tool. Safer_RAIN preprocessing was done in 112 seconds and each simulation lasted around 45 seconds. A Generalized Pareto distribution function was fitted to the 10 000 water depth values in each cell of the grid. Pluvial flood hazard maps were obtained by estimating the T-year water depth in each cell of the grid.


Samela et al. (2020). Safer_RAIN: A DEM-Based Hierarchical Filling-&-Spilling Algorithm for Pluvial Flood Hazard Assessment and Mapping across Large Urban Areas, Water, 12, 1514.

How to cite: Mediero, L., Soriano, E., Oria, P., Bagli, S., Castellarin, A., Garrote, L., Mazzoli, P., Mysiak, J., Pasetti, S., Persiano, S., Santillán, D., and Schröter, K.: A stochastic methodology for pluvial flood mapping in urban areas with a fast-processing DEM-based flooding algorithm , EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10187, https://doi.org/10.5194/egusphere-egu21-10187, 2021.

Tomohiro Tanaka, Keiko Kiyohara, and Yasuto Tachikawa

Against flood disasters to be intensified in a future climate, we are required to implement adaptation strategies on a limited budget. In urban areas, heavy rainfall-based floods are classified into two types: pluvial and fluvial floods. It is well known that fluvial floods cause deeper inundation and stronger fluid force while pluvial ones occur more frequently. Such hydrodynamic characteristics have been intensively discussed in a literature; however, their impact and the resulting damage have not yet been examined in a comprehensive manner due to small samples of storm events in one region that leads to high uncertainty in frequency analysis. In the context of climate change impact assessment on extreme events, considerable ensembles of climate data have become available, contributing to smaller uncertainty in frequency analysis of flood damages. This study presents a case study of frequency estimation of fluvial and pluvial floods in an urban area set in Nagoya City, Japan. We applied a large ensemble climate simulation database, d4PDF, to a combined pluvial and fluvial flood model, from which we derived flood risk curves for each type of flooding. The results indicated that pluvial flooding presents comparable economic risk to fluvial flooding (16% and 17% lesser damage at 50- and 100-year return periods, respectively) despite its significantly shallower flood depths (area with flood depth over 45 cm was only 10.5% and 5.4%, respectively). This is because pluvial floods widely occur over the city, including areas further away from the river. Furthermore, probably similar with other mega cities with long history, fluvial flood risk has been managed by settling the central economic district (originally the Nagoya Castle founded several centuries ago) on higher altitudes. The results suggest that pluvial flooding could have comparable economic risks to fluvial flooding in urban areas where major economic assets are widely sprawled over the city as well as historical countermeasures are implemented against fluvial flooding. Pluvial floods, countermeasures against which tend to be smaller than fluvial floods, should be managed at a comparable level in urban areas.

How to cite: Tanaka, T., Kiyohara, K., and Tachikawa, Y.: Deriving fluvial and pluvial flood risk curves using large ensemble climate simulation data with a fast 2-D flood model: A case study in Nagoya City, Japan, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3571, https://doi.org/10.5194/egusphere-egu21-3571, 2021.

Amit Singh and Sagar Chavan

The Kappa distribution is a versatile distribution and results in nine different distributions depending on its parameter values.The study presents an entropy-based method for estimating the parameters of the four parameters kappa distribution. At site data of the annual maximum flood of 30 sites of Krishna river basins are used for the study. The parameters estimated using the principle of maximum entropy (POME), method of moments, L-moments, and method of maximum likelihood is compared using Kolmogorov-Smirnov (K-S) test. The overall performance of the methods POME, MLE and L-moment are found to be comparable, whereas MOM performs with the highest bias; both the entropy method and the L-moment method allows the four-parameter kappa distribution to fit the data well and the combination of the two methods can further improve the parameter estimation of the four-parameter kappa distribution.

How to cite: Singh, A. and Chavan, S.: Estimation and Comparison of Entropy-Based Parameter Estimation for Kappa Distribution over Krishna River Basin, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-16127, https://doi.org/10.5194/egusphere-egu21-16127, 2021.