Articles | Volume 21, issue 12
https://doi.org/10.5194/hess-21-6461-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/hess-21-6461-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
18 Dec 2017
Research article |
| 18 Dec 2017
Does nonstationarity in rainfall require nonstationary intensity–duration–frequency curves?
Department of Civil Engineering, McMaster Water Resources and Hydrologic
Modelling Group, McMaster University, 1280 Main Street West, Hamilton, ON L8S 4L7, Canada
now at: GFZ German Research Centre for Geosciences, Sect. 5.4 Hydrology, 14473 Potsdam, Germany
Paulin Coulibaly
Department of Civil Engineering, McMaster Water Resources and Hydrologic
Modelling Group, McMaster University, 1280 Main Street West, Hamilton, ON L8S 4L7, Canada
Related authors
No articles found.
Olivier Champagne, M. Altaf Arain, Martin Leduc, Paulin Coulibaly, and Shawn McKenzie
Hydrol. Earth Syst. Sci., 24, 3077–3096, https://doi.org/10.5194/hess-24-3077-2020, https://doi.org/10.5194/hess-24-3077-2020, 2020
Short summary
Short summary
Using 50 members of one regional climate model and a processed-based hydrological model applied in four river basins in southern Ontario, this work focused on the winter streamflow projection uncertainties for the first half of 21st century. The results show a January–February increase of streamflow for the 50 projections due to early snowmelt and a rainfall increase. The streamflow projections are also modulated by the change of pressure patterns advecting different air masses over the region.
Olivier Champagne, Martin Leduc, Paulin Coulibaly, and M. Altaf Arain
Earth Syst. Dynam., 11, 301–318, https://doi.org/10.5194/esd-11-301-2020, https://doi.org/10.5194/esd-11-301-2020, 2020
Short summary
Short summary
Southern Ontario has seen more high flows in winter recently due to earlier snowmelt. We show that 10 mm of daily rain and temperature higher than 5 °C are necessary conditions to generate winter high flows in the historical period. These conditions are associated with high pressure on the east coast bringing warm and wet conditions from the south. In the future, as snowfall decreases, warm events will generate less high flows, while rainfall will become a greater high-flow contributor.
Sanjeev K. Jha, Durga L. Shrestha, Tricia A. Stadnyk, and Paulin Coulibaly
Hydrol. Earth Syst. Sci., 22, 1957–1969, https://doi.org/10.5194/hess-22-1957-2018, https://doi.org/10.5194/hess-22-1957-2018, 2018
Short summary
Short summary
The output from numerical weather prediction (NWP) models is known to have errors. River forecast centers in Canada mostly use precipitation forecasts directly obtained from American and Canadian NWP models. In this study, we evaluate the forecast performance of ensembles generated by a Bayesian post-processing approach in cold climates. We demonstrate that the post-processing approach generates bias-free forecasts and provides a better picture of uncertainty in the case of an extreme event.
Related subject area
Subject: Hydrometeorology | Techniques and Approaches: Stochastic approaches
Stochastic simulation of reference rainfall scenarios for hydrological applications using a universal multi-fractal approach
Atmospheric conditions favouring extreme precipitation and flash floods in temperate regions of Europe
A storm-centered multivariate modeling of extreme precipitation frequency based on atmospheric water balance
Probabilistic subseasonal precipitation forecasts using preceding atmospheric intraseasonal signals in a Bayesian perspective
Technical note: A stochastic framework for identification and evaluation of flash drought
Stochastic daily rainfall generation on tropical islands with complex topography
A gridded multi-site precipitation generator for complex terrain: An evaluation in the Austrian Alps
Modeling seasonal variations of extreme rainfall on different timescales in Germany
Compound flood potential from storm surge and heavy precipitation in coastal China: dependence, drivers, and impacts
Influence of ENSO and tropical Atlantic climate variability on flood characteristics in the Amazon basin
Conditional simulation of spatial rainfall fields using random mixing: a study that implements full control over the stochastic process
Comparison of statistical downscaling methods for climate change impact analysis on precipitation-driven drought
Technical Note: Temporal disaggregation of spatial rainfall fields with generative adversarial networks
A standardized index for assessing sub-monthly compound dry and hot conditions with application in China
Assessment of meteorological extremes using a synoptic weather generator and a downscaling model based on analogues
A new discrete multiplicative random cascade model for downscaling intermittent rainfall fields
Modelling rainfall with a Bartlett–Lewis process: new developments
Nonstationary stochastic rain type generation: accounting for climate drivers
Conditional simulation of surface rainfall fields using modified phase annealing
Climate influences on flood probabilities across Europe
Flood-related extreme precipitation in southwestern Germany: development of a two-dimensional stochastic precipitation model
A hybrid stochastic rainfall model that reproduces some important rainfall characteristics at hourly to yearly timescales
Mapping rainfall hazard based on rain gauge data: an objective cross-validation framework for model selection
On the skill of raw and post-processed ensemble seasonal meteorological forecasts in Denmark
Estimating radar precipitation in cold climates: the role of air temperature within a non-parametric framework
Dealing with non-stationarity in sub-daily stochastic rainfall models
Rainfall disaggregation for hydrological modeling: is there a need for spatial consistence?
Design water demand of irrigation for a large region using a high-dimensional Gaussian copula
Modeling the changes in water balance components of the highly irrigated western part of Bangladesh
A classification algorithm for selective dynamical downscaling of precipitation extremes
Seasonal streamflow forecasts in the Ahlergaarde catchment, Denmark: the effect of preprocessing and post-processing on skill and statistical consistency
Evaluation of ensemble precipitation forecasts generated through post-processing in a Canadian catchment
A nonparametric statistical technique for combining global precipitation datasets: development and hydrological evaluation over the Iberian Peninsula
Censored rainfall modelling for estimation of fine-scale extremes
An adaptive two-stage analog/regression model for probabilistic prediction of small-scale precipitation in France
Precipitation extremes on multiple timescales – Bartlett–Lewis rectangular pulse model and intensity–duration–frequency curves
A non-stationary stochastic ensemble generator for radar rainfall fields based on the short-space Fourier transform
Regionalizing nonparametric models of precipitation amounts on different temporal scales
A combined statistical bias correction and stochastic downscaling method for precipitation
Can local climate variability be explained by weather patterns? A multi-station evaluation for the Rhine basin
Precipitation ensembles conforming to natural variations derived from a regional climate model using a new bias correction scheme
Technical Note: The impact of spatial scale in bias correction of climate model output for hydrologic impact studies
Nonstationarity of low flows and their timing in the eastern United States
Climatological characteristics of raindrop size distributions in Busan, Republic of Korea
Correction of real-time satellite precipitation with satellite soil moisture observations
Stochastic approach to analyzing the uncertainties and possible changes in the availability of water in the future based on scenarios of climate change
Attribution of European precipitation and temperature trends to changes in synoptic circulation
Spatial and temporal variability of rainfall in the Nile Basin
Inter-comparison of statistical downscaling methods for projection of extreme precipitation in Europe
Imperfect scaling in distributions of radar-derived rainfall fields
Arun Ramanathan, Pierre-Antoine Versini, Daniel Schertzer, Remi Perrin, Lionel Sindt, and Ioulia Tchiguirinskaia
Hydrol. Earth Syst. Sci., 26, 6477–6491, https://doi.org/10.5194/hess-26-6477-2022, https://doi.org/10.5194/hess-26-6477-2022, 2022
Short summary
Short summary
Reference rainfall scenarios are indispensable for hydrological applications such as designing storm-water management infrastructure, including green roofs. Therefore, a new method is suggested for simulating rainfall scenarios of specified intensity, duration, and frequency, with realistic intermittency. Furthermore, novel comparison metrics are proposed to quantify the effectiveness of the presented simulation procedure.
Judith Meyer, Malte Neuper, Luca Mathias, Erwin Zehe, and Laurent Pfister
Hydrol. Earth Syst. Sci., 26, 6163–6183, https://doi.org/10.5194/hess-26-6163-2022, https://doi.org/10.5194/hess-26-6163-2022, 2022
Short summary
Short summary
We identified and analysed the major atmospheric components of rain-intense thunderstorms that can eventually lead to flash floods: high atmospheric moisture, sufficient latent instability, and weak thunderstorm cell motion. Between 1981 and 2020, atmospheric conditions became likelier to support strong thunderstorms. However, the occurrence of extreme rainfall events as well as their rainfall intensity remained mostly unchanged.
Yuan Liu and Daniel B. Wright
Hydrol. Earth Syst. Sci., 26, 5241–5267, https://doi.org/10.5194/hess-26-5241-2022, https://doi.org/10.5194/hess-26-5241-2022, 2022
Short summary
Short summary
We present a new approach to estimate extreme rainfall probability and severity using the atmospheric water balance, where precipitation is the sum of water vapor components moving in and out of a storm. We apply our method to the Mississippi Basin and its five major subbasins. Our approach achieves a good fit to reference precipitation, indicating that the rainfall probability estimation can benefit from additional information from physical processes that control rainfall.
Yuan Li, Zhiyong Wu, Hai He, and Hao Yin
Hydrol. Earth Syst. Sci., 26, 4975–4994, https://doi.org/10.5194/hess-26-4975-2022, https://doi.org/10.5194/hess-26-4975-2022, 2022
Short summary
Short summary
The relationship between atmospheric intraseasonal signals and precipitation is highly uncertain and depends on the region and lead time. In this study, we develop a spatiotemporal projection, based on a Bayesian hierarchical model (STP-BHM), to address the above challenge. The results suggest that the STP-BHM model is skillful and reliable for probabilistic subseasonal precipitation forecasts over China during the boreal summer monsoon season.
Yuxin Li, Sisi Chen, Jun Yin, and Xing Yuan
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2022-313, https://doi.org/10.5194/hess-2022-313, 2022
Revised manuscript accepted for HESS
Short summary
Short summary
Flash drought is referred to the rapid development of drought events with fast decline of soil moisture, which can pose serious impacts on agriculture, ecosystem, human health, and society. While flash drought have received much research attention, there is no consensus on its definition. Here we used a stochastic water balance framework to quantify the timing of soil moisture crossing any given thresholds, providing an efficient tool for diagnosing and monitoring flash drought.
Lionel Benoit, Lydie Sichoix, Alison D. Nugent, Matthew P. Lucas, and Thomas W. Giambelluca
Hydrol. Earth Syst. Sci., 26, 2113–2129, https://doi.org/10.5194/hess-26-2113-2022, https://doi.org/10.5194/hess-26-2113-2022, 2022
Short summary
Short summary
This study presents a probabilistic model able to reproduce the spatial patterns of rainfall on tropical islands with complex topography. It sheds new light on rainfall variability at the island scale, and explores the links between rainfall patterns and atmospheric circulation. The proposed model has been tested on two islands of the tropical Pacific, and demonstrates good skills in simulating both site-specific and island-scale rain behavior.
Hetal Dabhi, Mathias Rotach, and Michael Oberguggenberger
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2022-21, https://doi.org/10.5194/hess-2022-21, 2022
Revised manuscript accepted for HESS
Short summary
Short summary
High-resolution precipitation data consistent both in space and time for current and future climate are required for climate change impact assessments, but it is very challenging for complex topography. We present a model that generates synthetic gridded data of daily precipitation at 1 km spatial resolution using observed meteorological station data as input and provides data where historical observations are not available. We evaluate this model for a mountainous region in the European Alps.
Jana Ulrich, Felix S. Fauer, and Henning W. Rust
Hydrol. Earth Syst. Sci., 25, 6133–6149, https://doi.org/10.5194/hess-25-6133-2021, https://doi.org/10.5194/hess-25-6133-2021, 2021
Short summary
Short summary
The characteristics of extreme precipitation on different timescales as well as in different seasons are relevant information, e.g., for designing hydrological structures or managing water supplies. Therefore, our aim is to describe these characteristics simultaneously within one model. We find similar characteristics for short extreme precipitation at all considered stations in Germany but pronounced regional differences with respect to the seasonality of long-lasting extreme events.
Jiayi Fang, Thomas Wahl, Jian Fang, Xun Sun, Feng Kong, and Min Liu
Hydrol. Earth Syst. Sci., 25, 4403–4416, https://doi.org/10.5194/hess-25-4403-2021, https://doi.org/10.5194/hess-25-4403-2021, 2021
Short summary
Short summary
A comprehensive assessment of compound flooding potential is missing for China. We investigate dependence, drivers, and impacts of storm surge and precipitation for coastal China. Strong dependence exists between driver combinations, with variations of seasons and thresholds. Sea level rise escalates compound flood potential. Meteorology patterns are pronounced for low and high compound flood potential. Joint impacts from surge and precipitation were much higher than from each individually.
Jamie Towner, Andrea Ficchí, Hannah L. Cloke, Juan Bazo, Erin Coughlan de Perez, and Elisabeth M. Stephens
Hydrol. Earth Syst. Sci., 25, 3875–3895, https://doi.org/10.5194/hess-25-3875-2021, https://doi.org/10.5194/hess-25-3875-2021, 2021
Short summary
Short summary
We examine whether several climate indices alter the magnitude, timing and duration of floods in the Amazon. We find significant changes in both flood magnitude and duration, particularly in the north-eastern Amazon for negative SST years in the central Pacific Ocean. This response is not repeated when the negative anomaly is positioned further east. These results have important implications for both social and physical sectors working towards the improvement of flood early warning systems.
Jieru Yan, Fei Li, András Bárdossy, and Tao Tao
Hydrol. Earth Syst. Sci., 25, 3819–3835, https://doi.org/10.5194/hess-25-3819-2021, https://doi.org/10.5194/hess-25-3819-2021, 2021
Short summary
Short summary
Accurate spatial precipitation estimates are important in various fields. An approach to simulate spatial rainfall fields conditioned on radar and rain gauge data is proposed. Unlike the commonly used Kriging methods, which provide a Kriged mean field, the output of the proposed approach is an ensemble of estimates that represents the estimation uncertainty. The approach is robust to nonlinear error in radar estimates and is shown to have some advantages, especially when estimating the extremes.
Hossein Tabari, Santiago Mendoza Paz, Daan Buekenhout, and Patrick Willems
Hydrol. Earth Syst. Sci., 25, 3493–3517, https://doi.org/10.5194/hess-25-3493-2021, https://doi.org/10.5194/hess-25-3493-2021, 2021
Sebastian Scher and Stefanie Peßenteiner
Hydrol. Earth Syst. Sci., 25, 3207–3225, https://doi.org/10.5194/hess-25-3207-2021, https://doi.org/10.5194/hess-25-3207-2021, 2021
Short summary
Short summary
In hydrology, it is often necessary to infer from a daily sum of precipitation a possible distribution over the day – for example how much it rained in each hour. In principle, for a given daily sum, there are endless possibilities. However, some are more likely than others. We show that a method from artificial intelligence called generative adversarial networks (GANs) can
learnwhat a typical distribution over the day looks like.
Jun Li, Zhaoli Wang, Xushu Wu, Jakob Zscheischler, Shenglian Guo, and Xiaohong Chen
Hydrol. Earth Syst. Sci., 25, 1587–1601, https://doi.org/10.5194/hess-25-1587-2021, https://doi.org/10.5194/hess-25-1587-2021, 2021
Short summary
Short summary
We introduce a daily-scale index, termed the standardized compound drought and heat index (SCDHI), to measure the key features of compound dry-hot conditions. SCDHI can not only monitor the long-term compound dry-hot events, but can also capture such events at sub-monthly scale and reflect the related vegetation activity impacts. The index can provide a new tool to quantify sub-monthly characteristics of compound dry-hot events, which are vital for releasing early and timely warning.
Damien Raynaud, Benoit Hingray, Guillaume Evin, Anne-Catherine Favre, and Jérémy Chardon
Hydrol. Earth Syst. Sci., 24, 4339–4352, https://doi.org/10.5194/hess-24-4339-2020, https://doi.org/10.5194/hess-24-4339-2020, 2020
Short summary
Short summary
This research paper proposes a weather generator combining two sampling approaches. A first generator recombines large-scale atmospheric situations. A second generator is applied to these atmospheric trajectories in order to simulate long time series of daily regional precipitation and temperature. The method is applied to daily time series in Switzerland. It reproduces adequately the observed climatology and improves the reproduction of extreme precipitation values.
Marc Schleiss
Hydrol. Earth Syst. Sci., 24, 3699–3723, https://doi.org/10.5194/hess-24-3699-2020, https://doi.org/10.5194/hess-24-3699-2020, 2020
Short summary
Short summary
A new way to downscale rainfall fields based on the notion of equal-volume areas (EVAs) is proposed. Experiments conducted on 100 rainfall events in the Netherlands show that the EVA method outperforms classical methods based on fixed grid cell sizes, producing fields with more realistic spatial structures. The main novelty of the method lies in its adaptive sampling strategy, which avoids many of the mathematical challenges associated with the presence of zero rainfall values.
Christian Onof and Li-Pen Wang
Hydrol. Earth Syst. Sci., 24, 2791–2815, https://doi.org/10.5194/hess-24-2791-2020, https://doi.org/10.5194/hess-24-2791-2020, 2020
Short summary
Short summary
The randomised Bartlett–Lewis (RBL) model is widely used to synthesise rainfall time series with realistic statistical features. However, it tended to underestimate rainfall extremes at sub-hourly and hourly timescales. In this paper, we revisit the derivation of equations that represent rainfall properties and compare statistical estimation methods that impact model calibration. These changes effectively improved the RBL model's capacity to reproduce sub-hourly and hourly rainfall extremes.
Lionel Benoit, Mathieu Vrac, and Gregoire Mariethoz
Hydrol. Earth Syst. Sci., 24, 2841–2854, https://doi.org/10.5194/hess-24-2841-2020, https://doi.org/10.5194/hess-24-2841-2020, 2020
Short summary
Short summary
At subdaily resolution, rain intensity exhibits a strong variability in space and time due to the diversity of processes that produce rain (e.g., frontal storms, mesoscale convective systems and local convection). In this paper we explore a new method to simulate rain type time series conditional to meteorological covariates. Afterwards, we apply stochastic rain type simulation to the downscaling of precipitation of a regional climate model.
Jieru Yan, András Bárdossy, Sebastian Hörning, and Tao Tao
Hydrol. Earth Syst. Sci., 24, 2287–2301, https://doi.org/10.5194/hess-24-2287-2020, https://doi.org/10.5194/hess-24-2287-2020, 2020
Short summary
Short summary
For applications such as flood forecasting of urban- or town-scale distributed hydrological modeling, high-resolution quantitative precipitation estimation (QPE) with enough accuracy is the most important driving factor and thus the focus of this paper. Considering the fact that rain gauges are sparse but accurate and radar-based precipitation estimates are inaccurate but densely distributed, we are merging the two types of data intellectually to obtain accurate QPEs with high resolution.
Eva Steirou, Lars Gerlitz, Heiko Apel, Xun Sun, and Bruno Merz
Hydrol. Earth Syst. Sci., 23, 1305–1322, https://doi.org/10.5194/hess-23-1305-2019, https://doi.org/10.5194/hess-23-1305-2019, 2019
Short summary
Short summary
We investigate whether flood probabilities in Europe vary for different large-scale atmospheric circulation conditions. Maximum seasonal river flows from 600 gauges in Europe and five synchronous atmospheric circulation indices are analyzed. We find that a high percentage of stations is influenced by at least one of the climate indices, especially during winter. These results can be useful for preparedness and damage planning by (re-)insurance companies.
Florian Ehmele and Michael Kunz
Hydrol. Earth Syst. Sci., 23, 1083–1102, https://doi.org/10.5194/hess-23-1083-2019, https://doi.org/10.5194/hess-23-1083-2019, 2019
Short summary
Short summary
The risk estimation of precipitation events with high recurrence periods is difficult due to the limited timescale with meteorological observations and an inhomogeneous distribution of rain gauges, especially in mountainous terrains. In this study a spatially high resolved analytical model, designed for stochastic simulations of flood-related precipitation, is developed and applied to an investigation area in Germany but is transferable to other areas. High conformity with observations is found.
Jeongha Park, Christian Onof, and Dongkyun Kim
Hydrol. Earth Syst. Sci., 23, 989–1014, https://doi.org/10.5194/hess-23-989-2019, https://doi.org/10.5194/hess-23-989-2019, 2019
Short summary
Short summary
Rainfall data are often unavailable for the analysis of water-related problems such as floods and droughts. In such cases, researchers use rainfall generators to produce synthetic rainfall data. However, data from most rainfall generators can serve only one specific purpose; i.e. one rainfall generator cannot be applied to analyse both floods and droughts. To overcome this issue, we invented a multipurpose rainfall generator that can be applied to analyse most water-related problems.
Juliette Blanchet, Emmanuel Paquet, Pradeebane Vaittinada Ayar, and David Penot
Hydrol. Earth Syst. Sci., 23, 829–849, https://doi.org/10.5194/hess-23-829-2019, https://doi.org/10.5194/hess-23-829-2019, 2019
Short summary
Short summary
We propose an objective framework for estimating rainfall cumulative distribution functions in a region when data are only available at rain gauges. Our methodology allows us to assess goodness-of-fit of the full distribution, but with a particular focus on its tail. It is applied to daily rainfall in the Ardèche catchment in the south of France. Results show a preference for a mixture of Gamma distribution over seasons and weather patterns, with parameters interpolated with a thin plate spline.
Diana Lucatero, Henrik Madsen, Jens C. Refsgaard, Jacob Kidmose, and Karsten H. Jensen
Hydrol. Earth Syst. Sci., 22, 6591–6609, https://doi.org/10.5194/hess-22-6591-2018, https://doi.org/10.5194/hess-22-6591-2018, 2018
Short summary
Short summary
The present study evaluates the skill of a seasonal forecasting system for hydrological relevant variables in Denmark. Linear scaling and quantile mapping were used to correct the forecasts. Uncorrected forecasts tend to be more skillful than climatology, in general, for the first month lead time only. Corrected forecasts show a reduced bias in the mean; are more consistent; and show a level of accuracy that is closer to, although no higher than, that of ensemble climatology, in general.
Kuganesan Sivasubramaniam, Ashish Sharma, and Knut Alfredsen
Hydrol. Earth Syst. Sci., 22, 6533–6546, https://doi.org/10.5194/hess-22-6533-2018, https://doi.org/10.5194/hess-22-6533-2018, 2018
Short summary
Short summary
This study investigates the use of gauge precipitation and air temperature observations to ascertain radar precipitation in cold climates. The use of air temperature as an additional variable in a non-parametric model improved the estimation of radar precipitation significantly. Further, it was found that the temperature effects became insignificant when air temperature was above 10 °C. The findings from this study could be important for using radar precipitation for hydrological applications.
Lionel Benoit, Mathieu Vrac, and Gregoire Mariethoz
Hydrol. Earth Syst. Sci., 22, 5919–5933, https://doi.org/10.5194/hess-22-5919-2018, https://doi.org/10.5194/hess-22-5919-2018, 2018
Short summary
Short summary
We propose a method for unsupervised classification of the space–time–intensity structure of weather radar images. The resulting classes are interpreted as rain types, i.e. pools of rain fields with homogeneous statistical properties. Rain types can in turn be used to define stationary periods for further stochastic rainfall modelling. The application of rain typing to real data indicates that non-stationarity can be significant within meteorological seasons, and even within a single storm.
Hannes Müller-Thomy, Markus Wallner, and Kristian Förster
Hydrol. Earth Syst. Sci., 22, 5259–5280, https://doi.org/10.5194/hess-22-5259-2018, https://doi.org/10.5194/hess-22-5259-2018, 2018
Short summary
Short summary
Rainfall time series are disaggregated from daily to hourly values to be used for rainfall–runoff modeling of mesoscale catchments. Spatial rainfall consistency is implemented afterwards using simulated annealing. With the calibration process applied, observed runoff statistics (e.g., summer and winter peak flows) are represented well. However, rainfall datasets with under- or over-estimation of spatial consistency lead to similar results, so the need for a good representation can be questioned.
Xinjun Tu, Yiliang Du, Vijay P. Singh, Xiaohong Chen, Kairong Lin, and Haiou Wu
Hydrol. Earth Syst. Sci., 22, 5175–5189, https://doi.org/10.5194/hess-22-5175-2018, https://doi.org/10.5194/hess-22-5175-2018, 2018
Short summary
Short summary
For given frequencies of precipitation of a large region, design water demands of irrigation of the entire region among three methods, i.e., equalized frequency, typical year and most-likely weight function, slightly differed, but their alterations in sub-regions were complicated. A design procedure using the most-likely weight function in association with a high-dimensional copula, which built a linkage between regional frequency and sub-regional frequency of precipitation, is recommended.
A. T. M. Sakiur Rahman, M. Shakil Ahmed, Hasnat Mohammad Adnan, Mohammad Kamruzzaman, M. Abdul Khalek, Quamrul Hasan Mazumder, and Chowdhury Sarwar Jahan
Hydrol. Earth Syst. Sci., 22, 4213–4228, https://doi.org/10.5194/hess-22-4213-2018, https://doi.org/10.5194/hess-22-4213-2018, 2018
Edmund P. Meredith, Henning W. Rust, and Uwe Ulbrich
Hydrol. Earth Syst. Sci., 22, 4183–4200, https://doi.org/10.5194/hess-22-4183-2018, https://doi.org/10.5194/hess-22-4183-2018, 2018
Short summary
Short summary
Kilometre-scale climate-model data are of great benefit to both hydrologists and end users studying extreme precipitation, though often unavailable due to the computational expense associated with such high-resolution simulations. We develop a method which identifies days with enhanced risk of extreme rainfall over a catchment, so that high-resolution simulations can be performed only when such a risk exists, reducing computational expense by over 90 % while still well capturing the extremes.
Diana Lucatero, Henrik Madsen, Jens C. Refsgaard, Jacob Kidmose, and Karsten H. Jensen
Hydrol. Earth Syst. Sci., 22, 3601–3617, https://doi.org/10.5194/hess-22-3601-2018, https://doi.org/10.5194/hess-22-3601-2018, 2018
Short summary
Short summary
The skill of an experimental streamflow forecast system in the Ahlergaarde catchment, Denmark, is analyzed. Inputs to generate the forecasts are taken from the ECMWF System 4 seasonal forecasting system and an ensemble of observations (ESP). Reduction of biases is achieved by processing the meteorological and/or streamflow forecasts. In general, this is not sufficient to ensure a higher level of accuracy than the ESP, indicating a modest added value of a seasonal meteorological system.
Sanjeev K. Jha, Durga L. Shrestha, Tricia A. Stadnyk, and Paulin Coulibaly
Hydrol. Earth Syst. Sci., 22, 1957–1969, https://doi.org/10.5194/hess-22-1957-2018, https://doi.org/10.5194/hess-22-1957-2018, 2018
Short summary
Short summary
The output from numerical weather prediction (NWP) models is known to have errors. River forecast centers in Canada mostly use precipitation forecasts directly obtained from American and Canadian NWP models. In this study, we evaluate the forecast performance of ensembles generated by a Bayesian post-processing approach in cold climates. We demonstrate that the post-processing approach generates bias-free forecasts and provides a better picture of uncertainty in the case of an extreme event.
Md Abul Ehsan Bhuiyan, Efthymios I. Nikolopoulos, Emmanouil N. Anagnostou, Pere Quintana-Seguí, and Anaïs Barella-Ortiz
Hydrol. Earth Syst. Sci., 22, 1371–1389, https://doi.org/10.5194/hess-22-1371-2018, https://doi.org/10.5194/hess-22-1371-2018, 2018
Short summary
Short summary
This study investigates the use of a nonparametric model for combining multiple global precipitation datasets and characterizing estimation uncertainty. Inputs to the model included three satellite precipitation products, an atmospheric reanalysis precipitation dataset, satellite-derived near-surface daily soil moisture data, and terrain elevation. We evaluated the technique based on high-resolution reference precipitation data and further used generated ensembles to force a hydrological model.
David Cross, Christian Onof, Hugo Winter, and Pietro Bernardara
Hydrol. Earth Syst. Sci., 22, 727–756, https://doi.org/10.5194/hess-22-727-2018, https://doi.org/10.5194/hess-22-727-2018, 2018
Short summary
Short summary
Extreme rainfall is one of the most significant natural hazards. However, estimating very large events is highly uncertain. We present a new approach to construct intense rainfall using the structure of rainfall generation in clouds. The method is particularly effective at estimating short-duration extremes, which can be the most damaging. This is expected to have immediate impact for the estimation of very rare downpours, with the potential to improve climate resilience and hazard preparedness.
Jérémy Chardon, Benoit Hingray, and Anne-Catherine Favre
Hydrol. Earth Syst. Sci., 22, 265–286, https://doi.org/10.5194/hess-22-265-2018, https://doi.org/10.5194/hess-22-265-2018, 2018
Short summary
Short summary
We present a two-stage statistical downscaling model for the probabilistic prediction of local precipitation, where the downscaling statistical link is estimated from atmospheric circulation analogs of the current prediction day.
The model allows for a day-to-day adaptive and tailored downscaling. It can reveal specific predictors for peculiar and non-frequent weather configurations. This approach noticeably improves the skill of the prediction for both precipitation occurrence and quantity.
Christoph Ritschel, Uwe Ulbrich, Peter Névir, and Henning W. Rust
Hydrol. Earth Syst. Sci., 21, 6501–6517, https://doi.org/10.5194/hess-21-6501-2017, https://doi.org/10.5194/hess-21-6501-2017, 2017
Short summary
Short summary
A stochastic model for precipitation is used to simulate an observed precipitation series; it is compared to the original series in terms of intensity–duration frequency curves. Basis for the latter curves is a parametric model for the duration dependence of the underlying extreme value model allowing a consistent estimation of one single duration-dependent distribution using all duration series simultaneously. The stochastic model reproduces the curves except for very rare extreme events.
Daniele Nerini, Nikola Besic, Ioannis Sideris, Urs Germann, and Loris Foresti
Hydrol. Earth Syst. Sci., 21, 2777–2797, https://doi.org/10.5194/hess-21-2777-2017, https://doi.org/10.5194/hess-21-2777-2017, 2017
Short summary
Short summary
Stochastic generators are effective tools for the quantification of uncertainty in a number of applications with weather radar data, including quantitative precipitation estimation and very short-term forecasting. However, most of the current stochastic rainfall field generators cannot handle spatial non-stationarity. We propose an approach based on the short-space Fourier transform, which aims to reproduce the local spatial structure of the observed rainfall fields.
Tobias Mosthaf and András Bárdossy
Hydrol. Earth Syst. Sci., 21, 2463–2481, https://doi.org/10.5194/hess-21-2463-2017, https://doi.org/10.5194/hess-21-2463-2017, 2017
Short summary
Short summary
Parametric distribution functions are commonly used to model precipitation amounts at gauged and ungauged locations. Nonparametric distributions offer a more flexible way to model precipitation amounts. However, the nonparametric models do not exhibit parameters that can be easily regionalized for application at ungauged locations. To overcome this deficiency, we present a new interpolation scheme for nonparametric models and evaluate the usage of daily gauges for sub-daily resolutions.
Claudia Volosciuk, Douglas Maraun, Mathieu Vrac, and Martin Widmann
Hydrol. Earth Syst. Sci., 21, 1693–1719, https://doi.org/10.5194/hess-21-1693-2017, https://doi.org/10.5194/hess-21-1693-2017, 2017
Short summary
Short summary
For impact modeling, infrastructure design, or adaptation strategy planning, high-quality climate data on the point scale are often demanded. Due to the scale gap between gridbox and point scale and biases in climate models, we combine a statistical bias correction and a stochastic downscaling model and apply it to climate model-simulated precipitation. The method performs better in summer than in winter and in winter best for mild winter climate (Mediterranean) and worst for continental winter.
Aline Murawski, Gerd Bürger, Sergiy Vorogushyn, and Bruno Merz
Hydrol. Earth Syst. Sci., 20, 4283–4306, https://doi.org/10.5194/hess-20-4283-2016, https://doi.org/10.5194/hess-20-4283-2016, 2016
Short summary
Short summary
To understand past flood changes in the Rhine catchment and the role of anthropogenic climate change in extreme flows, an attribution study relying on a proper GCM (general circulation model) downscaling is needed. A downscaling based on conditioning a stochastic weather generator on weather patterns is a promising approach. Here the link between patterns and local climate is tested, and the skill of GCMs in reproducing these patterns is evaluated.
Kue Bum Kim, Hyun-Han Kwon, and Dawei Han
Hydrol. Earth Syst. Sci., 20, 2019–2034, https://doi.org/10.5194/hess-20-2019-2016, https://doi.org/10.5194/hess-20-2019-2016, 2016
Short summary
Short summary
A primary advantage of using model ensembles for climate change impact studies is to represent the uncertainties associated with models through the ensemble spread. Currently, most of the conventional bias correction methods adjust all the ensemble members to one reference observation. As a result, the ensemble spread is degraded during bias correction. However the proposed method is able to correct the bias and conform to the ensemble spread so that the ensemble information can be better used.
E. P. Maurer, D. L. Ficklin, and W. Wang
Hydrol. Earth Syst. Sci., 20, 685–696, https://doi.org/10.5194/hess-20-685-2016, https://doi.org/10.5194/hess-20-685-2016, 2016
Short summary
Short summary
To translate climate model output from its native coarse scale to a finer scale more representative of that at which societal impacts are experienced, a common method applied is statistical downscaling. A component of many statistical downscaling techniques is quantile mapping (QM). QM can be applied at different spatial scales, and here we study how skill varies with spatial scale. We find the highest skill is generally obtained when applying QM at approximately a 50 km spatial scale.
S. Sadri, J. Kam, and J. Sheffield
Hydrol. Earth Syst. Sci., 20, 633–649, https://doi.org/10.5194/hess-20-633-2016, https://doi.org/10.5194/hess-20-633-2016, 2016
Short summary
Short summary
Low flows are a critical part of the river flow regime but little is known about how they are changing in response to human influences and climate. We analyzed low flow records across the eastern US and identified sites that were minimally influenced by human activities. We found a general increasing trend in low flows across the northeast and decreasing trend across the southeast that are likely driven by changes in climate. The results have implications for how we manage our water resources.
S.-H. Suh, C.-H. You, and D.-I. Lee
Hydrol. Earth Syst. Sci., 20, 193–207, https://doi.org/10.5194/hess-20-193-2016, https://doi.org/10.5194/hess-20-193-2016, 2016
Short summary
Short summary
This paper was written to find the climatological characteristics of raindrop size distribution (DSD) with respect to the wind direction in Busan, Korea. The data were collected by POSS disdrometer during 4 years (2001–2004).
Busan shows the tendency of land-sea breeze. When sea wind blows during rainfall period, mean size and number concentration of raindrop are smaller and larger than that of land wind blows, respectively. It means that the features of DSD depend on the wind direction.
W. Zhan, M. Pan, N. Wanders, and E. F. Wood
Hydrol. Earth Syst. Sci., 19, 4275–4291, https://doi.org/10.5194/hess-19-4275-2015, https://doi.org/10.5194/hess-19-4275-2015, 2015
G. G. Oliveira, O. C. Pedrollo, and N. M. R. Castro
Hydrol. Earth Syst. Sci., 19, 3585–3604, https://doi.org/10.5194/hess-19-3585-2015, https://doi.org/10.5194/hess-19-3585-2015, 2015
Short summary
Short summary
The objective of this study was to analyze the changes and uncertainties related to water availability in the future, in the Ijuí River basin (south of Brazil), using a stochastic approach. In general the results showed a trend to increased flows. It can be concluded that there is a tendency to increase the hydrological variability during the period between 2011 and 2040, which indicates the possibility of occurrence of time series with more marked periods of droughts and floods.
A. K. Fleig, L. M. Tallaksen, P. James, H. Hisdal, and K. Stahl
Hydrol. Earth Syst. Sci., 19, 3093–3107, https://doi.org/10.5194/hess-19-3093-2015, https://doi.org/10.5194/hess-19-3093-2015, 2015
C. Onyutha and P. Willems
Hydrol. Earth Syst. Sci., 19, 2227–2246, https://doi.org/10.5194/hess-19-2227-2015, https://doi.org/10.5194/hess-19-2227-2015, 2015
Short summary
Short summary
Variability of rainfall in the Nile Basin was found linked to the large-scale atmosphere-ocean interactions. This finding is vital for a number of water management and planning aspects. To give just one example, it may help in obtaining improved quantiles for flood or drought/water scarcity risk management. This is especially important under conditions of (1) questionable data quality, and (2) data scarcity. These conditions are typical of the Nile Basin and inevitably need to be addressed.
M. A. Sunyer, Y. Hundecha, D. Lawrence, H. Madsen, P. Willems, M. Martinkova, K. Vormoor, G. Bürger, M. Hanel, J. Kriaučiūnienė, A. Loukas, M. Osuch, and I. Yücel
Hydrol. Earth Syst. Sci., 19, 1827–1847, https://doi.org/10.5194/hess-19-1827-2015, https://doi.org/10.5194/hess-19-1827-2015, 2015
M. J. van den Berg, L. Delobbe, and N. E. C. Verhoest
Hydrol. Earth Syst. Sci., 18, 5331–5344, https://doi.org/10.5194/hess-18-5331-2014, https://doi.org/10.5194/hess-18-5331-2014, 2014
Cited articles
Adamowski, K. and Bougadis, J.: Detection of trends in annual extreme rainfall, Hydrol. Process., 17, 3547–3560, 2003.
Agilan, V. and Umamahesh, N. V.: What are the best covariates for developing non-stationary rainfall Intensity–Duration–Frequency relationship?, Adv. Water Resour., 101, 11–22, 2017.
Ali, H. and Mishra, V.: Contrasting response of rainfall extremes to increase in surface air and dewpoint temperatures at urban locations in India, Sci. Rep.-UK, 7, 1228, https://doi.org/10.1038/s41598-017-01306-1, 2017.
ASCE: Standard Guidelines for the Design of Urban Stormwater Systems, Standard Guidelines for Installation of Urban Stormwater Systems, and Standard Guidelines for the Operation and Maintenance of Urban Stormwater Systems, ASCE/EWRI 45-05, 46-05, and 47-05, American Society of Civil Engineers, Reston, VA, available at: https://ascelibrary.org/doi/book/10.1061/9780784408063 (last access: 9 December 2016), 2006.
Baldwin, D. J. B., Desloges, J. R., and Band, L. E.: Physical geography of Ontario, in: Ecology of a Managed Terrestrial Landscape: Patterns and Processes of Forest Landscapes in Ontario, University of British Columbia Press, Vancouver, 2011.
Ban, N., Schmidli, J., and Schär, C.: Evaluation of the convection-resolving regional climate modeling approach in decade-long simulations, J. Geophys. Res.-Atmos., 119, 7889–7907, 2014.
Berg, P., Moseley, C., and Haerter, J. O.: Strong increase in convective precipitation in response to higher temperatures, Nat. Geosci., 6, 181–185, 2013.
Benjamini, Y. and Hochberg, Y.: Controlling the false discovery rate: a practical and powerful approach to multiple testing, J. Roy. Stat. Soc. B Met., 57, 289–300, 1995.
Berkley Earth: Local climate change: 44.20° N, 80.50° W, available at: http://berkeleyearth.lbl.gov, last access: December 2017.
Blenkinsop, S., Chan, S. C., Kendon, E. J., Roberts, N. M., and Fowler, H. J.: Temperature influences on intense UK hourly precipitation and dependency on large-scale circulation, Environ. Res. Lett., 10, 054021, 2015.
Bougadis, J. and Adamowski, K.: Scaling model of a rainfall intensity–duration–frequency relationship, Hydrol. Process., 20, 3747–3757, 2006.
Bourne, L. S. and Simmons, J.: New fault lines? Recent trends in the Canadian Urban System and their implications for planning and public policy, Can. J. Urban Res., 12, 22–47, 2003.
Burn, D. H. and Taleghani, A.: Estimates of changes in design rainfall values for Canada, Hydrol. Process., 27, 1590–1599, 2013.
Burnham, K. P. and Anderson, D. R.: Multimodel inference understanding AIC and BIC in model selection, Sociol. Methods Res., 33, 261–304, 2004.
Cannon, A. J.: A flexible nonlinear modelling framework for nonstationary generalized extreme value analysis in hydroclimatology, Hydrol. Process., 24, 673–685, https://doi.org/10.1002/hyp.7506, 2010.
Carvalho, L. M., Jones, C., and Liebmann, B.: Extreme precipitation events in southeastern South America and large-scale convective patterns in the South Atlantic convergence zone, J. Climate, 15, 2377–2394, 2002.
Castellarin, A., Kohnová, S., Gaál, L., Fleig, A., Salinas, J. L., Toumazis, A., Kjeldsen, T. R., and Macdonald, N.: Review of applied-statistical methods for flood-frequency analysis in Europe, available at: http://nora.nerc.ac.uk/19286/ (last access: 20 May 2017), 2012.
CCF (Canadian Climate Forum): Extreme Weather, 1, 1–4, Ottawa, available at: http://www.climateforum.ca/ (last access: December 2016), 2013.
CDD (Canadian Disaster Database): Public Safety Canada, available at: https://www.publicsafety.gc.ca/cnt/rsrcs/cndn-dsstr-dtbs/index-en.aspx (last access: December 2016), 2015.
Cheng, L. and AghaKouchak, A.: Nonstationary precipitation intensity-duration-frequency curves for infrastructure design in a changing climate, Sci. Rep.-UK, 4, 7093, https://doi.org/10.1038/srep07093, 2014.
Cheng, C. S., Li, G., Li, Q., and Auld, H.: A synoptic weather typing approach to simulate daily rainfall and extremes in Ontario, Canada: potential for climate change projections, J. Appl. Meteorol. Clim., 49, 845–866, https://doi.org/10.1175/2010JAMC2016.1, 2010.
Cheng, L., AghaKouchak, A., Gilleland, E., and Katz, R. W.: Non-stationary extreme value analysis in a changing climate, Climatic Change, 127, 353–369, 2014.
Chowdhury, A. and Mavrotas, G.: FDI and growth: what causes what?, World Econ., 29, 9–19, 2006.
Coles, S.: An Introduction to Statistical Modeling of Extreme Values, Springer, 1–183, 2001.
Coulibaly, P. and Shi, X.: Identification of the effect of climate change on future design standards of drainage infrastructure in Ontario, Rep. Prep. McMaster Univ. Funding Minist. Transp. Ont., 82, available at: http://www.cspi.ca/sites/default/files/download/Final_MTO_Report_June2005rv.pdf (last access: 9 December 2016), 2005.
Coulibaly, P., Burn, D., Switzman, H., Henderson, J., and Fausto, E.: A comparison of future IDF curves for Southern Ontario, Technical Report, McMaster University, Hamilton, available at: https://climateconnections.ca/wp-content/uploads/2014/01/IDF-Comparison-Report-and-Addendum.pdf (last access: 9 December 2016), 2015.
CSA (Canadian Standards Association): Technical Guide – Development, Interpretation and Use of Rainfall Intensity-duration-frequency (IDF) Information: Guideline for Canadian Water Resources Practitioners, CSA Group, Ottawa, 2010.
Dawson, C. W., Abrahart, R. J., and See, L. M.: HydroTest: A web-based toolbox of evaluation metrics for the standardised assessment of hydrological forecasts, Environ. Modell. Softw., 22, 1034–1052, https://doi.org/10.1016/j.envsoft.2006.06.008, 2007.
Dean, S. M., Rosier, S., Carey-Smith, T., and Stott, P. A.: The role of climate change in the two-day extreme rainfall in Golden Bay, New Zealand, December 2011, B. Am. Meteorol. Soc., 94, S61–S63, 2013.
De Carolis, L.: The urban heat island effect in Windsor, ON: an assessment of vulnerability and mitigation strategies, City Windsor Ont., 2012, 1–52, available at: https://www.citywindsor.ca/residents/environment/Environmental-Master- Plan/Documents/Urban Heat Island Report (2012).pdf, last access: December 2016.
Deng, Z., Qiu, X., Liu, J., Madras, N., Wang, X., and Zhu, H.: Trend in frequency of extreme precipitation events over Ontario from ensembles of multiple GCMs, Clim. Dynam., 46, 2909–2921, 2016.
Dickey, D. A. and Fuller, W. A.: Likelihood ratio statistics for autoregressive time series with a unit root, Econom. J. Econom. Soc., 49, 1057–1072, 1981.
Dixon, P. G. and Mote, T. L.: Patterns and causes of Atlanta's urban heat island–initiated precipitation, J. Appl. Meteorol., 42, 1273–1284, 2003.
Do, H. X., Westra, S., and Leonard, M.: A global-scale investigation of trends in annual maximum streamflow, J. Hydrol., 552, 28–43, 2017.
Donat, M. G., Lowry, A. L., Alexander, L. V., O'Gorman, P. A., and Maher, N.: More extreme precipitation in the world's dry and wet regions, Nat. Clim. Change, 6, 508–513, 2016.
Dritsakis, N.: Tourism as a Long-Run Economic Growth Factor: An Empirical Investigation for Greece Using Causality Analysis, Tour. Econ., 10, 305–316, https://doi.org/10.5367/0000000041895094, 2004.
Drobinski, P., Da Silva, N., Panthou, G., Bastin, S., Muller, C., Ahrens, B., Borga, M., Conte, D., Fosser, G., Giorgi, F., Güttler, I., Kotroni, V., Li, L., Morin, E., Önol, B., Quintana-Segui, P., Romera, R., and Torma, C. Z.: Scaling precipitation extremes with temperature in the Mediterranean: past climate assessment and projection in anthropogenic scenarios, Clim. Dynam., 1–21, https://doi.org/10.1007/s00382-016-3083-x , 2016.
Durrans, S. and Brown, P.: Estimation and internet-based dissemination of extreme rainfall information, Transp. Res. Rec. J. Transp. Res. Board, 1743, 41–48, 2001.
EC (Environment Canada): Documentation on Environment Canada Rainfall Intensity–DurationFrequency (IDF) Tables and Graphs V2.20, Government of Canada, 2012.
EC (Environment Canada): Documentation on Environment Canada Rainfall Intensity–DurationFrequency (IDF) Tables and Graphs V2.30, December, 2014, Government of Canada, available at: http://climate.weather.gc.ca/prods_servs/engineering_e.html (last access: December 2016), 2014.
ECCC (Environment and Climate Change Canada): Technical Documentation – Digital Archive of Canadian Climatological Data, Government of Canada, data available at: ftp://client_climate@ftp.tor.ec.gc.ca/Pub/Documentation_Technical/Technical_Documentation.pdf (last access: December 2016) from: https://www.canada.ca/en/environment-climate-change.html, 2017.
El Adlouni, S., Ouarda, T. B. M. J., Zhang, X., Roy, R., and Bobée, B.: Generalized maximum likelihood estimators for the nonstationary generalized extreme value model, Water Resour. Res., 43, W03410, https://doi.org/10.1029/2005WR004545, 2007.
IPCC (Intergovernmental Panel on Climate Change): Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation, A Special Report of Working Groups I and II of the Intergovernmental Panel on Climate Change, edited by: Field, C. B., Barros, V., Stocker, T. F., Qin, D., Dokken D. J., Ebi,K. L., Mastrandrea, M. D., Mach, K. J., Plattner, G.-K., Allen, S. K., Tignor, M., and Midgley, P. M., Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 582 pp., available at: https://www.ipcc.ch/pdf/special-reports/srex/SREX_Full_Report.pdf, 2012.
Fischer, E. M. and Knutti, R.: Observed heavy precipitation increase confirms theory and early models, Nat. Clim. Change, 6, 986–991, 2016.
Gan, T. Y., Gobena, A. K., and Wang, Q.: Precipitation of southwestern Canada: wavelet, scaling, multifractal analysis, and teleconnection to climate anomalies, J. Geophys. Res.-Atmos., 112, D10110, https://doi.org/10.1029/2006JD007157, 2007.
Ganguli, P., Kumar, D., and Ganguly, A. R.: US power production at risk from water stress in a changing climate, Sci. Rep.-UK, 7, 11983, https://doi.org/10.1038/s41598-017-12133-9, 2017.
Gershunov, A. and Barnett, T. P.: ENSO influence on intraseasonal extreme rainfall and temperature frequencies in the contiguous United States: observations and model results, J. Climate, 11, 1575–1586, 1998.
Gilleland, E. and Katz, R. W.: Extremes 2.0: an extreme value analysis package in R, J. Stat. Softw., 72, 1–39, https://doi.org/10.18637/jss.v072.i08, 2016.
Gimeno, R., Manchado, B., and Mìnguez, R.: Stationarity tests for financial time series, Physica A, 269, 72–78, https://doi.org/10.1016/S0378-4371(99)00081-3, 1999.
Gu, X., Zhang, Q., Singh, V. P., Xiao, M., and Cheng, J.: Nonstationarity-based evaluation of flood risk in the Pearl River basin: changing patterns, causes and implications, Hydrolog. Sci. J., 62, 246–258, 2017.
Gudmundsson, L., Bremnes, J. B., Haugen, J. E., and Engen-Skaugen, T.: Technical Note: Downscaling RCM precipitation to the station scale using statistical transformations – a comparison of methods, Hydrol. Earth Syst. Sci., 16, 3383–3390, 10.5194/hess-16-3383-2012, 2012.
Güntner, A., Olsson, J., Calver, A., and Gannon, B.: Cascade-based disaggregation of continuous rainfall time series: the influence of climate, Hydrol. Earth Syst. Sci., 5, 145–164, https://doi.org/10.5194/hess-5-145-2001, 2001.
Guo, X., Fu, D., and Wang, J.: Mesoscale convective precipitation system modified by urbanization in Beijing City, Atmos. Res., 82, 112–126, https://doi.org/10.1016/j.atmosres.2005.12.007, 2006.
Hamed, K. H. and Rao, A. R.: A modified Mann–Kendall trend test for autocorrelated data, J. Hydrol., 204, 182–196, 1998.
Hardwick Jones, R., Westra, S., and Sharma, A.: Observed relationships between extreme sub-daily precipitation, surface temperature, and relative humidity, Geophys. Res. Lett., 37, L22805, https://doi.org/10.1029/2010GL045081, 2010.
Hawkins, E. and Sutton, R.: The potential to narrow uncertainty in regional climate predictions, B. Am. Meteorol. Soc., 90, 1095–1107, 2009.
Hu, S.: Akaike information criterion, Cent. Res. Sci. Comput., NC State University, Raleigh, NC, available at: http://www4.ncsu.edu/~shu3/Presentation/AIC_2012.pdf (last access: 12 December 2016), 2007.
Hurvich, C. M. and Tsai, C.-L.: Model selection for extended quasi-likelihood models in small samples, Biometrics, 51, 1077–1084, 1995.
Ivancic, T. J. and Shaw, S. B.: Examining why trends in very heavy precipitation should not be mistaken for trends in very high river discharge, Climatic Change, 133, 681–693, 2015.
Jakob, D.: Nonstationarity in extremes and engineering design, in: Extremes in a Changing Climate, Springer, 363–417, 2013.
Jarvis, A., Reuter, H. I., Nelson, A., and Guevara, E.: Hole-filled SRTM for the globe Version 4, available at: http://www.cgiar-csi.org/data/srtm-90m-digital-elevation-database-v4-1 (last access: 13 December 2016), 2008.
Jebari, S., Berndtsson, R., Olsson, J., and Bahri, A.: Soil erosion estimation based on rainfall disaggregation, J. Hydrol., 436, 102–110, 2012.
Karmakar, S. and Simonovic, S.: Flood Frequency Analysis Using Copula with Mixed Marginal Distributions, Water Resour. Res. Rep., available at: http://ir.lib.uwo.ca/wrrr/19 (last access: 15 December 2016), 2007.
Katz, R. W. and Brown, B. G.: Extreme events in a changing climate: variability is more important than averages, Climatic Change, 21, 289–302, 1992.
Katz, R. W., Parlange, M. B., and Naveau, P.: Statistics of extremes in hydrology, Adv. Water Resour., 25, 1287–1304, 2002.
Kerr, D.: Some aspects of the geography of finance in Canada, Can. Geogr.-Geogr. Can., 9, 175–192, https://doi.org/10.1111/j.1541-0064.1965.tb00825.x, 1965.
Knutson, T. R., Zeng, F., and Wittenberg, A. T.: Seasonal and annual mean precipitation extremes occurring during 2013: a US focused analysis, B. Am. Meteorol. Soc., 95, S19–S23, 2014.
Kodra, E. and Ganguly, A. R.: Asymmetry of projected increases in extreme temperature distributions, Sci. Rep.-UK, 4, 5884, https://doi.org/10.1038/srep05884, 2014.
Komi, K., Amisigo, B. A., Diekkrüger, B., and Hountondji, F. C.: Regional flood frequency analysis in the Volta River Basin, West Africa, Hydrology, 3, 5, https://doi.org/10.3390/hydrology30100005, 2016.
Koutsoyiannis, D. and Montanari, A.: Negligent killing of scientific concepts: the stationarity case, Hydrolog. Sci. J., 60, 1174–1183, 2015.
Kumar, D. and Ganguly, A. R.: Intercomparison of model response and internal variability across climate model ensembles, Clim. Dynam., 1–13, https://doi.org/10.1007/s00382-017-3914-4, 2017.
Kunkel, K. E.: North American trends in extreme precipitation, Nat. Hazards, 29, 291–305, https://doi.org/10.1023/A:1023694115864, 2003.
Kwiatkowski, D., Phillips, P. C., Schmidt, P., and Shin, Y.: Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root?, J. Econ., 54, 159–178, 1992.
Lapen, D. R. and Hayhoe, H. N.: Spatial analysis of seasonal and annual temperature and precipitation normals in Southern Ontario, Canada, J. Great Lakes Res., 29, 529–544, https://doi.org/10.1016/S0380-1330(03)70457-2, 2003.
Lenderink, G. and van Meijgaard, E.: Increase in hourly precipitation extremes beyond expectations from temperature changes, Nat. Geosci., 1, 511–514, https://doi.org/10.1038/ngeo262, 2008.
Lenderink, G., Barbero, R., Loriaux, J. M., and Fowler, H. J.: Super-Clausius–Clapeyron scaling of extreme hourly convective precipitation and its relation to large-scale atmospheric conditions, J. Climate, 30, 6037–6052, https://doi.org/10.1175/JCLI-D-16-0808.1, 2017.
Li, H., Sheffield, J., and Wood, E. F.: Bias correction of monthly precipitation and temperature fields from Intergovernmental Panel on Climate Change AR4 models using equidistant quantile matching, J. Geophys. Res.-Atmos., 115, D10101, https://doi.org/10.1029/2009JD012882, 2010.
Lima, C. H., Kwon, H.-H., and Kim, J.-Y.: A Bayesian beta distribution model for estimating rainfall IDF curves in a changing climate, J. Hydrol., 540, 744–756, 2016.
Madsen, H., Arnbjerg-Nielsen, K., and Mikkelsen, P. S.: Update of regional intensity–duration–frequency curves in Denmark: tendency towards increased storm intensities, Atmos. Res., 92, 343–349, 2009.
Mailhot, A., Beauregard, I., Talbot, G., Caya, D., and Biner, S.: Future changes in intense precipitation over Canada assessed from multi-model NARCCAP ensemble simulations, Int. J. Climatol., 32, 1151–1163, 2012.
Maraun, D.: Bias correction, quantile mapping, and downscaling: revisiting the inflation issue, J. Climate, 26, 2137–2143, 2013.
Markose, S. and Alentorn, A.: The Generalized Extreme Value (GEV) distribution, implied tail index and option pricing, J. Deriv., 18, 35–60, 2005.
Martins, E. S. and Stedinger, J. R.: Generalized maximum-likelihood generalized extreme-value quantile estimators for hydrologic data, Water Resour. Res., 36, 737–744, 2000.
Meehl, G. A., Goddard, L., Murphy, J., Stouffer, R. J., Boer, G., Danabasoglu, G., Dixon, K., Giorgetta, M. A., Greene, A. M., Hawkins, E., Hegerl, G., Karoly, D., Keenlyside, N., Kimoto, M., Kirtman, B., Navarra, A., Pulwarty, R., Smith, D., Stammer, D., and Stockdale, T.: Decadal prediction, B. Am. Meteorol. Soc., 90, 1467–1485, https://doi.org/10.1175/2009BAMS2778.1, 2009.
Miao, C., Sun, Q., Borthwick, A. G. L., and Duan, Q.: Linkage between hourly precipitation events and atmospheric temperature changes over China during the warm season, Sci. Rep.-UK, 6, srep22543, https://doi.org/10.1038/srep22543, 2016.
Mikkelsen, P. S., Madsen, H., Arnbjerg-Nielsen, K., Rosbjerg, D., and Harremoës, P.: Selection of regional historical rainfall time series as input to urban drainage simulations at ungauged locations, Atmos. Res., 77, 4–17, https://doi.org/10.1016/j.atmosres.2004.10.016, 2005.
Miller, J. D., Kim, H., Kjeldsen, T. R., Packman, J., Grebby, S., and Dearden, R.: Assessing the impact of urbanization on storm runoff in a peri-urban catchment using historical change in impervious cover, J. Hydrol., 515, 59–70, https://doi.org/10.1016/j.jhydrol.2014.04.011, 2014.
Milly, P. C. D., Betancourt, J., Falkenmark, M., Hirsch, R. M., Kundzewicz, Z. W., Lettenmaier, D. P., and Stouffer, R. J.: Stationarity Is Dead: Whither Water Management?, Science, 319, 573–574, https://doi.org/10.1126/science.1151915, 2008.
Mishra, V., Dominguez, F., and Lettenmaier, D. P.: Urban precipitation extremes: How reliable are regional climate models?, Geophys. Res. Lett., 39, L03407, https://doi.org/10.1029/2011GL050658, 2012.
Moglen, G. E. and Schwartz, D. E.: Methods for adjusting US geological survey rural regression peak discharges in an urban setting, US Geological Survey Scientific Investigation Report 2006-5270, 1–55, 2006.
Mohsin, T. and Gough, W. A.: Characterization and estimation of Urban Heat Island at Toronto: impact of the choice of rural sites, Theor. Appl. Climatol., 108, 105–117, 2012.
Mölders, N. and Olson, M. A.: Impact of urban effects on precipitation in high latitudes, J. Hydrometeorol., 5, 409–429, 2004.
Mondal, A. and Mujumdar, P. P.: Modeling non-stationarity in intensity, duration and frequency of extreme rainfall over India, J. Hydrol., 521, 217–231, https://doi.org/10.1016/j.jhydrol.2014.11.071, 2015.
Montanari, A. and Koutsoyiannis, D.: Modeling and mitigating natural hazards: stationarity is immortal!, Water Resour. Res., 50, 9748–9756, 2014.
O'Gorman, P. A.: Precipitation extremes under climate change, Curr. Clim. Change Rep., 1, 49–59, https://doi.org/10.1007/s40641-015-0009-3, 2015.
O'Gorman, P. A. and Schneider, T.: The physical basis for increases in precipitation extremes in simulations of 21st-century climate change, P. Natl. Acad. Sci. USA, 106, 14773–14777, 2009.
Olsson, J.: Limits and characteristics of the multifractal behaviour of a high-resolution rainfall time series, Nonlinear Proc. Geoph., 2, 23–29, 1995.
Olsson, J.: Evaluation of a scaling cascade model for temporal rain- fall disaggregation, Hydrol. Earth Syst. Sci., 2, 19–30, https://doi.org/10.5194/hess-2-19-1998, 1998.
Paixao, E., Auld, H., Mirza, M. M. Q., Klaassen, J., and Shephard, M. W.: Regionalization of heavy rainfall to improve climatic design values for infrastructure: case study in Southern Ontario, Canada, Hydrol. Sci. J., 56, 1067–1089, https://doi.org/10.1080/02626667.2011.608069, 2011.
Papalexiou, S. M., Koutsoyiannis, D., and Makropoulos, C.: How extreme is extreme? An assessment of daily rainfall distribution tails, Hydrol. Earth Syst. Sci., 17, 851–862, https://doi.org/10.5194/hess-17-851-2013, 2013.
Partridge, M., Olfert, M. R., and Alasia, A.: Canadian cities as regional engines of growth: agglomeration and amenities, Can. J. Econ., 40, 39–68, https://doi.org/10.1111/j.1365-2966.2007.00399.x, 2007.
Pendergrass, A. G., Lehner, F., Sanderson, B. M., and Xu, Y.: Does extreme precipitation intensity depend on the emissions scenario?, Geophys. Res. Lett., 42, 8767–8774, 2015.
Petrow, T. and Merz, B.: Trends in flood magnitude, frequency and seasonality in Germany in the period 1951–2002, J. Hydrol., 371, 129–141, 2009.
Pettitt, A. N.: A non-parametric approach to the change-point problem, Appl. Statist., 126–135, 1979.
Pfahl, S., O'Gorman, P. A., and Fischer, E. M.: Understanding the regional pattern of projected future changes in extreme precipitation, Nat. Clim. Change, 7, 423–427, https://doi.org/10.1038/nclimate3287, 2017.
Pinheiro, E. C. and Ferrari, S. L. P.: A comparative review of generalizations of the Gumbel extreme value distribution with an application to wind speed data, J. Stat. Comput. Sim., 86, 2241–2261, https://doi.org/10.1080/00949655.2015.1107909, 2016.
Porporato, A. and Ridolfi, L.: Influence of weak trends on exceedance probability, Stoch. Hydrol. Hydraul., 12, 1–14, 1998.
Prein, A. F., Rasmussen, R. M., Ikeda, K., Liu, C., Clark, M. P., and Holland, G. J.: The future intensification of hourly precipitation extremes, Nat. Clim. Change, 7, 48–52, https://doi.org/10.1038/nclimate3168, 2016.
Prein, A. F., Liu, C., Ikeda, K., Trier, S. B., Rasmussen, R. M., Holland, G. J., and Clark, M. P.: Increased rainfall volume from future convective storms in the US, Nat. Clim. Change, 7, 880–884, https://doi.org/10.1038/s41558-017-0007-7, 2017.
Priestley, M. B. and Rao, T. S.: A test for non-stationarity of time-series, J. Roy. Stat. Soc. B Met., 31, 140–149, 1969.
Rana, A., Bengtsson, L., Olsson, J., and Jothiprakash, V.: Development of IDF-curves for tropical india by random cascade modeling, Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hessd-10-4709-2013, 2013.
Read, L. K. and Vogel, R. M.: Reliability, return periods, and risk under nonstationarity, Water Resour. Res., 51, 6381–6398, https://doi.org/10.1002/2015WR017089, 2015.
Reddy, M. J. and Ganguli, P.: Spatio-temporal analysis and derivation of copula-based intensity–area–frequency curves for droughts in western Rajasthan (India), Stoch. Env. Res. Risk A., 27, 1975–1989, 2013.
Renard, B., Sun, X., and Lang, M.: Bayesian methods for non-stationary extreme value analysis, in: Extremes in a Changing Climate, Springer, 39–95, 2013.
Rootzén, H. and Katz, R. W.: Design Life Level: quantifying risk in a changing climate, Water Resour. Res., 49, 5964–5972, https://doi.org/10.1002/wrcr.20425, 2013.
Rosner, A., Vogel, R. M., and Kirshen, P. H.: A risk-based approach to flood management decisions in a nonstationary world, Water Resour. Res., 50, 1928–1942, https://doi.org/10.1002/2013WR014561, 2014.
Ross, G. J., Tasoulis, D. K., and Adams, N. M.: Nonparametric monitoring of data streams for changes in location and scale, Technometrics, 53, 379–389, https://doi.org/10.1198/TECH.2011.10069, 2011.
Ruiz-Villanueva, V., Borga, M., Zoccatelli, D., Marchi, L., Gaume, E., and Ehret, U.: Extreme flood response to short-duration convective rainfall in South-West Germany, Hydrol. Earth Syst. Sci., 16, 1543–1559, https://doi.org/10.5194/hess-16-1543-2012, 2012.
Sadri, S., Kam, J., and Sheffield, J.: Nonstationarity of low flows and their timing in the eastern United States, Hydrol. Earth Syst. Sci., 20, 633–649, https://doi.org/10.5194/hess-20-633-2016, 2016.
Sanderson, M. and Gorski, R.: The effect of metropolitan Detroit–Windsor on precipitation, J. Appl. Meteorol., 17, 423–427, 1978.
Sandink, D., Simonovic, S. P., Schardong, A., and Srivastav, R.: A decision support system for updating and incorporating climate change impacts into rainfall intensity-duration-frequency curves: Review of the stakeholder involvement process, Environ. Modell. Softw., 84, 193–209, 2016.
SC (Statistics Canada): 2011 Census – Boundary files, Government of Canada, available at: http://www12.statcan.gc.ca/census-recensement/2011/geo/bound-limit/bound-limit-2011-eng.cfm, last access: November 2016.
Schaller, N., Kay, A. L., Lamb, R., Massey, N. R., van Oldenborgh, G. J., Otto, F. E. L., Sparrow, S. N., Vautard, R., Yiou, P., Ashpole, I., Bowery, A., Crooks, S. M., Haustein, K., Huntingford, C., Ingram, W. J., Jones, R. G., Legg, T., Miller, J., Skeggs, J., Wallom, D., Weisheimer, A., Wilson, S., Stott, P. A., and Allen, M. R.: Human influence on climate in the 2014 southern England winter floods and their impacts, Nat. Clim. Change, 6, 627–634, 2016.
Schroeer, K. and Kirchengast, G.: Sensitivity of extreme precipitation to temperature: the variability of scaling factors from a regional to local perspective, Clim. Dynam., 1–14, https://doi.org/10.1007/s00382-017-3857-9, 2017.
Sarhadi, A. and Soulis, E. D.: Time-varying extreme rainfall intensity-duration-frequency curves in a changing climate, Geophys. Res. Lett., 44, 2454–2463, https://doi.org/10.1002/2016GL072201, 2017.
Serinaldi, F. and Kilsby, C. G.: Stationarity is undead: Uncertainty dominates the distribution of extremes, Adv. Water Resour., 77, 17–36, 2015.
Serinaldi, F. and Kilsby, C. G.: The importance of prewhitening in change point analysis under persistence, Stoch. Env. Res. Risk A., 30, 763–777, https://doi.org/10.1007/s00477-015-1041-5, 2016.
Serinaldi, F., Kilsby, C. G., and Lombardo, F.: Untenable nonstationarity: An assessment of the fitness for purpose of trend tests in hydrology, Adv. Water Resour., 111, 132–155, https://doi.org/10.1016/j.advwatres.2017.10.015, 2018.
Shabbar, A., Bonsal, B., and Khandekar, M.: Canadian precipitation patterns associated with the Southern Oscillation, J. Climate, 10, 3016–3027, 1997.
Shaw, S. B., Royem, A. A., and Riha, S. J.: The relationship between extreme hourly precipitation and surface temperature in different hydroclimatic regions of the United States, J. Hydrometeorol., 12, 319–325, 2011.
Shephard, M. W., Mekis, E., Morris, R. J., Feng, Y., Zhang, X., Kilcup, K., and Fleetwood, R.: Trends in Canadian short-duration extreme rainfall: including an intensity–duration–frequency perspective, Atmos. Ocean, 52, 398–417, 2014.
Simonovic, S. P. and Peck, A.: Updated rainfall intensity duration frequency curves for the City of London under the changing climate, Department of Civil and Environmental Engineering, The University of Western Ontario, available at: http://ir.lib.uwo.ca/wrrr/29/ (last access: 13 January 2017), 2009.
Singh, J., Vittal, H., Karmakar, S., Ghosh, S., and Niyogi, D.: Urbanization causes nonstationarity in Indian Summer Monsoon Rainfall extremes, Geophys. Res. Lett., 43, 11269–11277, https://doi.org/10.1002/2016GL071238, 2016.
Stocker, T. F., Qin, D., Plattner, G. K., Tignor, M., Allen, S. K., Boschung, J., Nauels, A., Xia, Y., Bex, V., and Midgley, P. M.: Climate change 2013: the physical science basis. Intergovernmental panel on climate change, Working Group I Contribution to the IPCC Fifth Assessment Report (AR5), New York, 2013.
Svensson, C. and Jones, D. A.: Review of rainfall frequency estimation methods, J. Flood Risk Manag., 3, 296–313, 2010.
Switzman, H., Razavi, T., Traore, S., Coulibaly, P., Burn, D. H., Henderson, J., Fausto, E., and Ness, R.: Variability of future extreme rainfall statistics: comparison of multiple IDF projections, J. Hydrol. Eng., 22, 04017046, https://doi.org/10.1061/(ASCE)HE.1943-5584.0001561, 2017.
Teutschbein, C. and Seibert, J.: Bias correction of regional climate model simulations for hydrological climate-change impact studies: Review and evaluation of different methods, J. Hydrol., 456, 12–29, 2012.
TRCA (Toronto Region Conservation Authority): Resilient City: Preparing for Extreme Weather Events, City of Toronto, Canada, 2013.
Towler, E., Rajagopalan, B., Gilleland, E., Summers, R. S., Yates, D., and Katz, R. W.: Modeling hydrologic and water quality extremes in a changing climate: a statistical approach based on extreme value theory, Water Resour. Res., 46, W11504, https://doi.org/10.1029/2009WR008876, 2010.
Trenberth, K. E.: Atmospheric moisture recycling: role of advection and local evaporation, J. Climate, 12, 1368–1381, 1999.
Van Gelder, P., Wang, W., and Vrijling, J. K.: Statistical estimation methods for extreme hydrological events, in Extreme Hydrological Events: New Concepts for Security, Springer, 2006.
Villarini, G., Serinaldi, F., Smith, J. A., and Krajewski, W. F.: On the stationarity of annual flood peaks in the continental United States during the 20th century, Water Resour. Res., 45, W08417, https://doi.org/10.1029/2008WR007645, 2009a.
Villarini, G., Smith, J. A., Serinaldi, F., Bales, J., Bates, P. D., and Krajewski, W. F.: Flood frequency analysis for nonstationary annual peak records in an urban drainage basin, Adv. Water Resour., 32, 1255–1266, https://doi.org/10.1016/j.advwatres.2009.05.003, 2009b.
von Storch, H. and Navarra, A.: Analysis of Climate Variability: Applications of Statistical Techniques, Springer, 1–303, 1999.
Wasko, C. and Sharma, A.: Steeper temporal distribution of rain intensity at higher temperatures within Australian storms, Nat. Geosci., 8, 527–529, 2015.
Wasko, C. and Sharma, A.: Continuous rainfall generation for a warmer climate using observed temperature sensitivities, J. Hydrol., 544, 575–590, 2017.
Wang, X., Huang, G., Liu, J., Li, Z., and Zhao, S.: Ensemble projections of regional climatic changes over Ontario, Canada, J. Climate, 28, 7327–7346, 2015.
Westra, S. and Sisson, S. A.: Detection of non-stationarity in precipitation extremes using a max-stable process model, J. Hydrol., 406, 119–128, 2011.
Westra, S., Alexander, L. V., and Zwiers, F. W.: Global increasing trends in annual maximum daily precipitation, J. Climate, 26, 3904–3918, https://doi.org/10.1175/JCLI-D-12-00502.1, 2012.
Wilson, P. S. and Toumi, R.: A fundamental probability distribution for heavy rainfall, Geophys. Res. Lett., 32, L14812, https://doi.org/10.1029/2005GL022465, 2005.
Xie, H., Li, D., and Xiong, L.: Exploring the ability of the Pettitt method for detecting change point by Monte Carlo simulation, Stoch. Env. Res. Risk A., 28, 1643–1655, 2014.
Yilmaz, A. G. and Perera, B. J. C.: Extreme rainfall nonstationarity investigation and intensity–frequency–duration relationship, J. Hydrol. Eng., 19, 1160–1172, 2013.
Yilmaz, A. G., Hossain, I., and Perera, B. J. C.: Effect of climate change and variability on extreme rainfall intensity–frequency–duration relationships: a case study of Melbourne, Hydrol. Earth Syst. Sci., 18, 4065–4076, https://doi.org/10.5194/hess-18-4065-2014, 2014.
Yilmaz, A. G., Imteaz, M. A., and Perera, B. J. C.: Investigation of non-stationarity of extreme rainfalls and spatial variability of rainfall intensity–frequency–duration relationships: a case study of Victoria, Australia, Int. J. Climatol., 37, 430–442, https://doi.org/10.1002/joc.4716, 2017.
Yiou, P. and Cattiaux, J.: Contribution of atmospheric circulation to wet north European summer precipitation of 2012, B. Am. Meteorol. Soc., 94, S39, 2013.
Yue, S. and Wang, C. Y.: Power of the Mann–Whitney test for detecting a shift in median or mean of hydro-meteorological data, Stoch. Env. Res. Risk A., 16, 307–323, 2002.
Yue, S., Pilon, P., Phinney, B., and Cavadias, G.: The influence of autocorrelation on the ability to detect trend in hydrological series, Hydrol. Process., 16, 1807–1829, 2002.
Yue, S., Pilon, P., and Phinney, B. O. B.: Canadian streamflow trend detection: impacts of serial and cross-correlation, Hydrol. Sci. J., 48, 51–63, 2003.
Short summary
Using statistical models, we test whether nonstationary versus stationary models show any significant differences in terms of design storm intensity at different durations across Southern Ontario. We find that detectable nonstationarity in rainfall extremes does not necessarily lead to significant differences in design storm intensity, especially for shorter return periods. An update of 2–44 % is required in current design standards to mitigate the risk of storm-induced urban flooding.
Using statistical models, we test whether nonstationary versus stationary models show any...
