Stochastic generation of multi-site daily precipitation focusing on extreme events

Evin, Guillaume; Favre, Anne‐Catherine; Hingray, B.

doi:10.5194/hess-22-655-2018

Cited by 75 publications

(86 citation statements)

References 51 publications

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“…Suppose that (X 1 , … , X n ) represents our observed rainfall sample with cdf F. For precipitation data, Naveau et al (2016) noticed that the special case of G(u) = u with > 0 provided a decent fit for hourly and daily precipitation in France. Evin et al (2018) used this same G to model precipitation in Switzerland. Consequently, this parametric model for G appears to be a good starting point to give initial estimates for = ( , ) t .…”

Section: Initial Values For = ( ) Tmentioning

confidence: 99%

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Flexible semiparametric generalized Pareto modeling of the entire range of rainfall amount

et al. 2019

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Precipitation amounts at daily or hourly scales are skewed to the right, and heavy rainfall is poorly modeled by a simple gamma distribution. An important yet challenging topic in hydrometeorology is to find a probability distribution that is able to model well low, moderate, and heavy rainfall. To address this issue, we present a semiparametric distribution suitable for modeling the entire range of rainfall amount. This model is based on a recent parametric statistical model called the class of extended generalized Pareto distributions (EGPDs). The EGPD family is in compliance with extreme value theory for both small and large values, while it keeps a smooth transition between these tails and bypasses the hurdle of selecting thresholds to define extremes. In particular, return levels beyond the largest observation can be inferred. To add flexibility to this EGPD class, we propose to model the transition function in a nonparametric fashion. A fast and efficient nonparametric scheme based on Bernstein polynomial approximations is investigated. We perform simulation studies to assess the performance of our approach. It is compared to two parametric models: a parametric EGPD and the classical generalized Pareto distribution (GPD), the latter being only fitted to excesses above a high threshold. We also apply our semiparametric version of EGPD to a large network of 180 precipitation time series over France.

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Section: Initial Values For = ( ) Tmentioning

confidence: 99%

“…As mentioned in Evin, Favre, and Hingray (2018), stochastic precipitation generators have become useful tools in risk assessment studies. Realistic simulated precipitation draws are needed as inputs of conceptual hydrological models.…”

Section: Introductionmentioning

confidence: 99%

Flexible semiparametric generalized Pareto modeling of the entire range of rainfall amount

et al. 2019

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“…However, upper tail dependence can also be assumed to be present since extreme precipitation events, which might cause extreme flood events, have been shown to exhibit upper tail dependence (see e.g. Evin et al, 2018;Naveau et al, 2016 Spatial methods often relate the dependence between events at two stations to the distance between these stations. Traditionally, the Euclidean distance has been used to do so, which might not be very relevant in the case of floods since they evolve along a river network.…”

Section: Spatial Dependencementioning

confidence: 99%

Modeling the spatial dependence of floods using the Fisher copula

Brunner¹,

Furrer²,

Favre³

2018

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Abstract. Floods do often not only affect a single location but a whole region. Flood frequency analysis should therefore be undertaken at a regional scale which requires the considerations of the dependence of events at different locations. This dependence is often neglected even though its consideration is essential to derive reliable flood estimates. A model used in regional multivariate frequency analysis should ideally consider the dependence of events at multiple sites which might show dependence in the lower and/or upper tail of the distribution. We here seek at proposing a simple model that on the one hand 5 considers this dependence with respect to the network structure of the region and on the other hand, allows for the simulation of stochastic event sets at both gauged and ungauged locations. The new Fisher copula model is used for representing the spatial dependence of flood events in the nested Thur catchment in Switzerland. Flood event samples generated for the gauged stations using the Fisher copula are compared to samples generated by other dependence models allowing for modeling multivariate data including elliptical copulas, R-vine copulas, and max-stable models. The comparison of the dependence structures of 10 the generated samples shows that the Fisher copula is a suitable model for capturing the spatial dependence in the data. We therefore use the copula in a way such that it can be used in an interpolation context to simulate event sets comprising gauged and ungauged locations. The spatial event sets generated using the Fisher copula well capture the general dependence structure in the data and the upper tail dependence, which is of particular interest when looking at extreme flood events and when extrapolating to higher return periods. The Fisher copula is therefore a suitable model for the stochastic simulation of flood 15 event sets at multiple gauged and ungauged locations.

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“…Low probability and high impact extremes in hydrology, such as storms, play an important role in characterizing the hydrologic system and affecting water infrastructure design [1][2][3][4]. Capturing and defining these extremes is still a difficult task in hydrology because of the complexity of natural systems, as well as their variability in both space and time [5,6]. Compared to the prohibitive physical Different from most of the previous works, this study tries to evaluate and correlate surface and subsurface hydrological extreme events.…”

Section: Introductionmentioning

confidence: 99%

Statistical Analysis of Extreme Events in Precipitation, Stream Discharge, and Groundwater Head Fluctuation: Distribution, Memory, and Correlation

Dawley

Zhang

Liu

et al. 2019

Water

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Hydrological extremes in the water cycle can significantly affect surface water engineering design, and represents the high-impact response of surface water and groundwater systems to climate change. Statistical analysis of these extreme events provides a convenient way to interpret the nature of, and interaction between, components of the water cycle. This study applies three probability density functions (PDFs), Gumbel, stable, and stretched Gaussian distributions, to capture the distribution of extremes and the full-time series of storm properties (storm duration, intensity, total precipitation, and inter-storm period), stream discharge, lake stage, and groundwater head values observed in the Lake Tuscaloosa watershed, Alabama, USA. To quantify the potentially non-stationary statistics of hydrological extremes, the time-scale local Hurst exponent (TSLHE) was also calculated for the time series data recording both the surface and subsurface hydrological processes. First, results showed that storm duration was most closely related to groundwater recharge compared to the other storm properties, while intensity also had a close relationship with recharge. These relationships were likely due to the effects of oversaturation and overland flow in extreme total precipitation storms. Second, the surface water and groundwater series were persistent according to the TSLHE values, because they were relatively slow evolving systems, while storm properties were anti-persistent since they were rapidly evolving in time. Third, the stretched Gaussian distribution was the most effective PDF to capture the distribution of surface and subsurface hydrological extremes, since this distribution can capture the broad transition from a Gaussian distribution to a power-law one.process-based models requiring intensive data that are typically not available for many study sites, statistical analysis of hydrological extremes is an attractive tool to interpret these extreme events within and across systems from simple measurements [7-10].There are two major challenges when applying basic statistics to analyze hydrologic extremes. First, hydrologic processes in the water cycle are interconnected, while basic statistical analysis of extremes often does not consider multiple systems and tends to oversimplify the complexity of the correlated processes like precipitation and groundwater table fluctuations [11,12]. Understanding how the subtle properties of one system's extreme events can affect the other interconnected systems requires more in-depth analysis and use of advanced statistical techniques. Second, these basic statistical techniques often rely on assumptions or major simplifications of properties for water systems, such as stationarity in both space and time, which may not always be valid for real world dynamics [13][14][15]. These issues motivated this study.One example of the assumption/simplification used by basic statistical studies in hydrological extremes is the well-known Gumbel distribution. Statistics of extremes is one of th...

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Stochastic generation of multi-site daily precipitation focusing on extreme events

Cited by 75 publications

References 51 publications

Flexible semiparametric generalized Pareto modeling of the entire range of rainfall amount

Flexible semiparametric generalized Pareto modeling of the entire range of rainfall amount

Modeling the spatial dependence of floods using the Fisher copula

Statistical Analysis of Extreme Events in Precipitation, Stream Discharge, and Groundwater Head Fluctuation: Distribution, Memory, and Correlation

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