Return period of bivariate distributed extreme hydrological events

 Extreme hydrological events are inevitable and stochastic in nature. Characterized by multiple properties, the multivariate distribution is a better approach to represent this complex phenomenon than the univariate frequency analysis. However, it requires considerably more data and more sophisticated mathematical analysis. Therefore, a bivariate distribution is the most common method for modeling these extreme events. The return periods for a bivariate distribution can be defined using either separate single random variables or two joint random variables. In the latter case, the return periods can be defined using one random variable equaling or exceeding a certain magnitude and/or another random variable equaling or exceeding another magnitude or the conditional return periods of one random variable given another random variable equaling or exceeding a certain magnitude. In this study, the bivariate extreme value distribution with the Gumbel marginal distributions is used to model extreme flood events characterized by flood volume and flood peak. The proposed methodology is applied to the recorded daily streamflow from Ichu of the Pachang River located in Southern Taiwan. The results show a good agreement between the theoretical models and observed flood data. The author wishes to thank the two anonymous reviewers for their constructive comments that improving the quality of this work.     

Uncertainty and variability in bivariate modeling of hydrological droughts

There are two kinds of uncertainty factors in modeling the bivariate distribution of hydrological droughts: the alteration of predefined critical ratios for pooling droughts and excluding minor droughts and the temporal variability of univariate and/or bivariate characteristics of droughts due to the impact of human activities. Daily flow data covering a period of 56 hydrological years from two gauging stations from a humid region in South China are used. The influences of alterations of threshold values of flow and critical ratios of pooling droughts and excluding minor droughts on drought properties are analyzed. Six conventional univariate models and three Archimedean copulas are employed to fit the marginal and joint distributions of drought properties, the Kolmogorov–Smirnov and Anderson–Darling methods are used for testing the goodness-of-fit of the univariate model, and the Cramer-von Mises method based on Rosenblatt’s transform is applied for the test of the bivariate model. The change point analysis of the copula parameter of bivariate distribution of droughts is first made. Results demonstrate that both the statistical characteristics of each drought property and their bivariate joint distributions are sensitive to the critical ratio of excluding minor droughts. A model can be selected to fit the marginal distribution for drought deficit volume or maximum deficit, but it is not determined for drought duration with the lower ratios of the pooling and excluding droughts. The statistical uncertainty of drought duration makes the modeling of bivariate joint distribution of drought duration and deficit volume or of drought duration and maximum deficit undermined. Change points significantly occurred in the period from the late 1970s to the middle 1980s for a single drought property and the copula parameter of their joint distribution due to the impact of human activities. The difference between two subseries separated by the change point is remarkable in the magnitudes of drought properties and the joint return periods. A copula function can be selected to optimally fit the bivariate distribution, provided that the critical ratios of pooling and excluding droughts are great enough such as the optimal value of 0.4 in the case study. It is valuable that the modeling and designing of the bivariate joint correlation and distribution of drought properties can be performed on the subseries separated by the change point of the copula parameter.     

Exploring possible connections between hydrological extreme events and climate change in central south Chile

Abstract

Motivated by recent extreme flow events in the Mataquito River located in the Mediterranean region of Chile, we performed a detailed trend analysis of critical hydroclimatic variables based on observed daily flow, precipitation and temperature within the basin. For the period 1976–2008, positive trends in temperature were observed, especially during spring and summer months. At the same time, we found negative trends in the frequency and intensity of precipitation, especially during spring months. We observed an increasing difference between average streamflow in the rainy season as compared to the snowmelt season. Part of this trend is caused by larger flows during autumn months, although no positive precipitation trends are observed for these months. Finally, significant reductions in minimum flow during spring/summer and a disproportionate concentration of high-flow events occurring in the last 10 years were also identified. These high-flow events tend to happen during autumn months, and are associated with high precipitation and high minimum temperatures. Based on a simple assessment of changes in irrigated agriculture and land use, we concluded that other non-climatic factors seem not to be as relevant to the detected flow trends. All these results are in accord with future climate change scenarios that show an increase in temperature, a reduction in average precipitation and a reduction in snow accumulation. Such future scenarios could seriously hamper the development of economic activities in this basin, exemplifying also a fate that may be shared by other similar basins in Chile and in other regions of the world.

Editor Z.W. Kundzewicz

Citation Vicuña, S., Gironás, J., Meza, F.J., Cruzat, M.L., Jelinek, M., Bustos, E., Poblete, D., and Bambach, N., 2013. Exploring possible connections between hydrological extreme events and climate change in central south Chile. Hydrological Sciences Journal, 58 (8), 1598–1619.     

Variations and statistical probability characteristic analysis of extreme precipitation events under climate change in Haihe River Basin,China

The magnitude and frequency of regional extreme precipitation events may have variability under climate change. This study investigates the time–space variability and statistical probability characteristics of extreme precipitation under climate change in the Haihe River Basin. Hydrological alteration diagnosis methods are implemented to detect the occurrence time, style and degree of alteration such as trend and jump in the extreme precipitation series, and stationarity and serial independence are tested prior to frequency analysis. Then, the historical extreme precipitation frequency and spatio‐temporal variations analyses are conducted via generalized extreme value and generalized Pareto distributions. Furthermore, the occurrence frequency of extreme precipitation events in future is analysed on the basis of the Fourth Assessment Report of the Intergovermental Panel on Climate Change multi‐mode climate models under different greenhouse gases emission scenarios (SRES‐A2, A1B and B1). Results indicate that (1) in the past, alteration of extreme precipitation mainly occurred in the area north of 38°N. Decreasing trends of extreme precipitation are detected at most stations, whereas jump alteration is not obvious at most stations. (2) Spatial variation of estimated extreme precipitation under different return periods shows similarity. Bounded by the Taihang Mountain–Yan Mountain, extreme rainfall in the Haihe River Basin gradually reduces from the southeast to the northwest, which is consistent with the geographical features of the Haihe River Basin. (3) In the future, extreme precipitation with return period 5–20 years accounts for a significant portion of the total occurrence times. The frequency of extreme precipitation events has an increase trend under A1B and A2 scenarios. The total occurrence times of extreme precipitation under A1B senario are not more than that under B1 senario until the 2030s. Copyright © 2012 John Wiley & Sons, Ltd.     

Temporal patterns of suspended sediment yield following moderate to extreme hydrological events recorded in varved lacustrine sediments

A 487‐year annually laminated (varved) sediment record from Nicolay Lake, Cornwall Island, in the Canadian High Arctic was evaluated to determine the impact that years with high sediment yields had on sediment yields in subsequent years. All of the 40 largest years showed evidence for increased sediment yield in the subsequent 10–30 years. The positive anomalies in lagging years were approximately scaled according to the size of the initiating year, although many intermediate years (25‐ to 100‐year recurrence) showed weak or variable responses. The smallest events considered (10‐ to 25‐year recurrence) showed a consistent, but low‐amplitude response. Additionally the 10‐year events revealed frequent negative sediment yield anomalies in the preceding decade. This behaviour was interpreted as a frequent sediment activation cycle initiated by the modest year, and leading to sediment yield hysteresis lasting 15–25 years. The largest years (greater than 50‐year recurrence) showed consistently above‐average sediment yields in the preceding decade, in part due to the frequent occurrence of moderate (Q₁₀) years. It is hypothesized that temporary storage of sediment and previous initiation of erosion sites resulted in extraordinary sediment yields during intense summer rainfall events. This study demonstrates the potential use of varved lake sediment records to improve our understanding of long‐term sediment dynamics. These records present an opportunity to further develop and test sediment dynamic and routing models to gain insight into the interaction of time and space in fluvial and sediment delivery processes. Copyright © 2002 John Wiley & Sons, Ltd.     

Frequency analysis of climate extreme events in Zanjan, Iran

In this study, generalized extreme value distribution (GEV) and generalized Pareto distribution (GPD) were fitted to the maximum and minimum temperature, maximum wind speed, and maximum precipitation series of Zanjan. Maximum (minimum) daily and absolute annual observations of Zanjan station from 1961 to 2011 were used. The parameters of the distributions were estimated using the maximum likelihood estimation method. Quantiles corresponding to 2, 5, 10, 25, 50, and 100 years return periods were calculated. It was found that both candidate distributions fitted to extreme events series, were statistically reasonable. Most of the observations from 1961 to 2011 were found to fall within 1–10 years return period. Low extremal index (θ) values were found for excess maximum and minimum temperatures over a high threshold, indicating the occurrence of consecutively high peaks. For the purpose of filtering the dependent observations to obtain a set of approximately independent threshold excesses, a declustering method was performed, which separated the excesses into clusters, then the de-clustered peaks were fitted to the GPD. In both models, values of the shape parameters of extreme precipitation and extreme wind speed were close to zero. The shape parameter was less negative in the GPD than the GEV. This leads to significantly lower return period estimates for high extremes with the GPD model.     

Uncertainty assessment in the prediction of extreme rainfall events: an example from the central Spanish Pyrenees

Extreme rainfall events occur frequently in the central Pyrenees, but they are responsible for mass movements and short, very intense erosion periods, accompanied at times by loss of human life and high costs of infrastructure. This paper tries to assess the existence of patterns in the spatial distribution of maximum precipitation. The calculation of return periods of the most intense rainfall demonstrates that in the Pyrenees it exhibits an erratic spatial and temporal distribution and can be extremely localized. In the case of precipitation between 150 and 200 mm in 24 h, some influence from the surrounding relief has been found, but this is not the case for precipitation exceeding 200 mm, characterized by the absence of patterns governing their spatial distribution. Geomorphological approaches are, therefore, the only way for assessing the areas more subject to hydromorphological risks. Copyright © 2000 John Wiley & Sons, Ltd.     

Entropy inference of recurrence models for variability analysis of extreme events

A complete methodology is developed to analyze the recurrence of extreme environmental events and its variability as time without further events elapses. Firstly we investigate the conditioned recurrence inference problem consisting in the selection of a probability model for the interarrival time between extreme events, given a contexto-factual evidence conditioned by the time elapsed since the last of such events. Two ways to include this condition can be considered, which yield alternative conditioned evidences and convert the former problem into two distinct ones, thus giving rise to a possible consistency violation. These problems are formalized within the logical probability framework, in a plausible logic language that allows a suitable expression of the available observational data. They are solved using the REF relative entropy method with fractile constraints, and their solutions are compared at all inference levels. It is concluded that the two conditioning ways are not really mutually exclusive and that a unique global solution to the conditioned inference can be obtained using this procedure. An example illustrates an application of the methodology to the variability analysis of the recurrence time between historical inundations of the Guadalquivir river in Spain, as time elapses with no new floods.Acknowledgments. Support for this work was provided by DGI of Spain as the grant REN2000-2988-E/CLI and the research project REN2002-01337/CLI.     

Identification of hydrological neighborhoods for regional flood frequency analysis using statistical depth function

The adoption of hydrological neighborhoods is one of the common approaches employed for the delineation step in regional frequency analysis (RFA). Traditional methods proposed for building hydrological neighborhoods are mainly based on distance metrics. These methods have some limitations. They are not robust against outliers, they are not affine invariant and they require site characteristics to be normally distributed. To overcome these limitations, the present paper aims to propose a new robust method to identify the neighborhood of a target site. The proposed method is based on the statistical notion of depth function. More precisely, a similarity measure derived from depth functions is used to compute the similarities between the target sites and the gauged ones. A data set from the southern part of the province of Quebec (Canada) is used to compare the proposed method with traditional ones. The obtained results indicate that the depth-based method leads to neighborhoods that are more homogeneous and more efficient for quantile estimation, than those obtained by traditional methods. The triangular shape of neighborhoods obtained by the proposed approach makes it practical and flexible.     

Exploratory analysis of statistical post‐processing methods for hydrological ensemble forecasts

Despite many recent improvements, ensemble forecast systems for streamflow often produce under‐dispersed predictive distributions. This situation is problematic for their operational use in water resources management. Many options exist for post‐processing of raw forecasts. However, most of these have been developed using meteorological variables such as temperature, which displays characteristics very different from streamflow. In addition, streamflow data series are often very short or contain numerous gaps, thus compromising the estimation of post‐processing statistical parameters. For operational use, a post‐processing method has to be effective while remaining as simple as possible. We compared existing post‐processing methods using normally distributed and gamma‐distributed synthetic datasets. To reflect situations encountered with ensemble forecasts of daily streamflow, four normal distribution parameterizations and six gamma distribution parameterizations were used. Three kernel‐based approaches were tested, namely, the ‘best member’ method and two improvements thereof, and one regression‐based approach. Additional tests were performed to assess the ability of post‐processing methods to cope with short calibration series, missing values or small numbers of ensemble members. We thus found that over‐dispersion is best corrected by the regression method, while under‐dispersion is best corrected by kernel‐based methods. This work also shows key limitations associated with short data series, missing values, asymmetry and bias. One of the improved best member methods required longer series for the estimation of post‐processing parameters, but if provided with adequate information, yielded the best improvement of the continuous ranked probability score. These results suggest guidelines for future studies involving real operational datasets. Copyright © 2014 John Wiley & Sons, Ltd.     

Uncertainty analysis of statistical downscaling methods using Canadian Global Climate Model predictors

Three downscaling models, namely the Statistical Down‐Scaling Model (SDSM), the Long Ashton Research Station Weather Generator (LARS‐WG) model and an artificial neural network (ANN) model, have been compared in terms of various uncertainty attributes exhibited in their downscaled results of daily precipitation, daily maximum and minimum temperature. The uncertainty attributes are described by the model errors and the 95% confidence intervals in the estimates of means and variances of downscaled data. The significance of those errors has been examined by suitable statistical tests at the 95% confidence level. The 95% confidence intervals in the estimates of means and variances of downscaled data have been estimated using the bootstrapping method and compared with the observed data. The study has been carried out using 40 years of observed and downscaled daily precipitation data and daily maximum and minimum temperature data, starting from 1961 to 2000. In all the downscaling experiments, the simulated predictors of the Canadian Global Climate Model (CGCM1) have been used. The uncertainty assessment results indicate that, in daily precipitation downscaling, the LARS‐WG model errors are significant at the 95% confidence level only in a very few months, the SDSM errors are significant in some months, and the ANN model errors are significant in almost all months of the year. In downscaling daily maximum and minimum temperature, the performance of all three models is similar in terms of model errors evaluation at the 95% confidence level. But, according to the evaluation of variability and uncertainty in the estimates of means and variances of downscaled precipitation and temperature, the performances of the LARS‐WG model and the SDSM are almost similar, whereas the ANN model performance is found to be poor in that consideration. Further assessment of those models, in terms of skewness and average dry‐spell length comparison between observed and downscaled daily precipitation, indicates that the downscaled daily precipitation skewness and average dry‐spell lengths of the LARS‐WG model and the SDSM are closer to the observed data, whereas the ANN model downscaled precipitation underestimated those statistics in all months. Copyright © 2006 John Wiley & Sons, Ltd.     

Optimizing statistical classification accuracy of satellite remotely sensed imagery for supporting fast flood hydrological analysis

The aim of this study is to improve classification results of multispectral satellite imagery for supporting flood risk assessment analysis in a catchment area in Cyprus. For this purpose, precipitation and ground spectroradiometric data have been collected and analyzed with innovative statistical analysis methods. Samples of regolith and construction material were in situ collected and examined in the spectroscopy laboratory for their spectral response under consecutive different conditions of humidity. Moreover, reflectance values were extracted from the same targets using Landsat TM/ETM+ images, for drought and humid time periods, using archived meteorological data. The comparison of the results showed that spectral responses for all the specimens were less correlated in cases of substantial humidity, both in laboratory and satellite images. These results were validated with the application of different classification algorithms (ISODATA, maximum likelihood, object based, maximum entropy) to satellite images acquired during time period when precipitation phenomena had been recorded.     

Hydrological analysis of extreme rainfall events and severe rainstorms over Uttarakhand,India

ABSTRACT

Following the June 2013 disaster in the Uttarakhand Himalayas, many discussions are ongoing with regard to how climate change is seeking revenge on mankind by endowing us with disasters! The event was mostly linked with the occurrence of an extreme event due to climate change. In view of this, an attempt has been made in this paper to analyse the extreme rainfall events experienced by the Uttarakhand during 1901–2013 using more than 100 stations’ daily rainfall data. The study revealed that during the 113-year period, the highest numbers of extreme events were recorded during the decade 1961–1970, and to some extent in the decade 1981–1990. Thereafter, there is a decrease in extreme rainfall events. The comparative study of extreme events prior to 1901 showed that on 17–18 September 1880, a rainstorm which occurred in close vicinity to Uttarakhand caused serious floods and damage to lives and properties. The extreme rainfall recorded by some stations during this unprecedented rainstorm has not been surpassed to date.     

Application of isotope tracers in continental scale hydrological modeling

Isotope tracers are widely used to study hydrological processes in small catchments, but their use in continental-scale hydrological modeling has been limited. This paper describes the development of an isotope-enabled global water balance and transport model (iWBM/WTM) capable of simulating key hydrological processes and associated isotopic responses at the large scale. Simulations and comparisons of isotopic signals in precipitation and river discharge from available datasets, particularly the IAEA GNIP global precipitation climatology and the USGS river isotope dataset spanning the contiguous United States, as well as selected predictions of isotopic response in yet unmonitored areas illustrate the potential for isotopes to be applied as a diagnostic tool in water cycle model development. Various realistic and synthetic forcings of the global hydrologic and isotopic signals are discussed. The test runs demonstrate that the primary control on isotope composition of river discharge is the isotope composition of precipitation, with land surface characteristics and precipitation-amount having less impact. Despite limited availability of river isotope data at present, the application of realistic climatic and isotopic inputs in the model also provides a better understanding of the global distribution of isotopic variations in evapotranspiration and runoff, and reveals a plausible approach for constraining the partitioning of surface and subsurface runoff and the size and variability of the effective groundwater pool at the macro-scale.     

Extreme hydrological events,palaeo-information and climate change

Abstract

Extreme flood events have been and continue to be one of the most important natural hazards responsible for deaths and economic losses. Extreme floods result in direct destructive effects during the time of the event, and they also may be followed by a related chain of indirect calamities such as famines and epidemics that produce additional damages and suffering. Extreme hydrological events that have occurred in the historical past may also occur in the future. Knowledge about magnitudes and recurrence frequencies of past extreme hydrological events in most regions are too short to adequately evaluate potential magnitudes and recurrence frequencies of extreme hydrological events. Stationary climate in which the mean and variance do not change over time is a basic underlying assumption of standard methodological procedures for estimating recurrence probabilities of extreme hydrological events. Palaeo-archives contained in river and lake sediments, fossil plant and animal matter, ice layers, and other natural archives show that the assumption of stationary climate is not valid when the time scale is extended beyond centuries and millennia. Records of past extreme floods that occurred long before the period of instrumentation can be reconstructed from the distribution of slackwater flood deposits or from derivation of water depths competent to transport the largest rocks found in flood deposited sediment. Palaeoflood records reconstructed from the Upper Mississippi and Lower Colorado River systems in the United States confirm nonstationary behaviour of the mean and variance in hydrological time series. These stratigraphic records have shown that even very modest climatic changes have resulted in very important changes in the magnitudes and recurrence frequencies of extreme floods. A close relationship was found between the palaeo-flood record of extreme floods in the Upper Mississippi River system and a palaeo-record of stable isotopes of oxygen and carbon preserved in speleothem calcite from a local cave. The relationship suggests that isotopic records elsewhere might be calibrated to provide insight about how future potential climate changes might impact extreme flood magnitudes and recurrence frequencies there. Atmospheric global circulation models (GCMs) mainly simulate average climatic conditions and are presently inadequate sources of information about how future climate changes might be represented at the extreme event scale. Palaeo-flood archives, however, provide basic information about how magnitudes and recurrence frequencies of extreme hydrological events responded to past climate changes and they also provide a reference base against which GCM simulations can be calibrated regionally and be better interpreted to decipher hydrological information at the extreme event scale.     

Estimation of extreme Component-wise Excess design realization: a hydrological application

The classic univariate risk measure in environmental sciences is the Return Period (RP). The RP is traditionally defined as “the average time elapsing between two successive realizations of a prescribed event”. The notion of design quantile related with RP is also of great importance. The design quantile represents the “value of the variable(s) characterizing the event associated with a given RP”. Since an individual risk may strongly be affected by the degree of dependence amongst all risks, the need for the provision of multivariate design quantiles has gained ground. In contrast to the univariate case, the design quantile definition in the multivariate setting presents certain difficulties. In particular, Salvadori, G., De Michele, C. and Durante F. define in the paper called “On the return period and design in a multivariate framework” (Hydrol Earth Syst Sci 15:3293–3305, 2011) the design realization as the vector that maximizes a weight function given that the risk vector belongs to a given critical layer of its joint multivariate distribution function. In this paper, we provide the explicit expression of the aforementioned multivariate risk measure in the Archimedean copula setting. Furthermore, this measure is estimated by using Extreme Value Theory techniques and the asymptotic normality of the proposed estimator is studied. The performance of our estimator is evaluated on simulated data. We conclude with an application on a real hydrological data-set.     

Formation of homogeneous regions for regional frequency analysis of extreme precipitation events in the Czech Republic

Extreme high precipitation amounts are among environmental events with the most disastrous consequences for human society. This paper deals with the identification of ‘homogeneous regions’ according to statistical characteristics of precipitation extremes in the Czech Republic, i.e. the basic and most important step toward the regional frequency analysis. Precipitation totals measured at 78 stations over 1961–2000 are used as an input dataset. Preliminary candidate regions are formed by the cluster analysis of site characteristics, using the average-linkage clustering and Ward’s method. Several statistical tests for regional homogeneity are utilized, based on the 10-yr event and the variation of L-moment statistics. In compliance with results of the tests, the area of the Czech Republic has been divided into four homogeneous regions. The findings are supported by simulation experiments proposed to evaluate stability of the test results. Since the regions formed reflect also climatological differences in precipitation regimes and synoptic patterns causing high precipitation amounts, their future application may not be limited to the frequency analysis of extremes.