Analysis Of Extreme Events Research Articles

A statistical analysis of extreme events in current variations due to internal waves from the Australian North West Shelf

Measurements of current fluctuations due to internal waves obtained from two fixed point moorings on the Australian North West Shelf have been analyzed with the aim of calculating the probability of short‐scale, large‐amplitude internal waves exceeding particular values. Such waves are generated as a result of breaking or hydrodynamical instability of the semidiurnal internal tide. The statistical stationarity of each record has been checked, and it is shown that the records can be used for the calculation of the frequency by which currents exceed a particular value for wave heights (double amplitudes) of less than 60 cm s−1. The theoretical forms for exceedance frequency from the theory of extreme statistics have been checked, and it is shown that for one location a power asymptotic provides a slightly better descriptor of the statistics than an exponential asymptotic and for the other location an exponential asymptotic is found to provide the better fit. The exceedance frequency for internal waves near the Australian North West Shelf is found to be less than 1.3 waves per hour. The exceedance probability for each location has been calculated using Poisson statistics.

Sensitivity analysis of extreme precipitation events

AbstractA sensitivity analysis of the frequency of extreme precipitation events is performed. Extreme events in the form of total precipitation (e.g. over a month or season) exceeding a relatively large threshold (i.e. extremely wet conditions) or falling below a relatively small threshold (i.e. extremely dry conditions) are treated. To allow for the positive skewness of the distribution of total precipitation, a power transformation to normality is used. The relative sensitivities of extreme precipitation events to the median and to the scale parameter of this distribution are examined. It is shown that these relative sensitivities are both generally greater the more extreme the event. Moreover, the relative sensitivity to the scale is greater than that corresponding to the median for extreme wet events, whereas the opposite is true for extreme dry events. These theoretical results are illustrated through use of a network of precipitation observations in Spain.

Hydrologic controls of large floods in a small basin: central Appalachian case study

This paper reports the results of empirical and model-based analysis of extreme flood events observed in a small basin. The study catchment, WE-38 Mahantango Creek (7.2 km 2), is situated in the North Appalachian Valley and Ridge province of eastern Pennsylvania. Data from four rain gauges and one water level station are available at 5 min intervals. From the observations, 12 flood events were selected for detailed analysis. The data include tropical storm Agnes (21–24 June 1972), which was responsible for one of the most devastating floods in the region. Model-based analysis of hydrologic response is used to study the dominating runoff processes in the catchment. In this study, we use a distributed version of Topmodel to model runoff generation, and a lumped hillslope and channel routing model to model overland flow and channel flow. The runoff generation model relies on a topographic index to predict saturation excess runoff and on Philip's infiltration equation to predict infiltration excess runoff. The runoff routing model is based on the channel network width function and on the drainage basin hillslope function. The relative roles of initial conditions, soil properties and rainfall rates in determining hydrologic response in the basin are investigated. The flood frequency distribution seems to be insensitive to scaled maximum rainfall intensity. However, the flood frequency distribution is strongly affected by the scaled initial storage capacity. Simulated hydrograph characteristics, such as peak discharge, are very sensitive to the overland flow velocity parameter in the routing model.

Estimating future sea level extremes under conditions of sea level rise

Standard techniques of extreme event analysis involve making the assumption that future annual maxima can be approximated as independent random variables from a common distribution. This approach is not applicable to the investigation of future extreme sea levels, given the possibility of greenhouse-related sea level rise. Instead, design criteria for coastal structures must allow for future maxima to be generated from a sequence of different distributions. Analysis is still quite straightforward in principle, and attention is drawn to some basic statistical results for generating design estimates when the distributions of maxima differ just in the magnitude of the location parameter. An example from Adelaide, South Australia, is used to illustrate the generation and application of predictive models under the multi-distributional framework. Given sea level rise, quantiles of extreme magnitudes are suggested as being of more practical value in design work than return period magnitudes.

Toward a general procedure for analysis of extreme random events in the earth sciences

Engineering and scientific approaches to design magnitude estimation are briefly revisited. Some defense is offered for use of annual maxima in design as if they were variables from a common distribution. However, to assume any particular form of distribution tail beyond the largest data value is not justifiable, regardless of the degree of data support over the main body of the distribution. An alternative approach to the design problem is suggested through use of parameter-free nonparametric estimation using the kernel method. Some simulation results are presented which suggest that the parameter-free approach is worthy of further development. A particular advantage of nonparametric methods is that competing estimators can be checked against parametric distributions, leading to a progressive improvement in estimator accuracy.

Risk‐based analysis of extreme events

Mathematical expectation has traditionally been used in solving risk‐based decision making problems. However, this concept is not appropriate for decision making that affects public policy because it conceals extremes by commensurating events of different magnitudes and probabilities of occurrence. If a decision maker instead uses an expected value function in addition to a conditional expectation that captures extreme and catastrophic events, he will gain a more meaningful and more encompassing representation of the trade‐offs at hand. A theory relating conditional expectation to the statistics of extremes is developed in this paper. This expectation can now be viewed as the conditional expected risk given the occurrence of an event with a return period that equals or exceeds n years. The theory highlights the importance of using both the conditional and the unconditional expected risk in decision making. This fact has previously been recognized in the partitioned multi‐objective risk method (PMRM), a risk analysis methodology based on the concept of conditional expectation. The theory proposed in this paper provides a formulation for analyzing the sensitivity of subjectively chosen parameters in the PMRM. This theory will also simplify the practical implementation of the method.

Parameter and Quantile Estimation for the Generalized Pareto Distribution

The generalized Pareto distribution is a two-parameter distribution that contains uniform, exponential, and Pareto distributions as special cases. It has applications in a number of fields, including reliability studies and the analysis of environmental extreme events. Maximum likelihood estimation of the generalized Pareto distribution has previously been considered in the literature, but we show, using computer simulation, that, unless the sample size is 500 or more, estimators derived by the method of moments or the method of probability-weighted moments are more reliable. We also use computer simulation to assess the accuracy of confidence intervals for the parameters and quantiles of the generalized Pareto distribution.

Parameter and Quantile Estimation for the Generalized Pareto Distribution

The generalized Pareto distribution is a two-parameter distribution that contains uniform, exponential, and Pareto distributions as special cases. It has applications in a number of fields, including reliability studies and the analysis of environmental extreme events. Maximum likelihood estimation of the generalized Pareto distribution has previously been considered in the literature, but we show, using computer simulation, that, unless the sample size is 500 or more, estimators derived by the method of moments or the method of probability-weighted moments are more reliable. We also use computer simulation to assess the accuracy of confidence intervals for the parameters and quantiles of the generalized Pareto distribution.

Return period analysis of extreme rainfall events

The return periods analysis of extreme events of rainfall for selected 15 stations of Krishna river basin have been studied and presented in this paper. The annual one-day rainfall data for 60-years (1901-60) was used for the study. The rainfall estimates were computed for different return periods using tow different distribution and Fisher & Tipett type II distribution. Return periods corresponding to highest recorded rainfall were interpolated for both the distributions. Results show that while Gumbel’s distribution seems to indicate very high return periods of extreme events, the Fisher & Tipett type-II distribution provides lower estimates of the recurrence interval. As rainfall events are randomly distributed in nature, the return periods of outliers should also be determined with reasonable accuracy. The present study shows that the rainfall estimates for different return periods as obtained by using Fisher & Tipett type II distribution technique are much higher than those obtained by using Gumbel;s technique. It is suggested that Fisher & Tipett type II distribution may be preferred for evaluating the return periods of extreme rainfall events to Gumbel distribution.

A New Technique for the Analysis of Extreme Rainfall with Application to Lagos Metropolis, Nigeria

This paper focuses on the use of the principle of maximum entropy as an alternative technique for the parameter estimation of the Extreme Value Type – 1 (EV1) distribution or Gumbel distribution often used for the analysis and forecast of extreme events. A case study is made of storm rainfall analysis for Lagos metropolis using the available rainfall data for Ikeja, Oshodi and Lagos Mainland as obtained from Akanbi (1982). For comparison purposes, the parameters of the EV1 distribution is also obtained using the Maximum Likelihood Method. The later being one of the most reliable techniques and perhaps the most widely used for parameter estimation of the EV1 distribution. This exercise has made it possible to demonstrate in some ways the superiority of the maximum entropy method over existing methods used for statistical simulation of extreme events.

TVA Hydro Scheduling Model: Practical Aspects

Computer programs and mathematical methods have been developed to model long term week-to-week variations in water level, discharge and electrical generation for the 42 reservoirs operated by TVA. The model has an interactive structure with CRT graphics for easy use by TVA reservoir management personnel to evaluate the impact of new operating requirements on established objectives, check reservoir system status to warn of possible future problems, forecast reservoir systems operation and develop new long range operation guides. Notable features of the model include: (1) the observation of important system operating constraints and priorities, (2) extreme event analysis capability, (3) a special linear programming structure that provides the flexibility to modify operating objectives and experiment with new types of long range efficiency guides, and (4) interactive CRT graphical output analysis.