Statistics Of Extreme Events Research Articles

Projection of extreme temperatures in Hong Kong in the 21st century

The possible changes in the frequency of extreme temperature events in Hong Kong in the 21st century were investigated by statistically downscaling 26 sets of the daily global climate model projections (a combination of 11 models and 3 greenhouse gas emission scenarios, namely A2, A1B, and B1) of the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. The models’ performance in simulating the past climate during 1971–2000 has also been verified and discussed. The verification revealed that the models in general have an acceptable skill in reproducing past statistics of extreme temperature events. Moreover, the models are more skillful in simulating the past climate of the hot nights and cold days than that of the very hot days. The projection results suggested that, in the 21st century, the frequency of occurrence of extremely high temperature events in Hong Kong would increase significantly while that of the extremely low temperature events is expected to drop significantly. Based on the multi-model scenario ensemble mean, the average annual numbers of very hot days and hot nights in Hong Kong are expected to increase significantly from 9 days and 16 nights in 1980–1999 to 89 days and 137 nights respectively in 2090–2099. On the other hand, the average annual number of cold days will drop from 17 days in 1980–1999 to about 1 day in 2090–2099. About 65 percent of the model-scenario combinations indicate that there will be on average less than one cold day in 2090–2099. While all the model-emission scenarios in general have projected consistent trends in the change of temperature extremes in the 21st century, there is a large divergence in the projections between different model/emission scenarios. This reflects that there are still large uncertainties in the model simulation of the future climate of extreme temperature events.

Long-Term Statistics and Extreme Waves of Sea Storms

AbstractA stochastic model of sea storms for describing long-term statistics of extreme wave events is presented. The formulation generalizes Boccotti’s equivalent triangular storm model by describing an actual storm history in the form of a generic power law. The latter permits the derivation of analytical solutions for the return periods of extreme wave events and associated statistical properties. Lastly, the relative validity of the new model and its predictions is assessed by analyzing wave measurements retrieved from two NOAA National Oceanographic Data Center (NODC) buoys in the Atlantic and Pacific Oceans.

Statistics of Extreme Events in Airgap Measurements

The paper presents a study of the extreme value statistics related to airgap measurements on a scale model of a semisubmersible platform subjected to random waves in a wave basin. Relative wave elevation records corresponding to totally 24 h storm duration are considered, made up by 8×3 h realizations. The focus is on a comparison of two alternative methods for the prediction of extreme values from finite recordings at two different locations at the platform. One is a standard method used in the wave basin, making use of a Weibull-tail fitting procedure. The other is a novel method based on the level upcrossing function combined with an optimization procedure that allows prediction at extreme response levels. Similar results are obtained in the mean values by the two methods, while the latter shows less variability in the predictions from single 3 h records.

To what extent does variability of historical rainfall series influence extreme event statistics of sewer system surcharge and overflows?

In urban drainage modelling long-term extreme statistics has become an important basis for decision-making e.g. in connection with renovation projects. Therefore it is of great importance to minimize the uncertainties with regards to long-term prediction of maximum water levels and combined sewer overflow (CSO) in drainage systems. These uncertainties originate from large uncertainties regarding rainfall inputs, parameters, and assessment of return periods. This paper investigates how the choice of rainfall time series influences the extreme events statistics of max water levels in manholes and CSO volumes. Traditionally, long-term rainfall series, from a local rain gauge, are unavailable. In the present case study, however, long and local rain series are available. 2 rainfall gauges have recorded events for approximately 9 years at 2 locations within the catchment. Beside these 2 gauges another 7 gauges are located at a distance of max 20 kilometers from the catchment. All gauges are included in the Danish national rain gauge system which was launched in 1976. The paper describes to what extent the extreme events statistics based on these 9 series diverge from each other and how this diversity can be handled, e.g. by introducing an "averaging procedure" based on the variability within the set of statistics. All simulations are performed by means of the MOUSE LTS model.

Finite-size effects on the statistics of extreme events in the BTW model

The BTW Abelian sandpile model is a prominent example of systems showing self-organised criticality (SOC) in the infinite size limit. We study finite-size effects with special focus on the statistics of extreme events, i.e., of particularly large avalanches. Not only the avalanche size probability distribution, but also the mutual independence of large avalanches in the critical state is affected by finite-size effects. Instead of a Poissonian recurrencetime distribution, in the finite system we find a repulsion of extreme events that depends on the avalanche size and not on the respective probability. The dependence of these effects on the system size is investigated and some data collapse is found. Our results imply that SOC is an unsuitable mechanism for the explanation of extreme events which occur in clusters.

Expected impacts of climate change on extreme climate events

An overview of the expected change of climate extremes during this century due to greenhouse gases and aerosol anthropogenic emissions is presented. The most commonly used methodologies rely on the dynamical or statistical downscaling of climate projections, performed with coupled atmosphere–ocean general circulation models. Either of dynamical or of statistical type, downscaling methods present strengths and weaknesses, but neither their validation on present climate conditions, nor their potential ability to project the impact of climate change on extreme event statistics allows one to give a specific advantage to one of the two types. The results synthesized in the last IPCC report and more recent studies underline a convergence for a very likely increase in heat wave episodes over land surfaces, linked to the mean warming and the increase in temperature variability. In addition, the number of days of frost should decrease and the growing season length should increase. The projected increase in heavy precipitation events appears also as very likely over most areas and also seems linked to a change in the shape of the precipitation intensity distribution. The global trends for drought duration are less consistent between models and downscaling methodologies, due to their regional variability. The change of wind-related extremes is also regionally dependent, and associated to a poleward displacement of the midlatitude storm tracks. The specific study of extreme events over France reveals the high sensitivity of some statistics of climate extremes at the decadal time scale as a consequence of regional climate internal variability.

The climate station of the University of Hohenheim: analyses of air temperature and precipitation time series since 1878

At the University of Hohenheim (UHOH), one of the longest records in Germany concerning meteorological surface data exists. Since the late nineteenth century, time series of several surface variables such as temperature, precipitation, wind and relative humidity have been measured. Particularly, since 1878, almost continuous time series of temperature and precipitation are available. We are focusing our analysis on temperature as well as on precipitation. We demonstrate that the UHOH data provide another homogeneous, and from other sources, independent time record. Its errors are also well specified. Long time series are essential for investigating climate trends as well as statistics of extreme events. We are investigating trends in temperature and compare these to climatologies. We observe an increase in temperature of about 0.6 °C between 1971 and 2000 in comparison to the average between 1878 and 2002. Not only this amount but also the shape of the temperature curve are in striking agreement with trends assessed by the Intergovernmental Panel on Climate Change in the Northern Hemisphere. It shows also the same behavior of the Climate Research Unit (CRU) climatology using the grid point surrounding our measurement site. This demonstrates a low influence of local effects on the temperature trend at our measurement site. It also indicates that temperature fields have a large spatial correlation length. We found a reduction of 2.2 frost days and a reduction of 1.2 ice days per decade. In the summer of 2003, the mean temperature was 21.8 °C, which was 5 standard deviations larger than the mean value of 16.9 °C between 1878 and 2002. The precipitation patterns at our site show a significant increase of precipitation in winter, whereas in summer a trend is not significant. Particularly in winter, we find an increase of 12%. We also detected indications of a shift of precipitation to more extreme values. Copyright © 2006 Royal Meteorological Society.

Recent advances in flood forecasting and flood risk assessment

Abstract. Recent large floods in Europe have led to increased interest in research and development of flood forecasting systems. Some of these events have been provoked by some of the wettest rainfall periods on record which has led to speculation that such extremes are attributable in some measure to anthropogenic global warming and represent the beginning of a period of higher flood frequency. Whilst current trends in extreme event statistics will be difficult to discern, conclusively, there has been a substantial increase in the frequency of high floods in the 20th century for basins greater than 2x105 km2. There is also increasing that anthropogenic forcing of climate change may lead to an increased probability of extreme precipitation and, hence, of flooding. There is, therefore, major emphasis on the improvement of operational flood forecasting systems in Europe, with significant European Community spending on research and development on prototype forecasting systems and flood risk management projects. This Special Issue synthesises the most relevant scientific and technological results presented at the International Conference on Flood Forecasting in Europe held in Rotterdam from 3-5 March 2003. During that meeting 150 scientists, forecasters and stakeholders from four continents assembled to present their work and current operational best practice and to discuss future directions of scientific and technological efforts in flood prediction and prevention. The papers presented at the conference fall into seven themes, as follows.

The Big Flood: North Sea storm surge

In the 50 years since the catastrophic southern North Sea storm surge of 31 January-1 February 1953, there have been technological advances in the engineering of flood protection, increased understanding of physical processes in shallow seas and estuaries, and developments in the mathematical statistics of extreme events. This introductory paper reviews how the scientific understanding of surge events, their impacts and the human responses to them is evolving on many fronts, often across disciplinary boundaries. The question of how the long-term nature of the problem itself will be influenced by possible climate, land use and policy changes is addressed, along with their associated uncertainties.

Long-range correlations and rare events in boundary layer wind fields

We analyse the statistics of extreme events in the boundary layer wind fields. We focus on the wind speeds that are long-term correlated and show that its distribution of the return intervals of rare events is a stretched exponential and the stretching exponent, to within the numerical errors, is identical to the long-term correlation exponent γ. We also analyse correlations among the return intervals which are themselves long-term correlated with an exponent close to γ. This work complements the results obtained by Bunde et al. (Physica A 330 (2003) 1).

The origin of [formula omitted] fluctuations and scale transformations of time series at nonequilibrium phase transitions

Investigations of the dynamics of heat and mass transfer show that in crisis and transient conditions one can observe high-energy fluctuations with a power spectrum inversely proportional to the frequency (flicker or 1 / f fluctuations). Such a spectrum presupposes energy transient from high to lower frequency modes and the possibility of large-scale catastrophic events in a system. Theory shows that such fluctuations arise in a system owing to the simultaneous progress of interacting phase transitions in the presence of a white noise of sufficient intensity. The distributions functions of fluctuations during scale transformations of a system of stochastic equations describing the 1 / f noise generations have been investigated. It is shown that the Gaussian distributions of a random process with a 1 / f spectrum under a roughness of a scale change to exponential distribution characteristic of the statistics of extreme events. The probability of such events should be taken into account in predicting the stability of different heat transfer regimes.

Long-range correlations and rare events in boundary layer wind fields

We analyse the statistics of extreme events in the boundary layer wind fields. We focus on the wind speeds that are long-term correlated and show that its distribution of the return intervals of rare events is a stretched exponential and the stretching exponent, to within the numerical errors, is identical to the long-term correlation exponent γ . We also analyse correlations among the return intervals which are themselves long-term correlated with an exponent close to γ . This work complements the results obtained by Bunde et al. (Physica A 330 (2003) 1).

Canopy gaps to climate change - extreme events, ecology and evolution.

Canopy gaps to climate change - extreme events, ecology and evolution.

The Characteristics of Cold Air Outbreaks over the Eastern Highlands of Kenya

Climatological statistics of extreme temperature events over Kenya are established from the analysis of daily and monthly maximum temperatures for a representative station (Nairobi Dagoretti Corner) over the period 1956–1997.

Risk analysis using stochastic reliability methods applied to two cases of deterministic water quality models

For the computation of extreme event statistics with respect to pollutant loads and environmental effects, the uncertainty in model parameters of deterministic models and the inherent stochastic variability in input variables have to be taken into account. Two stochastic reliability methods—combinations of the First Order Reliability Method (FORM) with Directional Simulation with Importance Sampling (FORM/DIS) or with Latin Hypercube Sampling (FORM/LHS)—were used for risk analysis related to acute environmental effects. The range of probabilities of exceedence at which these combined methods are more efficient than crude Monte Carlo simulation (CMC) or Latin Hypercube Sampling (LHS) only, was investigated. Their efficiency in relation to the required number of model simulations to accurately estimate the small exceedence probabilities of extremes compared to that of Monte Carlo simulation was demonstrated with two case studies: (1) to estimate exceedence probabilities of limit pollutant concentrations in a lake after a loading event using a simple numerical model. At exceedence probabilities smaller than 0.1 both FORM/DIS and FORM/LHS gave more accurate results than crude Monte Carlo simulation, and this improvement increased rapidly with decreasing probabilities. (2) to estimate the frequencies of occurrence of extremely low dissolved oxygen (DO) concentrations in a stream receiving multiple COD loads from combined sewer overflows and storm water outlets using a D issolved O xygen S tream MO del (DOSMO). In this example the relationships between stochastic parameters and the model output are strongly non-linear and the number of loading events that determine the in-stream DO concentration is variable. Here, FORM/LHS was more efficient than than FORM/DIS in estimating very small probabilities. A general limit value for the probability of exceedence below which FORM/LHS or FORM/DIS were more efficient than Crude Monte Carlo simulation and Latin Hypercube Sampling could not be given, but they were lower for the complex stream DO model than for the simple lake model. Based on these very different case studies it is concluded that the methods can generally be applied to a large variety of numerical models within the field of environmental engineering.

Connection between dispersive transport and statistics of extreme events

A length dependence of the effective mobility in the form of a power law, B∼L1−1/α, is observed in dispersive transport in amorphous substances, with 0<α<1. We deduce this behavior as a simple consequence of the statistical theory of extreme events. We derive various quantities related to the largest value in samples of n trials, for the exponential and power-law probability densities of the individual events.

Preliminary climatology of southern Africa extreme weather: 1973?1992

Preliminary climatological statistics of extreme weather events over the southern Africa region are established through analysis of daily weather maps of the South African Weather Bureau for a twenty year peiod, 1973–1992. Influences of global warming and inter-annual variability imposed by El Nino events, amongst others, are sought. Notable trends include a decrease in the frequency of station days with rainfall > 70 mm and an increase in station days with temperature > 38°C. Correlations offer some insights to extreme climate associations. Lows over the land in the west and over the sea to the east display consistent interannual variability, despite opposing rainfall regimes. Agreement in extreme temperature statistics in all regions suggest that drought is widespread over southern Africa. Rainfall in the north is negatively related to lows over the sea to the south. A potential mechanism underlying the inverse relationship between midlatitude and sub-tropical storminess is the development of a vorticity dipole associated with the westerly jet stream. This is investigated in an El Nino-influenced case study.

Rank‐ordering statistics of extreme events: Application to the distribution of large earthquakes

Rank‐ordering statistics provide a perspective on the rare, largest elements of a population, whereas the statistics of cumulative distributions are dominated by the more numerous small events. The exponent of a power law distribution can be determined with good accuracy by rank‐ordering statistics from the observation of only a few tens of the largest events. Using analytical results and synthetic tests, we quantify the systematic and the random errors. We also study the case of a distribution defined by two branches, each having a power law distribution, one defined for the largest events and the other for smaller events, with application to the worldwide (Harvard) and southern California earthquake catalogs. In the case of the Harvard moment catalog, we make more precise earlier claims of the existence of a transition of the earthquake magnitude distribution between small and large earthquakes; the b values are b2 = 2.3 ± 0.3 for large shallow earthquakes and b1 = 1.00 ± 0.02 for smaller shallow earthquakes. However, the crossover magnitude between the two distributions is ill defined. The data available at present do not provide a strong constraint on the crossover which has a 50% probability of being between magnitudes 7.1 and 7.6 for shallow earthquakes; this interval may be too conservatively estimated. Thus any influence of a universal geometry of rupture on the distribution of earthquakes worldwide is ill defined at best. We caution that there is no direct evidence to confirm the hypothesis that the large‐moment branch is indeed a power law. In fact, a gamma distribution fits the entire suite of earthquake moments from the smallest to the largest satisfactorily. There is no evidence that the earthquakes of the southern California catalog have a distribution with two branches or that a rolloff in the distribution is needed; for this catalog, b = 1.00 ± 0.02 up to the largest magnitude observed, MW ≃ 7.5; hence we conclude that the thickness of the seismogenic layer has no observable influence whatsoever on the frequency distribution in this region.

Modeling geomorphic processes

The surface of the earth is largely molded by erosional and depositional processes, these processes yield complex structures but within the complexity there is order. The concept of fractals was first introduced in terms of the self-similarity of landforms and spectral studies of both topography and bathymetry often yield self-affine fractals. Drainage networks play an essential role in the evolution of landforms and drainage networks are a classic example of fractal trees. A number of models have recently been proposed for the evolution of drainage networks; a very simple approach that is quite realistic and reproduces observed statistics is based on diffusion limited aggregation. The erosion necessary to produce landforms is attributed to floods with the great floods doing most of the erosion. The statistics of floods and droughts is quite controversial with the applicability of Hurst exponents uncertain; an essential question is whether extreme floods obey fractal (power law) statistics or logarithmic statistics. A tremendous amount of data on paleoweather and climate resides in the sedimentary record; but there are always uncertainties with regard to the completeness of the sedimentary record. Modeling should be possible using the basic concepts of time series but the applicable time series are more likely to be log normal than Gaussian. The statistics of extreme events under such circumstances remain uncertain.

Causal Stochastic Simulation of Dissolved Oxygen Depletion in Rivers Receiving Combined Sewer Overflows

A method for stochastic analysis of the effect of combined sewer overflows on the dissolved oxygen concentration in receiving rivers is developed. The method is based on repeated operation of the water quality model MOUSE-DOSMO. Each operation of this model covers a series of overflow events calculated by the MOUSE-SAMBA runoff model based on a historical rainfall record. For each event selected input data and model parameters in both models are drawn from fundamental statistical distributions by a simple Monte Carlo method. These data and parameters vary from event to event in each series. Each operation of the MOUSE-DOSMO model results in an extreme event statistics on dissolved oxygen minimum values -while repeated operation of the model yields extreme event percentiles by means of which a probability-based assessment of the model result may be performed.