Dan Rosbjerg

Prediction in partial duration series with generalized pareto‐distributed exceedances

As a generalization of the common assumption of exponential distribution of the exceedances in partial duration series the generalized Pareto distribution has been adopted. Estimators for the parameters are presented using estimation by both method of moments and probability-weighted moments. The corresponding estimators for the T-year event are given and approximate expressions for bias and variance of the estimators are derived in both cases. Using the mean square error of the T-year event estimator as a performance index it is shown that the method of moments is preferable to the probability-weighted moments. Maintaining the generalized Pareto distribution as the parent exceedance distribution the T-year event is estimated assuming the exceedances to be exponentially distributed. For moderately long-tailed exceedance distributions and small to moderate sample sizes it is found, by comparing mean square errors of the T-year event estimators, that the exponential distribution is preferable to the correct generalized Pareto distribution despite the introduced model error and despite a possible rejection of the exponential hypothesis by a test of significance. For moderately short-tailed exceedance distributions (with physically justified upper limit) the correct exceedance distribution should be applied despite a possible acceptance of the exponential assumption by a test of significance.

Generalized least squares and empirical bayes estimation in regional partial duration series index‐flood modeling

A regional estimation procedure that combines the index-flood concept with an empirical Bayes method for inferring regional information is introduced. The model is based on the partial duration series approach with generalized Pareto (GP) distributed exceedances. The prior information of the model parameters is inferred from regional data using generalized least squares (GLS) regression. Two different Bayesian T-year event estimators are introduced: a linear estimator that requires only some moments of the prior distributions to be specified and a parametric estimator that is based on specified families of prior distributions. The regional method is applied to flood records from 48 New Zealand catchments. In the case of a strongly heterogeneous intersite correlation structure, the GLS procedure provides a more efficient estimate of the regional GP shape parameter as compared to the usually applied weighted regional average. If intersite dependence is ignored, the uncertainty of the regional estimator may be seriously underestimated and erroneous conclusions with respect to regional homogeneity may be drawn. The GLS procedure is shown to provide a general framework for a reliable evaluation of parameter uncertainty as well as for an objective appraisal of regional homogeneity. A comparison of the two different Bayesian T-year event estimators reveals that generally the simple linear estimator is adequate.

Estimation in partial duration series with independent and dependent peak values

Partial duration series with exponentially distributed peak exceedance values and Poissonian occurrence times have been studied in the case of both independent and dependent peak values. Especially the variance of the T-yr. estimate has been considered, an a previously unexplained disagreement between theory-based and Monte Carlo-based variance calculations in the independent case has been accounted for. In the dependent case a formula for the variance of the T-yr. estimate has been developed and shown to be in fine agreement with Monte Carlo-based variance calculations. Finally, a general formula for the distribution of the annual maximum covering also the dependent case has been derived, and the use of the formula has been exemplified.

The partial duration series method in regional index-flood modeling

A regional index-flood method based on the partial duration series model is introduced. The model comprises the assumptions of a Poisson-distributed number of threshold exceedances and generalized Pareto (GP) distributed peak magnitudes. The regional T-year event estimator is based on a regional estimate of the GP shape parameter. Analytical approximations of bias and variance of the regional T-year event estimator are deduced. The performance of the regional method is evaluated in the case of regional heterogeneity and intersite dependence. For small to moderate sample sizes, the regional estimator is superior to the at-site estimator even in extremely heterogenous regions, the performance of the regional estimator being relatively better in regions with a negative shape parameter. When the record length increases, the relative performance of the regional estimator decreases, but it is still preferable to at-site estimation in moderately heterogeneous and homogeneous regions for large sample sizes. Modest intersite dependence has only a small effect on the performance of the regional index-flood estimator.

Choice of reliability, resilience and vulnerability estimators for risk assessments of water resources systems / Choix d’estimateurs de fiabilité, de résilience et de vulnérabilité pour les analyses de risque de systèmes de ressources en eau

Abstract Abstract Definitions and estimators of water resources system reliability (the probability that the system will remain in a non-failure state), resilience (the ability of the system to return to non-failure state after a failure has occurred) and vulnerability (the likely damage of a failure event) have been thoroughly investigated. A behaviour analysis addressing monotonic behaviour, overlap and correlation between the estimators was carried out by routing time series of monthly runoff through a reservoir with a specified storage volume that is operated according to a fixed operation policy. Estimation based on historical time series is shown to be problematic and a procedure encompassing generation of synthetic time series with a length of at least 1000 years is recommended in order to stabilize the estimates. Moreover, the strong correlation between resilience and vulnerability may suggest that resilience should not be explicitly accounted for.

Modelling of transport and biogeochemical processes in pollution plumes: Vejen landfill, Denmark

A biogeochemical transport code is used to simulate leachate attenuation, biogeochemical processes, and development of redox zones in a pollution plume downstream of the Vejen landfill in Denmark. Calibration of the degradation parameters resulted in a good agreement with the observed distribution in the plume of a number of species, such as dissolved organic carbon (DOC), Fe2+, NO3−, HCO3−, SO42−, CH4, and pH. The simulated redox zones agree with observations confirming that the Fe-reducing zone played an important role in the attenuation of the DOC plume. Effective first-order rate constants for every redox zone were determined giving DOC half-lives ranging from 100 to 1–2 days going from the methanogenic to the aerobic zone. The order of decrease in DOC half-lives from the anaerobic to the aerobic zone corresponds to findings at other landfills.

Uncertainty measures of regional flood frequency estimators

Regional flood frequency models have different assumptions regarding homogeneity and inter-site independence. Thus, uncertainty measures of T-year event estimators are not directly comparable. However, having chosen a particular method, the reliability of the estimate should always be stated, e.g. in terms of a standard error. For this reason, and also for assistance in choice of method, approximate variances of the T-year event estimate have been deduced for five different regional models.

Optimization of Conventional Rule Curves Coupled with Hedging Rules for Reservoir Operation

As a common approach to reservoir operating policies, water levels at the end of each time interval should be kept at or above the rule curve. In this study, the policy is captured using rationing of the target yield to reduce the intensity of severe water shortages. For this purpose, a hybrid model is developed to optimize simultaneously both the conventional rule curve and the hedging rule. In the compound model, a simple genetic algorithm is coupled with a simulation program, including an inner linear programming algorithm. In this way, operational policies are imposed by priority concepts to achieve the optimal water allocation and the target storage levels for reservoirs. As a case study, a multipurpose, multireservoir system in southern Iran is selected. The results show that the model has good performance in extracting the optimum policy for reservoir operation under both normal and drought conditions.

Use of a two-component exponential distribution in partial duration modelling of hydrological droughts in Zimbabwean rivers.

Abstract An investigation of hydrological droughts has been conducted, based on the truncation level approach: each drought event is characterized by its duration and deficit volume. The truncation level is defined to reflect the expected natural water availability and, therefore, is evaluated monthly as a fixed percentile of the monthly flow-duration curve. Thus, the problem of expected zero flow of ephemeral rivers during the dry season is taken care of. The data material consists of daily discharge data from ten Zimbabwean rivers, and both ephemeral and perennial rivers are included in the analysis. The partial duration series approach is used to predict the severity of future droughts, i.e. the T-year events. The two-component exponential distribution is adopted as exceedence distribution for both duration and deficit volume. The parameters of the two-component exponential distribution are estimated using the maximum likelihood method. A method for calculating the T-year event and an approximate expression of the uncertainty of the T-year events have been developed. An observed problem of underestimation of observed deficit volumes is reduced by the introduction of censoring in the partial duration series. A better description of the observed events has been obtained by censoring the duration and deficit volume series. A relationship between optimal censoring and the coefficient of variation of the drought series has been indicated.

Estimation of regional intensity-duration-frequency curves for extreme precipitation

Regional estimation of extreme precipitation from a high resolution rain gauge network in Denmark is considered. The applied extreme value model is based on the partial duration series (PDS) approach in which all events above a certain threshold level are modelled. For a preliminary assessment of regional homogeneity and identification of a proper regional distribution L-moment analysis is applied. To analyse the regional variability in more detail, a generalised least squares regression analysis is carried out that relates the PDS model parameters to climatic and physiographic characteristics. The analysis reveals that the mean annual number of extreme events varies significantly within the region, and a large part of this variability can be explained by the mean annual rainfall. The mean value of the exceedance magnitudes can be assumed constant for intensities with durations less than one hour. For larger durations a pronounced metropolitan effect is evident, the mean intensities in the Copenhagen area being significantly larger than found in the rest of the country. With respect to second and higher order moments the region can be considered homogeneous for intensities with durations less than 24 hours. A regional parent distribution is identified as the generalised Pareto distribution.