Partial Duration Series Approach Research Articles

Application of Regional Climatic Models to Assess the Performance Evaluation of Changes on Flood Frequency in Woybo Catchment, Ethiopia

Climate change increases the possibility in varying rainfall and temperature that needs a detail study to estimate flood frequency under changing climate for the Woybo catchment in the Omo River basin of Ethiopia. The impact on flood frequency was evaluated using multiple climate models under RCP4.5 and RCP8.5 emission scenarios for 2020s, 2050s, and 2080s compared to 1976–2005. Hydrologic Engineering Center of Hydrologic Modeling System (HEC‐HMS) was used to simulate streamflow after sensitivity analysis, calibration, and validation of the model for the catchment. Flood frequency analysis was initiated after discharge through a longer section followed by frequency analysis by partial duration series approach which provides a better result even though threshold selection is cumbersome. The results from the nonparametric Mann–Kendall test illustrate a slight increase in annual rainfall. The projected flow is expected to increase in autumn, summer, and annually by 8.34, 13.54, and 5.02% in the 2050s and 12.20, 18.06, and 11.87% in 2080s, respectively, under RCP4.5, while it is likely to increase in summer and annually by 15.66 and 5.82% in 2050s and 10.55 and 29.51% in 2080s, respectively, under RCP8.5. Flood frequency was analyzed by using Gumbel’s method. The flood magnitude predicts a positive change for 10, 50, 100, 200, 500, and 1000 years recurrent periods under both scenarios. This research paves way to reduce the negative impacts of flooding and plays a vital role in providing estimates of recurrence floods which are used in designing roads, dams, and bridges for sustainable water resources management.

Flood frequency estimation and uncertainty in arid/semi-arid regions

At site flood frequency analysis (FFA) in arid/semi-arid watersheds poses unique challenges to researchers and practitioners due to the generally limited data records. This study presents a comprehensive evaluation of FFA in arid/semi-arid watersheds in relation to the unique characteristics of these regions, such as the limited number of floods occurring each year and the large variability of the flood peak discharges. Study cases in Israel and the US are examined and compared with non-arid watersheds, characterized by Mediterranean climate, and with synthetic flood records.Results show that the tail of extreme value distributions describing arid/semi-arid watersheds is found to be heavier than the one describing Mediterranean watersheds. The number of yearly floods and the variability of flood peak discharge are shown to have a crucial impact on the accuracy of the quantile estimates with smaller number of events per year and larger coefficient of variation of flood peak discharge being related to larger errors in the estimated quantiles. Partial duration series approach provides a slightly reduced bias in the estimates, but should not be blindly preferred over annual maxima series as it presents comparable estimation uncertainty. In general, the generalized extreme value and the generalized Pareto distribution are found to be non-optimal choices for the examined arid/semi-arid watersheds.

Analysis of air/river maximum daily temperature characteristics using the peaks over threshold approach

AbstractThe understanding of river temperature is very important when assessing fish habitat conditions in terms of fish growth as well as fish distribution within river systems. The quantification of extreme water temperatures is also important, especially when studying the suitability of thermal habitats during high air/water temperature events. The present study deals with the analysis of extreme air and water temperatures using the partial duration series approach, also known as the peak over threshold (POT) approach. The advantage of the POT approach is that extreme air and water temperatures can be described not only in magnitude but also in duration and degree day accumulation for each event. In the present study, 74 years of air temperature data (Miramichi meteorological station) were analysed as well as 21 years of river temperature data from the Little Southwest Miramichi River. For example, results showed that the 0.01 exceedance probability (F(x) = .99) for maximum daily air temperature event was calculated at 38.4°C whereas for the same exceedance probability, the maximum daily water temperature event was slightly lower at 32.7°C. The duration of events varied between 1 and 5 days for air temperature and between 1 and 7 days for water temperature. Maximum daily water temperature exceeding 30°C generally occurred over a period of 3 days or more, and the degree day accumulation was higher than 6°C·day. This study showed that the POT approach was effective in quantifying both air and water temperature extremes within the Miramichi River study area.

Sensitivity of flood frequency analysis to data record, statistical model, and parameter estimation methods: An evaluation over the contiguous United States

ABSTRACTThe current statistical methods applied in flood frequency analysis require long data records to obtain reliable estimates, particularly for long return periods. Moreover, the choice of the statistical model and the parameter estimation procedure may introduce uncertainty in the estimates. In this work, we investigate the sensitivity of flood frequency analysis to various sample sizes, statistical models, and parameter estimation methods over six major hydrological regions in the contiguous United States. Results show that flood frequency estimates based on annual maximum series approach convergence to the reference values (estimates derived from 70 years record) in terms of median for 35‐year or longer records. However, the uncertainty remains significant and a record of 35 years (20 years) is associated with ~50% (100%) larger uncertainty on the estimated 100‐year flood. The generalised extreme value distribution combined with maximum likelihood estimation method is associated with the largest uncertainty, while the log‐Pearson type III exhibits comparable bias and smaller uncertainty. Application of the partial duration series approach to 20‐year records shows no significant advantage. Our findings suggest that the hydroclimatic characteristics of the catchments exhibit limited impact on the uncertainty.

Extreme weather exposure identification for road networks – a comparative assessment of statistical methods

Abstract. The assessment of road infrastructure exposure to extreme weather events is of major importance for scientists and practitioners alike. In this study, we compare the different extreme value approaches and fitting methods with respect to their value for assessing the exposure of transport networks to extreme precipitation and temperature impacts. Based on an Austrian data set from 25 meteorological stations representing diverse meteorological conditions, we assess the added value of partial duration series (PDS) over the standardly used annual maxima series (AMS) in order to give recommendations for performing extreme value statistics of meteorological hazards. Results show the merits of the robust L-moment estimation, which yielded better results than maximum likelihood estimation in 62 % of all cases. At the same time, results question the general assumption of the threshold excess approach (employing PDS) being superior to the block maxima approach (employing AMS) due to information gain. For low return periods (non-extreme events) the PDS approach tends to overestimate return levels as compared to the AMS approach, whereas an opposite behavior was found for high return levels (extreme events). In extreme cases, an inappropriate threshold was shown to lead to considerable biases that may outperform the possible gain of information from including additional extreme events by far. This effect was visible from neither the square-root criterion nor standardly used graphical diagnosis (mean residual life plot) but rather from a direct comparison of AMS and PDS in combined quantile plots. We therefore recommend performing AMS and PDS approaches simultaneously in order to select the best-suited approach. This will make the analyses more robust, not only in cases where threshold selection and dependency introduces biases to the PDS approach but also in cases where the AMS contains non-extreme events that may introduce similar biases. For assessing the performance of extreme events we recommend the use of conditional performance measures that focus on rare events only in addition to standardly used unconditional indicators. The findings of the study directly address road and traffic management but can be transferred to a range of other environmental variables including meteorological and hydrological quantities.

A regional and nonstationary model for partial duration series of extreme rainfall

AbstractRegional extreme value models for estimation of extreme rainfall intensities are widely applied, but their underlying assumption of stationarity is challenged. Many recent studies show that the rainfall extremes worldwide exhibit a nonstationary behavior. This paper presents a spatiotemporal model of extreme rainfall. The framework is built on a partial duration series approach with a nonstationary, regional threshold value. The model is based on generalized linear regression solved by generalized estimation equations. It allows a spatial correlation between the stations in the network and accounts furthermore for variable observation periods at each station and in each year. Marginal regional and temporal regression models solved by generalized least squares are used to validate and discuss the results of the full spatiotemporal model. The model is applied on data from a large Danish rain gauge network for four durations ranging from 10 min to 24 h. The observation period differs between stations, and the number of stations with more than 10 years of observations has increased over the years. A spatiotemporal model for the threshold is suggested, applying the mean annual precipitation and time as the explanatory variables in the regional and temporal domain, respectively. Further analysis of partial duration series with nonstationary and regional thresholds shows that the mean exceedances also exhibit a significant variation in space and time for some rainfall durations, while the shape parameter is found to be constant.

Quantification of climate change effects on extreme precipitation used for high resolution hydrologic design

Design of urban drainage structures should include the climatic changes anticipated over the technical lifetime of the system. In Northern Europe climate changes implies increasing occurrences of extreme rainfall. Three approaches to quantify the impact of climate changes on extreme rainfall are studied, all based on output from historical rain series of the present climate and output from Regional Climate Models. Two models are applied, one being based on an extreme value model, the Partial Duration Series Approach, and the other based on a stochastic rainfall generator model. Finally an approach is based on identification of areas, where the present climate resembles the anticipated future climate for the region in question. The results indicate that design intensities in Denmark are likely to be increased by 10–50% within the next 100 years. The increase in design intensities depend on the duration and the return period in question.

Large scale modelling of bankfull flow: An example for Europe

► Bankfull flow was modelled on continental scale applying the partial duration series. ► An increasing threshold censoring procedure was applied. ► The setting of an appropriate threshold is more crucial than the distribution function. ► The partial duration series provided slightly better results than annual maxima. ► Bias corrected, daily climate input data led to more accurate results. Bankfull flow is a relevant parameter in the field of large scale modelling especially for the analysis of environmental flows and flood related hydrological processes. In our case, bankfull flow data were required within the SCENES project in order to analyse ecological important inundation events at selected grid cells of a European raster. In practise, the determination of bankfull flow is a complex task even on local scale. Subsequent to a literature survey of bankfull flow studies, this paper describes a method which can be applied to estimate bankfull flow on a global or continental grid cell raster. The method is based on the partial duration series approach taking into account a 40-years time series of daily discharge data modelled by the global water model WaterGAP. An increasing threshold censoring procedure, a declustering scheme and the generalised Pareto distribution are applied. Modelled bankfull flow values are then validated by different efficiency criteria against bankfull flows observed at gauging stations in Europe. Thereby, the impact of (i) the applied distribution function, (ii) the threshold setting in the partial duration series, (iii) the climate input data and (iv) applying the annual maxima series are evaluated and compared to the proposed approach. The results show that bankfull flow can be reasonably estimated with a high model efficiency ( E 1 = 0.71) and weighted correlation ( ωr 2 = 0.90) as well as a systematic overestimation of 22.8%. Finally it turned out that in our study focusing on hydrological extremes, the appliance of the daily climate input data is a basic requirement. While the choice of the distribution function had no significant impact on the final results, the threshold setting in the partial duration series was crucial.

Regional Frequency Analysis of Droughts in Portugal

This study investigated the frequency of droughts for the period September 1910 to October 2004 in mainland Portugal, based on monthly precipitation data from 144 rain gauges distributed across the country. The drought events were characterized using the standardized precipitation index (SPI) applied to time scales of 1, 3, 6 and 12 consecutive months. Based on the SPI time scale series a regional frequency analysis of drought magnitudes was undertaken using two approaches: annual maximum series (AMS) and partial duration series (PDS). Three spatially defined regions (north, central and south) were identified by cluster analysis and analyzed for homogeneity. Maps of drought magnitude were developed using a kriging technique for several return periods. Similar uniform spatial patterns were found throughout the country using the AMS and PDS approaches. For several SPI time scales a comparison of the observed and estimated maximum magnitude (269-year empirical return period) showed that the AMS combined with the selected probability distribution models (Pearson type III, general Pareto and Kappa) provided better results than the PDS approach combined with the same models. A general and simplified characterization of drought duration revealed a relatively uniform pattern of droughts events across the country.

Potential future increase in extreme one-hour precipitation events over Europe due to climate change

In this study the potential increase of extreme precipitation in a future warmer European climate has been examined. Output from the regional climate model (RCM) HIRHAM4 covering Europe has been analysed for two periods, a control period 1961-1990 and a scenario 2071-2100, the latter following the IPCC scenario A2. The model has a resolution of about 12 km, which is unique compared with existing RCM studies that typically operate at 25-50 km scale, and make the results relevant to hydrological phenomena occurring at the spatial scale of the infrastructure designed to drain off rainfall in large urban areas. Extreme events with one- and 24-hour duration were extracted using the Partial Duration Series approach, a Generalized Pareto Distribution was fitted to the data and T-year events for return periods from 2 to 100 years were calculated for the control and scenario period in model cells across Europe. The analysis shows that there will be an increase of the intensity of extreme events generally in Europe; Scandinavia will experience the highest increase and southern Europe the lowest. A 20 year 1-hour precipitation event will for example become a 4 year event in Sweden and a 10 year event in Spain. Intensities for short durations and high return periods will increase the most, which implies that European urban drainage systems will be challenged in the future.

Determination of bankfull discharge magnitude and frequency: comparison of methods on 16 gravel‐bed river reaches

AbstractBankfull discharge is identified as an important parameter for studying river morphology, sediment motion, flood dynamics and their ecological impacts. In practice, the determination of this discharge and its hydrological characteristics is not easy, and a choice has to be made between several existing methods. To evaluate the impact of the choice of methods, five bankfull elevation definitions and four hydrological characterizations (determination of duration and frequency of exceedance applied to instantaneous or mean daily data) were compared on 16 gravel‐bed river reaches located in France (the catchment sizes vary from 10 km2 to 1700 km2). The consistency of bankfull discharge estimated at reach scale and the hydraulic significance of the five elevation definitions were examined. The morphological definitions (Bank Inflection, Top of Bank) were found more relevant than the definitions based on a geometric criterion. The duration of exceedance was preferred to recurrence intervals (partial duration series approach) because it is not limited by the independency of flood events, especially for low discharges like those associated with the Bank Inflection definition. On average, the impacts of the choice of methods were very important for the bankfull discharge magnitude (factor of 1·6 between Bank Inflection and Top of Bank) and duration of exceedance or frequency (respectively a factor 1·8 and 1·9 between mean daily and instantaneous discharge data). The choice of one combination of methods rather than another can significantly modify the conclusions of a comparative analysis in terms of bankfull discharge magnitude and its hydrological characteristics, so that one must be cautious when comparing results from different studies that use different methods. Copyright © 2006 John Wiley & Sons, Ltd.

Can continuous streamflow data support flood frequency analysis? An alternative to the partial duration series approach

Common procedures for flood frequency modeling are based on analysis of series of annual maxima (AMS) of the instantaneous discharge. A practical alternative to AMS series is usually considered when the record length is short. In this case, analysis of partial duration series (PDS) on continuous streamflow records allows one to increase the available information by using more than one flood peak per year. In this paper, the analysis of continuous streamflow data is reconsidered from the beginning: a filtered peaks over threshold (FPOT) procedure is proposed as an alternative to the PDS approach, and objective criteria are devised for choosing a reasonable threshold and for determining the average annual number of events λ. The revised procedure demonstrates that there is no need for specific limitations on the magnitude of λ to preserve the basic hypotheses of the marked point process build in the PDS procedure. The proposed FPOT method is applied to 33 time series of daily runoff from rivers of northwestern Italy. Significant advantages over the classical PDS method are demonstrated, both in terms of physical interpretability of the parameters and efficiency of the estimates.

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

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.

Multivariate Modeling of Flood Flows

A systematic methodology for multivariate modeling of flood flows based on the partial duration series approach and bivariate normal distribution has been developed. The methodology provides univariate and bivariate modeling of flood characteristics and offers various possibilities of probability interpretation, which is not possible by conventional flood frequency methods. The two-step power transformation method has been used for normalization of the variables, required for the application of bivariate normal distribution. The application and validation of the methodology have been made by using daily flows of the Narmada River in Garudeshwar (India) and synthetically generated data.

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.

Properties of extreme point rainfall II: Parametric data interpretation and regional uncertainty assessment

As an alternative to the traditional non-parametric method the partial duration series approach with exponentially distributed exceedances is used to model extreme values of depth and maximum 10 min intensity per rainfall event, measured at gauges placed at different locations in Denmark. A statistically significant regional variation is documented and shown to be of importance to engineering application. The apparent variability is divided into sampling uncertainty and uncertainty caused by true regional variability. Further, a method for assessing the total inherent design uncertainty, taking into account a possible intersite dependence structure, is developed. Adding one total design standard deviation to the regionally averaged T-year events yields increased design values between 5 and 17%. This result brings up a number of questions with respect to application of historical rainfall data in urban storm drainage design and analysis.

Evaluation of risk concepts in partial duration series

Conventional design practice aims at obtaining optimal estimates of floods with specified exceedance probabilities. Such estimates are, however, known on the average to be exceeded more frequently than expected. Alternatively, methods focusing on the expected exceedance probability can be used. Two different methods are considered here; the first is based on the sample distribution of true exceedance probabilities. The second is a Bayesian analogue using the likelihood function and a noninformative prior to describe the variability of exceedance probabilities. Appropriate analytical solutions are presented in both cases using the partial duration series approach.

Some remarks on the truncation used in partial flood series models

In the partial duration series approach to the problem of flood analysis, the truncation level above which streamflow is regarded as flood flow plays a key role. In the absence of a systematic and well defined method for selecting such a level in practice, it is desirable to know how different choices effect the obtained results. We base our mathematical investigation on some commonly used partial flood series models to show that once the time‐dependent Poisson process, used in modeling flood frequency is found applicable with a certain truncation level, then it should remain so with any higher truncation level. We also point out that this same property holds true for the exponential distribution widely used in the study of flood magnitude. At the end of our investigation we give a number of remarks on some problems involved in the practical application of partial duration series models.