Non-stationary Flood Frequency Analysis Research Articles

An Adaptive Metropolis-Hastings Optimization Algorithm of Bayesian Estimation in Non-Stationary Flood Frequency Analysis

Global climate changing and human activities have altered the assumption of stationarity, and intensified the variation of hydrological process in recent decades. It is essential to make progress in accommodating appropriate models to the changing environment where non-stationary models are taken into account. The developing adapted Bayesian inference offers an attractive framework to estimate non-stationary models, when compared with conventional maximum likelihood estimation (MLE). As the inseparable companions of Bayesian inference, an efficient MCMC sampler are expected to be built. However, proper tunings are needed for the sampler to improve the performance by integrating adaptive algorithm and optimization method. A Bayesian approach with the adaptive Metropolis-Hastings optimization (AM-HO) algorithm is adopted to estimate the parameters and quantify the uncertainty in a two-parameter non-stationary Lognormal distribution model. To verify the performance of the developed model, simulation experiments and practical applications are implemented to fit annual maximum flood series of two gauges in Hanjiang River basin. From the point view of parameters estimation, both Bayesian and MLE methods perform similarly. However, Bayesian method is more attractive and reliable than MLE on uncertainty quantification, which provides a relative narrow intervals to be beneficial for risk analysis and water resource management.

Parsimonious nonstationary flood frequency analysis

Abstract There is now widespread awareness of the impact of anthropogenic influences on extreme floods (and droughts) and thus an increasing need for methods to account for such influences when estimating a frequency distribution. We introduce a parsimonious approach to nonstationary flood frequency analysis (NFFA) based on a bivariate regression equation which describes the relationship between annual maximum floods, x, and an exogenous variable which may explain the nonstationary behavior of x. The conditional mean, variance and skewness of both x and y = ln (x) are derived, and combined with numerous common probability distributions including the lognormal, generalized extreme value and log Pearson type III models, resulting in a very simple and general approach to NFFA. Our approach offers several advantages over existing approaches including: parsimony, ease of use, graphical display, prediction intervals, and opportunities for uncertainty analysis. We introduce nonstationary probability plots and document how such plots can be used to assess the improved goodness of fit associated with a NFFA.

A comparison of three approaches to non-stationary flood frequency analysis

Non-stationary flood frequency analysis (FFA) is applied to statistical analysis of seasonal flow maxima from Polish and Norwegian catchments. Three non-stationary estimation methods, namely, maximum likelihood (ML), two stage (WLS/TS) and GAMLSS (generalized additive model for location, scale and shape parameters), are compared in the context of capturing the effect of non-stationarity on the estimation of time-dependent moments and design quantiles. The use of a multimodel approach is recommended, to reduce the errors due to the model misspecification in the magnitude of quantiles. The results of calculations based on observed seasonal daily flow maxima and computer simulation experiments showed that GAMLSS gave the best results with respect to the relative bias and root mean square error in the estimates of trend in the standard deviation and the constant shape parameter, while WLS/TS provided better accuracy in the estimates of trend in the mean value. Within three compared methods the WLS/TS method is recommended to deal with non-stationarity in short time series. Some practical aspects of the GAMLSS package application are also presented. The detailed discussion of general issues related to consequences of climate change in the FFA is presented in the second part of the article entitled “Around and about an application of the GAMLSS package in non-stationary flood frequency analysis”.

Around and about an application of the GAMLSS package to non-stationary flood frequency analysis

The non-stationarity of hydrologic processes due to climate change or human activities is challenging for the researchers and practitioners. However, the practical requirements for taking into account non-stationarity as a support in decision-making procedures exceed the up-to-date development of the theory and the of software. Currently, the most popular and freely available software package that allows for non-stationary statistical analysis is the GAMLSS (generalized additive models for location, scale and shape) package. GAMLSS has been used in a variety of fields. There are also several papers recommending GAMLSS in hydrological problems; however, there are still important issues which have not previously been discussed concerning mainly GAMLSS applicability not only for research and academic purposes, but also in a design practice. In this paper, we present a summary of our experiences in the implementation of GAMLSS to non-stationary flood frequency analysis, highlighting its advantages and pointing out weaknesses with regard to methodological and practical topics.

Comparison of Two Nonstationary Flood Frequency Analysis Methods within the Context of the Variable Regime in the Representative Polish Rivers

Changes in river flow regime resulted in a surge in the number of methods of non-stationary flood frequency analysis. Common assumption is the time-invariant distribution function with time-dependent location and scale parameters while the shape parameters are time-invariant. Here, instead of location and scale parameters of the distribution, the mean and standard deviation are used. We analyse the accuracy of the two methods in respect to estimation of time-dependent first two moments, time-invariant skewness and time-dependent upper quantiles. The method of maximum likelihood (ML) with time covariate is confronted with the Two Stage (TS) one (combining Weighted Least Squares and L-moments techniques). Comparison is made by Monte Carlo simulations. Assuming parent distribution which ensures the asymptotic superiority of ML method, the Generalized Extreme Value distribution with various values of linearly changing in time first two moments, constant skewness, and various time-series lengths are considered. Analysis of results indicates the superiority of TS methods in all analyzed aspects. Moreover, the estimates from TS method are more resistant to probability distribution choice, as demonstrated by Polish rivers’ case studies.

An at-site flood estimation method in the context of nonstationarity I. A simulation study

Summary The stationarity of annual flood peak records is the traditional assumption of flood frequency analysis. In some cases, however, as a result of land-use and/or climate change, this assumption is no longer valid. Therefore, new statistical models are needed to capture dynamically the change of probability density functions over time, in order to obtain reliable flood estimation. In this study, an innovative method for nonstationary flood frequency analysis was presented. Here, the new method is based on detrending the flood series and applying the L-moments along with the GEV distribution to the transformed “stationary” series (hereafter, this is called the LM-NS). The LM-NS method was assessed through a comparative study with the maximum likelihood (ML) method for the nonstationary GEV model, as well as with the stationary (S) GEV model. The comparative study, based on Monte Carlo simulations, was carried out for three nonstationary GEV models: a linear dependence of the mean on time (GEV1), a quadratic dependence of the mean on time (GEV2), and linear dependence in both the mean and log standard deviation on time (GEV11). The simulation results indicated that the LM-NS method performs better than the ML method for most of the cases studied, whereas the stationary method provides the least accurate results. An additional advantage of the LM-NS method is to avoid the numerical problems (e.g., convergence problems) that may occur with the ML method when estimating parameters for small data samples.

Non-Stationary Flood Frequency Analysis in the Ouémé River Basin, Benin Republic

A statistical model to predict the probability and magnitude of floods in non-stationary conditions is presented. The model uses a time-dependent and/or covariate-dependent generalized extreme value (GEV) distribution to fit the annual maximal (AM) discharge, and it is applied to five gauging stations in the Ouémé River Basin in Benin Republic, West Africa. Different combinations of the model parameters, which vary with respect to time and/or climate covariates, were explored with the stationary model based on three criteria of goodness of fit. The non-stationary model more adequately explains a substantial amount of variation in the data. The GEV-1 model, which incorporates a linear trend in its location parameter, surpasses the other models. Non-stationary return levels for different return periods have been proposed for the study area. This case study tested the hypothesis of stationarity in estimating flood events in the basin and it demonstrated the strong need to account for changes over time when performing flood frequency analyses.

Nonstationary Flood Frequency Analysis for Annual Flood Peak Series, Adopting Climate Indices and Check Dam Index as Covariates

Traditionally, flood frequency analysis under the assumption of stationarity has been a cornerstone and there is mature technology applied in practice. However, recent evidences of the impact of climate variability and anthropogenic factors have thrown into question the applicability of stationary hypothesis. In this study, Kendall’s tau and Spearman’s rho correlation test were adopted to detect the relationship between climate indices (PDO, NAO, AO, NPO and ENSO) and annual flood peak data. The test results showed that NPO and Nino3 had significant correlations with the flood peak which could prove the climate cause of non-stationarity. Nino3 is used herein to describe ENSO. We also proposed a check dam index (CDIp) to represent the effect of human activities that caused nonstationarity on flood. The CDIp was based on the estimated storage capacity and drainage area of large number of check dams and small hydraulic structures. A framework for nonstationary flood frequency analysis was developed through Generalized Additive Models in Location, Scale and Shape (GAMLSS), and two models based on GAMLSS were applied to the annual flood peak. The model results that incorporated climate indices (NPO and Nino3) and CDIp as covariates in the parameters of the selected distribution exhibited an undulate behavior, which could better describe nonstationarity than the model with only time dependence. For a reservoir index (RI) proposed by Lopez and Frances (2013) which is similar to CDIp, we established two contrast models and the result revealed that CDIp is superior to RI. These results highlight the necessity of flood frequency analysis under nonstationary conditions, and alternative definitions of return period should be adapted.

Hierarchical Bayesian clustering for nonstationary flood frequency analysis: Application to trends of annual maximum flow in Germany

AbstractEspecially for extreme precipitation or floods, there is considerable spatial and temporal variability in long term trends or in the response of station time series to large‐scale climate indices. Consequently, identifying trends or sensitivity of these extremes to climate parameters can be marked by high uncertainty. When one develops a nonstationary frequency analysis model, a key step is the identification of potential trends or effects of climate indices on the station series. An automatic clustering procedure that effectively pools stations where there are similar responses is desirable to reduce the estimation variance, thus improving the identification of trends or responses, and accounting for spatial dependence. This paper presents a new hierarchical Bayesian approach for exploring homogeneity of response in large area data sets, through a multicomponent mixture model. The approach allows the reduction of uncertainties through both full pooling and partial pooling of stations across automatically chosen subsets of the data. We apply the model to study the trends in annual maximum daily stream flow at 68 gauges over Germany. The effects of changing the number of clusters and the parameters used for clustering are demonstrated. The results show that there are large, mainly upward trends in the gauges of the River Rhine Basin in Western Germany and along the main stream of the Danube River in the south, while there are also some small upward trends at gauges in Central and Northern Germany.

Flood Frequency Analysis Considering Probability Distribution and Return Period under Non-stationary Condition

This study performed the non-stationary flood frequency analysis considering time-varying parameters of a probability density function. Also, return period and risk under non-stationary condition were estimated. A stationary model and three non-stationary models using Generalized Extreme Value(GEV) were developed. The only location parameter was assumed as time-varying parameter in the first model. In second model, the only scale parameter was assumed as time-varying parameter. Finally, the both parameters were assumed as time varying parameter in the last model. Relative likelihood ratio test and Akaike information criterion were used to select appropriate model. The suggested procedure in this study was applied to eight multipurpose dams in South Korea. Using relative likelihood ratio test and Akaike information criterion it is shown that the inflow into the Hapcheon dam and the Seomjingang dam were suitable for non-stationary GEV model but the other six dams were suitable for stationary GEV model. Also, it is shown that the estimated return period under non-stationary condition was shorter than those estimated under stationary condition.

Non-Stationary Annual Maximum Flood Frequency Analysis Using the Norming Constants Method to Consider Non-Stationarity in the Annual Daily Flow Series

Flood frequency analysis is concerned with fitting a probability distribution to observed data to make predictions about the occurrence of floods in the future. Under conditions of climate change, or other changes to the water cycle that impact flood runoff, the flood series is likely to exhibit non-stationarity, in which case the return period of a flood event of a certain magnitude would change over time. In non-stationary flood frequency analysis, it is customary to examine only the non-stationarity of annual maximum flood data. We developed a way of considering the effect of non-stationarity in the annual daily flow series on the non-stationarity in the annual maximum flood series, which we termed the norming constants method (NCM) of non-stationary flood frequency analysis (FFA). After developing and explaining a framework for application of the method, we tested it using data from the Wei River, China. After detecting significant non-stationarity in both the annual maximum daily flood series and the annual daily flow series, application of the method revealed superior model performance compared to modelling the annual maximum daily flood series under the assumption of stationarity, and the result was further improved if explanatory climatic variables were considered. We conclude that the NCM of non-stationary FFA has potential for widespread application due to the now generally accepted weakness of the assumption of stationarity of flood time series.

Evaluation of Nonstationarity in Annual Maximum Flood Series and the Associations with Large-scale Climate Patterns and Human Activities

Recent evidences of the impact of regional climate variability, coupled with the intensification of human activities, have led hydrologists to study flood regime without applying the hypothesis of stationarity. In this study, identification of nonstationarity was conducted in the form of both trend and change point in the mean of the annual maximum flood magnitudes, using Mann-Kendall and Pettitt test, respectively in Wangkuai reservoir watershed, China. The annual maximum flood series exhibited a significant decreasing trend, and the timing of change point was detected in 1979, which was consistent with the construction of large numbers of check dams and small hydraulic structures. A correlation test (Pearson correlation test) between large-scale oceanic-atmospheric patterns (El Nino Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO), North Pacific Oscillation (NPO), North Atlantic Oscillation (NAO), Atlantic Oscillation (AO)) and annual maximum flood peaks was adopted to assess the climatic causes of nonstationary flood series. It was found that NPO, NAO and AO had significant correlations with flood peak, but ENSO and PDO could not explain the variations of flood peak. In the case of human-induced nonstationarity, we proposed 2 new indices to represent the effect of human activities on flood. The new indices were proposed based on the storage capacity and drainage area of the large numbers of check dams and small hydraulic structures which were estimated with no observed data. The identification of nonstationarity for flood series and the climatic and human-induced causes could provide useful information in nonstationary flood frequency analysis.

Non-stationary flood frequency analysis in continental Spanish rivers, using climate and reservoir indices as external covariates

Abstract. Recent evidences of the impact of persistent modes of regional climate variability, coupled with the intensification of human activities, have led hydrologists to study flood regime without applying the hypothesis of stationarity. In this study, a framework for flood frequency analysis is developed on the basis of a tool that enables us to address the modelling of non-stationary time series, namely, the "generalized additive models for location, scale and shape" (GAMLSS). Two approaches to non-stationary modelling in GAMLSS were applied to the annual maximum flood records of 20 continental Spanish rivers. The results of the first approach, in which the parameters of the selected distributions were modelled as a function of time only, show the presence of clear non-stationarities in the flood regime. In a second approach, the parameters of the flood distributions are modelled as functions of climate indices (Arctic Oscillation, North Atlantic Oscillation, Mediterranean Oscillation and the Western Mediterranean Oscillation) and a reservoir index that is proposed in this paper. The results when incorporating external covariates in the study highlight the important role of interannual variability in low-frequency climate forcings when modelling the flood regime in continental Spanish rivers. Also, with this approach it is possible to properly introduce the impact on the flood regime of intensified reservoir regulation strategies. The inclusion of external covariates permits the use of these models as predictive tools. Finally, the application of non-stationary analysis shows that the differences between the non-stationary quantiles and their stationary equivalents may be important over long periods of time.

A nonstationary flood frequency analysis method to adjust for future climate change and urbanization

Many current flood management policies and designs are based on an estimate of the 100-yr flood, an event that has a 1% chance of occurring in a given year. Existing methods to estimate the 100-yr flood, however, assume flood records are stationary even though multiple nonstationary factors, such as climate change and urbanization, influence measured hydrologic data. The goal of this study was to develop and apply a nonstationary flood frequency analysis method that accounts for multiple nonstationary factors. The method adjusts a measured flood record to urbanization and climate conditions for a future design year to account for the effects of changes in conditions from the year that each flood was measured to a selected design year. The method was applied to the Little Patuxent River in Guilford, Maryland, and the results showed a 30.2% increase in the 100-yr flood for the design year 2100. The developed method is intended to begin a discussion among engineers, scientists, and policy makers in regards to incorporating the issue of nonstationarity due to multiple factors into future policies and designs.

On seasonal approach to nonstationary flood frequency analysis

Annual peak flow series of Polish rivers are mixtures of summer and winter flows. Seasonal series are expected to be more homogeneous than annual series in respect of both the distribution and trend in time. Consequently, a seasonal maxima approach to stationary flood frequency analysis (FFA), which increases accuracy of quantile estimates in comparison to the annual maxima approach when the underlying distributions hold, has been introduced by Polish Hydrological Service. The set of Polish data of seasonal and annual maxima have been examined for their homogeneity regarding the distribution type and trend in mean and standard deviation. Large spatial variability of seasonal and annual distribution type as well as of linear trend estimates have been observed. Seasonal variation of trends requires seasonal approach for non-stationary FFA which is presented here and illustrated by a case study. Nonstationary FFA is performed for winter and summer peaks separately and time-dependent annual peak flow quantiles are computed by union formula of two independent events. Applied estimation techniques of NFFA and standard error evaluation by a bootstrap technique are briefly described.