Ewa Bogdanowicz

Climate Change Impact on Hydrological Extremes: Preliminary Results from the Polish-Norwegian Project

This paper presents the background, objectives, and preliminary outcomes from the first year of activities of the Polish–Norwegian project CHIHE (Climate Change Impact on Hydrological Extremes). The project aims to estimate the influence of climate changes on extreme river flows (low and high) and to evaluate the impact on the frequency of occurrence of hydrological extremes. Eight “twinned” catchments in Poland and Norway serve as case studies. We present the procedures of the catchment selection applied in Norway and Poland and a database consisting of near-natural ten Polish and eight Norwegian catchments constructed for the purpose of climate impact assessment. Climate projections for selected catchments are described and compared with observations of temperature and precipitation available for the reference period. Future changes based on those projections are analysed and assessed for two periods, the near future (2021–2050) and the far-future (2071–2100). The results indicate increases in precipitation and temperature in the periods and regions studied both in Poland and Norway.

Generalized Exponential Distribution in Flood Frequency Analysis for Polish Rivers

Many distributions have been used in flood frequency analysis (FFA) for fitting the flood extremes data. However, as shown in the paper, the scatter of Polish data plotted on the moment ratio diagram shows that there is still room for a new model. In the paper, we study the usefulness of the generalized exponential (GE) distribution in flood frequency analysis for Polish Rivers. We investigate the fit of GE distribution to the Polish data of the maximum flows in comparison with the inverse Gaussian (IG) distribution, which in our previous studies showed the best fitting among several models commonly used in FFA. Since the use of a discrimination procedure without the knowledge of its performance for the considered probability density functions may lead to erroneous conclusions, we compare the probability of correct selection for the GE and IG distributions along with the analysis of the asymptotic model error in respect to the upper quantile values. As an application, both GE and IG distributions are alternatively assumed for describing the annual peak flows for several gauging stations of Polish Rivers. To find the best fitting model, four discrimination procedures are used. In turn, they are based on the maximized logarithm of the likelihood function (K procedure), on the density function of the scale transformation maximal invariant (QK procedure), on the Kolmogorov-Smirnov statistics (KS procedure) and the fourth procedure based on the differences between the ML estimate of 1% quantile and its value assessed by the method of moments and linear moments, in sequence (R procedure). Due to the uncertainty of choosing the best model, the method of aggregation is applied to estimate of the maximum flow quantiles.

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.

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”.

The impact of seasonal flood peak dependence on annual maxima design quantiles

ABSTRACT If the maximum annual peak flow series are a mixture of summer and winter flows, a seasonal approach to flood frequency analysis is necessary. While considering seasonal maxima as mutually independent events, the annual maxima distribution is defined as the product of seasonal distributions. However, if the independency assumption does not hold, a bivariate approach with dependent margins should be applied, i.e. the copula approach. The impact of dependency on design quantiles is investigated here in the context of the Fréchet-Hoeffding inequality defining copula bounds and the definition of dependency. The results of the two approaches are compared using six catchments in the San River basin, where in four cases the dependency of seasonal maxima has been identified as positive significant and no strong dominance of any one season is observed. The product model leads to higher estimates of design quantiles than do models where the dependency is taken into account and, therefore, is safe. EDITOR R. Woods ASSOCIATE EDITOR A. Fiori

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.

On the Run Length in Annual Maximum Flow Series in the Middle Vistula Basin in the Context of Climate Change Impact

This chapter presents an application of the 1st order Markov model to the description of flood-poor and flood-rich period length. The flood-poor and flood-rich periods are defined as a sequence of successive years with maximum flows lower (for flood-poor) or greater (for flood-rich) than the specified threshold. The theoretical distributions for two chosen thresholds (median and upper quartile) are compared with empirical distributions for the series of annual flow maxima at Warsaw gauging station, representative for the Middle Vistula River reach, in order to determine an indicator for the assessment of changes in flood regime under the future climate. The results have shown that serial dependency in Warsaw maximum flow series—the longest series in Poland—is rather weak and the run length distributions are not significantly affected by this dependency. The longest flood-poor period of 19 years has been found for the upper quartile threshold.