Wyniki wyszukiwania - BazTech

1

Comparison of conventional and differential evolution based parameter estimation methods on the food frequency analysis

Yilmaz Muhammet, Tosunoglu Fatih, Demirel Mehmet Cüneyd

Acta Geophysica

|

2021

|

Vol. 69, no. 5

1887--1900

EN

Accurate estimation of food frequency is an important task for water resources management. This starts with appropriate selection of probability distribution to food samples (annual maximum flows) that is of great importance for food frequency analysis (FFA). In order to reach the most precise estimation, the probability distribution of the considered time series should be well defined and its parameters should be more accurately estimated. First time in the FFA literature, a differential evolution-based parameter estimation method is applied to obtain the parameters of probability distribution functions and is compared with the traditional maximum likelihood method (MLM) in the present study. For this purpose, eleven distributions have been used to describe the annual maximum food series of nine gauging sites, with the performance of each distribution being investigated based on six criteria. The results revealed that a single distribution cannot be specified as the best-ft distribution for the study area. Moreover, it has been found that the applied approach improves the probability prediction of foods better than MLM method for efficient design of hydraulic structures, risk analysis and floodplain management.

2

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

Debele S. E., Bogdanowicz E., Strupczewski W. G.

Acta Geophysica

|

2017

|

Vol. 65, no. 4

885--892

EN

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 nonstationarity as a support in decision-making procedures exceed the up-todate development of the theory and the of software. Currently, the most popular and freely available software package that allows for nonstationary 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.

3

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

Debele S. E., Strupczewski W. G., Bogdanowicz E.

Acta Geophysica

|

2017

|

Vol. 65, no. 4

863--883

EN

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”.

4

Zastosowanie metody uogólnionych momentów do estymacji kwantyli przepływów maksymalnych wybranych rozkładów o grubych ogonach

Kochanek K., Feluch W.

Przegląd Geofizyczny

|

2016

|

Z. 3-4

171--193

PL

W pracy przedstawiamy metodę estymacji kwantyli powodziowych za pomocą uogólnionych momentów jako alternatywę dla klasycznych metod estymacji, czyli metody momentów, momentów liniowych i największej wiarygodności. W swoich teoretycznych założeniach metoda uogólnionych momentów, uwalniając się od założeń naturalnych potęg momentów, umożliwia utrzymanie tych potęg na możliwie niskim poziomie, przez co minimalizuje błędy pomiarowe oraz niejednorodności próby losowej. Wyprowadzono wzory na momenty generalizowane dla trzech często stosowanych w analizie częstości powodzi modeli charakteryzujących się grubym ogonem: rozkłady Log-Gumbela, Log-Logistyczny i Weibulla. Za pomocą metody symulacyjnej Monte Carlo obliczono błędy systematyczne i średnie błędy kwadratowe kwantyli o okresie powtarzalności 10 i 100 lat. Wyliczenia pokazały, że metoda dla wybranych wartości rzędów momentów może stanowić alternatywę dla metod klasycznych. Dodatkowo przeprowadzono obliczenia na podstawie ciągu przepływów maksymalnych z profilu Warszawa-Nadwilanówka, które wykazały, że metoda uogólnionych momentów nie powinna być stosowana dla rozkładu Weibulla.

EN

This paper considers the estimation of the flood quantiles by means of the method of generalized moments which is the alternative for classical methods of estimation, namely methods of moments, linear moments and maximum likelihood. Theoretically the method of generalised moments is released from the assumption of the natural powers of moments and enables to keep these powers as low as possible diminishing the measurement errors and errors stemming from the heterogeneity of the random sample. The equations for the generalised moments for the three heavy-tailed models commonly used in the flood frequency analysis: log-Gumbel, Log-Logistic and Weibull. We used the Monte Carlo simulations to calculate the mean square errors of quantiles of the 10- and 100-year floods. The calculations revealed, that the method of generalised moments for certain range of powers can be an alternative for classical methods. Additionally, we carried out the calculations for the annual maximum flows for the Warsaw-Nadwilanówka at the River Vistula, which revealed that method of generalised moments should not be used for the Weibull model.

5

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

Strupczewski W. G., Kochanek K., Bogdanowicz E., Markiewicz I., Feluch W.

Acta Geophysica

|

2016

|

Vol. 64, no. 1

206--236

EN

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.

6

Are parsimonious FF models more reliable than true ones? II. Comparative assessment of the performance of simple models versus the parent distributions

Kochanek K., Strupczewski W. G., Singh V. P., Węglarczyk S.

Acta Geophysica Polonica

|

2005

|

Vol. 53, nr 4

437-457

EN

Applying the methodology described in Strupczewski et al. (2005a; this issue), the performance of various parsimonious models combined with three estima-tion methods versus Flood Parent Distributions is comparatively assessed by simulation experiments. Moments (MOM), L-moments (LMM) and maximum likelihood (MLM) are used as alternative methods. Five four-parameter Specific Wakeby Distributions (SWaD) are employed to serve as Flood Parent Distributions and forty Distribution/Estimation (D/E) procedures are included in respect to the estimation of upper quantiles. The relative bias (RB), relative root mean square error (RRMSE) and reliability of procedures are used for the assessment of the relative performance of alternative procedures. Parsimonious two-parameter models generally perform better for hydrological sample sizes than their three-parameter counterparts with respect to RRMSE. How-ever, the best performing procedures differ for various SWaDs. As far as estimation methods are concerned, MOM usually produces the smallest values of both RB and RRMSE of upper quantiles for all competing methods. The second place in rank is occupied by LMM, whereas, MLM produces usually the highest values. Considerable influence of sampling bias on the value of the total bias has been ascertained. The improper choice of a model fitted to SWaD samples causes that the reliability of some three-parameter parsimonious D/E procedures does not always rise with the sample size. Also odd is that True model does not always give one hundred percent reliability for very large samples, as it should. This means that estimating algorithms still require improvements.

7

Are parsimonious FF models more reliable than true ones? I. Accuracy of Quantiles and Moments Estimation (AQME) - method of assessment

Strupczewskiwgs@igf.edu.pl W. G., Kochanek K., Singh V. P., Węglarczyk S.

Acta Geophysica Polonica

|

2005

|

Vol. 53, nr 4

419-436

EN

Applying the methodology described in Strupczewski et al. (2005a; this is-sue), the performance of various parsimonious models combined with three estimation methods versus Flood Parent Distributions is comparatively assessed by simulation experiments. Moments (MOM), L-moments (LMM) and maximum likelihood (MLM) are used as alternative methods. Five four-parameter Specific Wakeby Distributions (SWaD) are employed to serve as Flood Parent Distributions and forty Distribution/Estimation (D/E) procedures are included in respect to the estimation of upper quantiles. The relative bias (RB), relative root mean square error (RRMSE) and reliability of procedures are used for the assessment of the relative performance of alternative procedures. Parsimonious two-parameter models generally perform better for hydrological sample sizes than their three-parameter counterparts with respect to RRMSE. How-ever, the best performing procedures differ for various SWaDs. As far as estimation methods are concerned, MOM usually produces the smallest values of both RB and RRMSE of upper quantiles for all competing methods. The second place in rank is occupied by LMM, whereas, MLM produces usually the highest values. Considerable influence of sampling bias on the value of the total bias has been ascertained. The improper choice of a model fitted to SWaD samples causes that the reli-ability of some three-parameter parsimonious D/E procedures does not always rise with the sample size. Also odd is that True model does not always give one hundred percent reliability for very large samples, as it should. This means that estimating algorithms still require improvements.

8

Model error in flood frequency estimation

Strupczewski W., Węglarczyk S., Singh V.

Acta Geophysica Polonica

|

2002

|

Vol. 50, nr 2

279-319

EN

Asymptotic bias in large quantiles and moments for three parameter estimation methods, including the maximum likelihood method (MLM), moments method (MOM) and linear moments method (LMM), is derived when a probability distribution function (PDF) is falsely assumed. It is illustrated using an alternative set of PDFs consisting of five two-parameter PDFs that are lower-bounded at zero, i.e., Log-Gumbel (LG), Log-logistic (LL), Log-normal (LN), Linear Diffusion (LD) and Gamma (Ga) distribution functions. The stress is put on applicability of LG and LL in the real conditions, where the hypothetical distribution (H) differs from the true one (T). Therefore, the following cases are considered: H=LG; T=LL, LN, LD and Ga, and H=LL, LN, LD and Ga, T=LG. It is shown that for every pair (H; T) and for every method, the relative bias (RB) of moments and quantiles corresponding to the upper tail is an increasing function of the true value of the coefficient of variation (cv), except that RB of moments for MOM is zero. The value of RB is smallest for MOM and the largest for MLM. The bias of LMM occupies an intermediate position. Since MLM used as the approximation method is irreversible, the asymptotic bias of the MLM-estimate of any statistical characteristic is not asymmetric as is for the MOM and LMM. MLM turns out to be the worst method if the assumed LG or LL distribution is not the true one. It produces a huge bias of upper quantiles, which is at least one order higher than that of the other two methods. However, the reverse case, i.e., acceptance of LN, LD or Ga as a hypothetical distribution while LG or LL as the true one, gives the MLM-bias of reasonable magnitude in upper quantiles. Therefore, one should be highly reluctant in choosing the LG and LL in flood frequency analysis, especially if MLM is to be applied.