Nonstationary Flood Frequency Analysis Based On Annual Daily Flow Series

In frequency analysis of annual maximum flood series(AMFS),it is mechanismbased and significant to incorporate the information of the underlying "ordinary" daily streamflow events for more accurate flood risk estimation and management.In previous studies relevant to flood nonstationarity,the classical norming constants method(CNCM)has been used to derive statistical parameters of annual maximum flood distribution from daily streamflow distribution.However,C-NCM does not flexibly consider the feasible range of the scale parameter of annual maximum flood distributions,which might lead to the inability to provide sufficient and reliable models to fit AMFS.This paper is aimed to investigate the potential of another two norming constants methods in fitting annual maximum floods,i.e.,the Hall's norming constants method(H-NCM)and the Fisher and Tippetts' norming constants method(FT-NCM)respectively.A comparative study of these three methods is carried out.Taking into account the characteristics of flood seasonality,based on the theory of H-NCM,a modified directional statistics method(MDS)is adopted to classify seasonal flood in nonstationary flood frequency analysis,and the traditional relative frequency method(RF)and directional statistics method(DS)is used for comparative study.This paper selected hydrological streamflow series of 77 stations in the Yangtze and Yellow River basins,China.The main findings and conclusions are summarized as follows:(1)The results of nonstationary test for hydro-meteorological series,using nonparametric method and time-varying moment method in the paper,show that the annual daily flow series(ADFS)or AMFS of Huaxian station and another nine stations are detected significant decreasing or increasing.The relative humidity of a few stations in the middle and lower reaches of the Yangtze River had a decreasing trend.Except for the annual maximum daily precipitation of some stations in the middle and lower reaches of the Yangtze River,the others keep stationary.Influenced by the global warming,statistics of temperature in nearly all study areas demonstrated significant upward trends.The nonstationary detection of hydro-meteorological series based on time-varying moment method is consistent with the results of non-parametric method.The Lognormal distribution outperforms in the candidate probability distributions in modelling the hydro-meteorological seies,followed by the Gamma distribution.Nonparametric method has simple and robust characteristics when detecting the nonstationarity of the first-order moment parameter(i.e.,mean)of the series,but it has limited ability to detect high-order moments(eg.variance).The time-varying momeonts method can objectively prefer the trend model or the change point model by information criterion.Therefore,the time-varying moment model is more reliable than the non-parametric method to identify the nonstationarity of hydro-meteorological series.(2)Modelling the ADFS with a single probability distribution is challenging.Firstly,to graphically identify candidate probability distributions,theoretical Lmoment ratios of different distributions are compared with sample L-moment ratios.The preliminary analysis is carried out to identify the potential of distributions,and five candidate distributions,namely GEV distribution,the generalized Pareto distribution(GPA),Lognormal distribution(LNO),Pearson type III distribution(PE3),and Kappa distribution(KAP)are selected.The results indicate that the KPA appears to provide the best fit to samples,followed by the LNO and GPA.However,through the model NSE values,the LNO distribution is the optimal distribution,followed by the GPA,KAP and PE3 distributions.The error-duration curvs show that,except for the LNO distribution,the others perform poor in estimating the high and low flows of the tail of ADFS.Specificlly,the GEV distribution overestimates the low flows,and the GPA,PE3 and KAP distributions underestimate the low flows;The PE3 distribution overestimates the high flows,and the other three types of distirbutions underestimate it.The modeling results indicate that KAP distribution modelling the middle flows is robust,and the confidence interval of residuals is narrow.In general,it is difficult to estimate the ADFS with a single probability distribution,especially at the tail of flow variation.However,it is still recommended the LNO distribution as the optimal probability distribution in modelling.(3)The nonstationary flood frequency analysis(NFFA)is conducted by NCM based on the theory of maximum domain of attraction of Gumbel distribution.The results show that H-NCM outperforms both C-NCM and FT-NCM for the stations with relatively low skewness coefficient of AMFS.It is found that the NCM is applicatable when the empirical skew coefficient of the flood series is smaller than the theoretical skew coefficient of the Gumbel distribution.Considering the first moment(mean)and the second moment(variation coefficient)of the sample,the method is also related to the magnitude and variation of in practical application.When empolying physical covariates as explanatory variables,all models perform better than the stationary ones.However,a few models are better than nonstationary models without considering covariates.Nevertheless,choosing appropriate covariates from various meteorological factors or human activity factors to optimize the model increases the physical significance in NFFA.(4)Considering the impact of seasonal floods,the relative frequency method(RF),directional statistics method(DS)and modified directional statistics method(MDS)are used to indentify the flood season.The results show that the beginning and ending time of flood season in the most stations of southern Yangtze River Basin is from the May to August,and some stations delay until mid-September.The northern Yellow River basin generally has a flood season from early July to mid-September.The DS method is more objective than the RF method.The MDS method is more reasonable when using the H-NCM method to consider the flood distribution in the flood season.In the NFFA based on the H-NCM method,the RF,DS and MDS methods perform seemly,but are better than the models of ignorance of seasonal flood(ISF).The evaluate the models,the MDS method performes best.The correlation between the model NSE values and statistics of AMFS is analyzed.It has the same results with conclusion aforementioned.Compared with the ISF models,the “abnormal” scatters of the models in NSE is significantly reduced when considering the flood season.To summary,the MDS method is recommended from comprehensive consideration in physical mechanism behind.