| Hydrometeorological frequency calculation is widely used in hydraulic design and planning.By calculating a certain return period of the hydrologic frequency under the design value,or calculate a certain level of return period,it may have an important guiding significance in estimating the future hydrological situation,planning the water resources,exploiting the groundwater and controlling the flood disaster.Standard for Hydrologic Calculation of Water Resources and Hydropower Engineering requires that the hydrological and meteorological data used in the engineering design should meet the requirements of reliability,representativeness and stationarity inspection,and the 30-year hydrological and meteorological sequence can be used as the shortest sequence in the engineering design of most areas of China.However,affected by human activities and climate change,hydrological cycle has been seriously destroyed and the stationarity of runoff sequence has been seriously damaged.At the same time,the representativeness of hydrometeorological series cannot be guaranteed due to the uneven construction time,hydrological data collection equipment,measurement technology and other phenomena in different regions,as well as the serious missing measurements.The applicability of 30-year series in the calculation of hydrological and meteorological frequency under the current changing environment needs to be discussed.In addition,the sampling error in short samples will affect the sequence stationary test results based on statistical methods,which also causes serious interference to the selection of hydrometeorological frequency calculation methods.Based on the above and aimed on the low representativeness of short hydro-meteorological sample,firstly in this article we proposed a new method for sample expansion and improving the representativeness.By the way of mathematical simulation experiment and comparing with a traditional sample expansion method,which is calling Bootstrap,we proved the effectiveness in the process of this method in the expansion of short sample.After determining that the new sample expansion method can effectively improve the representativeness of small samples,six representative gauges in different basins and regions nationwide were selected to calculate the design values of the annual maximum daily rainfall with the return period of 100 years and 50 years respectively.In addition,based on the problem of sampling error in short samples,another mathematical simulation experiment was designed to analyze the impact of sampling error on the judgment of sample stationarity,then the EMD decomposition and crossover reconstruction method would be used to calculate the design frequency of these short samples.The main contents and conclusions of this paper are as follows:(1)Considering the selection problem of the stopping criteria and the end effect existing in the empirical mode decomposition method and on the basic of others’ research results,in this paper,the double EMD decomposition method was put forward,which means a sequence would be decomposed twice.At the first time,the SD stopping criteria would be used in the EMD method to decompose the sequence into IMFs and monotonous residual,then the IMFs would be reconstructed into a new series.After this,the TVF-EMD method would be used in the new series to carry out the second decomposition,and all the components by this method can be treated as the IMFs.At the same time,in order to reduce the influence of end effect on component orthogonality,this paper chose to combine two methods to inhibit the end effect,namely,mirror extension method and RBF neural network.Compared with other methods,combined method has better effect in the process of inhibiting end effect.By upgrading the traditional EMD decomposition method,technical support and guarantee can be provided for the new capacity enlargement method based on EMD decomposition proposed in the paper.(2)According to the EMD decomposition and genetic theory,when a sample is not mutated and with stationary distribution,the sequence itself carried by hydrological genes come from the same distribution in the whole.If the sequence were divided into n series,the decomposed IMFs and residuals from each segment could be seen as part of hydrological genes of the matrix.Therefore,based on the theory of genetic hybridization,a large number of new samples could be generated after free combination of hydrological genes,and the new samples must be similar to the matrix.On the other words,they were subject to the same hydrometeorological overall distribution.After removing the outliers in the offspring,the remaining samples were expanded new samples after EMD decomposition.Through this method,the recessive hydrological genes of initial sample can be combined in cross show in the new generation.Comparing with the Bootstrap method,the expanding samples generated by EMD decomposition and crossover reconstruction could break the interval limit of the original sequence and generate more maximum or minimum values,which is more similar to the overall distribution.However,Bootstrap method only carried out multiple resampling in the original sample,which could not break the interval limit of the original sample,and it would break the distribution scheme of the original sequence when expanding.Therefore,the expanding samples generated by the EMD method were more representative than the original samples or the Bootstrap expanding samples.(3)To prove the capacity and efficiency of the EMD decomposition and crossover reconstruction method used in the short samples,and discuss the rationality of 30-year hydrometeorological sequence used in hydrometeorological frequency calculation,this paper designed a mathematical simulation experiment for analysis and calculation.A group of large samples of normal distribution with a certain mean and standard deviation were randomly generated,and M-K and Pettitt tests confirmed that the long sequence had no obvious regression or step change and met the assumption of stationarity.Adapted this sequence into an overall distribution,set the sample length to be 20~60 and the step length to be 10,and selected multiple samples by random sampling method.In addition,M-K and Pettitt tests were also performed on all sub-samples in order to determine the stationary distribution.Finally,100 sub-samples of different lengths were selected for sample expansion.The mean and standard deviation of each sub-sample were calculated,and the design values were calculated with the return period of 1000 years and 100 years respectively.After calculating the statistical values of samples expanded by two different sample expansion methods,the Z test and T test were be adapted to check the similarity of the mean and standard deviation of the sub-samples,the two expansion samples and the overall distribution respectively.The overall distributed design value was used to measure the quality of the sample expansion.Finally,the K-S test were used to check the similarity between the subsample,the two expanded samples and the overall distribution respectively.The final results showed that rather than the sub-samples and Bootstrap expanding samples,the EMD decomposition and crossover reconstruction method reflected higher applicability and efficiency in the expansion process of multiple sets of sub-samples of different lengths.Although the change of mean values after using new expanding method was not obvious,the standard deviation was closer to the overall distribution and the more accurate design values would be made.At the same time,there was little difference between the Z test and the F test results of the two expanded samples,among which the Z test pass rate was generally low,however,caused by the excessive length,which does not mean that the mean similarity was decreased.The similarities between the expansion samples under the new expanding method and the overall distribution were significantly higher than that the Bootstrap expansion sample,shown by K-S test.In addition,when the sample length is 30 or above,the K-S test pass rate of both the sub-samples or the expanded samples remains at a high level.In stark contrast,the K-S test pass rate of the sub-samples and their expanded samples with a length of 20 is low,and their representativeness cannot be guaranteed.Therefore,in most regions of China,it is reasonable to select 30 years as the shortest sample length that can be applied in engineering design,and at the same time,the sub-sample of 30 years will have higher representativeness through the EMD decomposition and crossover reconstruction method.(4)In recent years,extreme rainfall events were occurred frequently in China,and the safety of people’s lives and property has been seriously threatened by the rainfall events themselves and the subsequent floods and urban waterlogging disasters.Based on this,the return period of the annual maximum daily precipitation was set as the research index of extreme precipitation events,six representative hydrometeorological stations in different basins and regions in China were selected for calculation.It has been shown that the rainfall sequence length of each station was 60 years,and multiple groups of samples of 30,40 and 50 years were selected by means of sliding window.After that,EMD decomposition and crossover reconstruction method was adapted for sample expansion,and K-S test were used to find the minimum samples that could be used for frequency calculation in different regions.It was shown that except Lintao gauge,the 30-year samples of the other five stations were representative of the 60-year sequences.Due to the two statistical outliers were appeared in the measured series of Lintao station,the frequency calculation of this station was divided into two types: outliers existed and outliers eliminated.The reference of most water conservancy engineering construction would be provided by the former type,while a few engineering designs with short design period would be mainly served by the second type.At the same time,due to the existence of measured outliers,the 30-year samples from Lintao gauge were no longer representative.Based on the calculation results of six sites,if there were no longer sequences,the expanded samples of 60-year maximum daily rainfall sequences,which were produced by EMD decomposition and crossover reconstruction method,would be the true design values of six sites.When the total series met the stationary distribution hypothesis,and there was no obvious physical mechanism to cause the variation,due to the sampling error,the short samples were failed in the non-stationary test based on statistical principles.At this time,if the non-stationary hydrometeorological frequency calculation methods were used to calculate the return period or design value,the result would have a large error compared with the overall distribution.Therefore,in this paper,the method of mathematical simulation experiment was used again.Under the condition that the whole was known and stationary distribution was satisfied,the sub-samples of different lengths by sliding window may be non-stationary due to the sampling error.At this time,the mixed distribution model and the EMD decomposition and crossover reconstruction method were respectively used for sample expansion and design values calculation.The former was based on the non-stationary theory,while the latter indicated that the sample sampling error was not truly non-consistency.It could be shown at the final results that the designed values of the expanded samples were obviously better than that of the mixed distribution model.Therefore,the sampling error would interfere with the non-stationary test results,and it was unreasonable to directly calculate the design value by using the nonstationary hydrometeorological frequency calculation method without considering the physical results.At the same time,the design values of small samples in Shaoguan station and Shenyang station that did not pass the stationary test were calculated,and the results were found to be completely consistent with the results of mathematical simulation experiment,the calculation results of the expansion samples were still closer to the overall distribution. |
PDF Full Text Request