In order to assess the effects of calibration data series length on the performance and optimal parameter values of a hydrological model in ungauged or data-limited catchments (data are non-continuous and fragmental ...In order to assess the effects of calibration data series length on the performance and optimal parameter values of a hydrological model in ungauged or data-limited catchments (data are non-continuous and fragmental in some catchments), we used non-continuous calibration periods for more independent streamflow data for SIMHYD (simple hydrology) model calibration. Nash-Sutcliffe efficiency and percentage water balance error were used as performance measures. The particle swarm optimization (PSO) method was used to calibrate the rainfall-runoff models. Different lengths of data series ranging from one year to ten years, randomly sampled, were used to study the impact of calibration data series length. Fifty-five relatively unimpaired catchments located all over Australia with daily precipitation, potential evapotranspiration, and streamflow data were tested to obtain more general conclusions. The results show that longer calibration data series do not necessarily result in better model performance. In general, eight years of data are sufficient to obtain steady estimates of model performance and parameters for the SIMHYD model. It is also shown that most humid catchments require fewer calibration data to obtain a good performance and stable parameter values. The model performs better in humid and semi-humid catchments than in arid catchments. Our results may have useful and interesting implications for the efficiency of using limited observation data for hydrological model calibration in different climates.展开更多
The existing pattern matching methods of multivariate time series can hardly measure the similarity of multivariate hydrological time series accurately and efficiently.Considering the characteristics of multivariate h...The existing pattern matching methods of multivariate time series can hardly measure the similarity of multivariate hydrological time series accurately and efficiently.Considering the characteristics of multivariate hydrological time series,the continuity and global features of variables,we proposed a pattern matching method,PP-DTW,which is based on dynamic time warping.In this method,the multivariate time series is firstly segmented,and the average of each segment is used as the feature.Then,PCA is operated on the feature sequence.Finally,the weighted DTW distance is used as the measure of similarity in sequences.Carrying out experiments on the hydrological data of Chu River,we conclude that the pattern matching method can effectively describe the overall characteristics of the multivariate time series,which has a good matching effect on the multivariate hydrological time series.展开更多
Water level prediction of river runoff is an important part of hydrological forecasting.The change of water level not only has the trend and seasonal characteristics,but also contains the noise factors.And the water l...Water level prediction of river runoff is an important part of hydrological forecasting.The change of water level not only has the trend and seasonal characteristics,but also contains the noise factors.And the water level prediction ability of a single model is limited.Since the traditional ARIMA(Autoregressive Integrated Moving Average)model is not accurate enough to predict nonlinear time series,and the WNN(Wavelet Neural Network)model requires a large training set,we proposed a new combined neural network prediction model which combines the WNN model with the ARIMA model on the basis of wavelet decomposition.The combined model fit the wavelet transform sequences whose frequency are high with the WNN,and the scale transform sequence which has low frequency is fitted by the ARIMA model,and then the prediction results of the above are reconstructed by wavelet transform.The daily average water level data of the Liuhe hydrological station in the Chu River Basin of Nanjing are used to forecast the average water level of one day ahead.The combined model is compared with other single models with MATLAB,and the experimental results show that the accuracy of the combined model is improved by 7%compared with the traditional wavelet network under the appropriate wavelet decomposition function and the combined model parameters.展开更多
Time series analysis plays an important role in hydrologic forecasting,while the key to this analysis is to establish a proper model.This paper presents a time series neural network model with back propagation proced...Time series analysis plays an important role in hydrologic forecasting,while the key to this analysis is to establish a proper model.This paper presents a time series neural network model with back propagation procedure for hydrologic forecasting.Free from the disadvantages of previous models,the model can be parallel to operate information flexibly and rapidly.It excels in the ability of nonlinear mapping and can learn and adjust by itself,which gives the model a possibility to describe the complex nonlinear hydrologic process.By using directly a training process based on a set of previous data, the model can forecast the time series of stream flow.Moreover,two practical examples were used to test the performance of the time series neural network model.Results confirm that the model is efficient and feasible.展开更多
This paper firstly analyses the hydrologic characteristics of the major rivers around the Taklimakan Desert with the method of mathematical statistics. Secondly, structure features of annual runoff series of these riv...This paper firstly analyses the hydrologic characteristics of the major rivers around the Taklimakan Desert with the method of mathematical statistics. Secondly, structure features of annual runoff series of these rivers are discussed both in the domain and in frequency domain with the method of time series analysis. Fain the analysis, it can be learnt that the nature quantity of water in the rivers in this area is generally steady and the annual runoff series of rivers is mostly independment stationary random sequence. Therefore, this paper can Provide scientific basis for runoff variation law research and reasonal exploitation and utilization of water resource in this area.展开更多
Statistical analyses and descriptive characterizations are sometimes assumed to be offering information on time series forecastability.Despite the scientific interest suggested by such assumptions,the relationships be...Statistical analyses and descriptive characterizations are sometimes assumed to be offering information on time series forecastability.Despite the scientific interest suggested by such assumptions,the relationships between descriptive time series features(e.g.,temporal dependence,entropy,seasonality,trend and linearity features)and actual time series forecastability(quantified by issuing and assessing forecasts for the past)are scarcely studied and quantified in the literature.In this work,we aim to fill in this gap by investigating such relationships,and the way that they can be exploited for understanding hydroclimatic forecastability and its patterns.To this end,we follow a systematic framework bringing together a variety of–mostly new for hydrology–concepts and methods,including 57 descriptive features and nine seasonal time series forecasting methods(i.e.,one simple,five exponential smoothing,two state space and one automated autoregressive fractionally integrated moving average methods).We apply this framework to three global datasets originating from the larger Global Historical Climatology Network(GHCN)and Global Streamflow Indices and Metadata(GSIM)archives.As these datasets comprise over 13,000 monthly temperature,precipitation and river flow time series from several continents and hydroclimatic regimes,they allow us to provide trustable characterizations and interpretations of 12-month ahead hydroclimatic forecastability at the global scale.We first find that the exponential smoothing and state space methods for time series forecasting are rather equally efficient in identifying an upper limit of this forecastability in terms of Nash-Sutcliffe efficiency,while the simple method is shown to be mostly useful in identifying its lower limit.We then demonstrate that the assessed forecastability is strongly related to several descriptive features,including seasonality,entropy,(partial)autocorrelation,stability,(non)linearity,spikiness and heterogeneity features,among others.We further(i)show that,if such descriptive information is available for a monthly hydroclimatic time series,we can even foretell the quality of its future forecasts with a considerable degree of confidence,and(ii)rank the features according to their efficiency in explaining and foretelling forecastability.We believe that the obtained rankings are of key importance for understanding forecastability.Spatial forecastability patterns are also revealed through our experiments,with East Asia(Europe)being characterized by larger(smaller)monthly temperature time series forecastability and the Indian subcontinent(Australia)being characterized by larger(smaller)monthly precipitation time series forecastability,compared to other continental-scale regions,and less notable differences characterizing monthly river flow from continent to continent.A comprehensive interpretation of such patters through massive feature extraction and feature-based time series clustering is shown to be possible.Indeed,continental-scale regions characterized by different degrees of forecastability are also attributed to different clusters or mixtures of clusters(because of their essential differences in terms of descriptive features).展开更多
This study aims at establishing if climate change exists in the Niger Delta environment using non-stationary rainfall Intensity-Duration-Frequency (IDF) modelling incorporating time-variant parameters. To compute the ...This study aims at establishing if climate change exists in the Niger Delta environment using non-stationary rainfall Intensity-Duration-Frequency (IDF) modelling incorporating time-variant parameters. To compute the intensity levels, the open-access R-studio software was used based on the General Extreme Value (GEV) distribution function. Among the four linear parameter models adopted for integrating time as a covariate, the fourth linear model incorporating scale and location with the shape function constant produced the least corrected Akaike Information Criteria (AICc), varying between 306.191 to 101.497 for 15 and 1440 minutes, respectively, selected for calibration of the GEV distribution equation. The non-stationary intensities yielded higher values above those of stationary models, proving that the assumption of stationary IDF models underestimated extreme events. The difference of 13.71 mm/hr (22.71%) to 14.26 mm/hr (17.0%) intensities implies an underestimation of the peak flood from a stationary IDF curve. The statistical difference at a 95% confidence level between stationary and non-stationary models was significant, confirming evidence of climatic change influenced by time-variant parameters. Consequently, emphasis should be on applying shorter-duration storms for design purposes occurring with higher intensities to help reduce the flood risk and resultant infrastructural failures.展开更多
To analyze and simulate non-stationary time series with finite length, the statistical characteris- tics and auto-regressive (AR) models of non-stationary time series with finite length are discussed and stud- ied. ...To analyze and simulate non-stationary time series with finite length, the statistical characteris- tics and auto-regressive (AR) models of non-stationary time series with finite length are discussed and stud- ied. A new AR model called the time varying parameter AR model is proposed for solution of non-stationary time series with finite length. The auto-covariances of time series simulated by means of several AR models are analyzed. The result shows that the new AR model can be used to simulate and generate a new time series with the auto-covariance same as the original time series. The size curves of cocoon filaments re- garded as non-stationary time series with finite length are experimentally simulated. The simulation results are significantly better than those obtained so far, and illustrate the availability of the time varying parameter AR model. The results are useful for analyzing and simulating non-stationary time series with finite length.展开更多
Estimating the design flood under nonstationary conditions is challenging. In this study, a sample reconstruction approach was developed to transform a nonstationary series into a stationary one in a future time windo...Estimating the design flood under nonstationary conditions is challenging. In this study, a sample reconstruction approach was developed to transform a nonstationary series into a stationary one in a future time window (FTW). In this approach, the first-order moment (EFTW) of an extreme flood series in the FTW was used, and two possible methods of estimating EFTW values in terms of point values and confidence intervals were developed. Three schemes were proposed to analyze the uncertainty of design flood estimation in terms of sample representativeness, uncertainty from EFTW estimation, and both factors, respectively. To investigate the performance of the sample reconstruction approach, synthesis experiments were designed based on the annual peak series of the Little Sugar Creek in the United States. The results showed that the sample reconstruction approach performed well when the high-order moment of the series did not change significantly in the specified FTW. Otherwise, its performance deteriorated. In addition, the uncertainty of design flood estimation caused by sample representativeness was greater than that caused by EFTW estimation.展开更多
This paper considers the problem of smoothing a non-stationary time series(having either deterministic and/or stochastic trends) using the discrete cosine transform(DCT).The DCT is a powerful tool which has found frui...This paper considers the problem of smoothing a non-stationary time series(having either deterministic and/or stochastic trends) using the discrete cosine transform(DCT).The DCT is a powerful tool which has found fruitful applications in filtering and smoothing as it can closely approximate the optimal Karhunen-Loeve transform(KLT).In fact,it is known that it almost corresponds to the KLT for first-order autoregressive processes with a root close to unity:This is the case with most economic and financial time series.A number of new results are derived in the paper:(a) The explicit form of the linear smoother based on the DCT,which is found to have time-varying weights and that uses all observations;(b) the extrapolation of the DCT-smoothed series;(c) the form of the average frequency response function,which is shown to approximate the frequency response of the ideal low pass filter;(d) the asymptotic distribution of the DCT coefficients under the assumptions of deterministic or stochastic trends;(e) two news method for selecting an appropriate degree of smoothing,in general and under the assumptions in(d).These findings are applied and illustrated using several real world economic and financial time series.The results indicate that the DCT-based smoother that is proposed can find many useful applications in economic and financial time series.展开更多
Wavelet regression(WR)models are used commonly for hydrologic time series forecasting,but they could not consider uncertainty evaluation.In this paper the AM-MCMC(adaptive Metropolis-Markov chain Monte Carlo)algorithm...Wavelet regression(WR)models are used commonly for hydrologic time series forecasting,but they could not consider uncertainty evaluation.In this paper the AM-MCMC(adaptive Metropolis-Markov chain Monte Carlo)algorithm was employed to wavelet regressive modeling processes,and a model called AM-MCMC-WR was proposed for hydrologic time series forecasting.The AM-MCMC algorithm is used to estimate parameters’uncertainty in WR model,based on which probabilistic forecasting of hydrologic time series can be done.Results of two runoff data at the Huaihe River watershed indicate the identical performances of AM-MCMC-WR and WR models in gaining optimal forecasting result,but they perform better than linear regression models.Differing from the WR model,probabilistic forecasting results can be gained by the proposed model,and uncertainty can be described using proper credible interval.In summary,parameters in WR models generally follow normal probability distribution;series’correlation characters determine the optimal parameters values,and further determine the uncertain degrees and sensitivities of parameters;more uncertain parameters would lead to more uncertain forecasting results and hard predictability of hydrologic time series.展开更多
基金supported by the National Basic Research Program of China (the 973 Program,Grant No.2010CB951102)the National Supporting Plan Program of China (Grants No.2007BAB28B01 and 2008BAB42B03)the National Natural Science Foundation of China (Grant No. 50709042),and the Regional Water Theme in the Water for a Healthy Country Flagship
文摘In order to assess the effects of calibration data series length on the performance and optimal parameter values of a hydrological model in ungauged or data-limited catchments (data are non-continuous and fragmental in some catchments), we used non-continuous calibration periods for more independent streamflow data for SIMHYD (simple hydrology) model calibration. Nash-Sutcliffe efficiency and percentage water balance error were used as performance measures. The particle swarm optimization (PSO) method was used to calibrate the rainfall-runoff models. Different lengths of data series ranging from one year to ten years, randomly sampled, were used to study the impact of calibration data series length. Fifty-five relatively unimpaired catchments located all over Australia with daily precipitation, potential evapotranspiration, and streamflow data were tested to obtain more general conclusions. The results show that longer calibration data series do not necessarily result in better model performance. In general, eight years of data are sufficient to obtain steady estimates of model performance and parameters for the SIMHYD model. It is also shown that most humid catchments require fewer calibration data to obtain a good performance and stable parameter values. The model performs better in humid and semi-humid catchments than in arid catchments. Our results may have useful and interesting implications for the efficiency of using limited observation data for hydrological model calibration in different climates.
文摘The existing pattern matching methods of multivariate time series can hardly measure the similarity of multivariate hydrological time series accurately and efficiently.Considering the characteristics of multivariate hydrological time series,the continuity and global features of variables,we proposed a pattern matching method,PP-DTW,which is based on dynamic time warping.In this method,the multivariate time series is firstly segmented,and the average of each segment is used as the feature.Then,PCA is operated on the feature sequence.Finally,the weighted DTW distance is used as the measure of similarity in sequences.Carrying out experiments on the hydrological data of Chu River,we conclude that the pattern matching method can effectively describe the overall characteristics of the multivariate time series,which has a good matching effect on the multivariate hydrological time series.
文摘Water level prediction of river runoff is an important part of hydrological forecasting.The change of water level not only has the trend and seasonal characteristics,but also contains the noise factors.And the water level prediction ability of a single model is limited.Since the traditional ARIMA(Autoregressive Integrated Moving Average)model is not accurate enough to predict nonlinear time series,and the WNN(Wavelet Neural Network)model requires a large training set,we proposed a new combined neural network prediction model which combines the WNN model with the ARIMA model on the basis of wavelet decomposition.The combined model fit the wavelet transform sequences whose frequency are high with the WNN,and the scale transform sequence which has low frequency is fitted by the ARIMA model,and then the prediction results of the above are reconstructed by wavelet transform.The daily average water level data of the Liuhe hydrological station in the Chu River Basin of Nanjing are used to forecast the average water level of one day ahead.The combined model is compared with other single models with MATLAB,and the experimental results show that the accuracy of the combined model is improved by 7%compared with the traditional wavelet network under the appropriate wavelet decomposition function and the combined model parameters.
文摘Time series analysis plays an important role in hydrologic forecasting,while the key to this analysis is to establish a proper model.This paper presents a time series neural network model with back propagation procedure for hydrologic forecasting.Free from the disadvantages of previous models,the model can be parallel to operate information flexibly and rapidly.It excels in the ability of nonlinear mapping and can learn and adjust by itself,which gives the model a possibility to describe the complex nonlinear hydrologic process.By using directly a training process based on a set of previous data, the model can forecast the time series of stream flow.Moreover,two practical examples were used to test the performance of the time series neural network model.Results confirm that the model is efficient and feasible.
文摘This paper firstly analyses the hydrologic characteristics of the major rivers around the Taklimakan Desert with the method of mathematical statistics. Secondly, structure features of annual runoff series of these rivers are discussed both in the domain and in frequency domain with the method of time series analysis. Fain the analysis, it can be learnt that the nature quantity of water in the rivers in this area is generally steady and the annual runoff series of rivers is mostly independment stationary random sequence. Therefore, this paper can Provide scientific basis for runoff variation law research and reasonal exploitation and utilization of water resource in this area.
基金Funding from the Italian Ministry of Environment, Land and Sea Protection (MATTM) for the Sim PRO project (2020–2021) is acknowledged by (in alphabetical order): S. Grimaldi, G. Papacharalampous and E. Volpifunding from the Italian Ministry of Education, University and Research (MIUR), in the frame of the Departments of Excellence Initiative 2018–2022, attributed to the Department of Engineering of Roma Tre Universityfunding from the EU Horizon 2020 project CLINT (Climate Intelligence: Extreme events detection, attribution and adaptation design using machine learning) under Grant Agreement 101003876
文摘Statistical analyses and descriptive characterizations are sometimes assumed to be offering information on time series forecastability.Despite the scientific interest suggested by such assumptions,the relationships between descriptive time series features(e.g.,temporal dependence,entropy,seasonality,trend and linearity features)and actual time series forecastability(quantified by issuing and assessing forecasts for the past)are scarcely studied and quantified in the literature.In this work,we aim to fill in this gap by investigating such relationships,and the way that they can be exploited for understanding hydroclimatic forecastability and its patterns.To this end,we follow a systematic framework bringing together a variety of–mostly new for hydrology–concepts and methods,including 57 descriptive features and nine seasonal time series forecasting methods(i.e.,one simple,five exponential smoothing,two state space and one automated autoregressive fractionally integrated moving average methods).We apply this framework to three global datasets originating from the larger Global Historical Climatology Network(GHCN)and Global Streamflow Indices and Metadata(GSIM)archives.As these datasets comprise over 13,000 monthly temperature,precipitation and river flow time series from several continents and hydroclimatic regimes,they allow us to provide trustable characterizations and interpretations of 12-month ahead hydroclimatic forecastability at the global scale.We first find that the exponential smoothing and state space methods for time series forecasting are rather equally efficient in identifying an upper limit of this forecastability in terms of Nash-Sutcliffe efficiency,while the simple method is shown to be mostly useful in identifying its lower limit.We then demonstrate that the assessed forecastability is strongly related to several descriptive features,including seasonality,entropy,(partial)autocorrelation,stability,(non)linearity,spikiness and heterogeneity features,among others.We further(i)show that,if such descriptive information is available for a monthly hydroclimatic time series,we can even foretell the quality of its future forecasts with a considerable degree of confidence,and(ii)rank the features according to their efficiency in explaining and foretelling forecastability.We believe that the obtained rankings are of key importance for understanding forecastability.Spatial forecastability patterns are also revealed through our experiments,with East Asia(Europe)being characterized by larger(smaller)monthly temperature time series forecastability and the Indian subcontinent(Australia)being characterized by larger(smaller)monthly precipitation time series forecastability,compared to other continental-scale regions,and less notable differences characterizing monthly river flow from continent to continent.A comprehensive interpretation of such patters through massive feature extraction and feature-based time series clustering is shown to be possible.Indeed,continental-scale regions characterized by different degrees of forecastability are also attributed to different clusters or mixtures of clusters(because of their essential differences in terms of descriptive features).
文摘This study aims at establishing if climate change exists in the Niger Delta environment using non-stationary rainfall Intensity-Duration-Frequency (IDF) modelling incorporating time-variant parameters. To compute the intensity levels, the open-access R-studio software was used based on the General Extreme Value (GEV) distribution function. Among the four linear parameter models adopted for integrating time as a covariate, the fourth linear model incorporating scale and location with the shape function constant produced the least corrected Akaike Information Criteria (AICc), varying between 306.191 to 101.497 for 15 and 1440 minutes, respectively, selected for calibration of the GEV distribution equation. The non-stationary intensities yielded higher values above those of stationary models, proving that the assumption of stationary IDF models underestimated extreme events. The difference of 13.71 mm/hr (22.71%) to 14.26 mm/hr (17.0%) intensities implies an underestimation of the peak flood from a stationary IDF curve. The statistical difference at a 95% confidence level between stationary and non-stationary models was significant, confirming evidence of climatic change influenced by time-variant parameters. Consequently, emphasis should be on applying shorter-duration storms for design purposes occurring with higher intensities to help reduce the flood risk and resultant infrastructural failures.
基金Supported by the Natural Science Foundation of Jiangsu Province(No. L0313419913)
文摘To analyze and simulate non-stationary time series with finite length, the statistical characteris- tics and auto-regressive (AR) models of non-stationary time series with finite length are discussed and stud- ied. A new AR model called the time varying parameter AR model is proposed for solution of non-stationary time series with finite length. The auto-covariances of time series simulated by means of several AR models are analyzed. The result shows that the new AR model can be used to simulate and generate a new time series with the auto-covariance same as the original time series. The size curves of cocoon filaments re- garded as non-stationary time series with finite length are experimentally simulated. The simulation results are significantly better than those obtained so far, and illustrate the availability of the time varying parameter AR model. The results are useful for analyzing and simulating non-stationary time series with finite length.
基金supported by the National Key Research and Development Program of China(Grant No.2018YFC1508001)the National Natural Science Foundation of China(Grant No.51709073)the Fundamental Research Funds for the Central Universities of China(Grant No.B220202031).
文摘Estimating the design flood under nonstationary conditions is challenging. In this study, a sample reconstruction approach was developed to transform a nonstationary series into a stationary one in a future time window (FTW). In this approach, the first-order moment (EFTW) of an extreme flood series in the FTW was used, and two possible methods of estimating EFTW values in terms of point values and confidence intervals were developed. Three schemes were proposed to analyze the uncertainty of design flood estimation in terms of sample representativeness, uncertainty from EFTW estimation, and both factors, respectively. To investigate the performance of the sample reconstruction approach, synthesis experiments were designed based on the annual peak series of the Little Sugar Creek in the United States. The results showed that the sample reconstruction approach performed well when the high-order moment of the series did not change significantly in the specified FTW. Otherwise, its performance deteriorated. In addition, the uncertainty of design flood estimation caused by sample representativeness was greater than that caused by EFTW estimation.
文摘This paper considers the problem of smoothing a non-stationary time series(having either deterministic and/or stochastic trends) using the discrete cosine transform(DCT).The DCT is a powerful tool which has found fruitful applications in filtering and smoothing as it can closely approximate the optimal Karhunen-Loeve transform(KLT).In fact,it is known that it almost corresponds to the KLT for first-order autoregressive processes with a root close to unity:This is the case with most economic and financial time series.A number of new results are derived in the paper:(a) The explicit form of the linear smoother based on the DCT,which is found to have time-varying weights and that uses all observations;(b) the extrapolation of the DCT-smoothed series;(c) the form of the average frequency response function,which is shown to approximate the frequency response of the ideal low pass filter;(d) the asymptotic distribution of the DCT coefficients under the assumptions of deterministic or stochastic trends;(e) two news method for selecting an appropriate degree of smoothing,in general and under the assumptions in(d).These findings are applied and illustrated using several real world economic and financial time series.The results indicate that the DCT-based smoother that is proposed can find many useful applications in economic and financial time series.
基金supported by the National Natural Science Foundation of China(41201036)the Opening Fund of Key Laboratory for Land Surface Process and Climate Change in Cold and Arid Regions,Chinese Academy of Sciences(LPCC201203)
文摘Wavelet regression(WR)models are used commonly for hydrologic time series forecasting,but they could not consider uncertainty evaluation.In this paper the AM-MCMC(adaptive Metropolis-Markov chain Monte Carlo)algorithm was employed to wavelet regressive modeling processes,and a model called AM-MCMC-WR was proposed for hydrologic time series forecasting.The AM-MCMC algorithm is used to estimate parameters’uncertainty in WR model,based on which probabilistic forecasting of hydrologic time series can be done.Results of two runoff data at the Huaihe River watershed indicate the identical performances of AM-MCMC-WR and WR models in gaining optimal forecasting result,but they perform better than linear regression models.Differing from the WR model,probabilistic forecasting results can be gained by the proposed model,and uncertainty can be described using proper credible interval.In summary,parameters in WR models generally follow normal probability distribution;series’correlation characters determine the optimal parameters values,and further determine the uncertain degrees and sensitivities of parameters;more uncertain parameters would lead to more uncertain forecasting results and hard predictability of hydrologic time series.