Estimation of trend and expectation of periodically correlated time series

An applied statistical analysis is considered of periodically correlated time series with the known correlation period T. The statistical estimates are suggested of the trend (of nonrandom additive component) and mathematical expectation (of seasonal or daily component) of the time series under investigation.     

基于模糊时间序列的华南台风登陆时最大风速极值预测模型

利用1995—2017年登陆华南地区的台风登陆时最大风速极值数据,构建基于模糊时间序列的台风登陆时最大风速极值预测模型,并将该模型与传统时间序列ARIMA模型作对比。其预测结果表明,模糊时间序列的平均绝对误差、平均相对误差和均方根误差分别为2.621 m·s-1、0.066和2.727 m·s-1,预测的精确度明显高于传统时间序列ARIMA模型,同时也表明将模糊时间序列应用于登陆时最大风速极值的预测能够获得较理想的预测结果。     

Statistical modeling of extreme value behavior in North American tree-ring density series

Many analyses of the paleoclimate record include conclusions about extremes, with a focus on the unprecedented nature of recent climate events. While the use of extreme value theory is becoming common in the analysis of the instrumental climate record, applications of this framework to the spatio-temporal analysis of paleoclimate records remain limited. This article develops a Bayesian hierarchical model to investigate spatially varying trends and dependencies in the parameters characterizing the distribution of extremes of a proxy data set, and applies it to the site-wise decadal maxima and minima of a gridded network of temperature sensitive tree ring density time series over northern North America. The statistical analysis reveals significant spatial associations in the temporal trends of the location parameters of the generalized extreme value distributions: maxima are increasing as a function of time, with stronger increases in the north and east of North America; minima are significantly increasing in the west, possibly decreasing in the east, and exhibit no changes in the center of the region. Results indicate that the distribution varies as a function of both space and time, with tree ring density maxima becoming more extreme as a function of time and minima having diverging temporal trends, by spatial location. Results of this proxy-only analysis are a first step towards directly reconstructing extremal climate behavior, as opposed to mean climate behavior, by linking extremes in the proxy record to extremes in the instrumental record.     

Rainfall uncertainty in the Mediterranean: time series, uncertainty, and extreme events

Temporal precipitation irregularities, extreme rainfall, or droughts represent great climate concerns and have major impacts on the natural environment. The present study focuses on 41 stations spread over the entire Mediterranean region. The datasets contain daily rainfall totals, with a median length of 56?years within the period of 1931?C2006. The study aims at detecting significant trends in the time series and the uncertainties of four parameters: annual rainfall total, number of rain spells, the rain-spells yields, and rainy season length. In addition, it aims to detect significant temporal changes in the occurrence of extreme events of these parameters. Several methodologies have been used in this study, and the main conclusion is that despite the general assumption of tremendous changes in the rainfall regime, no significant temporal trends or uncertainty trends were found in most of the stations, neither in their annual totals, their number of rain spells, and their rain-spell yields, nor in their rainy season length. However, in the few cases that a significant trend was detected, former years tended to be wetter, longer, and with more abundant rain spells, while the opposite is seen in the later years; and uncertainty, tends to increase more than to decrease.     

Effect of the plume rise and wind speed on extreme value of air pollutant concentration

Summary Extreme values of the ground level concentration of air pollutants were evaluated as a function of plume rise Δh, and wind speed in two cases. Firstly, when a plume rise depends on the downwind distance x, and secondly, with a constant plume rise (i.e., independent on x). Also, the extreme values for the effective stack height were evaluated for different stability classes. The maximum value of the ground level concentration was obtained in unstable stability when plume rise depends on x and in the neutral stability when plume rise independent on x. Also, in stable case, the extreme values of the ground level concentration of air pollutants showed similar values in the two cases when plume rise depends on x, and with constant plume rise. Finally, it was found that the extreme value of the ground level concentration occurred near the stack and after that it was decreases in all stabilities.     

Trend analysis of long-term temperature time series in the Greater Toronto Area (GTA)

As the majority of the world’s population is living in urban environments, there is growing interest in studying local urban climates. In this paper, for the first time, the long-term trends (31–162 years) of temperature change have been analyzed for the Greater Toronto Area (GTA). Annual and seasonal time series for a number of urban, suburban, and rural weather stations are considered. Non-parametric statistical techniques such as Mann–Kendall test and Theil-Sen slope estimation are used primarily for the assessing of the significance and detection of trends, and the sequential Mann test is used to detect any abrupt climate change. Statistically significant trends for annual mean and minimum temperatures are detected for almost all stations in the GTA. Winter is found to be the most coherent season contributing substantially to the increase in annual minimum temperature. The analyses of the abrupt changes in temperature suggest that the beginning of the increasing trend in Toronto started after the 1920s and then continued to increase to the 1960s. For all stations, there is a significant increase of annual and seasonal (particularly winter) temperatures after the 1980s. In terms of the linkage between urbanization and spatiotemporal thermal patterns, significant linear trends in annual mean and minimum temperature are detected for the period of 1878–1978 for the urban station, Toronto, while for the rural counterparts, the trends are not significant. Also, for all stations in the GTA that are situated in all directions except south of Toronto, substantial temperature change is detected for the periods of 1970–2000 and 1989–2000. It is concluded that the urbanization in the GTA has significantly contributed to the increase of the annual mean temperatures during the past three decades. In addition to urbanization, the influence of local climate, topography, and larger scale warming are incorporated in the analysis of the trends.     

Comparison of missing value imputation methods in time series: the case of Turkish meteorological data

This study aims to compare several imputation methods to complete the missing values of spatio–temporal meteorological time series. To this end, six imputation methods are assessed with respect to various criteria including accuracy, robustness, precision, and efficiency for artificially created missing data in monthly total precipitation and mean temperature series obtained from the Turkish State Meteorological Service. Of these methods, simple arithmetic average, normal ratio (NR), and NR weighted with correlations comprise the simple ones, whereas multilayer perceptron type neural network and multiple imputation strategy adopted by Monte Carlo Markov Chain based on expectation–maximization (EM-MCMC) are computationally intensive ones. In addition, we propose a modification on the EM-MCMC method. Besides using a conventional accuracy measure based on squared errors, we also suggest the correlation dimension (CD) technique of nonlinear dynamic time series analysis which takes spatio–temporal dependencies into account for evaluating imputation performances. Depending on the detailed graphical and quantitative analysis, it can be said that although computational methods, particularly EM-MCMC method, are computationally inefficient, they seem favorable for imputation of meteorological time series with respect to different missingness periods considering both measures and both series studied. To conclude, using the EM-MCMC algorithm for imputing missing values before conducting any statistical analyses of meteorological data will definitely decrease the amount of uncertainty and give more robust results. Moreover, the CD measure can be suggested for the performance evaluation of missing data imputation particularly with computational methods since it gives more precise results in meteorological time series.     

Extreme value analysis in the Danube lower basin discharge time series in the twentieth century

The daily discharge time series in the lower Danube basin (Orsova) have been considered for the 1900–2005 period. The extreme value theory (EVT) is applied for the study of daily discharges incorporating some covariates. Two methods are applied for fitting the data to an extreme value distribution: block maxima and peaks over thresholds (POT). Using the block maxima approach associated with the use of the generalised extreme value (GEV) distribution, monthly and seasonal maxima of daily discharge for 1900–2005 have been analysed. Separately the monthly maxima of daily discharge for the 1958–2001 was analysed in order to be compatible with atmospheric circulation available from ERA-40. For performing parameter estimation, the maximum likelihood estimation (MLE) method was used. From the three possible types of GEV distribution, a Weibull distribution fits both the monthly and seasonal maxima of the daily discharges very well. The North Atlantic Oscillation (NAO) and the first ten principal components (PC) of the decomposition in multi-variate empirical orthogonal functions (MEOF) of three atmospheric fields (sea level pressure, 500 hPa and 500–1000 hPa thickness) over the Atlantic-European region (ERA-40), have been introduced as covariates. An improvement over the model without the covariate is found by incorporating NAO as the covariate in location parameter, especially for the spring maxima having the NAO as predictor during the winter. Related to atmospheric circulation influence, the most significant results are obtained by incorporating the first 10 PCs of the MEOF in the location parameter of GEV distribution within a month before the month of the discharge level. Regarding the POT approach associated with generalised Pareto distribution (GPD), different thresholds have been tested for daily discharges in the period 1900–2005, where the maxima were fitted by a bounded (or beta) distribution.     

基于陆基GNSS的电离层时间序列预报研究

为讨论不同时间序列模型对电离层垂直总电子含量（VTEC）的预报效果,在平静电离层条件下,采用载波相位平滑伪距法解算单站上空的电离层VTEC值,分别利用自回归积分滑动平均模型（ARIMA）与Holt-Winters指数平滑模型进行逐站建模,通过时长为9 d的样本序列实现3 d预报,并对预报值进行系统评估.结果表明,时间序列模型能够较好地反映预报期内的电离层VTEC变化情况,均方根误差均值不超5 TECU.此外,Holt-Winters乘法模型的预报值偏差最大,加法模型次之,ARIMA模型在11个测站的相对精度都高于Holt-Winters指数平滑模型,且其均方根误差峰值最小,具有最高的预报精度.     

气象时间序列规则发现及其应用

1时间序列及挖掘 时间序列是指将某一指标在不同时间上的不同数值，按照时间的先后顺序排列而成的数列。随着信息技术的广泛使用以及人们获取数据手段的多样化，人类所拥有的时间序列信息急剧增加。按照研究对象和问题的不同，可以得到各种时间序列。例如产品销售记录、股票价格数据、气象数据、医疗信息等。目前计算机存储的数据中，时间序列数据占据了相当大（约80％）的比例，面对如此海量的时间序列数据，人们想找到有效的方法或技术来揭示这些数据内部所隐藏的知识或信息。例如股票经纪人想从某一种股票每日收盘价格的历史记录中发现其变化规律，以预测该股票未来行情走势；气象工作者想从降水量的历史变化中发现其变化规律，以预测未来降水量的变化趋势等等。     

Volatility modeling of rainfall time series

Networks of rain gauges can provide a better insight into the spatial and temporal variability of rainfall, but they tend to be too widely spaced for accurate estimates. A way to estimate the spatial variability of rainfall between gauge points is to interpolate between them. This paper evaluates the spatial autocorrelation of rainfall data in some locations in Peninsular Malaysia using geostatistical technique. The results give an insight on the spatial variability of rainfall in the area, as such, two rain gauges were selected for an in-depth study of the temporal dependence of the rainfall data-generating process. It could be shown that rainfall data are affected by nonlinear characteristics of the variance often referred to as variance clustering or volatility, where large changes tend to follow large changes and small changes tend to follow small changes. The autocorrelation structure of the residuals and the squared residuals derived from autoregressive integrated moving average (ARIMA) models were inspected, the residuals are uncorrelated but the squared residuals show autocorrelation, and the Ljung–Box test confirmed the results. A test based on the Lagrange multiplier principle was applied to the squared residuals from the ARIMA models. The results of this auxiliary test show a clear evidence to reject the null hypothesis of no autoregressive conditional heteroskedasticity (ARCH) effect. Hence, it indicates that generalized ARCH (GARCH) modeling is necessary. An ARIMA error model is proposed to capture the mean behavior and a GARCH model for modeling heteroskedasticity (variance behavior) of the residuals from the ARIMA model. Therefore, the composite ARIMA–GARCH model captures the dynamics of daily rainfall in the study area. On the other hand, seasonal ARIMA model became a suitable model for the monthly average rainfall series of the same locations treated.     

地面自动站气压的台站极值检查方法研究

根据压高公式,利用2000多个国家级台站海拔高度和本站气压观测资料,得到了自动站本站气压的台站极值检查方法,称为“台站海拔高度统计法”。首先由观测资料得到台站海拔高度和本站气压的指数经验公式,此经验公式可以计算出本站气压的估计值;然后由经验公式,选 ,可以估算出0.01信度下本站气压的取值范围,其中剩余均方差的估算方法类同本站气压的估计方法。使用台站海拔高度统计法依次对国家基准站、国家级台站以及区域自动站定时气压进行试验,试验效果良好。此方法可以用于气象业务中实时和非实时气压质量控制流程中的台站气压极值检查。     

Reconstruction and analysis of two long-term precipitation time series: Alpe Devero and Domodossola (Italian Western Alps)

With this study, we analyzed two long-term precipitation time series recorded at Alpe Devero and Domodossola (Italian Western Alps) for two periods (1916–2010 and 1872–2010, respectively). The aims of the study were: to create the first precipitation time series covering more than 50?years for Alpe Devero, to extend and update the precipitation time series for Domodossola, to detect changes by means of trend analysis on the precipitation time series. After an accurate analysis of the metadata and the measurements recorded at each station, a trend analysis was performed on both datasets. The results showed a statistically significant decline in winter, summer, and annual precipitation at Alpe Devero and a nonsignificant decrease in seasonal and annual precipitation at Domodossola. Covering more than 90?years, the long-term precipitation time series at Alpe Devero and Domodossola represent unique data sets for this sector of Italian Western Alps. Continuing updating of the data could provide a useful resource for climate change studies in this area and, within a wider perspective, in Alpine regions.     

Spatiotemporal long-term trends of extreme wind characteristics over the Black Sea

In this study, long-term change of wind characteristics on the Black Sea has been investigated using two widely used data sources, i.e., European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-Interim and National Centers for Environmental Prediction/Climate Forecast System Reanalysis (NCEP/CFSR), spanning 40 years between 1979 and 2018. Spatial and seasonal variability of climatic features such as the wind speed, direction, number and duration of storms, and wind power density are discussed. Wind climate is characterized by strong, durable and stable winds in the northern and western Black Sea, and relatively weak, short-lived and highly-variable winds in the eastern Black Sea. These long-term wind patterns indicate that the eastern part of the basin is likely to be subjected to the impacts of climate change. Long-term stable and strong wind conditions in the southwest part indicate reliable, persistent and sustainable wind energy potential. Long-term and seasonal variation of wind power density (WPD) at 110 m altitude over the Black Sea is investigated. There is a significant difference in WPD values between winter and summer seasons, with around 2.8 times larger WPD in winter than that in summer. In the western Black Sea, narrow confidence intervals observed in each season indicate a low level of variation during a season and ensures stable wind power conditions.     

四川盆地短历时强降水极值分布的研究

运用广义帕雷托分布(GPD)和广义极值分布(GEV),借助于L-矩的参数估计方法,对四川盆地12站的小时极端降水量进行拟合,并对两种模型的拟合效果进行比较。运用Hill图,结合统计量D*来确定GPD的最佳门限值是合适的,选出的样本是独立的。各站的小时极端降水概率分布均符合GPD和GEV,但GPD模型的拟合精度要优于GEV模型。利用两种模型推算出各站给定重现期的最大小时降水量,其中泸州50 a一遇和100 a一遇的降水极值分位数都超过了100 mm,除了遂宁站外,两种模型估计出的极值分位数的相对误差基本都在10%以下。通过分析,GPD推算的结果更加可靠。     

On clustering of non-stationary meteorological time series

A method for clustering of multidimensional non-stationary meteorological time series is presented. The approach is based on optimization of the regularized averaged clustering functional describing the quality of data representation in terms of several regression models and a metastable hidden process switching between them. Proposed numerical clustering algorithm is based on application of the finite element method (FEM) to the problem of non-stationary time series analysis. The main advantage of the presented algorithm compared to Hidden Markov Models (HMMs) and to finite mixture models is that no a priori assumptions about the probability model for the hidden and observed processes (e.g., Markovianity or stationarity) are necessary for the proposed method. Another attractive numerical feature of the discussed algorithm is the possibility to choose the optimal number of metastable clusters and a natural opportunity to control the fuzziness of the resulting decomposition a posteriory, based on the statistical distinguishability of the resulting persistent cluster states. The resulting FEM-K-trends algorithm is compared with some standard fuzzy clustering methods on toy model examples and on analysis of multidimensional historical temperature data locally in Europe and on the global temperature data set.     

峡谷地形对两次极端降水的作用

利用地面加密自动站、常规观测资料、NCEP再分析资料和两种模式产品,对发生在宜昌峡谷地区2016年7月7日局地极端短时强降水过程和2018年4月22日稳定性极端降水过程形成原因及模式预报性能进行检验分析。结果表明:(1)强的块状回波稳定少动,造成7月7日高效率的对流降水。4月22日降水既有沿山中尺度对流回波造成的对流降水,也有螺旋状涡旋回波形成的锋面层状云降水。(2)山谷风形成中尺度切变线,触发对流,中尺度切变线发展为中尺度涡旋使对流加强是极端短时降水形成的主要原因。(3)地形强迫抬升使对流降水强度明显增大,锋面层状云回波受地形阻挡影响长时间维持是稳定性极端降水形成主要原因。(4)地形相差大的地区模式预报性能差异较大,模式对复杂地形下的对流降水预报偏弱,导致系统强度出现差异,进而影响降水强度预报。