Improving the methodology for spectral analysis of climatic time series

The paper discusses a methodology able to estimate both the discrete and continuous spectra without any assumption on the shape of spectral densities. The approach to estimate the spectral density is based on a robust smoothing of the periodogram. Bandwidth, a quantity similar to the width of spectral windows traditionally used in spectral analysis, is estimated locally in contrast to intuitively chosen global window lengths. Detection and estimation of frequencies forming discrete spectra are also addressed. The procedure is applied to Central England temperature (CEt), North Atlantic Oscillation (NAO) index and Oxygen Isotope of North Greenland Ice Core Project (δ¹⁸O of NGRIP) data. Annual and half annual cycles were detected in CEt data, whilst 118.2- and 41.7-ky cycles were found in δ¹⁸O of NGRIP. This latter periodicity is almost as intense as the dominant longer cycle. Several local peaks of spectral densities were recognised in each time series that mostly cover earlier results. However, a few previous findings at low frequencies have not been reinforced by the present method. Identification of modest local peaks or discrete amplitudes at low frequencies is an extremely challenging task as climatic data generally have spectral densities rising to low frequencies.     

Time trend estimation with breaks in temperature time series

This paper deals with the modelling of the global and northern and southern hemispheric anomaly temperature time series using a novel technique based on segmented trends and fractional integration. We use a procedure that permits us to estimate linear time trends and orders of integration at various subsamples, where the periods for the changing trends are endogenously determined by the model. Moreover, we use a non-parametric approach (Bloomfield P, Biometrika, 60:217–226, 1973) for modelling the I(0) deviation term. The results show that the three series (global, northern and southern temperatures) can be well described in terms of fractional integration with the orders of integration around 0.5 in the three cases. The coefficients associated to the time trends are statistically significant in all subsamples for the three series, especially during the final part of the sample, giving then some support to the global warming theories.     

小波频率估计方法及其在通信信号检测中的应用

小波变换作为新的信号分析工具,受到学者们的重视,然而如何将小波尺度与频率联系起来,是一个亟待解决的问题.为了求解小波的中心频率,提出了一种基于正弦波的模型,并将模型推广到任意采样间隔与任意小波尺度.由于模型的非凸性,传统的基于梯度的优化方法容易陷入局部最优,因此提出了一种基于Rossler吸引子的粒子群算法.实验给出了常见小波的频率值,并通过一个通信信号检测的例子证明了该方法的有效性.     

Testing for nonlinearity in European climatic time series by the method of surrogate data

Summary Using temperature and pressure records from Czech meteorological stations and NCEP/NCAR reanalysis series, we tested for the presence of detectable nonlinearity in univariate and multivariate climatic time series. The method of surrogate data was utilized for nonlinearity detection – results of nonlinear prediction for the original series were compared to the results for series whose nonlinear structure was randomized. The prediction was done by means of local linear models in the reconstructed phase space. None or very weak nonlinearity was found in the single (univariate) series, and pressure series generally exhibited stronger nonlinearity than series of temperature (daily mean, minimum or maximum). Distinct nonlinearity was found in all tested multivariate systems, especially when both temperatures and pressures were used simultaneously to form the phase space. Nonlinearity tests were carried out for 30-year and 10-year-long datasets and nonlinear behavior was generally more apparent in the longer versions. In addition, the tested systems showed more substantial nonlinearity when the success of short-range prediction was used as the discriminating statistic; with an increase of the prediction time, detectable nonlinearity became weaker and it disappeared completely for long-term prediction.     

Prediction of nonstationary climatic series

Summary Most of the stochastic prediction methods are developed for stationary time series. However, many climatic series show clear evidence of non-stationarity. In such cases, methods based on the stationarity assumptions would be inappropriate. Alternative methods such as those based on stochastic approximation are preferable in these cases because they are based on adaptive learning principles. These methods have not been applied and their suitability not tested with nonstationary climatic time series.In the stochastic approximation method, the deterministic component of a nonstationary time series is estimated by first predicting the two steps ahead value of a time series. The two steps-ahead forecast may involve a term characterizing the trend in the time series. The two steps-ahead predictor is corrected to obtain the one step ahead prediction by using a gain sequence.The dynamic stochastic approximation method is used herein to predict non-stationary climatic time series. Daily minimum temperature series at West Lafayette, Indiana, U.S.A. and seasonal temperature and precipitation series at Evansville, Indiana, U.S.A. are used in the study. For data trends, an improved dynamic stochastic approximation method, called the modified dynamic stochastic approximation method gives more accurate predictions. If the method is used for seasonal data, then it can be used to track the time varying mean value.With 6 Figures     

多变量时间序列滑动窗口异常点的检测

针对多变量时间序列(MTS)的异常点的探测问题,提出了采用由粗到细的二次探测方案.基于滑动窗口数据的置信区间,构造了变化趋势值特征和相对变化趋势值特征分别用于二次探测,同时研究了特征的快速提取算法.通过对OPEN3000数据监测系统采集的事故发生前后某市城南变电站各设备表的数据集进行异常点探测,结果表明提出的算法能够快速准确地探测出异常点的位置.     

相关时延估计在宽带干涉仪闪电观测中的应用

针对噪声对宽带干涉仪测角的干扰,提出了互相关测角算法.该方法避开频域分析,计算简单.通过仿真试验表明其抗干扰较强,具有一定的精度.通过本方法对人工引雷数据分析,能够明显定位直窜先导-继后回击过程,为宽带干涉仪测角提供了一个新思路.     

EOF analysis of a time series with application to tsunami detection

Fragments of deep-ocean tidal records up to 3 days long belong to the same functional sub-space, regardless of the record’s origin. The tidal sub-space basis can be derived via Empirical Orthogonal Function (EOF) analysis of a tidal record of a single buoy. Decomposition of a tsunami buoy record in a functional space of tidal EOFs presents an efficient tool for a short-term tidal forecast, as well as for an accurate tidal removal needed for early tsunami detection and quantification [Tolkova, E., 2009. Principal component analysis of tsunami buoy record: tide prediction and removal. Dyn. Atmos. Oceans 46 (1–4), 62–82] EOF analysis of a time series, however, assumes that the time series represents a stationary (in the weak sense) process. In the present work, a modification of one-dimensional EOF formalism not restricted to stationary processes is introduced. With this modification, the EOF-based de-tiding/forecasting technique can be interpreted in terms of a signal passage through a filter bank, which is unique for the sub-space spanned by the EOFs. This interpretation helps to identify a harmonic content of a continuous process whose fragments are decomposed by given EOFs. In particular, seven EOFs and a constant function are proved to decompose 1-day-long tidal fragments at any location. Filtering by projection into a reduced sub-space of the above EOFs is capable of isolating a tsunami wave within a few millimeter accuracy from the first minutes of the tsunami appearance on a tsunami buoy record, and is reliable in the presence of data gaps. EOFs with ∼$\sim$3-day duration (a reciprocal of either tidal band width) allow short-term (24.75 h in advance) tidal predictions using the inherent structure of a tidal signal. The predictions do not require any a priori knowledge of tidal processes at a particular location, except for recent 49.5 h long recordings at the location.     

气候突变的定义和检测方法

气候突变现象及其理论的研究是近代气候学一个新兴的研究领域.本文是气候突变研究评述的第一部分,着重讨论了突变,主要是气候突变的定义和气候突变信号的各种检测方法.把气候突变归纳为四类,即均值突变、变率突变、转折突变和翘翘板(seasaw)突变.并通过Mann-Kendall法的检测,发现在本世纪20年代经历了一次全球范围的气候突变.     

习水县水资源气候背景及其演变趋势

利用习水1959年以来年、季降水等资料,对习水县降水的长期变化趋势和年际变化作较全面的分析,并作出未来5年内的降水趋势预测,为水资源可持续开发利用提供科学依据.     

Quasi-periodicities in Chinese precipitation time series

Summary Although climate change deeply affects China, climatic time series are expected to show quasi-periodic behavior. This hypothesis has been tested by means of Autocorrelation Spectral Analysis (ASA) to detect quasi-periodicities in precipitation time series of 132 climate stations spread over China for the period from 1951 to 2002. A Continuous Wavelet Transform (CWT) has also been applied in order to examine if these quasi-periods are stable in time. Finally, it has been tested whether precipitation series recorded at neighboring stations show similar spectral behavior and can thus be grouped. All in all, our hypothesis regarding quasi-periodicities has been verified. Most of the time series show significant quasi-periods. A 2–3 year quasi-periodicity is predominant in many different regions of China. The result of ASA is that precipitation series from neighboring stations often show similar quasi-periods and therefore a grouping seems to be justified. However, the outcome of CWT provides more detailed information. In north-eastern China several series show similar quasi-periods which are statistically significant at different times; here, a grouping would be incorrect. In addition, the results of CWT show a less uniform pattern of quasi-periods in the southern inland regions. Whereas ASA shows a relatively uniform pattern of 2–3 year quasi-periods, CWT detects 2–3, 4–5 and 6–7 year quasi-periods. Nevertheless, although the quasi-periods are detected as being unstable, time series from neighboring stations sometimes show analogous significant quasi-periods within the same time frame and can thus be grouped. This can be seen in the northern part of central China, near the border to North Korea and along the coast of the South China Sea. Authors’ addresses: Heike Hartmann, Lorenz King, Department of Geography, Justus Liebig University, Senckenbergstra?e 1, 35390 Giessen, Germany; Stefan Becker, Department of Geography & Urban Planning, University of Wisconsin-Oshkosh, Oshkosh, WI 54901, U.S.A.     

气候大气和海洋的临界时间跨度与非线性作用结构

研究了气候海洋与大气的临界时间跨度及其非线性作用的大致结构。与预报的空间分辩率及系统的非线性强度相联系，气候大气和海洋的临界时间跨度可反映系统可预报的相对时间尺度。对于具有同样空间特征尺度的大气和海洋，海洋的最小临界时间跨度约是大气的9倍（可达数日至数十日）。一般（外源变化缓慢的）气候海洋与大气的一阶非线性越强，其临界时间跨度越小。气候海洋与大气非线性作用的大致结构是：通常与科里奥利力对流体运动的规范作用（如地转运动）有关，非线性作用随纬度增加而减弱。距平流场的切变结构及其沿经向与纬向上强度的比较直接改变气候大气和海洋的非线性作用（比如，向东的距平环流强度与经向环流强度相当时，非线性作用最强），较强的外部驱动（风应力和压弹梯度力）使非线性作用加大等等。     

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.     

Analysis of the climatic signal in the South Dome,Greenland ice core

The purpose of this research was to investigate the statistical relationship between an oxygen isotope chronology from southern Greenland and climatic variables recorded at a coastal village. The response of the oxygen isotope time series to monthly temperature and precipitation data was calculated using a combination of principal components factor analysis and multiple regression analysis. Orthogonal eigenvectors extracted from 35 yr of climatic data reliably explained 59% of the temporal variance in mean annual oxygen isotope values. The response functions demonstrate an apparent seasonal reversal in the relationship between oxygen isotope values and temperature, with the response varying between a positive (direct) relationship in winter, spring, and autumn, and a negative (indirect) relationship in summer. The results, and their implications, are shown to be useful in the historical climatic reconstruction of the South Greenland region.     

Measuring persistence in time series of temperature anomalies

Studies on persistence are important for the clarification of statistical properties of the analyzed time series and for understanding the dynamics of the systems which create these series. In climatology, the analysis of the autocorrelation function has been the main tool to investigate the persistence of a time series. In this paper, we propose to use a more sophisticated econometric instrument. Using this tool, we obtain an estimate of the persistence in global land and ocean and hemispheric temperature time series.     

Non-stationarity of the signal and noise characteristics of seasonal precipitation anomalies

In order to improve seasonal-to-interannual precipitation forecasts and their application by decision makers, there is a clear need to understand when, where, and to what extent seasonal precipitation anomalies are driven by potentially predictable surface–atmosphere interactions versus to chaotic interannual atmospheric dynamics. Using a simple Monte Carlo approach, interannual variability and linear trends in the SST-forced signal and potential predictability of boreal winter precipitation anomalies is examined in an ensemble of twentieth century AGCM simulations. Signal and potential predictability are shown to be non-stationary over more than 80% of the globe, while chaotic noise is shown to be stationary over most of the globe. Correlation analysis with respect to magnitudes of the four leading modes of global SST variability suggests that interannual variability and trends in signal and potential predictability over 35% of the globe is associated with ENSO-related SST variability; signal and potential predictability are not significantly associated with SST modes characterized by a global SST trend, North Atlantic SST variability, and North Pacific SST variability, respectively. Results suggest that mechanisms other than SST variability contribute to the non-stationarity of signal and noise characteristics of hydroclimatic variability over mid- and high-latitude regions.     

Calibration of the climatic signal in a new pollen sequence from La Grande Pile

A new core, GPXX, from La Grande Pile (Vosges, France) has enabled a more precise evaluation of pollen data concerning the last climatic cycle at this site and has enabled reconstruction of the monthly temperature and precipitation. This paper shows that the various components of the reconstructed climatic signal are clearly separated and that they are coherent with the vegetation dynamics. The Eemian interglacial was influenced first by an oceanic climate and second by a more continental one. The two interstadials, St-Germain I and II, were mainly continental. These three temperate periods ended with a cool and humid transition period dominated by boreal forests, which may have been favourable to ice accretion. The Dansgaard-Oeschger oscillations from 55 to 25 Kyr BP are not significantly recorded in La Grande Pile.Contribution to Clima Locarno — Past and Present Climate Dynamics; Conference September 1990, Swiss Academy of Sciences — National Climate Program