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.     

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.     

Assessing levels of uncertainty in recent temperature time series

 We examine to what degree we can expect to obtain accurate temperature trends for the last two decades near the surface and in the lower troposphere. We compare temperatures obtained from surface observations and radiosondes as well as satellite-based measurements from the Microwave Soundings Units (MSU), which have been adjusted for orbital decay and non-linear instrument-body effects, and reanalyses from the European Centre for Medium-Range Weather Forecasts (ERA) and the National Centre for Environmental Prediction (NCEP). In regions with abundant conventional data coverage, where the MSU has no major influence on the reanalysis, temperature anomalies obtained from microwave sounders, radiosondes and from both reanalyses agree reasonably. Where coverage is insufficient, in particular over the tropical oceans, large differences are found between the MSU and either reanalysis. These differences apparently relate to changes in the satellite data availability and to differing satellite retrieval methodologies, to which both reanalyses are quite sensitive over the oceans. For NCEP, this results from the use of raw radiances directly incorporated into the analysis, which make the reanalysis sensitive to changes in the underlying algorithms, e.g. those introduced in August 1992. For ERA, the bias-correction of the one-dimensional variational analysis may introduce an error when the satellite relative to which the correction is calculated is biased itself or when radiances change on a time scale longer than a couple of months, e.g. due to orbit decay. ERA inhomogeneities are apparent in April 1985, October/November 1986 and April 1989. These dates can be identified with the replacements of satellites. It is possible that a negative bias in the sea surface temperatures (SSTs) used in the reanalyses may have been introduced over the period of the satellite record. This could have resulted from a decrease in the number of ship measurements, a concomitant increase in the importance of satellite-derived SSTs, and a likely cold bias in the latter. Alternately, a warm bias in SSTs could have been caused by an increase in the percentage of buoy measurements (relative to deeper ship intake measurements) in the tropical Pacific. No indications for uncorrected inhomogeneities of land surface temperatures could be found. Near-surface temperatures have biases in the boundary layer in both reanalyses, presumably due to the incorrect treatment of snow cover. The increase of near-surface compared to lower tropospheric temperatures in the last two decades may be due to a combination of several factors, including high-latitude near-surface winter warming due to an enhanced NAO and upper-tropospheric cooling due to stratospheric ozone decrease. Received: 5 May 1999 / Accepted: 15 December 1999     

Robust estimation of background noise and signal detection in climatic time series

We present a new technique for isolating climate signals in time series with a characteristic red noise background which arises from temporal persistence. This background is estimated by a robust procedure that, unlike conventional techniques, is largely unbiased by the presence of signals immersed in the noise. Making use of multiple-taper spectral analysis methods, the technique further provides for a distinction between purely harmonic (periodic) signals, and broader-band (quasiperiodic) signals. The effectiveness of our signal detection procedure is demonstrated with synthetic examples that simulate a variety of possible periodic and quasiperiodic signals immersed in red noise. We apply our methodology to historical climate and paleoclimate time series examples. Analysis of a 3 million year sediment core reveals significant periodic components at known astronomical forcing periodicities and a significant quasiperiodic 100 year peak. Analysis of a roughly 1500 year tree-ring reconstruction of Scandinavian summer temperatures suggests significant quasiperiodic signals on a near-century timescale, an interdecadal 16–18 year timescale, within the interannual El Niño/Southern Oscillation (ENSO) band, and on a quasibiennial timescale. Analysis of the 144 year record of Great Salt Lake monthly volume change reveals a significant broad band of significant interdecadal variability, ENSO-timescale peaks, an annual cycle and its harmonics. Focusing in detail on the historical estimated global-average surface temperature record, we find a highly significant secular trend relative to the estimated red noise background, and weakly significant quasiperiodic signals within the ENSO band. Decadal and quasibiennial signals are marginally significant in this series.     

Multi-sliding time windows based changing trend of mean temperature and its association with the global-warming hiatus

Based on three global annual mean surface temperature time series and three Chinese annual mean surface air temperature time series, climate change trends on multiple timescales are analyzed by using the trend estimation method of multi-sliding time windows. The results are used to discuss the so-called global-warming hiatus during 1998–2012. It is demonstrated that different beginning and end times have an obvious effect on the results of the trend estimation, and the implications are particularly large when using a short window. The global-warming hiatus during 1998–2012 is the result of viewing temperature series on short timescales; and the events similar to it, or the events with even cold tendencies, have actually occurred many times in history. Therefore, the global-warming hiatus is likely to be a periodical feature of the long-term temperature change. It mainly reflects the decadal variability of temperature, and such a phenomenon in the short term does not alter the overall warming trend in the long term.     

资料均一化对沈阳站气温趋势和城市化偏差分析的影响

利用国家气象信息中心2013年发布的逐日均一化气温资料,对沈阳站资料均一化处理前后平均气温和极端气温指数序列的线性趋势及其城市化影响偏差进行了比较评价。结果表明:1)资料均一化处理对日最高气温及其衍生的极端气温指数序列趋势估计的影响较弱,但对日最低气温及其衍生的极端气温指数序列趋势估计具有显著影响。2)经资料均一化处理后,平均气温序列中的城市化影响偏差有所增大,平均最低气温序列中的城市化影响偏差增大尤其明显;与冷事件有关的极端气温指数序列的城市化影响偏差数值有所减小,与暖事件有关的极端气温指数序列的城市化影响偏差数值有所增加。3)资料均一化处理有效纠正了因迁站等原因造成的地面气温观测记录中的非均一性,但却在很大程度上还原了城市站地面气温观测记录中的城市化影响偏差。     

Complexity analysis of the air temperature and the precipitation time series in Serbia

Regional Atmospheric Modeling System (RAMS) was applied to the study of the effect of the topographical altitude of the Tibetan Plateau (TP) on a severe drought event which took place in eastern China from November 2008 to January 2009. Two simulations of this drought event were conducted: a control simulation (CNTRL run) using original model settings and a sensitive simulation (TOPO run), where no change other than to reduce the TP topography by 50 %. The results show that the CNTRL simulation validates RAMS by reproducing this drought event fairly accurately. However, as part of the TOPO simulation, the total heat flux showed a decrease over most parts of the TP, latent heat flux underwent a significant increase over the southeastern TP, contrary to sensible heat, and a universal decrease over eastern China; this led to an increase in precipitation over the southeastern TP and a decrease in precipitation over eastern China. The decrease of total heat flux over the TP is collocated with an anomalous anticyclonic circulation from the TP to the coasts of southeastern China. Changes in atmospheric circulation and low-level water vapor transport pathways were consistent with changes in precipitation. In general, reducing the topographical altitude of the TP worsens drought in eastern China and moreover causes a significant decrease in precipitation over southern China.     

Statistical time series decomposition into significant components and application to European temperature

Summary Time series of observed monthly mean temperatures of European stations and at grid points are decomposed into different kinds of trends (linear, progressive, degressive), constant or significantly changing annual cycles, episodic and harmonic components, extreme events and noise. A stepwise regression is used to test whether the components are significant. Special emphasis is given to extreme events which we distinguish from extreme values. While extreme values may likely occur by chance, it is very unlikely that extreme events would be in accordance with the features of the time series. On one hand, extreme events alter the estimates (and test results) of trends and other components. On the other hand, such components have to be known to recognize extreme events. To deal with this problem, an iterative procedure is introduced that converges fast to robust estimates of all the components. Applying this procedure to the last 100 years of European temperatures reveals that the phase of the annual cycle is shifted backward within the year in western Europe but foreward in eastern Europe. In the latter region, the amplitude of the annual cycle has also increased significantly. Most of the trend components found in the time series are positive and linear. Nearly all detected extreme events are cold events which occurred in winter. Their number has significantly grown. Significant harmonic components with a period of 92.3 months (about 7.7 years) are found mainly in northern and western Europe. Received August 15, 2000 Revised June 20, 2001     

Probabilistic projections of regional temperature and precipitation extending from observed time series

Probabilistic projections of change in regional temperature and precipitation previously derived allow for the range of sensitivities to global warming simulated by CMIP3 models. However, the changes were relative to an idealized base climate for 1980–1999, disregarding observed trends, such as those in rainfall in some Australian regions. Here we propose a method that represents projections for both forced change and decadal means as time series that extend from the observed series, illustrated using data for central Victoria. The main idea is to estimate the time-evolving underlying (or forced) past climate then convert this to a series of absolute values, by using the mean of the full observational record. We again use the pattern scaling assumption, and combine the CMIP3 sensitivities used for future change with a global warming series beginning at 1900. Like the confidence interval of regression theory, the analysis gives an estimate of the range of the underlying climate at each decade. This range can be augmented to allow for natural variability. A Bayesian theory can be applied to combine the model-based sensitivity with that estimated from observations. The time series are modified and the persistence of current observed anomalies considered, ultimately merging the probabilistic projections with the observed record. For some other cases, such as rainfall in southwest and north Australia and temperature in the state of Iowa, the two sensitivity estimates appear less compatible, and possible additional forcings are considered. Examples of the potential use of such time series are presented.     

Ground observed climatology and trend in snow cover phenology across China with consideration of snow-free breaks

Accurate understanding of snow cover phenology and its changes is important to hydrological processes and climate system. Having recognized the potential uncertainties in remote sensing snow cover products, we used daily snow depth observations from 514 meteorological stations across China to investigate the spatiotemporal variations in snow cover phenology during 1970–2014. Climatologically, the snow cover onset date (D_o) and end date (D_e) as well as the number of snow cover days (D_s) depended on latitude at most stations outside of the Tibetan Plateau (TP). For the high-elevation stations, which were mainly in the TP, multiple snow-free breaks (SFBs) during the cold season made D_s insensitive to D_o and D_e. Furthermore, the number of SFBs (D_b) increased significantly with the rise in elevation, explaining why higher altitudes in TP did not necessarily have greater D_s values despite the earlier D_o and later D_e values. From 1970 to 2014, most stations in China exhibited delayed D_o and advanced D_e due mainly to the increased temperature, but such trends were significant at only 10.5% and 15.4% of the stations, respectively. During the same period, shortened D_s primarily occurred south of ~ 40° N, whereas the opposite ones dominated north of ~ 40° N. Most stations (except those in Hexi Corridor) with significant growth in D_s were characterized by delayed D_o and advanced D_e. Such a phenomenon of “increased snow cover days during shortened cold season” was due to the significant shrinkage in D_b values. The spatial pattern of the trends in annual total snow depth overall follows that of D_s, suggesting that the D_s, when takes SFBs into consideration, could be an indicator of variations of snow water resources in China. The trends in D_o, D_e and D_s were not elevation dependent in TP.

     

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.     

Exploring Granger causality between global average observed time series of carbon dioxide and temperature

Detection and attribution methodologies have been developed over the years to delineate anthropogenic from natural drivers of climate change and impacts. A majority of prior attribution studies, which have used climate model simulations and observations or reanalysis datasets, have found evidence for human-induced climate change. This papers tests the hypothesis that Granger causality can be extracted from the bivariate series of globally averaged land surface temperature (GT) observations and observed CO₂ in the atmosphere using a reverse cumulative Granger causality test. This proposed extension of the classic Granger causality test is better suited to handle the multisource nature of the data and provides further statistical rigor. The results from this modified test show evidence for Granger causality from a proxy of total radiative forcing (RC), which in this case is a transformation of atmospheric CO₂, to GT. Prior literature failed to extract these results via the standard Granger causality test. A forecasting test shows that a holdout set of GT can be better predicted with the addition of lagged RC as a predictor, lending further credibility to the Granger test results. However, since second-order-differenced RC is neither normally distributed nor variance stationary, caution should be exercised in the interpretation of our results.     

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.     

On the time-varying trend in global-mean surface temperature

The Earth has warmed at an unprecedented pace in the decades of the 1980s and 1990s (IPCC in Climate change 2007: the scientific basis, Cambridge University Press, Cambridge, 2007). In Wu et al. (Proc Natl Acad Sci USA 104:14889–14894, 2007) we showed that the rapidity of the warming in the late twentieth century was a result of concurrence of a secular warming trend and the warming phase of a multidecadal (~65-year period) oscillatory variation and we estimated the contribution of the former to be about 0.08°C per decade since ~1980. Here we demonstrate the robustness of those results and discuss their physical links, considering in particular the shape of the secular trend and the spatial patterns associated with the secular trend and the multidecadal variability. The shape of the secular trend and rather globally-uniform spatial pattern associated with it are both suggestive of a response to the buildup of well-mixed greenhouse gases. In contrast, the multidecadal variability tends to be concentrated over the extratropical Northern Hemisphere and particularly over the North Atlantic, suggestive of a possible link to low frequency variations in the strength of the thermohaline circulation. Depending upon the assumed importance of the contributions of ocean dynamics and the time-varying aerosol emissions to the observed trends in global-mean surface temperature, we estimate that up to one third of the late twentieth century warming could have been a consequence of natural variability.     

Indications of change of climate from the analysis of air temperature time series in Athens,Greece

Air temperature data of Athens are analysed to point out the variations caused by natural controls and anthropogenic activities. The study of the temperature records from 1858 to 1982 at Athens, on the southeast coast of Greece, supports the findings of earlier studies which indicate that the period of the 1920's to the 1950's were, climatologically, warmer than the preceding 60 yr and after about 1960. In particular, minimum temperatures show an increase from the 1920's to the 1980's, possibly due to the urbanization of the area. The climatological trends are clearly indicated in the data, when averaged over 30 yr and/or a numerical low-pass filtering technique is used. However, the sizes of the trends in climate are smaller than the interannual variations in the temperature measures. Over periods of several generations these small variations in climate cannot have had any effect on human activity when compared with the large effects caused by the interannual variability in the temperature.     

基于小波和M-K方法的商丘气温时间序列分析

利用1955-2011年商丘气象站地面逐日气象数据,集成Morlet小波分析法、Mann-Kendall分析法、回归分析法、变异系数等方法,分析商丘气温序列的年、季周期变化特征、突变特征、变化趋势特征及年际变率特征。结果表明：根据回归分析、5 a滑动平均分析,商丘年平均气温呈增加趋势,年际变化倾向率为0.17 ℃/10 a;各季节气温变化趋势差异明显,夏季气温呈下降趋势,年际变化倾向率为-0.08 ℃/10 a,冬春秋季气温呈增加趋势,冬季增温最为显著,冬季气温年际变化倾向率为0.35 ℃/10 a。根据Mann-Kendall分析,年平均气温突变点为1992年,夏季气温不存在明显突变,冬季气温突变点为1986年。根据小波分析,20世纪50-80年代商丘年平均气温存在准17 a周期信号,之后该周期信号消失,80年代和90年代出现准32 a周期信号,在本研究的整个时间序列上存在准5 a和准2 a周期信号,周期信号显示未来几年可能会出现低温年。商丘年平均气温的年际变异系数为0.04,年际变率较小,年际变化较平稳。商丘作为重要的粮食生产基地,集成多种方法的气温变化特征和趋势预测分析,对该区域的农业种植活动具有重要的指导意义。     

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.