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     

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.     

Seasonal forecasting of air temperature anomalies using the time analog method

Proposed is a method of forecasting the monthly mean air temperature anomalies for three months of the moving season based on the statistical analysis of the array of analogous processes of temperature variations specially selected for the initial season using the operational forecast for the first ten-day period of prognostic period being available by the beginning of the forecast. The array of analogous processes is used for revealing the most frequently observed values of temperature anomalies in the future. The overall station-by-station analysis gives a field of anomaly forecast for the CIS territory for three forthcoming months and for a season. Presented is the assessment of forecasts issued from January 2007 to December 2010 using the real ten-day period forecasts. The estimates of forecasts based on the model using the normals for 1979?C2007 are also considered.     

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.     

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.     

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     

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.     

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.     

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.     

CFSv2 prediction skill of stratospheric temperature anomalies

This study evaluates the prediction skill of stratospheric temperature anomalies by the Climate Forecast System version 2 (CFSv2) reforecasts for the 12-year period from January 1, 1999 to December 2010. The goal is to explore if the CFSv2 forecasts for the stratosphere would remain skillful beyond the inherent tropospheric predictability time scale of at most 2 weeks. The anomaly correlation between observations and forecasts for temperature field at 50 hPa (T50) in winter seasons remains above 0.3 over the polar stratosphere out to a lead time of 28 days whereas its counterpart in the troposphere at 500 hPa drops more quickly and falls below the 0.3 level after 12 days. We further show that the CFSv2 has a high prediction skill in the stratosphere both in an absolute sense and in terms of gain over persistence except in the equatorial region where the skill would mainly come from persistence of the quasi-biennial oscillation signal. We present evidence showing that the CFSv2 forecasts can capture both timing and amplitude of wave activities in the extratropical stratosphere at a lead time longer than 30 days. Based on the mass circulation theory, we conjecture that as long as the westward tilting of planetary waves in the stratosphere and their overall amplitude can be captured, the CFSv2 forecasts is still very skillful in predicting zonal mean anomalies even though it cannot predict the exact locations of planetary waves and their spatial scales. This explains why the CFSv2 has a high skill for the first EOF mode of T50, the intraseasonal variability of the annular mode while its skill degrades rapidly for higher EOF modes associated with stationary waves. This also explains why the CFSv2’s skill closely follows the seasonality and its interannual variability of the meridional mass circulation and stratosphere polar vortex. In particular, the CFSv2 is capable of predicting mid-winter polar stratosphere warming events in the Northern Hemisphere and the timing of the final polar stratosphere warming in spring in both hemispheres 3–4 weeks in advance.     

Synoptic-scale anomalies of Lake Ladoga surface temperature fields

Results of studying characteristic features of variability of the water surface temperature fields of Lake Ladoga during the open water period are presented. Anomalies and extreme deviations of real spatial distributions from those typical of the scales of synoptic variability are estimated. Typical surface temperature distribution of Lake Ladoga during an open water period occupies not more than 20% of the lake area. The near-shore shallow water area is characterized as an area of most anomalous water temperature distribution. The abnormality extent changes from month to month. July is the most anomalous month of the open water period.     

Propagation of the sea-surface temperature anomalies in the Tropical Atlantic

Summary The evolving modes of the sea-surface temperature (SST) in the Tropical Atlantic on the short interannual (IA) timescale were obtained by performing the extended empirical orthogonal function (EEOF) analyses on this variable separately for the 106-year (1871–1976) and 20-year (1881–1900; 1901–1920; 1921–1940; 1941–1960) periods. The equatorial and inter-hemispheric patterns manifest in the first EEOF mode of each analysis as part of the short IA evolution of the SST anomalies in the Tropical Atlantic. Another outstanding feature of the first EEOF mode of each analysis concerns the propagations of the SST anomalies in the meridional direction within the 20°N–20°S band and in the zonal direction in the sector 40°W–20°W. For all analyses, the SST anomalies propagate northward from the equator to 15°N and southward from 20°N to 15°N, with the same sign anomalies merging approximately at 15°N. On the other hand, the SST anomalies propagate westward in the sector 40°W–20°W with a propagation rate close to that of the phase speed of the fastest baroclinic Rossby wave in the ocean. So, the observed propagations of the SST anomalies in the 20°N–20°S band might result from the combined effect of the surface oceanic currents in this band and the baroclinic Rossby waves in the ocean.     

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.     

Detecting primary precursors of January surface air temperature anomalies in China

This study aims to detect the primary precursors and impact mechanisms for January surface temperature anomaly (JSTA) events in China against the background of global warming, by comparing the causes of two extreme JSTA events occurring in 2008 and 2011 with the common mechanisms inferred from all typical episodes during 1979–2008. The results show that these two extreme events exhibit atmospheric circulation patterns in the mid–high latitudes of Eurasia, with a positive anomaly center over the Ural Mountains and a negative one to the south of Lake Baikal (UMLB), which is a pattern quite similar to that for all the typical events. However, the Eurasian teleconnection patterns in the 2011 event, which are accompanied by a negative phase of the North Atlantic Oscillation, are different to those of the typical events and the 2008 event. We further find that a common anomalous signal appearing in early summer over the tropical Indian Ocean may be responsible for the following late-winter Eurasian teleconnections and the associated JSTA events in China. We show that sea surface temperature anomalies (SSTAs) in the preceding summer over the western Indian Ocean (WIO) are intimately related to the UMLB-like circulation pattern in the following January. Positive WIOSSTAs in early summer tend to induce strong UMLB-like circulation anomalies in January, which may result in anomalously or extremely cold events in China, which can also be successfully reproduced in model experiments. Our results suggest that the WIOSSTAs may be a useful precursor for predicting JSTA events in China.     

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.