This is a list of papers on global warming detection from global temperature series (i.e. papers that estimate if global warming signal can be statistically significantly distinguished from random noise). The list is not complete, and will most likely be updated in future in order to make it more thorough and more representative.

**UPDATE** (July 24, 2013): Foster & Rahmstorf (2011) added.

A Bayesian approach to detecting change points in climatic records – Ruggieri (2012) “Given distinct climatic periods in the various facets of the Earth’s climate system, many attempts have been made to determine the exact timing of ‘change points’ or regime boundaries. However, identification of change points is not always a simple task. A time series containing N data points has approximately N_{k} distinct placements of k change points, rendering brute force enumeration futile as the length of the time series increases. Moreover, how certain are we that any one placement of change points is superior to the rest? This paper introduces a Bayesian Change Point algorithm which provides uncertainty estimates both in the number and location of change points through an efficient probabilistic solution to the multiple change point problem. To illustrate its versatility, the Bayesian Change Point algorithm is used to analyse both the NOAA/NCDC annual global surface temperature anomalies time series and the much longer δ^{18}O record of the Plio-Pleistocene.” *Eric Ruggieri, International Journal of Climatology, DOI: 10.1002/joc.3447.*

Global temperature evolution 1979–2010 – Foster & Rahmstorf (2011) “We analyze five prominent time series of global temperature (over land and ocean) for their common time interval since 1979: three surface temperature records (from NASA/GISS, NOAA/NCDC and HadCRU) and two lower-troposphere (LT) temperature records based on satellite microwave sensors (from RSS and UAH). All five series show consistent global warming trends ranging from 0.014 to 0.018 K yr^{−1}. When the data are adjusted to remove the estimated impact of known factors on short-term temperature variations (El Niño/southern oscillation, volcanic aerosols and solar variability), the global warming signal becomes even more evident as noise is reduced. Lower-troposphere temperature responds more strongly to El Niño/southern oscillation and to volcanic forcing than surface temperature data. The adjusted data show warming at very similar rates to the unadjusted data, with smaller probable errors, and the warming rate is steady over the whole time interval. In all adjusted series, the two hottest years are 2009 and 2010.” *Grant Foster and Stefan Rahmstorf 2011 Environ. Res. Lett. 6 044022 doi:10.1088/1748-9326/6/4/044022.* [Full text]

Detecting abrupt climate changes on different time scales – Matyasovszky (2011) “Two concepts are introduced for detecting abrupt climate changes. In the first case, the sampling frequency of climate data is high as compared to the frequency of climate events examined. The method is based on a separation of trend and noise in the data and is applicable to any dataset that satisfies some mild smoothness and statistical dependence conditions for the trend and the noise, respectively. We say that an abrupt change occurs when the first derivative of the trend function has a discontinuity and the task is to identify such points. The technique is applied to Northern Hemisphere temperature data from 1850 to 2009, Northern Hemisphere temperature data from proxy data, a.d. 200–1995 and Holocene δ^{18}O values going back to 11,700 years BP. Several abrupt changes are detected that are, among other things, beneficial for determining the Medieval Warm Period, Little Ice Age and Holocene Climate Optimum. In the second case, the sampling frequency is low relative to the frequency of climate events studied. A typical example includes Dansgaard–Oeschger events. The methodology used here is based on a refinement of autoregressive conditional heteroscedastic models. The key element of this approach is the volatility that characterises the time-varying variance, and abrupt changes are defined by high volatilities. The technique applied to δ^{18}O values going back to 122,950 years BP is suitable for identifying DO events. These two approaches for the two cases are closely related despite the fact that at first glance, they seem quite different.” *István Matyasovszky, Theoretical and Applied Climatology, Volume 105, Numbers 3-4 (2011), 445-454, DOI: 10.1007/s00704-011-0401-4.*

Testing for Deterministic Trends in Global Sea Surface Temperature – Barbosa (2011) “Long-term variability in global sea surface temperature (SST) is often quantified by the slope from a linear regression fit. Attention is then focused on assessing the statistical significance of the derived slope parameter, but the adequacy of the linear model itself, and the inherent assumption of a deterministic linear trend, is seldom tested. Here, a parametric statistical test is applied to test the hypothesis of a linear deterministic trend in global sea surface temperature. The results show that a linear slope is not adequate for describing the long-term variability of sea surface temperature over most of the earth’s surface. This does not mean that sea surface temperature is not increasing, rather that the increase should not be characterized by the slope from a linear fit. Therefore, describing the long-term variability of sea surface temperature by implicitly assuming a deterministic linear trend can give misleading results, particularly in terms of uncertainty, since the actual increase could be considerably larger than the one predicted by a deterministic linear model.” *Barbosa, Susana M., 2011: Testing for Deterministic Trends in Global Sea Surface Temperature. J. Climate, 24, 2516–2522. doi: http://dx.doi.org/10.1175/2010JCLI3877.1.*

1963: The break point of the Northern Hemisphere temperature trend during the twentieth century – Ivanov & Evtimov (2010) “Besides gradually, climate can also change abruptly. The global surface temperature series is a major indicator of such changes. Using rigorous statistical tools, we show that during the twentieth century the time series of annual Northern Hemisphere surface temperature is well described by a trend-stationary process, but the trend line breaks in 1963. After six transitory years, in 1970, the temperature course locks up into a new regime with a triple linear warming rate. For the emergence and abruptness of the break we reveal the key roles of the Mount Agung eruption and the interannual to interdecadal changes of the major modes and patterns of climate variability. We offer an abrupt climate shift scenario based on the adaptivity of climatic regimes against instant external forcings.” *Martin A. Ivanov, Stilian N. Evtimov, International Journal of Climatology, Volume 30, Issue 11, pages 1738–1746, September 2010, DOI: 10.1002/joc.2002.*

Warming Break Trends and Fractional Integration in the Northern, Southern, and Global Temperature Anomaly Series – Gil-Alana (2008) “This paper deals with the estimation of time trends in temperature anomaly series. However, instead of imposing that the estimated residuals from the time trends are covariance stationary processes with spectral density that is positive and finite at the zero frequency [I(0)], the author allows them to be fractionally integrated. In this context, a new procedure for testing fractional integration with segmented trends is applied to the northern, southern, and global temperature anomaly series. The results show that the three series are fractionally integrated, and the warming effects are substantially higher after the break in all cases.” *Gil-Alana, Luis A., 2008: Warming Break Trends and Fractional Integration in the Northern, Southern, and Global Temperature Anomaly Series. J. Atmos. Oceanic Technol., 25, 570–578. doi: http://dx.doi.org/10.1175/2007JTECHA1025.1.* [Full text]

Semiparametric estimation and testing of the trend of temperature series – Gao & Hawthorne (2006) “The application of a partially linear model to global and hemispheric temperature series is proposed. Partially linear modelling allows the trend to take a very general form rather than imposing the restriction of linearity seen in existing studies. The removal of the linearity restriction is based on the fact that it is well accepted that a significant trend is present in global temperature series. The model will allow for the data to ‘speak for themselves’ with regard to the form of the trend. The results initially reveal that a linear trend does not approximate well the behaviour of global or hemispheric temperature series. This is further confirmed through a formal testing procedure. The results suggest that little faith should be instilled in long-term forecasts of temperatures in which the trend of global and hemispheric series is assumed to be linear. All the current evidence suggest that temperatures will continue to rise in an unknown and probably nonlinear fashion.” *Jiti Gao, Kim Hawthorne, The Econometrics Journal, Volume 9, Issue 2, pages 332–355, July 2006, DOI: 10.1111/j.1368-423X.2006.00188.x.*

Are winters getting warmer? – Vogelsang & Franses (2006) “We examine whether any trends in monthly temperatures are the same through-out the year for various lengthy series. The data concern the world, the northern and southern hemispheres, and about three centuries of data for the United Kingdom and the Netherlands. For the empirical exercise, we rely on new and accurate tests which have been recently developed. These tests do not have standard distributions, so that critical values have to be tabulated. The empirical findings include significant worldwide temperature increases, differences across months for the northern hemisphere, and warming winters for the UK and the Netherlands.” *Timothy J. Vogelsang, Philip Hans Franses, Environmental Modelling & Software, Volume 20, Issue 11, November 2005, Pages 1449–1455, http://dx.doi.org/10.1016/j.envsoft.2004.09.016.*

Tests of common deterministic trend slopes applied to quarterly global temperature data – Fomby & Vogelsang (2003) “We examine the global warming temperature data sets of Jones et al. (1999) and Vinnikov et al. (1994) in the context of the multivariate deterministic trend-testing framework of Franses and Vogelsang (2002). We find that, across all seasons, global warming seems to be present for the globe and for the northern and southern hemispheres. Globally and within hemispheres, it appears that seasons are not warming equally fast. In particular, winters appear to be warming faster than summers. Across hemispheres, it appears that the winters in the northern and southern hemispheres are warming equally fast whereas the remaining seasons appear to have unequal warming rates. The results obtained here seem to coincide with the findings of Kaufmann and Stern (2002) who use cointegration analysis and find that the hemispheres are warming at different rates.” *Thomas B. Fomby, Timothy J. Vogelsang, (2003) “TESTS OF COMMON DETERMINISTIC TREND SLOPES APPLIED TO QUARTERLY GLOBAL TEMPERATURE DATA”, , Vol. Iss: 17, pp.29 – 43, doi: 10.1016/S0731-9053(03)17002-8.*

The Application of Size-Robust Trend Statistics to Global-Warming Temperature Series – Fomby & Vogelsang (2002) “In this note, new evidence is provided confirming that global temperature series spanning back to the mid-1800s have statistically significant positive trends. Although there is a growing consensus that global temperatures are on the rise systematically, some recent studies have pointed out that strong serial correlation (or a unit root) in global temperature data could, in theory, generate spurious evidence of a significant positive trend. In other words, strong serially correlated data can mimic trending behavior over fixed periods of time. A serial-correlation–robust trend test recently was proposed that controls for the possibility of spurious evidence due to strong serial correlation. This new test is valid whether the errors are stationary or have a unit root (strong serial correlation). This test also has the attractive feature that it does not require estimates of serial correlation nuisance parameters. The test is applied to six annual global temperature series, and it provides strong evidence that global temperature series have positive trends that are statistically significant even when controlling for the possibility of strong serial correlation. The point estimates of the rate of increase in the trend suggest that temperatures have risen about 0.5°C (1.0°F) 100 yr^{−1}. If the analysis is restricted to twentieth-century data, many of the point estimates are closer to 0.6°C.” *Fomby, Thomas B., Timothy J. Vogelsang, 2002: The Application of Size-Robust Trend Statistics to Global-Warming Temperature Series. J. Climate, 15, 117–123, doi: http://dx.doi.org/10.1175/1520-0442(2002)0152.0.CO;2.* [Full text]

Structural Time Series Models and Trend Detection in Global and Regional Temperature Series – Zheng & Basher (1999) “A unified statistical approach to identify suitable structural time series models for annual mean temperature is proposed. This includes a generalized model that can represent all the commonly used structural time series models for trend detection, the use of differenced series (successive year-to-year differences), and explicit methods for comparing the validity of no-trend nonstationary residuals models relative to trend models. Its application to Intergovernmental Panel on Climate Change global and latitude-belt temperature series reveals that a linear trend model (starting in 1890, with Southern Oscillation index signal removal and a red noise residuals process) is the optimal model for much of the globe, from the Northern Hemisphere Tropics to the Southern Hemisphere midlatitudes, but that a random stationary increment process (with no deterministic trend) is preferred for the northern part of the Northern Hemisphere. The result for the higher northern latitudes appears to be related to the greater climate variability there and does not exclude the possibility of a trend being present. The hemispheric and global series will contain a mixture of the two processes but are dominated by and best represented by the linear trend model. The latitudinal detectability of trends is oppositely matched to where GCMs indicate greatest anthropogenic trend, that is, it is best for the Tropics rather than for the high latitudes. The results reinforce the view that the global temperatures are affected by a long-term trend that is not of natural origin.” *Zheng, Xiaogu, Reid E. Basher, 1999: Structural Time Series Models and Trend Detection in Global and Regional Temperature Series. J. Climate, 12, 2347–2358, doi: http://dx.doi.org/10.1175/1520-0442(1999)0122.0.CO;2.* [Full text]

Trend Estimation and Regression Analysis in Climatological Time Series: An Application of Structural Time Series Models and the Kalman Filter – Visser & Molenaar (1995) “The detection of trends in climatological data has become central to the discussion on climate change due to the enhanced greenhouse effect. To prove detection, a method is needed (i) to make inferences on significant rises or declines in trends, (ii) to take into account natural variability in climate series, and (iii) to compare output from GCMs with the trends in observed climate data. To meet these requirements, flexible mathematical tools are needed. A structural time series model is proposed with which a stochastic trend, a deterministic trend, and regression coefficients can be estimated simultaneously. The stochastic trend component is described using the class of ARIMA models. The regression component is assumed to be linear. However, the regression coefficients corresponding with the explanatory variables may be time dependent to validate this assumption. The mathematical technique used to estimate this trend-regression model is the Kaiman filter. The main features of the filter are discussed. Examples of trend estimation are given using annual mean temperatures at a single station in the Netherlands (1706–1990) and annual mean temperatures at Northern Hemisphere land stations (1851–1990). The inclusion of explanatory variables is shown by regressing the latter temperature series on four variables: Southern Oscillation index (SOI), volcanic dust index (VDI), sunspot numbers (SSN), and a simulated temperature signal, induced by increasing greenhouse gases (GHG). In all analyses, the influence of SSN on global temperatures is found to be negligible. The correlations between temperatures and SOI and VDI appear to be negative. For SOI, this correlation is significant, but for VDI it is not, probably because of a lack of volcanic eruptions during the sample period. The relation between temperatures and GHG is positive, which is in agreement with the hypothesis of a warming climate because of increasing levels of greenhouse gases. The prediction performance of the model is rather poor, and possible explanations are discussed.” *Visser, H., J. Molenaar, 1995: Trend Estimation and Regression Analysis in Climatological Time Series: An Application of Structural Time Series Models and the Kalman Filter. J. Climate, 8, 969–979, doi: http://dx.doi.org/10.1175/1520-0442(1995)0082.0.CO;2.* [Full text]

Selecting a Model for Detecting the Presence of a Trend – Woodward & Gray (1995) “The authors consider the problem of determining whether the upward trending behavior in the global temperature anomaly series should be forecast to continue. To address this question, the generic problem of determining whether an observed trend in a time series realization is a random (i.e., short-term) trend or a deterministic (i.e., permanent) trend is considered. The importance of making this determination is that forecasts based on these two scenarios are dramatically different. Forecasts based on a series with random trends will not predict the observed trend to continue, while forecasts based on a model with deterministic trend will forecast the trend to continue into the future. In this paper, the authors consider an autoregressive integrated moving average (ARIMA) model and a “deterministic forcing function + autoregressive (AR) noise” model as possible random trend and deterministic trend models, respectively, for realizations displaying trending behavior. A bootstrap-based classification procedure for classifying an observed time series realization as ARIMA or “function + AR” using linear and quadratic forcing functions is introduced. A simulation study demonstrates that the procedure is useful in distinguishing between realizations from these two models. A unit-root test is also examined in an effort to distinguish between these two types of models. Using the techniques developed here, the temperature anomaly series are classified as ARIMA (i.e., having random trends).” *Woodward, Wayne A., H. L. Gray, 1995: Selecting a Model for Detecting the Presence of a Trend. J. Climate, 8, 1929–1937, doi: http://dx.doi.org/10.1175/1520-0442(1995)0082.0.CO;2.* [Full text]

Global Warming and the Problem of Testing for Trend in Time Series Data – Woodward & Gray (1993)“In recent years a number of statistical tests have been proposed for testing the hypothesis that global warming is occurring. The standard approach is to examine one or two of the more prominent global temperature datasets by letting *Y _{t} = a + bt + E_{t}*, where

*Y*represents the temperature at time

_{t}*t*and

*E*represents error from the trend line, and to test the hypothesis that b = 0. Several authors have applied these tests for trend to determine whether or not a significant long-term or deterministic trend exists, and have generally concluded that there is a significant deterministic trend in the data. However, we show that certain autoregressive-moving average (ARMA) models may also be very reasonable models for these data due to the random trends present in their realizations. In this paper, we provide simulation evidence to show that the tests for trend detect a deterministic trend in a relatively high percentage of realizations from a wide range of ARMA models, including those obtained for the temperature series, for which it is improper to forecast a trend to continue over more than a very short time period. Thus, we demonstrate that trend tests based on models such as

_{t}*Y*, where

_{t}= a + bt + E_{t}*Y*for the purpose of prediction or inference concerning future behavior should be used with caution. Of course, the projections that the warming trend will extend into the future are largely based on such factors as the buildup of atmospheric greenhouse gases. We have shown here, however, that based solely on the available temperature anomaly series, it is difficult to conclude that the trend will continue over any extended length of time.”

_{t}*Woodward, Wayne A., H. L. Gray, 1993: Global Warming and the Problem of Testing for Trend in Time Series Data. J. Climate, 6, 953–962, doi: http://dx.doi.org/10.1175/1520-0442(1993)0062.0.CO;2.*[Full text]

Climate spectra and detecting climate change – Bloomfield & Nychka (1992) “Part of the debate over possible climate changes centers on the possibility that the changes observed over the previous century are natural in origin. This raises the question of how large a change could be expected as a result of natural variability. If the climate measurement of interest is modelled as a stationary (or related) Gaussian time series, this question can be answered in terms of (a) the way in which change is estimated, and (b) the spectrum of the time series. These computations are illustrated for 128 years of global temperature data using some simple measures of change and for a variety of possible temperature spectra. The results highlight the time scales on which it is important to know the magnitude of natural variability. The uncertainties in estimates of trend are most sensitive to fluctuations in the temperature series with periods from approximately 50 to 500 years. For some of the temperature spectra, it was found that the standard error of the least squares trend estimate was 3 times the standard error derived under the naïve assumption that the temperature series was uncorrelated. The observed trend differs from zero by more than 3 times the largest of the calculated standard errors, however, and is therefore highly significant.” *Peter Bloomfield and Douglas Nychka, Climatic Change, Volume 21, Number 3 (1992), 275-287, DOI: 10.1007/BF00139727.*

Trends in global temperature – Bloomfield (1992) “Statistical models consisting of a trend plus serially correlated noise may be fitted to observed climate data such as global surface temperature, the trend and noise representing systematic change and other variations, respectively. When such a model is fitted, the estimated character of the noise determines the precision of the estimated trend, and hence the precision of the estimate of the magnitude of the systematic change in the variable considered. The results of fitting such models to global temperature imply that there is uncertainty in the amount of temperature change over the past century of up to ± 0.2 °C, but that the change of around one half of a degree Celsius is significantly different from zero. The statistical models for climate variability also imply that the observed temperature data provide only imprecise information about the climate sensitivity. This is defined here as the equilibrium response of global temperature to a doubling of the atmospheric concentration of carbon dioxide. The temperature changes observed to date are compatible with a wide range of climate sensitivities, from 0.7 °C to 2.2 °C. When data uncertainties are taken into account, the interval widens even further.” *Peter Bloomfield, Climatic Change, Volume 21, Number 1 (1992), 1-16, DOI: 10.1007/BF00143250.*

Inference about trends in global temperature data – Galbraith & Green (1992) “Interpretation of the effects of increasing atmospheric carbon dioxide on temperature is made more difficult by the fact that it is unclear whether sufficient global warming has taken place to allow a statistically significant finding of any upward trend in the temperature series. We add to the few existing statistical results by reporting tests for both deterministic and stochastic non-stationarity (trends) in time series of global average temperature. We conclude that the statistical evidence is sufficient to reject the hypothesis of a stochastic trend; however, there is evidence of a trend which could be approximated by a deterministic linear model.” *John W. Galbraith and Christopher Green, Climatic Change, Volume 22, Number 3 (1992), 209-221, DOI: 10.1007/BF00143028.*

Interdecadal oscillations and the warming trend in global temperature time series – Ghil & Vautard (1991) “THE ability to distinguish a warming trend from natural variability is critical for an understanding of the climatic response to increasing greenhouse-gas concentrations. Here we use singular spectrum analysis1 to analyse the time series of global surface air tem-peratures for the past 135 years, allowing a secular warming trend and a small number of oscillatory modes to be separated from the noise. The trend is flat until 1910, with an increase of 0.4 °C since then. The oscillations exhibit interdecadal periods of 21 and 16 years, and interannual periods of 6 and 5 years. The interannual oscillations are probably related to global aspects of the El Niño-Southern Oscillation (ENSO) phenomenon. The interdecadal oscillations could be associated with changes in the extratropical ocean circulation. The oscillatory components have combined (peak-to-peak) amplitudes of >0.2 °C, and therefore limit our ability to predict whether the inferred secular warming trend of 0.005 °Cyr^{−1} will continue. This could postpone incontrovertible detection of the greenhouse warming signal for one or two decades.” *M. Ghil & R. Vautard, Nature 350, 324 – 327 (28 March 1991); doi:10.1038/350324a0.* [Full text]

Global Warming as a Manifestation of a Random Walk – Gordon (1991) “Global and hemispheric series of surface temperature anomalies are examined in an attempt to isolate any specific features of the structure of the series that might contribute to the global warming of about 0.5°C which has been observed over the past 100 years. It is found that there are no significant differences between the means of the positive and negative values of the changes in temperature from one year to the next; neither do the relative frequencies of the positive and negative values differ from the frequencies that would be expected by chance with a probability near 0.5. If the interannual changes are regarded as changes of unit magnitude and plotted in a Cartesian frame of reference with time measured along the x axis and yearly temperature differences along the y axis, the resulting path closely resembles the kind of random walk that occurs during a coin-tossing game. We hypothesize that the global and hemispheric temperature series are the result of a Markov process. The climate system is subjected to various forms of random impulses. It is argued that the system fails to return to its former state after reacting to an impulse but tends to adjust to a new state of equilibrium as prescribed by the shock. This happens because a net positive feedback accompanies each shock and slightly alters the environmental state.” *Gordon, A. H., 1991: Global Warming as a Manifestation of a Random Walk. J. Climate, 4, 589–597, doi: http://dx.doi.org/10.1175/1520-0442(1991)0042.0.CO;2.* [Full text]

Detecting CO_{2}-induced climatic change – Wigley & Jones (1981) “Although it is widely believed that increasing atmospheric CO_{2} levels will cause noticeable global warming, the effects are not yet detectable, possibly because of the ‘noise’ of natural climatic variability. An examination of the spatial and seasonal distribution of signal-to-noise ratio shows that the highest values occur in summer and annual mean surface temperatures averaged over the Northern Hemisphere or over mid-latitudes. The spatial and seasonal characteristics of the early twentieth century warming were similar to those expected from increasing CO_{2} based on an equilibrium response model. This similarity may hinder the early detection of CO_{2} effects on climate.” *T. M. L. Wigley & P. D. Jones, Nature 292, 205 – 208 (16 July 1981); doi:10.1038/292205a0.*