How unusual is the recent series of warm years?

Climatic Change, 2000

Non-stationary time series such as global and hemispheric temperatures, greenhouse gas concentrations, solar irradiance, and anthropogenic sulfate aerosols, may contain stochastic trends (the simplest stochastic trend is a random walk) which, due to their unique patterns, can act as a signal of the influence of other variables on the series in question. Two or more series may share a common stochastic trend, which indicates that either one series causes the behavior of the other or that there is a common driving variable. Recent developments in econometrics allow analysts to detect and classify such trends and analyze relationships among series that contain stochastic trends. We apply some univariate autoregression based tests to evaluate the presence of stochastic trends in several time series for temperature and radiative forcing. The temperature and radiative forcing series are found to be of different orders of integration which would cast doubt on the anthropogenic global warming hypothesis. However, these tests can suffer from size distortions when applied to noisy series such as hemispheric temperatures. We, therefore, use multivariate structural time series techniques to decompose Northern and Southern Hemisphere temperatures into stochastic trends and autoregressive noise processes. These results show that there are two independent stochastic trends in the data. We investigate the possible origins of these trends using a regression method. Radiative forcing due to greenhouse gases and solar irradiance can largely explain the common trend. The second trend, which represents the non-scalar non-stationary differences between the hemispheres, reflects radiative forcing due to tropospheric sulfate aerosols. We find similar results when we use the same techniques to analyze temperature data generated by the Hadley Centre GCM SUL experiment.

Journal of Climate, 2002

In this paper we apply some recently proposed size robust trend function tests to seven global temperature series. The tests are valid for general forms of serial correlation in the errors and do not require estimates of serial correlation nuisance parameters in order to carry out asymptotically valid inference. Perhaps more importantly, the tests are valid whether the errors are stationary or have a unit root. This is an important property as conventional trend function tests become oversized when errors have a unit root or are highly persistent. It is this undesirable property of conventional tests that had raised doubts about the empirical validity of a positive trend in global temperature series. Using the robust trend statistics, we find strong evidence to suggest that typical global temperature series spanning back to the mid 1800's have positive trends that are statistically significant. This suggests that average global temperatures are indeed on the rise as widely believed. The point estimates of the rate of increase in the trend suggest that temperatures have risen only about 0.5 degrees Celsius (1.0 degree Fahrenheit) per 100 years.

Geophys. Res. Lett., 33, L06718, doi:10.1029/ 2005GL025591., 2006

We have analyzed six recently reconstructed records (Jones et al., 1998; Mann et al., 1999; Briffa, 2000; Esper et al., 2002; McIntyre and McKitrick, 2003; and Moberg et al., 2005) of the Northern Hemisphere temperatures and found that all are governed by long-term persistence. Due to the long-term persistence, the mean temperature variations s(m,L) between L years, obtained from moving averages over m years, are considerably larger than for uncorrelated or shortterm correlated records. We compare the values for s(m, L) with the most recent temperature changes DTi(m, L) in the corresponding instrumental record and determine the year ic where DTi(m, L)/s(m, L) exceeds a certain threshold and the first year id when this could be detected. We find, for example, that for the climatologically relevant parameters m = 30, L = 100, and the threshold 2.5, the values (ic, id) range, for all records, between (1976, 1990) for Mann et al. (1999) and (1988, 2002) for Jones et al. (1998). Accordingly, the hypothesis that at least part of the recent warming cannot be solely related to natural factors, may be accepted with a very low risk, independently of the database used.

Earth System Dynamics Discussions, 2014

Various interpretations of the notion of a trend in the context of global warming are discussed, contrasting the difference between viewing a trend as the deterministic response to an external forcing and viewing it as a slow variation which can be separated from the background spectral continuum of long-range persistent climate noise. The emphasis in this paper is on the latter notion, and a general scheme is presented for testing a multi-parameter trend model against a null hypothesis which models the observed climate record as an autocorrelated noise. The scheme is employed to the instrumental global sea-surface temperature record and the global land temperature record. A trend model comprising a linear plus an oscillatory trend with period of approximately 70 yr, and the statistical significance of the trends, are tested against three different null models: first-order autoregressive process, fractional Gaussian noise, and fractional Brownian motion. The parameters of the null m...

Interactions between externally forced and internally generated climate variations on decadal timescales is a major determinant of changing climate risk. Severe testing is applied to observed global and regional surface and satellite temperatures and modelled surface temperatures to determine whether these interactions are independent, as in the traditional signal-to-noise model, or whether they interact, resulting in step-like warming. The multistep bivariate test is used to detect step changes in temperature data. The resulting data are then subject to six tests designed to distinguish between the two statistical hypotheses, h step and h trend. Test 1: since the mid-20th century, most observed warming has taken place in four events: in 1979/80 and 1997/98 at the global scale, 1988/89 in the Northern Hemisphere and 1968–70 in the Southern Hemisphere. Temperature is more step-like than trend-like on a regional basis. Satellite temperature is more step-like than surface temperature. Warming from internal trends is less than 40 % of the total for four of five global records tested (1880–2013/14). Test 2: correlations between step-change frequency in observations and models (1880–2005) are 0.32 (CMIP3) and 0.34 (CMIP5). For the period 1950–2005, grouping selected events (1963/64, 1968–70, 1976/77, 1979/80, 1987/88 and 1996–98), the correlation increases to 0.78. Test 3: steps and shifts (steps minus internal trends) from a 107-member climate model ensemble (2006–2095) explain total warming and equilibrium climate sensitivity better than internal trends. Test 4: in three regions tested, the change between stationary and non-stationary temperatures is step-like and attributable to external forcing. Test 5: step-like changes are also present in tide gauge observations, rainfall, ocean heat content and related variables. Test 6: across a selection of tests, a simple stepladder model better represents the internal structures of warming than a simple trend, providing strong evidence that the climate system is exhibiting complex system behaviour on decadal timescales. This model indicates that in situ warming of the atmosphere does not occur; instead, a store-and-release mechanism from the ocean to the atmosphere is proposed. It is physically plausible and theoretically sound. The presence of step-like – rather than gradual – warming is important information for characterising and managing future climate risk.

Geophysical Research Letters, 2019

• The incomplete sampling of the surface temperature of earths surface affects the estimation of trends in the global mean. • The changing availability of temperature observations over time influences the variance of the data sample. • An inhomogeneity in the data in terms of changing variance affects the trend estimate for the global mean temperature.

This communication aims to identify and utilize persistent features of global atmospheric temperature for predicting underlying fluctuating phenomena. A graphical method, Loess plot is used to show the presence of some degree of non-linearity in global temperature dynamics. Here we propose to split the average global temperature data set into three scale invariant temperature series on the basis of Hurst exponent in order to extract useful features of the physical system responsible for temperature anomalies. Global warming dynamics is revealed as possible Martingale and Markov stochastic processes. Different orders of Markov processes are examined for representative adequate models of the phenomenon. The models considered can be used both for short term and long-term temperature forecasts.

Weather and Climate Extremes

The Earth has warmed over the past century. The warming rate (amount of warming over a given period) varies in time and space. Observations show a recent increase in global mean warming rate, which is initially maintained in model projections, but which diverges substantially in future depending on the emissions scenario followed. Scenarios that stabilize forcing lead to much lower warming rates, as the rate depends on the change in forcing, not the amount. Warming rates vary spatially across the planet, but most areas show a shift toward higher warming rates in recent decades. The areal distribution of warming rates is also changing shape to include a longer tail in recent decades. Some areas of the planet are already experiencing extreme warming rates of about 1 C/decade. The fat tail in areal distribution of warming rates is pronounced in model runs when the forcing and global mean warming rate is increasing, and indicates a climate state more prone to regime transitions. The areaproportion of the Earth displaying warming/cooling trends is shown to be directly related to the global mean warming rate, especially for trends of length 15 years and longer. Since the global mean warming rate depends on the forcing rate, the proportion of warming/cooling trend areas in future also depends critically on the choice of future forcing scenario.

Geophysical Research Letters, 2014

Observed trends in the intensity of hot and cold extremes as well as in dry spell length and heavy precipitation intensity are often not significant at local scales. However, using a spatially aggregated perspective, we demonstrate that the probability distribution of observed local trends across the globe for the period 1960-2010 is clearly different to what would be expected from internal variability. We detect a distinct intensification of heavy precipitation events and hot extremes. We show that CMIP5 models generally capture the observed shift in the trend distribution but tend to underestimate the intensification of heavy precipitation and cold extremes and overestimate the intensification in hot extremes. Using an initial condition experiment sampling internal variability, we demonstrate that much of the local to regional differences in trends of extremes can be explained by internal variability, which can regionally mask or amplify the forced long-term trends for many decades.

Climatic Change, 2010

We evaluate the claim by Gay et al. (Clim Change 94:333-349, 2009) that "surface temperature can be better described as a trend stationary process with a one-time permanent shock" than efforts by Kaufmann et al. (Clim Change 77:249-278, 2006) to model surface temperature as a time series that contains a stochastic trend that is imparted by the time series for radiative forcing. We test this claim by comparing the in-sample forecast generated by the trend stationary model with a one-time permanent shock to the in-sample forecast generated by a cointegration/error correction model that is assumed to be stable over the 1870-2000 sample period. Results indicate that the in-sample forecast generated by the cointegration/error correction model is more accurate than the in-sample forecast generated by the trend stationary model with a one-time permanent shock. Furthermore, Monte Carlo simulations of the cointegration/error correction model generate time series for temperature that are consistent with the trend-stationary-with-a-break result generated by Gay et al. (Clim Change 94:333-349, 2009), while the time series for radiative forcing cannot be modeled as trend stationary with a one-time shock. Based on these results, we argue that modeling surface temperature as a time series that shares a stochastic trend with radiative forcing offers the possibility of greater insights regarding the potential causes of climate change and efforts to slow its progression.