Does temperature contain a stochastic trend: linking statistical results to physical mechanisms

By construction, the time series for radiative forcing that are used to run the 20c3m experiments, which are implemented by climate models, impart non-stationary movements (either stochastic or deterministic) to the simulated time series for global surface temperature. Here, we determine whether stochastic or deterministic trends are present in the simulated time series for global surface temperature by examining the time series for radiative forcing. Statistical tests indicate that the forcings contain a stochastic trend against the alternative hypothesis that the series are trend stationary with a one-time structural change. This result is consistent with the economic processes that impart a stochastic trend to anthropogenic emissions and the physical processes that integrate emissions in the atmosphere. Furthermore, the stochastic trend in the aggregate measure of radiative forcing also is present in the simulated time series for global surface temperature, which is consistent with the relation between these two variables that is represented by a zero dimensional energy balance model. Finally, we propose that internal weather variability imposed on the stochastic trend in radiative forcings is responsible for statistical results, which gives the impression that global surface temperature is trend stationary with a one-time structural change. We conclude that using the ideas of stochastic trends, cointegration, and error correction can generate reliable conclusions regarding the causes of changes in global surface temperature during the instrumental temperature record.     

Anthropogenic and natural causes of climate change

We test for causality between radiative forcing and temperature using multivariate time series models and Granger causality tests that are robust to the non-stationary (trending) nature of global climate data. We find that both natural and anthropogenic forcings cause temperature change and also that temperature causes greenhouse gas concentration changes. Although the effects of greenhouse gases and volcanic forcing are robust across model specifications, we cannot detect any effect of black carbon on temperature, the effect of changes in solar irradiance is weak, and the effect of anthropogenic sulfate aerosols may be only around half that usually attributed to them.     

Emissions, Concentrations, & Temperature: A Time Series Analysis

We use recent advances in time series econometrics to estimate the relation among emissions of CO₂ and CH₄, the concentration of these gases, and global surface temperature. These models are estimated and specified to answer two questions; (1) does human activity affect global surface temperature and; (2) does global surface temperature affect the atmospheric concentration of carbon dioxide and/or methane. Regression results provide direct evidence for a statistically meaningful relation between radiative forcing and global surface temperature. A simple model based on these results indicates that greenhouse gases and anthropogenic sulfur emissions are largely responsible for the change in temperature over the last 130 years. The regression results also indicate that increases in surface temperature since 1870 have changed the flow of carbon dioxide to and from the atmosphere in a way that increases its atmospheric concentration. Finally, the regression results for methane hint that higher temperatures may increase its atmospheric concentration, but this effect is not estimated precisely.     

Solar Forcing of Global Climate Change Since The Mid-17th Century

Spacecraft measurements of the sun's total irradiance since 1980 have revealed a long-term variation that is roughly in phase with the 11-year solar cycle. Its origin is uncertain, but may be related to the overall level of solar magnetic activity as well as to the concurrent activity on the visible disk. A low-pass Gaussian filtered time series of the annual sunspot number has been developed as a suitable proxy for solar magnetic activity that contains a long-term component related to the average level of activity as well as a short-term component related to the current phase of the 11-year cycle. This time series is also assumed to be a proxy for solar total irradiance, and the irradiance is reconstructed for the period since 1617 based on the estimate from climatic evidence that global temperatures during the Maunder Minimum of solar activity, which coincided with one of the coldest periods of the Little Ice Age, were about 1 °C colder than modern temperatures. This irradiance variation is used as the variable radiative forcing function in a one-dimensional ocean–climate model, leading to a reconstruction of global temperatures over the same period, and to a suggestion that solar forcing and anthropogenic greenhouse-gas forcing made roughly equal contributions to the rise in global temperature that took place between 1900 and 1955. The importance of solar variability as a factor in climate change over the last few decades may have been underestimated in recent studies.     

Does temperature contain a stochastic trend? Evaluating conflicting statistical results

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.     

Spatial asymmetry of temperature trends over India and possible role of aerosols

Dissimilarities in temperature trends in space and time over the Indian region have been examined to look for signatures of aerosols’ influence. Separate temperature time series for North and South India were constructed for dry (November–May) and wet (June–October) seasons. Temperature trend for the entire period 1901–2007 and different subperiods of 1901–1950, 1951–1990, 1971–2007, and 1991–2007 have been examined to isolate the aerosol and other greenhouse gas influences on temperatures. Maximum (daytime) temperatures during dry season corresponding to North and South India show significant warming trend of 0.8 and 1.0?°C per hundred years during the period 1901–2007, while minimum temperature shows nebulous trend of 0.2 and 0.3?°C per hundred years over North and South India, respectively. During the wet season, maximum temperature shows nearly half of dry season maximum temperature warming trend. However, asymmetry is observed in dry season maximum temperature trend during post-industrial period 1951–1990 wherein the North/South India shows decreasing/increasing trends, while during the recent period 1991–2007 trends are uniformly positive for both the regions. Spatial and temporal asymmetry in observed trends clearly point to the role of aerosols in lowering temperature trends over northern India. Atmospheric aerosols could cause a negative climate forcing that can modulate the regional surface temperature trends in a significant way. As this forcing acts differentially on day and night temperatures, trends in diurnal temperature range (DTR) provide a direct assessment of impacts of aerosols on temperature trends. Time series of diurnal temperature range for dry and wet seasons have been examined separately for North and South India. Over North India, the DTR for dry season has increased gradually during the period 1901–1970 and thereafter showed decreasing trend, while trends in temperature range over Southern India were almost opposite in phase with North India. The aerosol and greenhouse gases seem to play an important role in the spatial and temporal variability of temperature range over India.     

Inference about trends in global temperature data

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.The authors are grateful to the SSHRC (Green) and FCAR (Galbraith) for financial support under grants 10-89-0205 and NC-0047.     

Climatic trends

A 10,000-year long simulation has been made with the CSIRO Mark 2 coupled global atmospheric-oceanic model for present climatic conditions. The annual mean output from the model has been used to calculate global distributions of climatic trends. These trends were derived by linear regression using a least squares fit to a given climatic time series for a selected trend duration. Typically, this information cannot be obtained from the limited observational record, hence the simulation provides a documentation of many climatic trend characteristics not previously available. A brief examination of observed climatic trends is given to demonstrate the viability of the trend analysis. This is followed by a range of global trend distributions for various climatic variables and trend durations. At any one time only relatively small regions of the globe have trends significant at the 95% level. Markedly different trend patterns occur for a given trend duration computed for different times within the simulation. Decadal and multi-decadal trend patterns revealed consistent relationships for El Niño/Southern Oscillation (ENSO)-related climatic variables. It was found that within a given duration trend, noticeable shorter term counter-trends can exist, with the latter being much stronger. In general, a strong trend is indicative of a short duration, thus highlighting the danger of extrapolating such trends. Examination of time series of climatic trends emphasised the dominance of decadal variability and the essential residual nature of, especially longer term, trends. Rainfall trends over Australia are used to indicate the almost continent-wide changes that can occur in trend patterns within a few decades, in agreement with observation. The outcome emphasises that any changes in current, observed climatic trends should not automatically be attributed to greenhouse forcing. Importantly, it is noted that for conditions associated with naturally occurring climatic variability, the global mean of any climatic trend distribution should be zero or near zero. Departures from this situation imply the existence of an external forcing agency. Thousand year trends could be readily identified within the simulation, but the variations from millennium to millennium indicate the occurrence of secular variability. A probability density function distribution of 30-year duration trends within a selected millennium revealed a near-Gaussian outcome. This, together with other analyses, supports the conclusion that stochastic processes dominate the climatic variability within the simulation.     

近50年我国探空温度序列均一化及变化趋势

利用1958—2005年我国116个站探空温度序列研究了我国高空温度变化趋势。首先通过静力学质量控制和两相回归法对原始序列进行了均一化处理。我国探空温度序列存在明显的间断点, 间断点的订正对于序列的趋势影响较为显著。缺测率是影响我国探空温度序列应用性的重要因子, 也是区域平均趋势统计中台站取舍的指标, 减少台站总数会削弱我国对流层升温和平流层降温的变化趋势。分析表明: 70%作为最小资料有效率标准最为合理。为满足最小资料有效率, 选取92个站统计我国高空温度变化趋势的区域平均值。结果表明: 1958-2005年, 平流层下层和对流层上层降温, 对流层中、低层升温; 高空温度变化趋势与研究时段明显相关, 1958-1978年我国高空大气整层均为降温; 1979—2005年, 对流层中低层升温最为明显, 增暖的幅度随高度增加而减小, 400 hPa以上各层转为降温。对流层的升温始于20世纪80年代, 升温幅度与全球尺度的平均值有所不同。     

Warming of an elevated layer over Africa

This paper analyzes trends of temperatures over Africa and seeks to quantify the most significant processes. Observations of air temperature reveal significant warming trends in the 925–600 hPa layer over tropical west Africa and the east Atlantic. This is related to the influence of desert dust and biomass burning emissions on the atmospheric energy budget. We calculate a net radiative absorption of ～??20 W m^???2. The southern (northern) plume is rich in short-lived greenhouse gases (dust aerosols), and the atmospheric response, according to a simplified radiative transfer model, is a >3°C heating of the 2–4 km layer. The observed pattern of warming coincides with a mixture of dust, black carbon and short-lived greenhouse gases in space, time and height. Physical forcing provides a secondary source of regional warming, with sinking motions over the Sahel. The elevated warm layer stabilizes the lower atmosphere over and west of Africa, so drying trends may be anticipated.     

A transition from CMIP3 to CMIP5 for climate information providers: the case of surface temperature over eastern North America

The release of new data constituting the Coupled Model Intercomparison Project—Phase 5 (CMIP5) database is an important event in both climate science and climate services issues. Although users’ eagerness for a fast transition from CMIP3 to CMIP5 is expected, this change implies some challenges for climate information providers. The main reason is that the two sets of experiments were performed in different ways regarding radiative forcing and hence continuity between both datasets is partially lost. The objective of this research is to evaluate a metric that is independent of the amount and the evolution of radiative forcing, hence facilitating comparison between the two sets for surface temperature over eastern North America. The link between CMIP3 and CMIP5 data sets is explored spatially and locally (using the ratio of local to global temperatures) through the use of regional warming patterns, a relationship between the grid-box and the global mean temperature change for a certain time frame. Here, we show that local to global ratios are effective tools in making climate change information between the two sets comparable. As a response to the global mean temperature change, both CMIP experiments show very similar warming patterns, trends, and climate change uncertainty for both winter and summer. Sensitivity of the models to radiative forcing is not assessed. Real inter-model differences remain the largest source of uncertainty when calculating warming patterns as well as spatially-based patterns for the pattern scaling approach. This relationship between the datasets, which may escape users when they are provided with a single radiative forcing pathway, needs to be stressed by climate information providers.     

Review of simulations of climate variability and change with the GFDL R30 coupled climate model

A review is presented of the development and simulation characteristics of the most recent version of a global coupled model for climate variability and change studies at the Geophysical Fluid Dynamics Laboratory, as well as a review of the climate change experiments performed with the model. The atmospheric portion of the coupled model uses a spectral technique with rhomboidal 30 truncation, which corresponds to a transform grid with a resolution of approximately 3.75° longitude by 2.25° latitude. The ocean component has a resolution of approximately 1.875° longitude by 2.25° latitude. Relatively simple formulations of river routing, sea ice, and land surface processes are included. Two primary versions of the coupled model are described, differing in their initialization techniques and in the specification of sub-grid scale oceanic mixing of heat and salt. For each model a stable control integration of near millennial scale duration has been conducted, and the characteristics of both the time-mean and variability are described and compared to observations. A review is presented of a suite of climate change experiments conducted with these models using both idealized and realistic estimates of time-varying radiative forcing. Some experiments include estimates of forcing from past changes in volcanic aerosols and solar irradiance. The experiments performed are described, and some of the central findings are highlighted. In particular, the observed increase in global mean surface temperature is largely contained within the spread of simulated global mean temperatures from an ensemble of experiments using observationally-derived estimates of the changes in radiative forcing from increasing greenhouse gases and sulfate aerosols.     

A local climatic model of the temperature-cloudiness relationship

Summary Filtered secular series of temperature at Zagreb (Croatia) are negatively correlated with simultaneous series of solar radiation and positively correlated with cloudiness.The local balance of radiative fluxes, with cloudiness interference included, provides a basis for the evaluation of a local deterministic model, which can describe both the positive and negative impacts of cloud radiative forcing upon surface temperature. A theoretical temperature series, generated by the model simulation, proves a prevailing greenhouse effect of clouds upon recent climatic variations of temperature at Zagreb.With 5 Figures     

Simple indices of global climate variability and change Part II: attribution of climate change during the twentieth century

Five simple indices of surface temperature are used to investigate the influence of anthropogenic and natural (solar irradiance and volcanic aerosol) forcing on observed climate change during the twentieth century. These indices are based on spatial fingerprints of climate change and include the global-mean surface temperature, the land-ocean temperature contrast, the magnitude of the annual cycle in surface temperature over land, the Northern Hemisphere meridional temperature gradient and the hemispheric temperature contrast. The indices contain information independent of variations in global-mean temperature for unforced climate variations and hence, considered collectively, they are more useful in an attribution study than global mean surface temperature alone. Observed linear trends over 1950–1999 in all the indices except the hemispheric temperature contrast are significantly larger than simulated changes due to internal variability or natural (solar and volcanic aerosol) forcings and are consistent with simulated changes due to anthropogenic (greenhouse gas and sulfate aerosol) forcing. The combined, relative influence of these different forcings on observed trends during the twentieth century is investigated using linear regression of the observed and simulated responses of the indices. It is found that anthropogenic forcing accounts for almost all of the observed changes in surface temperature during 1946–1995. We found that early twentieth century changes (1896–1945) in global mean temperature can be explained by a combination of anthropogenic and natural forcing, as well as internal climate variability. Estimates of scaling factors that weight the amplitude of model simulated signals to corresponding observed changes using a combined normalized index are similar to those calculated using more complex, optimal fingerprint techniques.     

Detection and Adjustment of Undocumented Discontinuities in Chinese Temperature Series Using a Composite Approach

Annually averaged daily maximum and minimum surface temperatures from southeastern China were evaluated for artificial discontinuities using three different tests for undocumented changepoints. Changepoints in the time series were identified by comparing each target series to a reference calculated from values observed at a number of nearby stations. Under the assumption that no trend was present in the sequence of target-reference temperature differences, a changepoint was assigned to the target series when at least two of the three tests rejected the null hypothesis of no changepoint at approximately the same position in the difference series. Each target series then was adjusted using a procedure that accounts for discontinuities in average temperature values from nearby stations that otherwise could bias estimates of the magnitude of the target series step change. A spatial comparison of linear temperature trends in the adjusted annual temperature series suggests that major relative discontinuities were removed in the homogenization process. A greater number of relative change points were detected in annual average minimum than in average maximum temperature series. Some evidence is presented which suggests that minimum surface temperature fields may be more sensitive to changes in measurement practice than maximum temperature fields. In addition, given previous evidence of urban heat island (i.e., local) trends in this region, the assumption of no slope in a target-reference difference series is likely to be violated more frequently in minimum than in maximum temperature series. Consequently, there may be greater potential to confound trend and step changes in minimum temperature series.     

How robust is the long-run relationship between temperature and radiative forcing?

This paper examines the robustness of the long-run, cointegrating, relationship between global temperatures and radiative forcing. It is found that the temperature sensitivity to a doubling of radiative forcing is of the order of 2 ± 1°C. This result is robust across the sample period of 1850 to 2000, thus providing further confirmation of the quantitative impact of radiative forcing and, in particular, CO₂ forcing, on temperatures.     

Multi-fingerprint detection and attribution analysis of greenhouse gas, greenhouse gas-plus-aerosol and solar forced climate change

 A multi-fingerprint analysis is applied to the detection and attribution of anthropogenic climate change. While a single fingerprint is optimal for the detection of climate change, further tests of the statistical consistency of the detected climate change signal with model predictions for different candidate forcing mechanisms require the simultaneous application of several fingerprints. Model-predicted climate change signals are derived from three anthropogenic global warming simulations for the period 1880 to 2049 and two simulations forced by estimated changes in solar radiation from 1700 to 1992. In the first global warming simulation, the forcing is by greenhouse gas only, while in the remaining two simulations the direct influence of sulfate aerosols is also included. From the climate change signals of the greenhouse gas only and the average of the two greenhouse gas-plus-aerosol simulations, two optimized fingerprint patterns are derived by weighting the model-predicted climate change patterns towards low-noise directions. The optimized fingerprint patterns are then applied as a filter to the observed near-surface temperature trend patterns, yielding several detection variables. The space-time structure of natural climate variability needed to determine the optimal fingerprint pattern and the resultant signal-to-noise ratio of the detection variable is estimated from several multi-century control simulations with different CGCMs and from instrumental data over the last 136 y. Applying the combined greenhouse gas-plus-aerosol fingerprint in the same way as the greenhouse gas only fingerprint in a previous work, the recent 30-y trends (1966–1995) of annual mean near surface temperature are again found to represent a significant climate change at the 97.5% confidence level. However, using both the greenhouse gas and the combined forcing fingerprints in a two-pattern analysis, a substantially better agreement between observations and the climate model prediction is found for the combined forcing simulation. Anticipating that the influence of the aerosol forcing is strongest for longer term temperature trends in summer, application of the detection and attribution test to the latest observed 50-y trend pattern of summer temperature yielded statistical consistency with the greenhouse gas-plus-aerosol simulation with respect to both the pattern and amplitude of the signal. In contrast, the observations are inconsistent with the greenhouse-gas only climate change signal at a 95% confidence level for all estimates of climate variability. The observed trend 1943–1992 is furthermore inconsistent with a hypothesized solar radiation change alone at an estimated 90% confidence level. Thus, in contrast to the single pattern analysis, the two pattern analysis is able to discriminate between different forcing hypotheses in the observed climate change signal. The results are subject to uncertainties associated with the forcing history, which is poorly known for the solar and aerosol forcing, the possible omission of other important forcings, and inevitable model errors in the computation of the response to the forcing. Further uncertainties in the estimated significance levels arise from the use of model internal variability simulations and relatively short instrumental observations (after subtraction of an estimated greenhouse gas signal) to estimate the natural climate variability. The resulting confidence limits accordingly vary for different estimates using different variability data. Despite these uncertainties, however, we consider our results sufficiently robust to have some confidence in our finding that the observed climate change is consistent with a combined greenhouse gas and aerosol forcing, but inconsistent with greenhouse gas or solar forcing alone. Received: 28 April 1996 / Accepted: 27 January 1997     

North-Atlantic SST amplified recent wintertime European land temperature extremes and trends

Europe has been warming over the past 30?years. In particular all seasonal temperature records have been broken since 2003, which altered socio-economic and environmental systems. Since we expect this trend in both mean and extreme temperatures to continue along the twenty first century under enhanced radiative forcing, it is crucial to understand the underlying mechanisms of such climate variations to help in considering adaptation or mitigation strategies to reduce the impacts of a warmer climate. From a statistical analysis we show that the inter-annual variability of European seasonal temperatures can be reconstructed from North-Atlantic atmospheric circulation only, but not their recent trends and extreme seasons. Adding North-Atlantic sea-surface temperature (SST) as a predictor helps improving the reconstruction, especially in autumn and winter. Sensitivity experiments with the MM5 regional model over 2003?C2007 suggest that the anomalous SST enhance European land temperatures through the upper-air advection of heat and water vapor, interacting with radiative fluxes over the continent. This mechanism is pronounced in autumn and winter, where estimates of SST influence as obtained from MM5 are in agreement with those obtained from statistical regressions. We find a lesser SST influence in spring and summer, where local surface and radiative feedbacks are the main amplifiers of recent extremes.     

Temperature stabilization, ocean heat uptake and radiative forcing overshoot profiles

Political leaders in numerous nations argue for an upper limit of the global average surface temperature of 2 K above the pre-industrial level, in order to attempt to avoid the most serious impacts of climate change. This paper analyzes what this limit implies in terms of radiative forcing, emissions pathways and abatement costs, for a range of assumptions on rate of ocean heat uptake and climate sensitivity. The primary aim is to analyze the importance of ocean heat uptake for radiative forcing pathways that temporarily overshoot the long-run stabilization forcing, yet keep the temperature increase at or below the 2 K limit. In order to generate such pathways, an integrated climate-economy model, MiMiC, is used, in which the emissions pathways generated represent the least-cost solution of stabilizing the global average surface temperature at 2 K above the pre-industrial level. We find that the level of overshoot can be substantial. For example, the level of overshoot in radiative forcing in 2100 ranges from about 0.2 to 1 W/m2, where the value depends strongly and positively on the effective diffusivity of heat in the oceans. Measured in relative terms, the level of radiative forcing overshoot above its longrun equilibrium level in 2100 is 20% to 60% for high values of climate sensitivity (i.e., about 4.5 K) and 8% to 30% for low values of climate sensitivity (i.e., about 2 K). In addition, for cases in which the radiative forcing level can be directly stabilized at the equilibrium level associated with a specific climate sensitivity and the 2 K limit, the net present value abatement cost is roughly cut by half if overshoot pathways are considered instead of stabilization of radiative forcing at the equilibrium level without an overshoot.     

温室气体和硫酸盐气溶胶的辐射强迫作用

对GOALS4 .0海 陆 气耦合模式的相关部分进行了改进 ,主要改进包括温室气体的扩充和硫酸盐气溶胶“显式”方案的引入 ,并引入 2 0世纪温室气体的实际浓度变化以及硫循环模式模拟的硫酸盐气溶胶的三维全球浓度分布 ,模拟了温室气体和硫酸盐气溶胶造成的辐射强迫的空间分布和时间变化。全球平均的温室气体和硫酸盐气溶胶的辐射强迫分别为 2 .17W /m2 和 - 0 .2 9W /m2 ;温室气体造成的辐射强迫在空间上呈现明显的纬向结构 ,最大值 (大于 2 .5W/m2 )和最小值 (小于 1W /m2 )分别位于副热带和两极地区 ,在北半球主要工业区硫酸盐气溶胶的辐射强迫绝对值接近温室气体的辐射强迫值 (大于 - 2 .0W /m2 )。