Global Temperature Time Series Research Articles

Analysis of the stationarity and correlation of the global temperature and carbon dioxide time series

Background: The rapid and ongoing phenomenon of global warming has negatively impacted both the Earth’s environment and its inhabitants. Time series and regression analysis techniques play a significant role in weather forecasting and the interpretation of climate data. One of the key characteristics of time series analysis is stationarity. Methods: In this article, we explore how detrending and differencing techniques can be used to transform the time series of global temperature and carbon dioxide into stationary series. Regression models and goodness of fit tests were used to examine the relationship between carbon dioxide and data on global temperature. A cross-correlation time series model is also used to assess those time series’ lagging and leading characteristics. Results: The study of data on global temperature anomalies indicates that detrending and differencing are helpful in transforming temperature time series into stationary time series. However, the first differencing and detrending methods do not make the carbon dioxide time series stationary; instead, an alternate transformation is needed. Neither the carbon dioxide time series nor the global temperature time series lag or lead with regard to the cross-correlation function. Conclusions: In this article, we looked into stationarity and some other topics associated with correlation in terms of data on CO2 and global temperature. Stationarity is one of the important properties to check before conducting a more thorough investigation of the time series. To transform a non-stationary time series into a stationary one, there are numerous techniques available. However, in this article, we just pay attention to detrending and differencing and how those methods perform with respect to time series data for global temperature and carbon dioxide.

Examining global warming factors using self-organizing map and Granger causality network: a case from South Korea

BackgroundUnderstanding and patterning the possible causal variables of global warming is attributed to the development of effective prevention and mitigation strategies for climate change. Therefore, we aimed to pattern and visualize the possible causal variables of global warming and measure the causality between them.MethodsWe patterned and visualized the time series (103 years, from 1918 to 2020) of global surface temperature (GTemp) data with the gross domestic product (GDP) per capita, human population (Pop), and carbon dioxide (CO2) emissions of South Korea using a self-organizing map (SOM) and examined the causable local feature of global warming using the Granger causality (GC) test. The time-series data were trained and mapped in 4 × 4 SOM grids, and causality networks between variables were examined using multivariate Granger test statistics.ResultsSOM patterned 103 years of data, and a dominant cluster contained continuous time-series data from 2007 to 2020. Similarly, the CO2 emissions of South Korea were obtained as a predictable unidirectional causal variable for GTemp from GC analysis. Based on data from the past 34 years, significant causality (p-value = 0.01) was observed with the integrated effect of Pop, GDP, and CO2 on GTemp.ConclusionThis study patterned the time-series data using SOM and examined the causal relationship between variables using the GC test. The study framework could be used as a reference by future scholars, ecologists, and the United Nations Sustainable Development Goals.

Contributions of internal climate variability in driving global and ocean temperature variations using multi-layer perceptron neural network

Roles of internal climate variabilities regulating global and ocean temperature changes is a hot but complex issue of scientific concern, influencing the comprehensive policy-making in response to global and regional warming. In this study, the time series of monthly global and ocean mean surface temperature (GST and OST, respectively) since 1866 is successfully reconstructed via natural and anthropogenic forcing factors and internal climate variability by using a Multi-Layer Perceptron (MLP) neural network technique. The MLP demonstrates prominent monthly GST and OST reconstruction skills on both interannual and annual time scales. Most of the warming in GST and OST since 1866 is found to be attributable to anthropogenic forcing, while the multidecadal and interannual GST and OST variations are considerably dominated by Atlantic Multidecadal Oscillation (AMO). Internal climate variabilities like Interdecadal Pacific Oscillation (IPO) can amplify the GST and OST changes and explain the global warming slowdown since 1998. Southern Oscillation Index (SOI) performs a similar role as IPO but to a lesser extent. Changes in OST caused by solar forcing are more considerable than those in GST. Moreover, the ‘biased warmth’ during the Second World War is successfully reconstructed in MLP. AMO and IPO can explain most annual and even sub-annual temperature variations during this period, offering an explanation for the existence of this abnormal warm period other than that it was entirely caused by instrumental errors. The generally high accuracy of reconstructions on interannual and annual time scales can enhance the ability to monitor the prompt feedback of specific external radiative forcings and internal variabilities to changes in climate.

Trend locally stationary wavelet processes

Most time series observed in practice exhibit first‐ as well as second‐order non‐stationarity. In this article we propose a novel framework for modelling series with simultaneous time‐varying first‐ and second‐order structure, removing the restrictive zero‐mean assumption of locally stationary wavelet processes and extending the applicability of the locally stationary wavelet model to include trend components. We develop an associated estimation theory for both first‐ and second‐order time series quantities and show that our estimators achieve good properties in isolation of each other by making appropriate assumptions on the series trend. We demonstrate the utility of the method by analysing the global mean sea temperature time series, highlighting the impact of the changing climate.

Observations of planetary heating since the 1980s from multiple independent datasets

Time series of global mean surface temperature are widely used to measure the rate of climate change that results from Earth’s energy imbalance. However, studies based on climate model simulations suggest that on annual-to-decadal timescales global ocean heat content is a more reliable indicator. Here we examine the observational evidence for this, drawing together multiple datasets that span the past ∼30 years. This observational analysis strongly supports the model-based finding that global ocean heat content and sea level are more reliable than surface temperature for monitoring Earth’s energy accumulation on these timescales. Global ocean temperature anomalies in the 0–100 m and 100–250 m layers are negatively correlated (r = −0.36), primarily explained by the influence of the Tropical Pacific, and a clearer heating signal is revealed by integrating over deeper ocean layers. The striking agreement between multiple independent datasets represents unequivocal evidence of ongoing planetary heating.

Sensitivity of trends to estimation methods and quantification of subsampling effects in global radiosounding temperature and humidity time series

AbstractClimate trends estimated using historical radiosounding time series may be significantly affected by the choice of the regression method to use, as well as by a subsampling of the dataset often adopted in specific applications. These are contributions to the uncertainty of trend estimations, which have been quantified in literature, although on specific pairs of regression methods, and in the not very recent past characterized by smaller trends in temperature than those observed over the last two decades. This paper investigates the sensitivity of trend estimations to four linear regression methods (parametric and nonparametric) and to the artificial subsampling of the same dataset using historical radiosounding time series from 1978 onwards, available in the version 2 of the Integrated Global Radiosonde Archive (IGRA). Results show that long‐term decadal trends may have not negligible uncertainties related to the choice of the regression method, the percentage of data available, the amount of missing data and the number of stations selected in the dataset. The choice of the regression methods increases uncertainties in the decadal trends ranging from −0.10 to −0.01 K⋅da–1 for temperature in the lower stratosphere at 100 hPa and from 0.2 to 0.8% da–1 for relative humidity (RH) in the middle troposphere at 300 hPa. Differences can also increase up to 0.4 K⋅da–1 at 300 hPa when the amount of missing data exceeds 50% of the original dataset for temperature, while for RH, significant differences are observed in the lower troposphere at 925 hPa for almost all datasets. Finally, subsampling effects on trend estimation are quantified by artificially reducing the size of the IGRA dataset: Results show that subsampling effects on trend estimations when at least 60 stations, up to 76% of data available, are considered for temperature and at least 40 stations for RH.

A new energy-balance approach to linear filtering for estimating effective radiative forcing from temperature time series

Abstract. Reliable estimates of historical effective radiative forcing (ERF) are important for understanding the causes of past climate change and for constraining predictions of future warming. This study proposes a new linear-filtering method for estimating historical radiative forcing from time series of global mean surface temperature (GMST), using energy-balance models (EBMs) fitted to GMST from CO2-quadrupling general circulation model (GCM) experiments. We show that the response of any k-box EBM can be represented as an ARMA(k, k−1) (autoregressive moving-average) filter. We show how, by inverting an EBM's ARMA filter representation, time series of surface temperature may be converted into radiative forcing. The method is illustrated using three-box EBM fits to two recent Earth system models from CMIP5 and CMIP6 (Coupled Model Intercomparison Project). A comparison with published results obtained using the established ERF_trans method, a purely GCM-based approach, shows that our new method gives an ERF time series that closely matches the GCM-based series (correlation of 0.83). Time series of estimated historical ERF are obtained by applying the method to a dataset of historical temperature observations. The results show that there is clear evidence of a significant increase over the historical period with an estimated forcing in 2018 of 1.45±0.504 W m−2 when derived using the two Earth system models. This method could be used in the future to attribute past climate changes to anthropogenic and natural factors and to help constrain estimates of climate sensitivity.

Artificial intelligence reconstructs missing climate information

Historical temperature measurements are the basis of global climate datasets like HadCRUT4. This dataset contains many missing values, particularly for periods before the mid-twentieth century, although recent years are also incomplete. Here we demonstrate that artificial intelligence can skilfully fill these observational gaps when combined with numerical climate model data. We show that recently developed image inpainting techniques perform accurate monthly reconstructions via transfer learning using either 20CR (Twentieth-Century Reanalysis) or the CMIP5 (Coupled Model Intercomparison Project Phase 5) experiments. The resulting global annual mean temperature time series exhibit high Pearson correlation coefficients (≥0.9941) and low root mean squared errors (≤0.0547 °C) as compared with the original data. These techniques also provide advantages relative to state-of-the-art kriging interpolation and principal component analysis-based infilling. When applied to HadCRUT4, our method restores a missing spatial pattern of the documented El Nino from July 1877. With respect to the global mean temperature time series, a HadCRUT4 reconstruction by our method points to a cooler nineteenth century, a less apparent hiatus in the twenty-first century, an even warmer 2016 being the warmest year on record and a stronger global trend between 1850 and 2018 relative to previous estimates. We propose image inpainting as an approach to reconstruct missing climate information and thereby reduce uncertainties and biases in climate records. An artificial intelligence-based method may infill gaps in historical temperature data more effectively than conventional techniques. Application of this method reveals a stronger global warming trend between 1850 and 2018 than estimated previously.

Standard normal homogeneity test as a tool to detect change points in climate-related river discharge variation: case study of the Kupa River Basin

ABSTRACTThe study addresses homogeneity testing of annual discharge time series for eight hydrological stations and five annual climate time series for one weather station in the Kupa River Basin, between Slovenia and Croatia, and global annual average surface temperature time series for the period 1961–2010. The standard normal homogeneity test (SNHT) was used to detect both abrupt and gradual linear trend homogeneity breaks. The results reveal natural change points at the beginning of the 1980s. Absolute homogeneity testing of average annual weather station-level air pressure, annual precipitation, differences between precipitation totals and potential evapotranspiration and surface runoff from the independent observation time series confirmed an abrupt shift, also at the beginning of the 1980s. The trend of local air temperature for 1985–2000, which partly coincides with global surface temperature trend for 1974–2005, strengthened the river discharge regime shift since the beginning of the 1980s. These results could improve climate variation monitoring and estimation of the impact of climate variation on the environment in the area. Generally, an indication of climate regime change points and an assessment of their duration could provide significant benefits for the society.

Quantifying the importance of interannual, interdecadal and multidecadal climate natural variabilities in the modulation of global warming rates

Despite the monotonically rising greenhouse gas emission, global warming rate changes again and again, especially the slowdown during 1998–2013, challenging the current global temperature change mechanisms. Recently, different-scale natural climate variabilities have been individually recognized as the potential causes of global warming rate change, particularly the recent warming slowdown, but disagreements still exist on their relative importance. Here we quantify the contribution of interannual, interdecadal and multidecadal variabilities (IAV, IDV and MDV) in modulating the global warming rate during the period 1850–2017 via decomposing the global mean temperature timeseries derived from 12 datasets into several quasi-periodic fluctuations and a monotonical secular trend (ST) using the ensemble empirical mode decomposition method. Our results show that the IAV, IDV and MDV dominate the global warming rate change together, rather than one-scale variability alone. For example, during 1998–2013 both the IAV and IDV present obvious negative trends and combine to cut 59 ± 22% of global mean surface temperature (GMST) and 65 ± 38% of sea surface temperature (SST) positive trends which are caused by the steadily warming ST and the warming phase of MDV, thus causing an apparent warming slowdown during this period. Furthermore, we illustrate that the IAV, IDV and MDV mainly originate from the El Nino-Southern oscillation (ENSO), Pacific decadal oscillation (PDO) and Atlantic multidecadal oscillation (AMO), respectively. Our work partly reconciles the controversy over the importance of different-scale natural variabilities, and provides some insights for climate change attribution and prediction research.

Evaluating trends in time series of distributions: A spatial fingerprint of human effects on climate

We analyze a time series of global temperature anomaly distributions to identify and estimate persistent features in climate change. We employ a formal test for the existence of functional unit roots in the time series of these densities, and we develop a new test to distinguish functional unit roots from functional deterministic trends or explosive behavior. Results suggest that temperature anomalies contain stochastic trends (as opposed to deterministic trends or explosive roots), two trends are present in the Northern Hemisphere while one stochastic trend is present in the Southern Hemisphere, and the probabilities of observing moderately positive anomalies have increased. We postulate that differences in the pattern and number of unit roots in each hemisphere may be due to a natural experiment which causes human emissions of greenhouse gases and sulfur to be greater in the Northern Hemisphere, decreasing the mean temperature anomaly but increasing the spatial variance relative to the Southern Hemisphere. Together, these results are consistent with the theory of anthropogenic climate change.

Identifying the early 2000s hiatus associated with internal climate variability

This study focuses on re-examining the early 2000s hiatus and the associated key components of the global mean surface temperature (GMST) using multiscale statistics for five well-known gridded surface temperature and two reanalysis datasets. The hiatus is characterized as a near-zero trend on the decadal scale corresponding to the maximum P-value via an F-test in statistics. The results reveal that the hiatus exists in both the GMST and global mean air temperature (GMAT) time series, rather than in global warming component, which has maintained an approximately constant rate of change of approximately 0.08 °C/decade over the past three decades. The hiatus’s duration is different from that of time series such as 2002–2012/2001–2013/2002–2014 in HadCRUT4, NOAA-old, ERA-Interim and NCEP-R2. The newly gridded datasets with data infilling or bias correction for interpreting the sea surface temperature (SST) measurement from the old versions show a slightly higher trend from 2002–2012 than the hiatus, which is thus regarded as a slowdown. Comparison suggests that the hiatus should be during the period 2002–2012. Orthogonal wavelet decomposition of the temperature time series shows that the hiatus was merely a decadal balance between cooling from interannual variability and global warming, in addition to weak warming from interdecadal and multidecadal climate oscillations. In addition, the evolutions of the GMST’s interannual composites are well coincided with Niño3.4 SST anomalies, which is consistent with the numerical simulation performed by Kosaka and Xie in 2013. Hence, it is the anomalous El Niño Southern Oscillation (ENSO) events in the early 2000s that caused the hiatus despite a constant rate of global warming and the maximum magnitude of the multidecadal composite that led to the limited contribution to the trend during this period. The multidecadal composite follows a downward path, which implies that future climate conditions will likely rely on competition between multidecadal cooling and global warming if the multidecadal climate cycle repeats, as was experienced during the second half of the twentieth century.

Complexity Analysis of Global Temperature Time Series.

Climate has complex dynamics due to the plethora of phenomena underlying its evolution. These characteristics pose challenges to conducting solid quantitative analysis and reaching assertive conclusions. In this paper, the global temperature time series (TTS) is viewed as a manifestation of the climate evolution, and its complexity is calculated by means of four different indices, namely the Lempel–Ziv complexity, sample entropy, signal harmonics power ratio, and fractal dimension. In the first phase, the monthly mean TTS is pre-processed by means of empirical mode decomposition, and the TTS trend is calculated. In the second phase, the complexity of the detrended signals is estimated. The four indices capture distinct features of the TTS dynamics in a 4-dim space. Hierarchical clustering is adopted for dimensional reduction and visualization in the 2-dim space. The results show that TTS complexity exhibits space-time variability, suggesting the presence of distinct climate forcing processes in both dimensions. Numerical examples with real-world data demonstrate the effectiveness of the approach.

Nonlinear reconstruction of global climate leading modes on decadal scales

A nonlinear decomposition method is applied to the analysis of global sea surface temperature (SST) time series in different epochs related to the Pacific Decadal Oscillation (PDO) since the end of 19th century to present time. This method allows one to extract an optimal (small) number of global nonlinear teleconnection patterns associated with distinct dominant time scales from the original high-dimensional spatially extended data set. In particular, it enables us to reveal ENSO teleconnection patterns corresponding to different PDO cycles during the last 145 years, to uncover four climate shifts connected with PDO phase changes and to reconstruct the corresponding global PDO patterns. We find that SST teleconnections between the ENSO region, extra-tropical Pacific regions and the Indian ocean became fundamentally nonlinear since the second half of 20th century.

Multiscale Granger causality.

In the study of complex physical and biological systems represented by multivariate stochastic processes, an issue of great relevance is the description of the system dynamics spanning multiple temporal scales. While methods to assess the dynamic complexity of individual processes at different time scales are well established, multiscale analysis of directed interactions has never been formalized theoretically, and empirical evaluations are complicated by practical issues such as filtering and downsampling. Here we extend the very popular measure of Granger causality (GC), a prominent tool for assessing directed lagged interactions between joint processes, to quantify information transfer across multiple time scales. We show that the multiscale processing of a vector autoregressive (AR) process introduces a moving average (MA) component, and describe how to represent the resulting ARMA process using state space (SS) models and to combine the SS model parameters for computing exact GC values at arbitrarily large time scales. We exploit the theoretical formulation to identify peculiar features of multiscale GC in basic AR processes, and demonstrate with numerical simulations the much larger estimation accuracy of the SS approach compared to pure AR modeling of filtered and downsampled data. The improved computational reliability is exploited to disclose meaningful multiscale patterns of information transfer between global temperature and carbon dioxide concentration time series, both in paleoclimate and in recent years.

Multi‐decadal evolution characteristics of global surface temperature anomaly data shown by observation and CMIP5 models

ABSTRACTBased on methods of statistical analysis, the time series of global surface air temperature (SAT) anomalies from 1860 to 2014 has been defined by three types of phase changes that occur through the division of temperature changes into different stages. The characteristics of the three types of phase changes simulated by Coupled Model Inter‐Comparison Project (CMIP5) models were evaluated. The conclusion is as follows: the SAT from 1860 to 2014 can be divided into six stages according to trend differences, and this subdivision is proved to be statistically significant. Based on trend analysis and the distribution of slopes between any two points (two points' slope) in every stage, the six stages can be summarized as three phase changes of warming, cooling, and hiatus. Between 1860 and 2014, the world experienced three heating phases (1860–1878, 1909–1942, and 1975–2004), one cooling phase (1878–1909), and two hiatus phases (1942–1975 and 2004–2014). Using the definition method, whether the next year belongs to the previous phase can be estimated. Furthermore, the temperature in 2015 was used as an example to validate the feasibility of this method. The simulations of the heating period by CMIP5 models are well; however, the characteristics shown by SAT during the cooling and hiatus period cannot be represented by CMIP5 models. As such, the projections of future heating phases using the CMIP5 models are credible, but for cooling and hiatus events they are unreliable.

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

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

A comprehensive examination of global atmospheric CO2 teleconnections using wavelet-based multi-resolution analysis

Interannual variability of the atmospheric CO2 accumulation is at a similar magnitude of decadal average CO2 accumulation in the atmosphere. Part of observed variability in the atmospheric CO2 can be interpreted by large-scale climate variability. Teleconnection between the atmospheric CO2 anomalous tendency and selected large-scale coupled oceanic and atmospheric oscillations (AO, NAO, PDO, IOD, ENSO and SAM) are examined using wavelet-based multi-resolution analysis. The results indicate that all six oscillation indices appear to be associated with monthly CO2 concentration at most of the 13 examined stations. About 70 % of interannual variability of CO2 anomalous tendency at Mauna Loa and South Pole can be interpreted by the climatic indices. The temperature effects on the CO2 anomalous tendency are overall positive. At the monthly scale, they interpret 14 % variability in CO2 anomalous tendency in 1980–2011. At two high elevation stations (Mauna Loa and South Pole) with large footprints, the teleconnection signal is stronger (interpreting 20 and 25 % variability in monthly CO2 anomalous tendency, respectively). Including global mean monthly air temperature time series, slightly but significantly in the statistical sense, improves the proportion of monthly CO2 anomalous tendency being interpreted at most of the examined stations. The signs (positive vs. negative) in the association between monthly CO2 anomalous tendency and the significant climatic indices appear to reflect physical mechanisms leading to such teleconnections.

StructSSI: Simultaneous and Selective Inference for Grouped or Hierarchically Structured Data.

The 𝖱 package structSSI provides an accessible implementation of two recently developed simultaneous and selective inference techniques: the group Benjamini-Hochberg and hierarchical false discovery rate procedures. Unlike many multiple testing schemes, these methods specifically incorporate existing information about the grouped or hierarchical dependence between hypotheses under consideration while controlling the false discovery rate. Doing so increases statistical power and interpretability. Furthermore, these procedures provide novel approaches to the central problem of encoding complex dependency between hypotheses. We briefly describe the group Benjamini-Hochberg and hierarchical false discovery rate procedures and then illustrate them using two examples, one a measure of ecological microbial abundances and the other a global temperature time series. For both procedures, we detail the steps associated with the analysis of these particular data sets, including establishing the dependence structures, performing the test, and interpreting the results. These steps are encapsulated by 𝖱 functions, and we explain their applicability to general data sets.

Uncertainty in annual rankings from NOAA's global temperature time series

[1] Annual rankings of global temperature are an important component of climate monitoring. However, there is some degree of uncertainty for every yearly value in the global temperature time series, which leads to uncertainty in annual rankings as well. This study applies a Monte Carlo uncertainty analysis to the National Oceanic and Atmospheric Administration (NOAA) National Climatic Data Center's global land-ocean surface temperature (NOAATMP) time series. Accounting for persistence between years does not materially affect the results versus presuming statistical independence. The highest probabilities for the warmest year analysis (1880–2012) are associated with the years 2010 (~36%), 2005 (~28%), and 1998 (~11%). The current separation among the warmest observed years is relatively small compared to the standard errors of the NOAATMP time series. However, each year between 1997 and 2012 was warmer than the vast majority of all other years since 1880 at the 95% confidence level.