Trends of temperature variability: Which variability and what health implications?

A large majority of climate change studies carried out to date are on changes in mean climate, which have comparatively downplayed variability. In terms of trend analysis or forecast, the scientific output and common knowledge for global warming are much more robust than for changes in temperature variability. Quantification of temperature variability adds another dimension of temporal scale, requiring immense labor and presenting great uncertainty. Regardless, this endeavor is necessary since changes in ambient temperature variabilities could also contribute to current and future human health burden besides changes in mean quantities. Here, we review the current literature on trends of surface air temperature variability defined at a range of timescales, aiming to tease out the welter of evidence and thus improving the scientific recognition of changes in air temperature variability in the context of climate change. The findings of reviewed studies from numerous regions differ substantially over various temporal scales. In general, the ambient temperature variability on short time scales (e.g., diurnal or inter-day) shows a downward trend, while it is increasing on longer time scales (e.g., inter-annual). We then move beyond the review and deliver an extended discussion of potential implications for future research related to ambient temperature variability. We highlight the need to consider the methodological choices, especially timescales of interest, in the trend analysis as well as health impact studies. Continued research focusing on temperature variability at multiple timescales, with concerted efforts from scientists of all relevant stripes, is meaningful in synthesizing knowledge and reducing uncertainties surrounding air temperature variability.

Detecting causality from time series in a machine learning framework.

Detecting causality from observational data is a challenging problem. Here, we propose a machine learning based causality approach, Reservoir Computing Causality (RCC), in order to systematically identify causal relationships between variables. We demonstrate that RCC is able to identify the causal direction, coupling delay, and causal chain relations from time series. Compared to a well-known phase space reconstruction based causality method, Extended Convergent Cross Mapping, RCC does not require the estimation of the embedding dimension and delay time. Moreover, RCC has three additional advantages: (i) robustness to noisy time series; (ii) computational efficiency; and (iii) seamless causal inference from high-dimensional data. We also illustrate the power of RCC in identifying remote causal interactions of high-dimensional systems and demonstrate its usability on a real-world example using atmospheric circulation data. Our results suggest that RCC can accurately detect causal relationships in complex systems.

Evaluation of ENSO simulations in CMIP5 models: A new perspective based on percolation phase transition in complex networks.

In this study, the performance of CMIP5 models in simulating the El Niño-Southern Oscillation (ENSO) is evaluated by using a new metric based on percolation theory. The surface air temperatures (SATs) over the tropical Pacific Ocean are constructed as a SAT network, and the nodes within the network are linked if they are highly connected (e.g., high correlations). It has been confirmed from reanalysis datasets that the SAT network undergoes an abrupt percolation phase transition when the influences of the sea surface temperature anomalies (SSTAs) below are strong enough. However, from simulations of the CMIP5 models, most models are found incapable of capturing the observed phase transition at a proper critical point Pc. For the 15 considered models, four even miss the phase transition, indicating that the simulated SAT network is too stable to be significantly changed by the SSTA below. Only four models can be considered cautiously with some skills in simulating the observed phase transition of the SAT network. By comparing the simulated SSTA patterns with the node vulnerabilities, which is the chance of each node being isolated during a ENSO event, we find that the improperly simulated sea-air interactions are responsible for the missing of the observed percolation phase transition. Accordingly, a careful study of the sea-air couplers, as well as the atmospheric components of the CMIP5 models is suggested. Since the percolation phase transition of the SAT network is a useful phenomenon to indicate whether the ENSO impacts can be transferred remotely, it deserves more attention for future model development.

Quantifying distinct associations on different temporal scales: comparison of DCCA and Pearson methods.

Cross-correlation between pairs of variables takes multi-time scale characteristic, and it can be totally different on different time scales (changing from positive correlation to negative one), e.g., the associations between mean air temperature and relative humidity over regions to the east of Taihang mountain in China. Therefore, how to correctly unveil these correlations on different time scales is really of great importance since we actually do not know if the correlation varies with scales in advance. Here, we compare two methods, i.e. Detrended Cross-Correlation Analysis (DCCA for short) and Pearson correlation, in quantifying scale-dependent correlations directly to raw observed records and artificially generated sequences with known cross-correlation features. Studies show that 1) DCCA related methods can indeed quantify scale-dependent correlations, but not Pearson method; 2) the correlation features from DCCA related methods are robust to contaminated noises, however, the results from Pearson method are sensitive to noise; 3) the scale-dependent correlation results from DCCA related methods are robust to the amplitude ratio between slow and fast components, while Pearson method may be sensitive to the amplitude ratio. All these features indicate that DCCA related methods take some advantages in correctly quantifying scale-dependent correlations, which results from different physical processes.

Percolation Phase Transition of Surface Air Temperature Networks under Attacks of El Niño/La Niña.

In this study, sea surface air temperature over the Pacific is constructed as a network, and the influences of sea surface temperature anomaly in the tropical central eastern Pacific (El Niño/La Niña) are regarded as a kind of natural attack on the network. The results show that El Niño/La Niña leads an abrupt percolation phase transition on the climate networks from stable to unstable or metastable phase state, corresponding to the fact that the climate condition changes from normal to abnormal significantly during El Niño/La Niña. By simulating three different forms of attacks on an idealized network, including Most connected Attack (MA), Localized Attack (LA) and Random Attack (RA), we found that both MA and LA lead to stepwise phase transitions, while RA leads to a second-order phase transition. It is found that most attacks due to El Niño/La Niña are close to the combination of MA and LA, and a percolation critical threshold Pc can be estimated to determine whether the percolation phase transition happens. Therefore, the findings in this study may renew our understandings of the influence of El Niño/La Niña on climate, and further help us in better predicting the subsequent events triggered by El Niño/La Niña.

"Intrinsic" correlations and their temporal evolutions between winter-time PNA/EPW and winter drought in the west United States.

In this study, relations between winter-time Pacific-Northern America pattern (PNA)/East Pacific wave-train (EPW) and winter-time drought in the west United States over the period of 1951-2010 are analyzed. Considering traditional Pearson's Correlation Coefficient can be influenced by non-stationarity and nonlinearity, a recently proposed method, Detrended Partial-Cross-Correlation Analysis (DPCCA) is applied. With DPCCA, we analyzed the "intrinsic" correlations between PNA/EPW and the winter drought with possible effects of ENSO and PDO removed. We found, i) significant negative correlations between PNA/EPW and drought on time scales of 5-6 years after removing the effects of ENSO, ii) and significant negative correlations between PNA/EPW and drought on time scales of 15-25 years after removing the effects of PDO. By further studying the temporal evolutions of the "intrinsic" correlations, we found on time scales of 5-6 years, the "intrinsic" correlations between PNA/EPW and drought can vary severely with time, but for most time, the correlations are negative. While on interdecadal (15-25 years) time scales, after the effects of PDO removed, unlike the relations between PNA and drought, the "intrinsic" correlations between EPW and drought takes nearly homogeneous-sign over the whole period, indicating a better model can be designed by using EPW.

Beyond Benford's Law: Distinguishing Noise from Chaos.

Determinism and randomness are two inherent aspects of all physical processes. Time series from chaotic systems share several features identical with those generated from stochastic processes, which makes them almost undistinguishable. In this paper, a new method based on Benford's law is designed in order to distinguish noise from chaos by only information from the first digit of considered series. By applying this method to discrete data, we confirm that chaotic data indeed can be distinguished from noise data, quantitatively and clearly.

Detrended partial-cross-correlation analysis: a new method for analyzing correlations in complex system.

In this paper, a new method, detrended partial-cross-correlation analysis (DPCCA), is proposed. Based on detrended cross-correlation analysis (DCCA), this method is improved by including partial-correlation technique, which can be applied to quantify the relations of two non-stationary signals (with influences of other signals removed) on different time scales. We illustrate the advantages of this method by performing two numerical tests. Test I shows the advantages of DPCCA in handling non-stationary signals, while Test II reveals the "intrinsic" relations between two considered time series with potential influences of other unconsidered signals removed. To further show the utility of DPCCA in natural complex systems, we provide new evidence on the winter-time Pacific Decadal Oscillation (PDO) and the winter-time Nino3 Sea Surface Temperature Anomaly (Nino3-SSTA) affecting the Summer Rainfall over the middle-lower reaches of the Yangtze River (SRYR). By applying DPCCA, better significant correlations between SRYR and Nino3-SSTA on time scales of 6 ~ 8 years are found over the period 1951 ~ 2012, while significant correlations between SRYR and PDO on time scales of 35 years arise. With these physically explainable results, we have confidence that DPCCA is an useful method in addressing complex systems.

Extracting climate memory using Fractional Integrated Statistical Model: a new perspective on climate prediction.

Long term memory (LTM) in climate variability is studied by means of fractional integral techniques. By using a recently developed model, Fractional Integral Statistical Model (FISM), we in this report proposed a new method, with which one can estimate the long-lasting influences of historical climate states on the present time quantitatively, and further extract the influence as climate memory signals. To show the usability of this method, two examples, the Northern Hemisphere monthly Temperature Anomalies (NHTA) and the Pacific Decadal Oscillation index (PDO), are analyzed in this study. We find the climate memory signals indeed can be extracted and the whole variations can be further decomposed into two parts: the cumulative climate memory (CCM) and the weather-scale excitation (WSE). The stronger LTM is, the larger proportion the climate memory signals will account for in the whole variations. With the climate memory signals extracted, one can at least determine on what basis the considered time series will continue to change. Therefore, this report provides a new perspective on climate prediction.

Permutation entropy and statistical complexity quantifier of nonstationarity effect in the vertical velocity records.

How the nonstationarity in the atmosphere turbulent vertical velocity series affects its organization degree of multiscale structures is quantified by permutation entropy (PE) and complexity-entropy causality plane (CECP), and marked PE and CECP differences are detected between the nonstationary and stationary series. We find that the value of PE is lower in the nonstationary vertical velocity series than the stationary counterparts. Both types of series locate near the region of the higher complexity value in the CECP as chaotic systems, but the PE is smaller and the complexity degree is larger in the nonstationary series than the stationary with smaller time delays. Due to the close relationship between PE and the multiscale Shannon entropy, we show that the PE and CECP can be also taken as an indicator to quantify the different organization degrees of the multiscale structures existing between the stationary and nonstationary surface vertical velocity records.