Distribution of natural trends in long-term correlated records: a scaling approach

Statistical significance of PM2.5 and O3 trends in China under long-term memory effects

Over the past decade, the Chinese government has implemented the "Clean Air Action" measures to enhance the atmospheric environmental quality, primarily focusing on curbing PM2.5 and O3 concentrations. The efficacy of these strategies and the underlying causes (human factors or natural variability) of any observed increases or decreases in PM2.5 and O3 concentrations are of great importance. Examining the hourly PM2.5 and O3 concentration time series from six representative regions in China between 2015 and 2021 revealed an overall downward trend in PM2.5 concentrations. However, the O3 concentration time series indicated upward trends in some regions, except for the Northeast area (NE) and Sichuan Basin (SCB). In the context of conventional significance tests, the assumption is typically that the time series' samples are independent and therefore memoryless. However, in situations where the time series exhibits strong autocorrelation and limited sample size, this assumption can lead to an overestimation of the statistical significance of the linear trend. To account for this, we utilized a long-term memory model that can reproduce the long-term persistence of pollutant records to improve the accuracy of significance tests. By comparing the P-values of real and surrogate data generated by the long-term memory model, we found that only PM2.5 concentrations in the Pearl River Delta (PRD) were slightly insignificant. For the remaining five regions, the P-values of PM2.5 concentrations were smaller than the significant level of 0.05, suggesting that the observed downward trends in PM2.5 concentrations are not due to natural variability, thereby confirming the effectiveness of the government's policies aimed at curbing atmospheric particulate matter in recent years. Our results show that O3 pollution is significantly increasing only in the Beijing-Tianjin-Hebei (BTH) region, beyond natural variability. In contrast, the trends of O3 pollution in many regions of China are markedly impacted by natural and climate variability.

Statistical significance of seasonal warming/cooling trends

The question whether a seasonal climate trend (e.g., the increase of summer temperatures in Antarctica in the last decades) is of anthropogenic or natural origin is of great importance for mitigation and adaption measures alike. The conventional significance analysis assumes that (i) the seasonal climate trends can be quantified by linear regression, (ii) the different seasonal records can be treated as independent records, and (iii) the persistence in each of these seasonal records can be characterized by short-term memory described by an autoregressive process of first order. Here we show that assumption ii is not valid, due to strong intraannual correlations by which different seasons are correlated. We also show that, even in the absence of correlations, for Gaussian white noise, the conventional analysis leads to a strong overestimation of the significance of the seasonal trends, because multiple testing has not been taken into account. In addition, when the data exhibit long-term memory (which is the case in most climate records), assumption iii leads to a further overestimation of the trend significance. Combining Monte Carlo simulations with the Holm-Bonferroni method, we demonstrate how to obtain reliable estimates of the significance of the seasonal climate trends in long-term correlated records. For an illustration, we apply our method to representative temperature records from West Antarctica, which is one of the fastest-warming places on Earth and belongs to the crucial tipping elements in the Earth system.

Detecting anthropogenic footprints in sea level rise

While there is scientific consensus that global and local mean sea level (GMSL and LMSL) has risen since the late nineteenth century, the relative contribution of natural and anthropogenic forcing remains unclear. Here we provide a probabilistic upper range of long-term persistent natural GMSL/LMSL variability (P=0.99), which in turn, determines the minimum/maximum anthropogenic contribution since 1900. To account for different spectral characteristics of various contributing processes, we separate LMSL into two components: a slowly varying volumetric component and a more rapidly changing atmospheric component. We find that the persistence of slow natural volumetric changes is underestimated in records where transient atmospheric processes dominate the spectrum. This leads to a local underestimation of possible natural trends of up to ∼1 mm per year erroneously enhancing the significance of anthropogenic footprints. The GMSL, however, remains unaffected by such biases. On the basis of a model assessment of the separate components, we conclude that it is virtually certain (P=0.99) that at least 45% of the observed increase in GMSL is of anthropogenic origin.

The contribution of anthropogenic forcing to rising sea levels during the industrial era remains uncertain. Here, the authors provide a probabilistic evaluation and show that at least 45% of global mean sea level rise is of anthropogenic origin.

Significance of trends in long-term correlated records

We study the distribution P(x;α,L) of the relative trend x in long-term correlated records of length L that are characterized by a Hurst exponent α between 0.5 and 1.5. The relative trend x is the ratio between the strength of the trend Δ in the record measured by linear regression and the standard deviation σ around the regression line. We consider L between 400 and 2200, which is the typical length scale of monthly local and annual reconstructed global climate records. Extending previous work by Lennartz and Bunde [S. Lennartz and A. Bunde, Phys. Rev. E 84, 021129 (2011)] we show explicitly that x follows the Student's t distribution P∝[1+(x/a)2/l]-(l+1)/2, where the scaling parameter a depends on both L and α, while the effective length l depends, for α below 1.15, only on the record length L. From P we can derive an analytical expression for the trend significance S(x;α,L)=∫(-x)xP(x';α,L)dx' and the border lines of the 95% significance interval. We show that the results are nearly independent of the distribution of the data in the record, holding for Gaussian data as well as for highly skewed non-Gaussian data. For an application, we use our methodology to estimate the significance of central west Antarctic warming.

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.