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Register a new userMapping atmospheric waves and unveiling phase coherent structures in a global surface air temperature reanalysis dataset
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In the analysis of empirical signals, detecting correlations that capture genuine interactions between the elements of a complex system is a challenging task with applications across disciplines. Here we analyze a global data set of surface air temperature (SAT) with daily resolution. Hilbert analysis is used to obtain phase, instantaneous frequency and amplitude information of SAT seasonal cycles in different geographical zones. The analysis of the phase dynamics reveals large regions with coherent seasonality. The analysis of the instantaneous frequencies uncovers clean wave patterns formed by alternating regions of negative and positive correlations. In contrast, the analysis of the amplitude dynamics uncovers wave patterns with additional large-scale structures. These structures are interpreted as due to the fact that the amplitude dynamics is affected by processes that act in long and short time scales, while the dynamics of the instantaneous frequency is mainly governed by fast processes. Therefore, Hilbert analysis allows to disentangle climatic processes and to track planetary atmospheric waves. Our results are relevant for the analysis of complex oscillatory signals because they offer a general strategy for uncovering interactions that act at different time scales.
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Errors in applying regression models and wavelet filters used to analyze geophysical signals are discussed: (1) multidecadal natural oscillations (e.g. the quasi 60-year Atlantic Multidecadal Oscillation (AMO), North Atlantic Oscillation (NAO) and Pacific Decadal Oscillation (PDO)) need to be taken into account for properly quantifying anomalous accelerations in tide gauge records such as in New York City; (2) uncertainties and multicollinearity among climate forcing functions prevent a proper evaluation of the solar contribution to the 20th century global surface temperature warming using overloaded linear regression models during the 1900-2000 period alone; (3) when periodic wavelet filters, which require that a record is pre-processed with a reflection methodology, are improperly applied to decompose non-stationary solar and climatic time series, Gibbs boundary artifacts emerge yielding misleading physical interpretations. By correcting these errors and using optimized regression models that reduce multicollinearity artifacts, I found the following results: (1) the sea level in New York City is not accelerating in an alarming way, and may increase by about 350 mm from 2000 to 2100 instead of the previously projected values varying from 1130 mm to 1550 mm estimated using the methods proposed by Sallenger et al. (2012) and Boon (2012), respectively; (2) the solar activity increase during the 20th century contributed about 50% of the 0.8 K global warming observed during the 20th century instead of only 7-10% (IPCC, 2007; Benestad and Schmidt, 2009; Lean and Rind, 2009). These findings stress the importance of natural oscillations and of the sun to properly interpret climatic changes.
Uncovering meaningful regularities in complex oscillatory signals is a challenging problem with applications across a wide range of disciplines. Here we present a novel approach, based on the Hilbert transform (HT). We show that temporal periodicity can be uncovered by averaging the signal in a moving window of appropriated length, $tau$, before applying the HT. By analyzing the variation of the mean rotation period, $overline{T}$, of the Hilbert phase as a function of $tau$, we discover well-defined plateaus. In many geographical regions the plateau corresponds to the expected one-year solar cycle; however, in regions where SAT dynamics is highly irregular, the plateaus reveal non-trivial periodicities, which can be interpreted in terms of climatic phenomena such as El Ni~no. In these regions, we also find that Fourier analysis is unable to detect the periodicity that emerges when $tau$ increases and gradually washes out SAT variability. The values of $overline{T}$ obtained for different $tau$s are then given to a standard machine learning algorithm. The results demonstrate that these features are informative and constitute a new approach for SAT time series classification. To support these results, we analyse synthetic time series generated with a simple model and confirm that our method extracts information that is fully consistent with our knowledge of the model that generates the data. Remarkably, the variation of $overline{T}$ with $tau$ in the synthetic data is similar to that observed in real SAT data. This suggests that our model contains the basic mechanisms underlying the unveiled periodicities. Our results demonstrate that Hilbert analysis combined with temporal averaging is a powerful new tool for discovering hidden temporal regularity in complex oscillatory signals.
Emission metrics, a crucial tool in setting effective equivalences between greenhouse gases, currently require a subjective, arbitrary choice of time horizon. Here, we propose a novel framework that uses a specific temperature goal to calculate the time horizon that aligns with scenarios satisfying that temperature goal. We analyze the Intergovernmental Panel on Climate Change Special Report on Global Warming of 1.5 C Scenario Database 1 to find that justified time horizons for the 1.5 C and 2 C global warming goals of the Paris Agreement are 22 +/- 1 and 55 +/- 1 years respectively. We then use these time horizons to quantify time-dependent emission metrics. Using methane as an example, we find that emission metrics that align with the 1.5 C and 2 C warming goals respectively (using their associated time horizons) are 80 +/- 1 and 45 +/- 1 for the Global Warming Potential, 62 +/- 1 and 11 +/- 1 for the Global Temperature change Potential, and 89 +/- 1 and 50 +/- 1 for the integrated Global Temperature change Potential. Using the most commonly used time horizon, 100 years, results in underestimating methane emission metrics by 40-70% relative to the values we calculate that align with the 2 C goal.
We explore the possibility to identify areas of intense patch formation from floating items due to systematic convergence of surface velocity fields by means of a visual comparison of Lagrangian Coherent Structures (LCS) and estimates of areas prone to patch formation using the concept of Finite-Time Compressibility (FTC, a generalisation of the notion of time series of divergence). The LCSs are evaluated using the Finite Time Lyapunov Exponent (FTLE) method. The test area is the Gulf of Finland (GoF) in the Baltic Sea. A basin-wide spatial average of backward FTLE is calculated for the GoF for the first time. This measure of the mixing strength displays a clear seasonal pattern. The evaluated backward FTLE features are linked with potential patch formation regions with high FTC levels. It is shown that areas hosting frequent upwelling or downwelling have consistently stronger than average mixing intensity. The combination of both methods, FTC and LCS, has the potential of being a powerful tool to identify the formation of patches of pollution at the sea surface.
Based on data from the Japan Sea and the North Sea the occurrence of rogue waves is analyzed by a scale dependent stochastic approach, which interlinks fluctuations of waves for different spacings. With this approach we are able to determine a stochastic cascade process, which provides information of the general multipoint statistics. Furthermore the evolution of single trajectories in scale, which characterize wave height fluctuations in the surroundings of a chosen location, can be determined. The explicit knowledge of the stochastic process enables to assign entropy values to all wave events. We show that for these entropies the integral fluctuation theorem, a basic law of non-equilibrium thermodynamics, is valid. This implies that positive and negative entropy events must occur. Extreme events like rogue waves are characterized as negative entropy events. The statistics of these entropy fluctuations changes with the wave state, thus for the Japan Sea the statistics of the entropies has a more pronounced tail for negative entropy values, indicating a higher probability of rogue waves.
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