Dynamical properties and extremes of Northern Hemisphere climate fields over the past 60 years

Abstract

Abstract. Atmospheric dynamics are described by a set of partial differential equations yielding an infinite-dimensional phase space. However, the actual trajectories followed by the system appear to be constrained to a finite-dimensional phase space, i.e. a strange attractor. The dynamical properties of this attractor are difficult to determine due to the complex nature of atmospheric motions. A first step to simplify the problem is to focus on observables which affect -or are linked to phenomena which affect -human welfare and activities, such as sea-level pressure, 2 m temperature, and precipitation frequency. We make use of recent advances in dynamical systems theory to estimate two instantaneous dynamical properties of the above fields for the Northern Hemisphere: local dimension and persistence. We then use these metrics to characterize the seasonality of the different fields and their interplay. We further analyse the large-scale anomaly patterns corresponding to phase-space extremes -namely time steps at which the fields display extremes in their instantaneous dynamical properties. The analysis is based on the NCEP/NCAR reanalysis data, over the period 1948-2013. The results show that (i) despite the high dimensionality of atmospheric dynamics, the Northern Hemisphere sea-level pressure and temperature fields can on average be described by roughly 20 degrees of freedom; (ii) the precipitation field has a higher dimensionality; and (iii) the seasonal forcing modulates the variability of the dynamical indicators and affects the occurrence of phase-space extremes. We further identify a number of robust correlations between the dynamical properties of the different variables.

An overview of the extremal index

“…All such dynamical quantities can be extracted by fits to universal extreme value distributions and are therefore readily available empirically 23 . This versatility is reflected in a large number of applications to geophysical flows, where local dimensions and persistence are associated with typical atmospheric configurations 25,26 , and extreme events 37 or dynamical shifts in turbulent boundary layers 55 can be detected.…”

“…Each time a point is visited, the internal state of the Markov process is updated according to the transition probabilities satisfying Eq. (25). With this thinning protocol set up, we can again examine the evolution of the renormalized waiting time density f p (t).…”

Correlation dimension and phase space contraction via extreme value theory

“…Therefore, our results cannot be used to estimate the dimension of the full atmospheric climate attractor. ii) Previous results [15,39,40] have shown that the estimates obtained for the daily dimensions are robust with respect to the changes in the datasets, resolution of the climate models, and are linearly insensitive to the size of the domain. This gives us confidence on the applicability of the numerical algorithm described in this paper for climate data since it is largely based on those used in [15,39,40].…”

Dynamical Systems Theory Sheds New Light on Compound Climate Extremes in Europe and Eastern North America

“…We also note that the α anomaly means related to wind extremes are higher than those for precipitation. This is not surprising, since precipitation has a noisy and fractal structure, which is reflected in the dynamical systems metrics (Faranda et al, 2017a). α anomaly means calculated for concurrent wet and windy extremes mostly reflect the patterns observed for the univariate extreme cases (Figure 3f).…”

“…They can thus be computed for any state ζ on the underlying attractor -a state in our case being a latitude-longitude map of one or more atmospheric variables at a given time. d and θ −1 have recently been applied to a range of different climate variables over different geographical domains and were found to successfully reflect large-scale features of atmospheric motions (Faranda et al, 2017a(Faranda et al, ,b, 2019a(Faranda et al, , 2020Messori et al, 2017;Rodrigues et al, 2018;Hochman et al, 2019a,b).…”