The paper reviews recent advances in studies of electric discharges in the stratosphere and mesosphere above thunderstorms, and their effects on the atmosphere. The primary focus is on the sprite discharge occurring in the mesosphere, which is the most commonly observed high altitude discharge by imaging cameras from the ground, but effects on the upper atmosphere by electromagnetic radiation from lightning are also considered. During the past few years, co-ordinated observations over Southern Europe have been made of a wide range of parameters related to sprites and their causative thunderstorms. Observations have been complemented by the modelling of processes ranging from the electric discharge to perturbations of trace gas concentrations in the upper atmosphere. Observations point to significant energy deposition by sprites in the neutral atmosphere as observed by infrasound waves detected at up to 1000 km distance, whereas elves and lightning have been shown significantly to affect ionization and heating of the lower ionosphere/mesosphere. Studies of the thunderstorm systems powering high altitude discharges show the important role of intracloud (IC) lightning in sprite generation as seen by the first simultaneous observations of IC activity, sprite activity and broadband, electromagnetic radiation in the VLF range. Simulations of sprite ignition suggest that, under certain conditions, energetic electrons in the runaway regime are generated in streamer discharges. Such electrons may be the source of X-and Gamma-rays observed in lightning, thunderstorms and the so-called Terrestrial Gamma-ray Flashes (TGFs) observed from space over thunderstorm regions. Model estimates of sprite perturbations to the global atmospheric electric circuit, trace gas concentrations and atmospheric dynamics suggest significant local perturbations, and possibly significant meso-scale effects, but negligible global effects.

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The adoption of the Kolmogorov-Sinai (KS) entropy is becoming a popular research tool among physicists, especially when applied to a dynamical system fitting the conditions of validity of the Pesin theorem. The study of time series that are a manifestation of system dynamics whose rules are either unknown or too complex for a mathematical treatment, is still a challenge since the KS entropy is not computable, in general, in that case. Here we present a plan of action based on the joint action of two procedures, both related to the KS entropy, but compatible with computer implementation through fast and efficient programs. The former procedure, called Compression Algorithm Sensitive To Regularity (CASToRe), establishes the amount of order by the numerical evaluation of algorithmic compressibility. The latter, called Complex Analysis of Sequences via Scaling AND Randomness Assessment (CASSANDRA), establishes the complexity degree through the numerical evaluation of the strength of an anomalous effect. This is the departure, of the diffusion process generated by the observed fluctuations, from ordinary Brownian motion. The CASSANDRA algorithm shares with CASToRe a connection with the Kolmogorov complexity. This makes both algorithms especially suitable to study the transition from dynamics to thermodynamics, and 1 the case of non-stationary time series as well. The benefit of the joint action of these two methods is proven by the analysis of artificial sequences with the same main properties as the real time series to which the joint use of these two methods will be applied in future research work.