Method for reconstructing nonlinear modes with adaptive structure from multidimensional data.

We present a detailed description of a new approach for the extraction of principal nonlinear dynamical modes (NDMs) from high-dimensional data. The method of NDMs allows the joint reconstruction of hidden scalar time series underlying the observational variability together with a transformation mapping these time series to the physical space. Special Bayesian prior restrictions on the solution properties provide an efficient recognition of spatial patterns evolving in time and characterized by clearly separated time scales. In particular, we focus on adaptive properties of the NDMs and demonstrate for model examples of different complexities that, depending on the data properties, the obtained NDMs may have either substantially nonlinear or linear structures. It is shown that even linear NDMs give us more information about the internal system dynamics than the traditional empirical orthogonal function decomposition. The performance of the method is demonstrated on two examples. First, this approach is successfully tested on a low-dimensional problem to decode a chaotic signal from nonlinearly entangled time series with noise. Then, it is applied to the analysis of 250-year preindustrial control run of the INMCM4.0 global climate model. There, a set of principal modes of different nonlinearities is found capturing the internal model variability on the time scales from annual to multidecadal.

The representation of ionospheric potential in the global chemistry-climate model SOCOL.

In this paper, we present the first results of the ionospheric potential (IP) calculations with the chemistry-climate model (CCM) SOCOL (Solar Climate Ozone Links). For the study, we exploit a parameterization of the difference in electric potential between Earth's surface and lower boundary of the ionosphere as a function of thunderstorm and electrified cloud properties. The model shows a good enough agreement with the IP obtained by balloon soundings. The simulated UT variation of IP exhibits a maximum at 20 Universal time (UT) and minimum at about 2 UT which agree with the UT cycle of the lightning activity. The obtained results allow understanding of IP variability pattern at diurnal, seasonal and annual timescales. We also compare our results with the IP simulated with the climate model INMCM4 using similar IP parameterization. The comparison shows a good agreement of UT cycles especially before 12 UT. Simulated IP annual cycle reaches its maximum in late spring in both models. However, the comparison also reveals some differences in amplitudes of IP variability on different time scales. The large deviations occur after 12 UT for all seasons except summer where the maximum of both results happens before 12 UT. The UT cycle of IP simulated with CCM SOCOL is in a better agreement with observations after 12 UT in terms of phase with similar timing of maximum values. The calculation of IP using climate models can help to fill up the gaps when the observed IP is not available. The interactive calculation of IP is also a step forward in coupling atmospheric and ionospheric processes.