Echo State Networks: analysis, training and predictive control

The goal of this paper is to investigate the theoretical properties, the training algorithm, and the predictive control applications of Echo State Networks (ESNs), a particular kind of Recurrent Neural Networks. First, a condition guaranteeing incremetal global asymptotic stability is devised. Then, a modified training algorithm allowing for dimensionality reduction of ESNs is presented. Eventually, a model predictive controller is designed to solve the tracking problem, relying on ESNs as the model of the system. Numerical results concerning the predictive control of a nonlinear process for pH neutralization confirm the effectiveness of the proposed algorithms for the identification, dimensionality reduction, and the control design for ESNs.Comment: 6 pages,5 figures, submitted to European Control Conference (ECC

Stringy origin of non-Abelian discrete flavor symmetries

We study the origin of non-Abelian discrete flavor symmetries in superstring theory. We classify all possible non-Abelian discrete flavor symmetries which can appear in heterotic orbifold models. These symmetries include D_4 and Delta(54). We find that the symmetries of the couplings are always larger than the symmetries of the compact space. This is because they are a consequence of the geometry of the orbifold combined with the space group selection rules of the string. We also study possible breaking patterns. Our analysis yields a simple geometric understanding of the realization of non-Abelian flavor symmetries.Comment: 27 pages, 4 figures, v2: matches version published in Nuclear Physics

Impact of different vertical transport representations on simulating process in the tropical tropopause layer (TTL)

The chemical and dynamical processes in the tropical tropopause layer (TTL) control the amount of radiatively active species like water vapour and ozone in the stratosphere, and hence turn out to be crucial for atmospheric trends and climate change. Chemistry transport models and chemistry climate models are suitable tools to understand these processes. But model results are subject to uncertainties arising from the parametrization of model physics. In this thesis the sensitivity of model predictions to the choice of the vertical transport representation will be analysed. Therefore, backtrajectories are calculated in the TTL, based on different diabatic and kinematic transport representations using ERA-Interim and operational ECMWF data. For diabatic transport on potential temperature levels, the vertical velocity is deduced from the ERA-Interim diabatic heat budget. For kinematic transport on pressure levels, the vertical wind is used as vertical velocity. It is found that all terms in the diabatic heat budget are necessary to cause transport from the troposphere to the stratosphere. In particular, clear-sky heating rates alone miss very important processes. Many characteristics of transport in the TTL turn out to depend very sensitively on the choice of the vertical transport representation. Timescales for tropical troposphere-tostratosphere transport vary between one and three months, with respect to the chosen representation. Moreover, for diabatic transport ascent is found throughout the upper TTL, whereas for kinematic transport regions of mean subsidence occur, particularly above the maritime continent. To investigate the sensitivity of simulated trace gas distributions in the TTL to the transport representation, a conceptual approach is presented to predict water vapour and ozone concentrations from backtrajectories, based on instantaneous freeze-drying and photochemical ozone production. It turns out that ozone predictions and vertical dispersion of the trajectories are highly correlated, rendering ozone an interesting tracer for aspects of transport in the TTL where water vapour is not sensitive. Consequently, dispersion and mean upwelling have similar effects on ozone profiles, with slower upwelling and larger dispersion both leading to higher ozone concentrations. Analyses of tropical upwelling based on mean transport characteristics (e.g., mean ascent rates) and model validation have to take into account this ambiguity. Predicted ozone concentrations for kinematic transport are robustly higher than for diabatic transport, due to larger trajectory dispersion caused by the larger inhomogeneity in the kinematic vertical velocity field. During the tropical SCOUT-O3 campaign, kinematic ozone predictions show an extreme high bias compared to in-situ observations. The high sensitivity of many characteristics of transport to the choice of the transport representation, demonstrates the need to better constrain transport in the TTL. Consequently, estimates of exact numbers from models, e.g., for timescales of transport, are not reliable and only a range of values can be given. However, there are robust features of tropical transport, not depending on the transport representation, as for example, a significant impact of monsoon driven horizontal in-mixing from the extratropics on the composition of the TTL. In fact, the annual cycle of ozone above the tropical tropopause is attributed, at least in ‘ECMWF-world’, to in-mixing of ozone-rich extratropical air during summer

CLaMS results used for age of air analysis in the report of assessment of the ESA Earth Explorer candidate mission CAIRT

<p>Results of the Chemical Lagrangian Model of the Stratosphere (CLaMS) used for age of air analysis in the report of assessment of the ESA Earth Explorer candidate mission CAIRT. Days of results: 2011-01-01, 2011-04-01, 2011-07-01, 2011-10-01 and 2019-09-23. Included trace gases: SF6, CFC-11, CFC-12, HCFC-22, N2O and CH4. The results also include the clock tracer BA, which can be converted into the precise mean age of or air of the model environment with the attached python script 'AOA2age_years.py'.</p&gt

3-D tomographic observations of Rossby wave breaking over the Northern Atlantic during the WISE aircraft campaign in 2017

We present measurements of ozone, water vapour and nitric acid in the upper troposphere/lower stratosphere (UTLS) over North Atlantic and Europe. The measurements were acquired with the Gimballed Limb Observer for Radiance Imaging of the Atmosphere (GLORIA) during the Wave Driven Isentropic Exchange (WISE) campaign in October 2017. GLORIA is an airborne limb imager capable of acquiring both 2-D data sets (curtains along the flight path) and, when the carrier aircraft is flying around the observed air mass, spatially highly resolved 3-D tomographic data. We show a case study of a Rossby wave (RW) breaking event observed during two subsequent flights two days apart. RW breaking is known to steepen tracer gradients and facilitate stratosphere-troposphere exchange (STE). Our measurements reveal complex spatial structures in stratospheric tracers (ozone and nitric acid) with multiple vertically stacked filaments. Backward trajectory analysis is used to demonstrate that these features are related to several previous Rossby wave breaking events and that the small-scale structure of the UTLS in the Rossby wave breaking region, which is otherwise very hard to observe, can be understood as stirring and mixing of air masses of tropospheric and stratospheric origin. It is also shown that a strong nitric acid enhancement observed just above the tropopause is likely a result of NOx production by lightning activity. The measurements showed signatures of enhanced mixing between stratospheric and tropospheric air near the polar jet with some transport of water vapour into the stratosphere. Some of the air masses seen in 3-D data were encountered again two days later, stretched to very thin filament (horizontal thickness down to 30&#8201;km at some altitudes) rich in stratospheric tracers. This repeated measurement allowed us to directly observe and analyse the progress of mixing processes in a thin filament over two days. Our results provide direct insight into small-scale dynamics of the UTLS in the Rossby wave breaking region, witch is of great importance to understanding STE and poleward transport in the UTLS.</p

Annual cycle of horizontal in-mixing into the lower tropical stratosphere

Based on the HALOE and SHADOZ observations of ozone (O-3) and on a simple conceptual model of transport and photochemistry, the seasonality of O-3 within the stratospheric part of the tropical tropopause layer (TTL) extending between 360 and 420 K potential temperature is discussed. We show that the seasonality of O-3 diagnosed on pressure (p) surfaces has a significantly larger annual cycle compared with the same kind of analysis on surfaces with constant potential temperature (theta), in particular around p = 80 hPa, where the strongest annual variation in tropical temperature occurs. Thus by using theta instead of p as the vertical coordinate, the (seasonal) adiabatic variability is removed, and consequently, a much smaller seasonal cycle of O-3 remains, which can be understood as a consequence of chemistry, cross-isentropic transport (upwelling), and horizontal, i.e., quasi-isentropic, transport (in-mixing). Furthermore, we show that the observed, theta-related seasonality of O-3, with highest values during boreal summer, cannot be understood only by photolytical O-3 production in slowly rising air masses, which are well isolated from the extratropics. By using the SHADOZ climatology at theta = 360 K and quantifying the photochemical production of O-3 in ascending air above theta = 360 K, we determine the residual variability between the observations (SHADOZ, HALOE) and the calculated O-3 values and, consequently, interpret this residuum as horizontal in-mixing from the extratropical stratosphere. We find that between 380 and 420 K, in-mixing contributes to about 40% of the observed O-3 mixing ratios during boreal summer

Investigating stratospheric circulation and chemistry changes over three decades with trace gas data from aircraft, large balloons, and AirCores

Laube et al. (2020) investigated stratospheric changes between 2009 and 2018 with halogenated trace gas data (CFC-11, CFC-12, H-1211, H-1301, HCFC-22, and SF6) from air samples collected via aircraft and AirCores, and compared the mixing ratios and average stratospheric transit times derived from these observations with those from a global model. We here expand this analysis in three ways: firstly, by adding data from further traces gases such as CFC-115, C2F6, and HCFC-142b to broaden the range of tropospheric trends and stratospheric lifetimes, both of which help to assess the robustness of inferred long-term trends in the stratosphere; secondly, by increasing the temporal span of the observations to nearly three decades using new AirCore observations as well as reanalysed archived air samples collected on board high altitude aircraft and large balloons in the 1990s and 2000s; and thirdly, by investigating the fractional release factors and mean ages of air derived from the aforementioned species as measures of their stratospheric chemistry and the strength of the Brewer-Dobson circulation. In combination with model data from the Chemical Langrangian Model of the Stratosphere (CLaMS) this unique data set allows for an unprecedented evaluation of stratospheric chemistry and dynamics in the mid-latitudes of the Northern Hemisphere

Investigating stratospheric circulation and chemistry changes over three decades with trace gas data from aircraft, large balloons, and AirCores

Laube et al. (2020) investigated stratospheric changes between 2009 and 2018 with halogenated trace gas data (CFC-11, CFC-12, H-1211, H-1301, HCFC-22, and SF6) from air samples collected via aircraft and AirCores, and compared the mixing ratios and average stratospheric transit times derived from these observations with those from a global model. We here expand this analysis in three ways: firstly, by adding data from further traces gases such as CFC-115, C2F6, and HCFC-142b to broaden the range of tropospheric trends and stratospheric lifetimes, both of which help to assess the robustness of inferred long-term trends in the stratosphere; secondly, by increasing the temporal span of the observations to nearly three decades using new AirCore observations as well as reanalysed archived air samples collected on board high altitude aircraft and large balloons in the 1990s and 2000s; and thirdly, by investigating the fractional release factors and mean ages of air derived from the aforementioned species as measures of their stratospheric chemistry and the strength of the Brewer-Dobson circulation. In combination with model data from the Chemical Langrangian Model of the Stratosphere (CLaMS) this unique data set allows for an unprecedented evaluation of stratospheric chemistry and dynamics in the mid-latitudes of the Northern Hemisphere