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  • 1
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: We study the Abraham model for N charges interacting with the Maxwell field. On the scale of the charge diameter, R ϕ, the charges are a distance ɛ-1 R ϕ apart and have a velocity with ɛ a small dimensionless parameter. We follow the motion of the charges over times of the order ɛ-3/2 R ϕ/c and prove that on this time scale their motion is well approximated by the Darwin Lagrangian. The mass is renormalized. The interaction is dominated by the instantaneous Coulomb forces, which are of the order ɛ2. The magnetic fields and first order retardation generate the Darwin correction of the order ɛ3. Radiation damping would be of the order ɛ7/2.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: We consider the system of a point particle, accelerated through a confining potential, and interacting with a scalar wave field. We prove that the periodic solutions of the linearized system (which has an eigenvalue embedded in the continuous spectrum) do not survive perturbation through the nonlinearity, if some “mode” of the wave field does not couple to the particle.
    Type of Medium: Electronic Resource
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  • 3
    Publication Date: 2016-11-24
    Description: A model simulation of the climate during Maunder Minimum (MM) (1645–1715) was performed using the Freie Universität Berlin Climate Middle Atmosphere Model (FUB-CMAM). A multi-year equilibrium integration with prescribed solar insolation, atmospheric composition and sea surface temperatures (SSTs) for MM conditions was compared with a present-day (PD) simulation. We find that during MM the stratosphere was significantly warmer (up to 3 K) than during PD, and dynamically more disturbed in winter. The warming is due to the dominant effect of the lower atmospheric CO2 concentration during MM, which leads to a reduced emission of long-wave radiation, and compensates the cooling due to the reduced solar irradiance. The troposphere was about 1–1.5 K cooler in the annual mean during MM. The global mean surface air temperature decreased by 0.86 K. Northern hemisphere winters were on average characterized by cooler and drier weather over the northern parts of the continents, with an increase in precipitation in the southern parts. These climate anomalies are shown to be related to a shift in the North Atlantic Oscillation (NAO) towards a predominantly low phase during MM. The simulated climate anomalies are in very good agreement with reconstructions from proxy-data. Changes in the dynamical coupling between the troposphere and stratosphere were found in the MM simulation, indicating the importance of the stratosphere for climate change.
    Type: Article , PeerReviewed
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  • 4
    Publication Date: 2019-04-24
    Type: Report , NonPeerReviewed
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  • 5
    ISSN: 1572-9222
    Keywords: Lyapunov exponents ; cocycle ; Oseledets' Multiplicative Ergodic Theorem ; non-smooth mechanical pendulum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider dynamical systems from mechanics for which, due to some non-smooth friction effects, Oseledets' Multiplicative Ergodic Theorem cannot be applied canonically to define Lyapunov exponents. For general non-smooth systems which fit into a natural formal framework, we construct a suitable cocycle which lives on a “good” invariant set of full Lebesgue measure. Afterwards, this construction is applied to investigate a pendulum with dry friction, described through the equation $$\ddot x + x + \operatorname{sgn} \dot x = \gamma \sin (\eta t)$$ . The Lyapunov exponents obtained by our construction show a good agreement with the dynamical behaviour of the system, and since we will prove that these Lyapunov exponents are always non-positive, we conclude that the system does not show “chaotic behaviour.”
    Type of Medium: Electronic Resource
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  • 6
    Publication Date: 2018-03-28
    Description: The impact of 11-year solar cycle variations on stratospheric ozone (O3) is studied with the Freie Universität Berlin Climate Middle Atmosphere Model with interactive chemistry (FUB-CMAM-CHEM). To consider the effect of variations in charged particle precipitation we included an idealized NO x source in the upper mesosphere representing relativistic electron precipitation (REP). Our results suggest that the NO x source by particles and its transport from the mesosphere to the stratosphere in the polar vortex are important for the solar signal in stratospheric O3. We find a positive dipole O3 signal in the annual mean, peaking at 40–45 km at high latitudes and a negative O3 signal in the tropical lower stratosphere. This is similar to observations, but enhanced due to the idealized NO x source and at a lower altitude compared to the observed minimum. Our results imply that this negative O3 signal arises partly via chemical effects.
    Type: Article , PeerReviewed
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  • 7
  • 8
    Publication Date: 2019-02-01
    Description: The impact of changes in incoming solar irradiance on stratospheric ozone abundances should be included in climate simulations to aid in capturing the atmospheric response to solar cycle variability. This study presents the first systematic comparison of the representation of the 11-year solar cycle ozone response (SOR) in chemistry–climate models (CCMs) and in pre-calculated ozone databases specified in climate models that do not include chemistry, with a special focus on comparing the recommended protocols for the Coupled Model Intercomparison Project Phase 5 and Phase 6 (CMIP5 and CMIP6). We analyse the SOR in eight CCMs from the Chemistry–Climate Model Initiative (CCMI-1) and compare these with results from three ozone databases for climate models: the Bodeker Scientific ozone database, the SPARC/Atmospheric Chemistry and Climate (AC&C) ozone database for CMIP5 and the SPARC/CCMI ozone database for CMIP6. The peak amplitude of the annual mean SOR in the tropical upper stratosphere (1–5hPa) decreases by more than a factor of 2, from around 5 to 2%, between the CMIP5 and CMIP6 ozone databases. This substantial decrease can be traced to the CMIP5 ozone database being constructed from a regression model fit to satellite and ozonesonde measurements, while the CMIP6 database is constructed from CCM simulations. The SOR in the CMIP6 ozone database therefore implicitly resembles the SOR in the CCMI-1 models. The structure in latitude of the SOR in the CMIP6 ozone database and CCMI-1 models is considerably smoother than in the CMIP5 database, which shows unrealistic sharp gradients in the SOR across the middle latitudes owing to the paucity of long-term ozone measurements in polar regions. The SORs in the CMIP6 ozone database and the CCMI-1 models show a seasonal dependence with enhanced meridional gradients at mid- to high latitudes in the winter hemisphere. The CMIP5 ozone database does not account for seasonal variations in the SOR, which is unrealistic. Sensitivity experiments with a global atmospheric model without chemistry (ECHAM6.3) are performed to assess the atmospheric impacts of changes in the representation of the SOR and solar spectral irradiance (SSI) forcing between CMIP5 and CMIP6. The larger amplitude of the SOR in the CMIP5 ozone database compared to CMIP6 causes a likely overestimation of the modelled tropical stratospheric temperature response between 11-year solar cycle minimum and maximum by up to 0.55K, or around 80% of the total amplitude. This effect is substantially larger than the change in temperature response due to differences in SSI forcing between CMIP5 and CMIP6. The results emphasize the importance of adequately representing the SOR in global models to capture the impact of the 11-year solar cycle on the atmosphere. Since a number of limitations in the representation of the SOR in the CMIP5 ozone database have been identified, we recommend that CMIP6 models without chemistry use the CMIP6 ozone database and the CMIP6 SSI dataset to better capture the climate impacts of solar variability. The SOR coefficients from the CMIP6 ozone database are published with this paper.
    Type: Article , PeerReviewed
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  • 9
    Publication Date: 2019-05-23
    Description: This paper describes the recommended solar forcing dataset for CMIP6 and highlights changes with respect to CMIP5. The solar forcing is provided for radiative properties, namely total solar irradiance (TSI), solar spectral irradiance (SSI), and the F10.7 index as well as particle forcing, including geomagnetic indices Ap and Kp, and ionization rates to account for effects of solar protons, electrons, and galactic cosmic rays. This is the first time that a recommendation for solar-driven particle forcing has been provided for a CMIP exercise. The solar forcing datasets are provided at daily and monthly resolution separately for the CMIP6 preindustrial control, historical (1850–2014), and future (2015–2300) simulations. For the preindustrial control simulation, both constant and time-varying solar forcing components are provided, with the latter including variability on 11-year and shorter timescales but no long-term changes. For the future, we provide a realistic scenario of what solar behavior could be, as well as an additional extreme Maunder-minimum-like sensitivity scenario. This paper describes the forcing datasets and also provides detailed recommendations as to their implementation in current climate models. For the historical simulations, the TSI and SSI time series are defined as the average of two solar irradiance models that are adapted to CMIP6 needs: an empirical one (NRLTSI2–NRLSSI2) and a semi-empirical one (SATIRE). A new and lower TSI value is recommended: the contemporary solar-cycle average is now 1361.0 W m−2. The slight negative trend in TSI over the three most recent solar cycles in the CMIP6 dataset leads to only a small global radiative forcing of −0.04 W m−2. In the 200–400 nm wavelength range, which is important for ozone photochemistry, the CMIP6 solar forcing dataset shows a larger solar-cycle variability contribution to TSI than in CMIP5 (50 % compared to 35 %). We compare the climatic effects of the CMIP6 solar forcing dataset to its CMIP5 predecessor by using time-slice experiments of two chemistry–climate models and a reference radiative transfer model. The differences in the long-term mean SSI in the CMIP6 dataset, compared to CMIP5, impact on climatological stratospheric conditions (lower shortwave heating rates of −0.35 K day−1 at the stratopause), cooler stratospheric temperatures (−1.5 K in the upper stratosphere), lower ozone abundances in the lower stratosphere (−3 %), and higher ozone abundances (+1.5 % in the upper stratosphere and lower mesosphere). Between the maximum and minimum phases of the 11-year solar cycle, there is an increase in shortwave heating rates (+0.2 K day−1 at the stratopause), temperatures ( ∼  1 K at the stratopause), and ozone (+2.5 % in the upper stratosphere) in the tropical upper stratosphere using the CMIP6 forcing dataset. This solar-cycle response is slightly larger, but not statistically significantly different from that for the CMIP5 forcing dataset. CMIP6 models with a well-resolved shortwave radiation scheme are encouraged to prescribe SSI changes and include solar-induced stratospheric ozone variations, in order to better represent solar climate variability compared to models that only prescribe TSI and/or exclude the solar-ozone response. We show that monthly-mean solar-induced ozone variations are implicitly included in the SPARC/CCMI CMIP6 Ozone Database for historical simulations, which is derived from transient chemistry–climate model simulations and has been developed for climate models that do not calculate ozone interactively. CMIP6 models without chemistry that perform a preindustrial control simulation with time-varying solar forcing will need to use a modified version of the SPARC/CCMI Ozone Database that includes solar variability. CMIP6 models with interactive chemistry are also encouraged to use the particle forcing datasets, which will allow the potential long-term effects of particles to be addressed for the first time. The consideration of particle forcing has been shown to significantly improve the representation of reactive nitrogen and ozone variability in the polar middle atmosphere, eventually resulting in further improvements in the representation of solar climate variability in global models.
    Type: Article , PeerReviewed , info:eu-repo/semantics/article
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  • 10
    Publication Date: 2006-11-01
    Description: Dynamical changes in the Arctic and Antarctic lower stratosphere from autumn to spring were analysed using the NCEP/NCAR, ERA40 and FUB stratospheric analyses for three periods: 1979–1999, 1979–2005, and 1965–2005. We found a weakening of the Arctic vortex in winter and a strengthening in spring between 1979/1980 and 1998/1999, with corresponding changes in the zonal mean circulation. The vortex formed earlier in autumn and broke down later in spring. These changes however were statistically not significant due to the high interannual dynamical variability in northern hemisphere (NH) winter and spring and the relatively short time series. In the Antarctic, the vortex formed earlier in autumn, intensified in late spring, and broke down later. The changes of the Antarctic vortex were at all levels and for both autumn and spring transitions larger and more significant than the changes of the Arctic vortex. These changes of the 1980s and early to mid 1990s were however not representative of a long-term change. The dynamically more active winters in the Arctic and Antarctic since 1998/1999 led to an enhanced weakening of the polar vortex in winter, and to a reduction of the polar vortex intensification in spring. As two of the recent Arctic major warmings occurred rather early in winter the polar vortex could recover in late winter and the delay in spring breakdown further increased. In contrast, the increase in Antarctic vortex persistence did no longer appear when including the recent winters due to the dominant impact of the three recent dynamically active Antarctic winters in 2000, 2002, and 2004. The long-term changes of 1965/1966–2005 were smaller in amplitude and partly opposite to the trends since the 1980s. There is no significant long-term change in the Arctic vortex lifetime or spring persistence, while the Antarctic vortex shows a long-term deepening and shift towards later spring transitions. The changes in the stratospheric dynamical situation could be attributed in both hemispheres to changes in the dynamical forcing from the troposphere. ©2006 Springer-Verlag
    Print ISSN: 0930-7575
    Electronic ISSN: 1432-0894
    Topics: Geosciences , Physics
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