Plane wave approximation of homogeneous Helmholtz solutions

In this paper, we study the approximation of solutions of the homogeneous Helmholtz equation Δu + ω 2 u = 0 by linear combinations of plane waves with different directions. We combine approximation estimates for homogeneous Helmholtz solutions by generalized harmonic polynomials, obtained from Vekua’s theory, with estimates for the approximation of generalized harmonic polynomials by plane waves. The latter is the focus of this paper. We establish best approximation error estimates in Sobolev norms, which are explicit in terms of the degree of the generalized polynomial to be approximated, the domain size, and the number of plane waves used in the approximations.

Plane wave approximation in linear elasticity

We consider the approximation of solutions of the time-harmonic linear elastic wave equation by linear combinations of plane waves. We prove algebraic orders of convergence both with respect to the dimension of the approximating space and to the diameter of the domain. The error is measured in Sobolev norms and the constants in the estimates explicitly depend on the problem wavenumber. The obtained estimates can be used in the h- and p-convergence analysis of wave-based finite element schemes.

Case-to-case variability of predictability of deep convection in a mesoscale model

Successful quantitative precipitation forecasts under convectively unstable conditions depend on the ability of the model to capture the location, timing and intensity of convection. Ensemble forecasts of two mesoscale convective outbreaks over the UK are examined with a view to understanding the nature and extent of their predictability. In addition to a control forecast, twelve ensemble members are run for each case with the same boundary conditions but with perturbations added to the boundary layer. The intention is to introduce perturbations of appropriate magnitude and scale so that the large-scale behaviour of the simulations is not changed. In one case, convection is in statistical equilibrium with the large-scale flow. This places a constraint on the total precipitation, but the location and intensity of individual storms varied. In contrast, the other case was characterised by a large-scale capping inversion. As a result, the location of individual storms was fixed, but their intensities and the total precipitation varied strongly. The ensemble shows case-to-case variability in the nature of predictability of convection in a mesoscale model, and provides additional useful information for quantitative precipitation forecasting.

Inter-hemispheric mesospheric coupling in a comprehensive middle atmosphere model

Observations of noctilucent clouds have revealed a surprising coupling between the winter stratosphere and the summer polar mesopause region. In spite of the great distance involved, this inter-hemispheric link has been suggested to be the principal reason for both the year-to-year variability and the hemispheric differences in the frequency of occurrence of these high-altitude clouds. In this study, we investigate the dynamical influence of the winter stratosphere on the summer mesosphere using simulations from the vertically extended version of the Canadian Middle Atmosphere Model (CMAM). We find that for both Northern and Southern Hemispheres, variability in the summer polar mesopause region from one year to another can be traced back to the planetary-wave flux entering the winter stratosphere. The teleconnection pattern is the same for both positive and negative wave-flux anomalies. Using a composite analysis to isolate the events, it is argued that the mechanism for interhemispheric coupling is a feedback between summer mesosphere gravity-wave drag (GWD) and zonal wind, which is induced by an anomaly in mesospheric cross-equatorial flow, the latter arising from the anomaly in winter hemisphere GWD induced by the anomaly in stratospheric conditions.

Vertical propagation of information in a middle atmosphere data assimilation system by gravity-wave drag feedbacks

The mesospheric response to the 2002 Antarctic Stratospheric Sudden Warming (SSW) is analysed using the Canadian Middle Atmosphere Model Data Assimilation System (CMAM-DAS), where it represents a vertical propagation of information from the observations into the data-free mesosphere. The CMAM-DAS simulates a cooling in the lowest part of the mesosphere which is accomplished by resolved motions, but which is extended to the mid- to upper mesosphere by the response of the model's non-orographic gravity-wave drag parameterization to the change in zonal winds. The basic mechanism is that elucidated by Holton consisting of a net eastward wave-drag anomaly in the mesosphere during the SSW, although in this case there is a net upwelling in the polar mesosphere. Since the zonal-mean mesospheric response is shown to be predictable, this demonstrates that variations in the mesospheric state can be slaved to the lower atmosphere through gravity-wave drag.

The role of increasing temperature variability in European summer heatwaves

Instrumental observations1, 2 and reconstructions3, 4 of global and hemispheric temperature evolution reveal a pronounced warming during the past 150 years. One expression of this warming is the observed increase in the occurrence of heatwaves5, 6. Conceptually this increase is understood as a shift of the statistical distribution towards warmer temperatures, while changes in the width of the distribution are often considered small7. Here we show that this framework fails to explain the record-breaking central European summer temperatures in 2003, although it is consistent with observations from previous years. We find that an event like that of summer 2003 is statistically extremely unlikely, even when the observed warming is taken into account. We propose that a regime with an increased variability of temperatures (in addition to increases in mean temperature) may be able to account for summer 2003. To test this proposal, we simulate possible future European climate with a regional climate model in a scenario with increased atmospheric greenhouse-gas concentrations, and find that temperature variability increases by up to 100%, with maximum changes in central and eastern Europe.

Climate variability-observations, reconstructions, and model simulations for the Atlantic-European and Alpine region from 1500-2100 AD

A detailed analysis is undertaken of the Atlantic-European climate using data from 500-year-long proxy-based climate reconstructions, a long climate simulation with perpetual 1990 forcing, as well as two global and one regional climate change scenarios. The observed and simulated interannual variability and teleconnectivity are compared and interpreted in order to improve the understanding of natural climate variability on interannual to decadal time scales for the late Holocene. The focus is set on the Atlantic-European and Alpine regions during the winter and summer seasons, using temperature, precipitation, and 500 hPa geopotential height fields. The climate reconstruction shows pronounced interdecadal variations that appear to “lock” the atmospheric circulation in quasi-steady long-term patterns over multi-decadal periods controlling at least part of the temperature and precipitation variability. Different circulation patterns are persistent over several decades for the period 1500 to 1900. The 500-year-long simulation with perpetual 1990 forcing shows some substantial differences, with a more unsteady teleconnectivity behaviour. Two global scenario simulations indicate a transition towards more stable teleconnectivity for the next 100 years. Time series of reconstructed and simulated temperature and precipitation over the Alpine region show comparatively small changes in interannual variability within the time frame considered, with the exception of the summer season, where a substantial increase in interannual variability is simulated by regional climate models.