Introductory remarks

The very first numerical models which were developed more than 20 years ago were drastic simplifications of the real atmosphere and they were mostly restricted to describe adiabatic processes. For prediction of a day or two of the mid tropospheric flow these models often gave reasonable results but the result deteriorated quickly when the prediction was extended further in time. The prediction of the surface flow was unsatisfactory even for short predictions. It was evident that both the energy generating processes as well as the dissipative processes have to be included in numerical models in order to predict the weather patterns in the lower part of the atmosphere and to predict the atmosphere in general beyond a day or two. Present-day computers make it possible to attack the weather forecasting problem in a more comprehensive and complete way and substantial efforts have been made during the last decade in particular to incorporate the non-adiabatic processes in numerical prediction models. The physics of radiational transfer, condensation of moisture, turbulent transfer of heat, momentum and moisture and the dissipation of kinetic energy are the most important processes associated with the formation of energy sources and sinks in the atmosphere and these have to be incorporated in numerical prediction models extended over more than a few days. The mechanisms of these processes are mainly related to small scale disturbances in space and time or even molecular processes. It is therefore one of the basic characteristics of numerical models that these small scale disturbances cannot be included in an explicit way. The reason for this is the discretization of the model's atmosphere by a finite difference grid or the use of a Galerkin or spectral function representation. The second reason why we cannot explicitly introduce these processes into a numerical model is due to the fact that some physical processes necessary to describe them (such as the local buoyance) are a priori eliminated by the constraints of hydrostatic adjustment. Even if this physical constraint can be relaxed by making the models non-hydrostatic the scale problem is virtually impossible to solve and for the foreseeable future we have to try to incorporate the ensemble or gross effect of these physical processes on the large scale synoptic flow. The formulation of the ensemble effect in terms of grid-scale variables (the parameters of the large-scale flow) is called 'parameterization'. For short range prediction of the synoptic flow at middle and high latitudes, very simple parameterization has proven to be rather successful.

Problems in four-dimensional data assimilation

With the introduction of new observing systems based on asynoptic observations, the analysis problem has changed in character. In the near future we may expect that a considerable part of meteorological observations will be unevenly distributed in four dimensions, i.e. three dimensions in space and one in time. The term analysis, or objective analysis in meteorology, means the process of interpolating observed meteorological observations from unevenly distributed locations to a network of regularly spaced grid points. Necessitated by the requirement of numerical weather prediction models to solve the governing finite difference equations on such a grid lattice, the objective analysis is a three-dimensional (or mostly two-dimensional) interpolation technique. As a consequence of the structure of the conventional synoptic network with separated data-sparse and data-dense areas, four-dimensional analysis has in fact been intensively used for many years. Weather services have thus based their analysis not only on synoptic data at the time of the analysis and climatology, but also on the fields predicted from the previous observation hour and valid at the time of the analysis. The inclusion of the time dimension in objective analysis will be called four-dimensional data assimilation. From one point of view it seems possible to apply the conventional technique on the new data sources by simply reducing the time interval in the analysis-forecasting cycle. This could in fact be justified also for the conventional observations. We have a fairly good coverage of surface observations 8 times a day and several upper air stations are making radiosonde and radiowind observations 4 times a day. If we have a 3-hour step in the analysis-forecasting cycle instead of 12 hours, which is applied most often, we may without any difficulties treat all observations as synoptic. No observation would thus be more than 90 minutes off time and the observations even during strong transient motion would fall within a horizontal mesh of 500 km * 500 km.

A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

The impedance boundary value problem for the Helmholtz equation in a half-plane

We prove unique existence of solution for the impedance (or third) boundary value problem for the Helmholtz equation in a half-plane with arbitrary L∞ boundary data. This problem is of interest as a model of outdoor sound propagation over inhomogeneous flat terrain and as a model of rough surface scattering. To formulate the problem and prove uniqueness of solution we introduce a novel radiation condition, a generalization of that used in plane wave scattering by one-dimensional diffraction gratings. To prove existence of solution and a limiting absorption principle we first reformulate the problem as an equivalent second kind boundary integral equation to which we apply a form of Fredholm alternative, utilizing recent results on the solvability of integral equations on the real line in [5].

Scattering by rough surfaces: the Dirichlet problem for the Helmholtz equation in a non-locally perturbed half-plane

We consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane, this problem arising in electromagnetic scattering by one-dimensional rough, perfectly conducting surfaces. We propose a new boundary integral equation formulation for this problem, utilizing the Green's function for an impedance half-plane in place of the standard fundamental solution. We show, at least for surfaces not differing too much from the flat boundary, that the integral equation is uniquely solvable in the space of bounded and continuous functions, and hence that, for a variety of incident fields including an incident plane wave, the boundary value problem for the scattered field has a unique solution satisfying the limiting absorption principle. Finally, a result of continuous dependence of the solution on the boundary shape is obtained.

The 20 February 2010 Madeira flash-floods: synoptic analysis and extreme rainfall assessment

This study aims to characterise the rainfall exceptionality and the meteorological context of the 20 February 2010 flash-floods in Madeira (Portugal). Daily and hourly precipitation records from the available rain-gauge station networks are evaluated in order to reconstitute the temporal evolution of the rainstorm, as its geographic incidence, contributing to understand the flash-flood dynamics and the type and spatial distribution of the associated impacts. The exceptionality of the rainstorm is further confirmed by the return period associated with the daily precipitation registered at the two long-term record stations, with 146.9 mm observed in the city of Funchal and 333.8 mm on the mountain top, corresponding to an estimated return period of approximately 290 yr and 90 yr, respectively. Furthermore, the synoptic associated situation responsible for the flash-floods is analysed using different sources of information, e.g., weather charts, reanalysis data, Meteosat images and radiosounding data, with the focus on two main issues: (1) the dynamical conditions that promoted such anomalous humidity availability over the Madeira region on 20 February 2010 and (2) the uplift mechanism that induced deep convection activity.

Synoptic-scale controls of persistent low temperature and icy weather over southern China in January 2008

In January 2008, central and southern China experienced persistent low temperatures, freezing rain, and snow. The large-scale conditions associated with the occurrence and development of these snowstorms are examined in order to identify the key synoptic controls leading to this event. Three main factors are identified: 1) the persistent blocking high over Siberia, which remained quasi-stationary around 65°E for 3 weeks, led to advection of dry and cold Siberian air down to central and southern China; 2) a strong persistent southwesterly flow associated with the western Pacific subtropical high led to enhanced moisture advection from the Bay of Bengal into central and southern China; and 3) the deep inversion layer in the lower troposphere associated with the extended snow cover over most of central and southern China. The combination of these three factors is likely responsible for the unusual severity of the event, and hence a long return period

The European storm Kyrill in January 2007: synoptic evolution, meteorological impacts and some considerations with respect to climate change

The synoptic evolution and some meteorological impacts of the European winter storm Kyrill that swept across Western, Central, and Eastern Europe between 17 and 19 January 2007 are investigated. The intensity and large storm damage associated with Kyrill is explained based on synoptic and mesoscale environmental storm features, as well as on comparisons to previous storms. Kyrill appeared on weather maps over the US state of Arkansas about four days before it hit Europe. It underwent an explosive intensification over the Western North Atlantic Ocean while crossing a very intense zonal polar jet stream. A superposition of several favourable meteorological conditions west of the British Isles caused a further deepening of the storm when it started to affect Western Europe. Evidence is provided that a favourable alignment of three polar jet streaks and a dry air intrusion over the occlusion and cold fronts were causal factors in maintaining Kyrill's low pressure very far into Eastern Europe. Kyrill, like many other strong European winter storms, was embedded in a pre-existing, anomalously wide, north-south mean sea-level pressure (MSLP) gradient field. In addition to the range of gusts that might be expected from the synoptic-scale pressure field, mesoscale features associated with convective overturning at the cold front are suggested as the likely causes for the extremely damaging peak gusts observed at many lowland stations during the passage of Kyrill's cold front. Compared to other storms, Kyrill was by far not the most intense system in terms of core pressure and circulation anomaly. However, the system moved into a pre-existing strong MSLP gradient located over Central Europe which extended into Eastern Europe. This fact is considered determinant for the anomalously large area affected by Kyrill. Additionally, considerations of windiness in climate change simulations using two state-of-the-art regional climate models driven by ECHAM5 indicate that not only Central, but also Eastern Central Europe may be affected by higher surface wind speeds at the end of the 21st century. These changes are partially associated with the increased pressure gradient over Europe which is identified in the ECHAM5 simulations. Thus, with respect to the area affected, as well as to the synoptic and mesoscale storm features, it is proposed that Kyrill may serve as an interesting study case to assess future storm impacts.

Analysis of frequency and intensity of European winter storm events from a multi-model perspective, at synoptic and regional scales

This study focuses on the analysis of winter (October-November-December-January-February-March; ONDJFM) storm events and their changes due to increased anthropogenic greenhouse gas concentrations over Europe. In order to assess uncertainties that are due to model formulation, 4 regional climate models (RCMs) with 5 high resolution experiments, and 4 global general circulation models (GCMs) are considered. Firstly, cyclone systems as synoptic scale processes in winter are investigated, as they are a principal cause of the occurrence of extreme, damage-causing wind speeds. This is achieved by use of an objective cyclone identification and tracking algorithm applied to GCMs. Secondly, changes in extreme near-surface wind speeds are analysed. Based on percentile thresholds, the studied extreme wind speed indices allow a consistent analysis over Europe that takes systematic deviations of the models into account. Relative changes in both intensity and frequency of extreme winds and their related uncertainties are assessed and related to changing patterns of extreme cyclones. A common feature of all investigated GCMs is a reduced track density over central Europe under climate change conditions, if all systems are considered. If only extreme (i.e. the strongest 5%) cyclones are taken into account, an increasing cyclone activity for western parts of central Europe is apparent; however, the climate change signal reveals a reduced spatial coherency when compared to all systems, which exposes partially contrary results. With respect to extreme wind speeds, significant positive changes in intensity and frequency are obtained over at least 3 and 20% of the European domain under study (35–72°N and 15°W–43°E), respectively. Location and extension of the affected areas (up to 60 and 50% of the domain for intensity and frequency, respectively), as well as levels of changes (up to +15 and +200% for intensity and frequency, respectively) are shown to be highly dependent on the driving GCM, whereas differences between RCMs when driven by the same GCM are relatively small.

The central European floods of August 2002: Part 2 - Synoptic causes and considerations with respect to climatic change

In the first part of this paper (Ulbrich et al. 2003), we gave a description of the August 2002 rainfall events and the resultant floods, in particular of the flood wave of the River Elbe. The extreme precipitation sums observed in the first half of the month were primarily associated with two rainfall episodes. The first episode occurred on 6/7 August 2002. The main rainfall area was situated over Lower Austria, the south-western part of the Czech Republic and south-eastern Germany. A severe flash flood was produced in the Lower Austrian Waldviertel (`forest quarter’ ). The second episode on 11± 13 August 2002 most severely affected the Erz Mountains and western parts of the Czech Republic. During this second episode 312mm of rain was recorded between 0600GMT on 12 August and 0600GMT on 13 August at the Zinnwald weather station in the ErzMountains, which is a new 24-hour record for Germany. The flash floods resulting from this rainfall episode and the subsequent Elbe flood produced the most expensive weatherrelated catastrophe in Europe in recent decades. In this part of the paper we discuss the meteorological conditions and physical mechanisms leading to the two main events. Similarities to the conditions that led to the recent summer floods of the River Oder in 1997 and the River Vistula in 2001 will be shown. This will lead us to a consideration of trends in extreme rainfall over Europe which are found in numerical simulations of anthropogenic climate change.

Application of the direct Liapunov method to the problem of symmetric stability in the atmosphere

The problem of symmetric stability is examined within the context of the direct Liapunov method. The sufficient conditions for stability derived by Fjørtoft are shown to imply finite-amplitude, normed stability. This finite-amplitude stability theorem is then used to obtain rigorous upper bounds on the saturation amplitude of disturbances to symmetrically unstable flows.By employing a virial functional, the necessary conditions for instability implied by the stability theorem are shown to be in fact sufficient for instability. The results of Ooyama are improved upon insofar as a tight two-sided (upper and lower) estimate is obtained of the growth rate of (modal or nonmodal) symmetric instabilities.The case of moist adiabatic systems is also considered.

Southern annular mode dynamics in observations and models, Part II: Eddy feedbacks

Many global climate models (GCMs) have trouble simulating Southern Annular Mode (SAM) variability correctly, particularly in the Southern Hemisphere summer season where it tends to be too persistent. In this two part study, a suite of experiments with the Canadian Middle Atmosphere Model (CMAM) is analyzed to improve our understanding of the dynamics of SAM variability and its deficiencies in GCMs. Here, an examination of the eddy-mean flow feedbacks is presented by quantification of the feedback strength as a function of zonal scale and season using a new methodology that accounts for intraseasonal forcing of the SAM. In the observed atmosphere, in the summer season, a strong negative feedback by planetary scale waves, in particular zonal wavenumber 3, is found in a localized region in the south west Pacific. It cancels a large proportion of the positive feedback by synoptic and smaller scale eddies in the zonal mean, resulting in a very weak overall eddy feedback on the SAM. CMAM is deficient in this negative feedback by planetary scale waves, making a substantial contribution to its bias in summertime SAM persistence. Furthermore, this bias is not alleviated by artificially improving the climatological circulation, suggesting that climatological circulation biases are not the cause of the planetary wave feedback deficiency in the model. Analysis of the summertime eddy feedbacks in the CMIP-5 models confirms that this is indeed a common problem among GCMs, suggesting that understanding this planetary wave feedback and the reason for its deficiency in GCMs is key to improving the fidelity of simulated SAM variability in the summer season.

The (il)logical problem of heritage speaker bilingualism and incomplete acquisition

This Forum challenges and problematizes the term incomplete acquisition, which has been widely used to describe the state of competence of heritage speaker (HS) bilinguals for well over a decade (see, e.g., Montrul, 2008). It is suggested and defended that HS competence, while often different from monolingual peers, is in fact not incomplete (given any reasonable definition by the word incomplete), but simply distinct for reasons related to the realities of their environment.