Finite departure from convective quasi-equilibrium: periodic cycle and discharge-recharge mechanism

A simple self–contained theory is proposed for describing life cycles of convective systems as a discharge–recharge process. A closed description is derived for the dynamics of an ensemble of convective plumes based on an energy cycle. The system consists of prognostic equations for the cloud work function and the convective kinetic energy. The system can be closed by intro ducing a functional relationship between the convective kinetic energy and the cloud–base mass flux. The behaviour of this system is considered under a bulk simplification. Previous cloud–resolving mo delling as well as bulk statistical theories for ensemble convective systems suggest that a plausible relationship would be to assume that the convective kinetic energy is linearly proportional to the cloud–base mass flux. As a result, the system reduces to a nonlinear dynamical system with two dependent variables, the cloud–base mass flux and the cloud work function. The fully nonlinear solution of this system always represents a periodic cycle regardless of the initial condition under constant large–scale forcing. Importantly, the inclusion of energy dissipation in this model does not in itself lead the system to an equilibrium.

Computational modes and grid imprinting on five quasi-uniform spherical C-grids

Currently, most operational forecasting models use latitude-longitude grids, whose convergence of meridians towards the poles limits parallel scaling. Quasi-uniform grids might avoid this limitation. Thuburn et al, JCP, 2009 and Ringler et al, JCP, 2010 have developed a method for arbitrarily-structured, orthogonal C-grids (TRiSK), which has many of the desirable properties of the C-grid on latitude-longitude grids but which works on a variety of quasi-uniform grids. Here, five quasi-uniform, orthogonal grids of the sphere are investigated using TRiSK to solve the shallow-water equations. We demonstrate some of the advantages and disadvantages of the hexagonal and triangular icosahedra, a Voronoi-ised cubed sphere, a Voronoi-ised skipped latitude-longitude grid and a grid of kites in comparison to a full latitude-longitude grid. We will show that the hexagonal-icosahedron gives the most accurate results (for least computational cost). All of the grids suffer from spurious computational modes; this is especially true of the kite grid, despite it having exactly twice as many velocity degrees of freedom as height degrees of freedom. However, the computational modes are easiest to control on the hexagonal icosahedron since they consist of vorticity oscillations on the dual grid which can be controlled using a diffusive advection scheme for potential vorticity.

Arctic Oscillation and Antarctic Oscillation in internal atmospheric variability

n this study, we investigated the features of Arctic Oscillation (AO) and Antarctic Oscillation (AAO), that is, the annular modes in the extratropics, in the internal atmospheric variability attained through an ensemble of integrations by an atmospheric general circulation model (AGCM) forced with the global observed SSTs. We focused on the interannual variability of AO/AAO, which is dominated by internal atmospheric variability. In comparison with previous observed results, the AO/AAO in internal atmospheric variability bear some similar characteristics, but exhibit a much clearer spatial structure: significant correlation between the North Pacific and North Atlantic centers of action, much stronger and more significant associated precipitation anomalies, and the meridional displacement of upper-tropospheric westerly jet streams in the Northern/Southern Hemisphere. In addition, we examined the relationship between the North Atlantic Oscillation (NAO)/AO and East Asian winter monsoon (EAWM). It has been shown that in the internal atmospheric variability, the EAWM variation is significantly related to the NAO through upper-tropospheric atmospheric teleconnection patterns.

Decadal to multidecadal variability and the climate change background

Three prominent quasi-global patterns of variability and change are observed using the Met Office's sea surface temperature (SST) analysis and almost independent night marine air temperature analysis. The first is a global warming signal that is very highly correlated with global mean SST. The second is a decadal to multidecadal fluctuation with some geographical similarity to the El Niño–Southern Oscillation (ENSO). It is associated with the Pacific Decadal Oscillation (PDO), and its Pacific-wide manifestation has been termed the Interdecadal Pacific Oscillation (IPO). We present model investigations of the relationship between the IPO and ENSO. The third mode is an interhemispheric variation on multidecadal timescales which, in view of climate model experiments, is likely to be at least partly due to natural variations in the thermohaline circulation. Observed climatic impacts of this mode also appear in model simulations. Smaller-scale, regional atmospheric phenomena also affect climate on decadal to interdecadal timescales. We concentrate on one such mode, the winter North Atlantic Oscillation (NAO). This shows strong decadal to interdecadal variability and a correspondingly strong influence on surface climate variability which is largely additional to the effects of recent regional anthropogenic climate change. The winter NAO is likely influenced by both SST forcing and stratospheric variability. A full understanding of decadal changes in the NAO and European winter climate may require a detailed representation of the stratosphere that is hitherto missing in the major climate models used to study climate change.

The structure of the optimal income tax in the quasi-linear model

Existing numerical characterizations of the optimal income tax have been based on a limited number of model specifications. As a result, they do not reveal which properties are general. We determine the optimal tax in the quasi-linear model under weaker assumptions than have previously been used; in particular, we remove the assumption of a lower bound on the utility of zero consumption and the need to permit negative labor incomes. A Monte Carlo analysis is then conducted in which economies are selected at random and the optimal tax function constructed. The results show that in a significant proportion of economies the marginal tax rate rises at low skills and falls at high. The average tax rate is equally likely to rise or fall with skill at low skill levels, rises in the majority of cases in the centre of the skill range, and falls at high skills. These results are consistent across all the specifications we test. We then extend the analysis to show that these results also hold for Cobb-Douglas utility.

A ‘Boscastle-type’ quasi-stationary convective system over the UK Southwest Peninsula

An investigation is presented of a quasi-stationary convective system (QSCS) which occurred over the UK Southwest Peninsula on 21 July 2010. This system was remarkably similar in its location and structure to one which caused devastating flash flooding in the coastal village of Boscastle, Cornwall on 16 August 2004. However, in the 2010 case rainfall accumulations were around four times smaller and no flooding was recorded. The more extreme nature of the Boscastle case is shown to be related to three factors: (1) higher rain rates, associated with a warmer and moister tropospheric column and deeper convective clouds; (2) a more stationary system, due to slower evolution of the large-scale flow; and (3) distribution of the heaviest precipitation over fewer river catchments. Overall, however, the synoptic setting of the two events was broadly similar, suggesting that such conditions favour the development of QSCSs over the Southwest Peninsula. A numerical simulation of the July 2010 event was performed using a 1.5-km grid length configuration of the Met Office Unified Model. This reveals that convection was repeatedly initiated through lifting of low-level air parcels along a quasi-stationary coastal convergence line. Sensitivity tests are used to show that this convergence line was a sea breeze front which temporarily stalled along the coastline due to the retarding influence of an offshore-directed background wind component. Several deficiencies are noted in the 1.5-km model’s representation of the storm system, including delayed convective initiation; however, significant improvements are observed when the grid length is reduced to 500 m. These result in part from an improved representation of the convergence line, which enhances the associated low-level ascent allowing air parcels to more readily reach their level of free convection. The implications of this finding for forecasting convective precipitation are discussed.

'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function

In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = n¡® for its connection to the Riemann zeta function on the line 1, 'f is bounded with k'f k = ³(®). For the unbounded case, we show that 'f : M2 ! M2 where M2 is the subset of l2 of multiplicative sequences, for many f 2 M2. Consequently, we study the `quasi'-norm sup kak = T a 2M2 k'fak kak for large T, which measures the `size' of 'f on M2. For the f(n) = n¡® case, we show this quasi-norm has a striking resemblance to the conjectured maximal order of j³(® + iT )j for ® > 12 .

One-port de-embedding technique for the quasi-optical characterization of integrated components

We describe a one-port de-embedding technique suitable for the quasi-optical characterization of terahertz integrated components at frequencies beyond the operational range of most vector network analyzers. This technique is also suitable when the manufacturing of precision terminations to sufficiently fine tolerances for the application of a TRL de-embedding technique is not possible. The technique is based on vector reflection measurements of a series of easily realizable test pieces. A theoretical analysis is presented for the precision of the technique when implemented using a quasi-optical null-balanced bridge reflectometer. The analysis takes into account quantization effects in the linear and angular encoders associated with the balancing procedure, as well as source power and detector noise equivalent power. The precision in measuring waveguide characteristic impedance and attenuation using this de-embedding technique is further analyzed after taking into account changes in the power coupled due to axial, rotational, and lateral alignment errors between the device under test and the instruments' test port. The analysis is based on the propagation of errors after assuming imperfect coupling of two fundamental Gaussian beams. The required precision in repositioning the samples at the instruments' test-port is discussed. Quasi-optical measurements using the de-embedding process for a WR-8 adjustable precision short at 125 GHz are presented. The de-embedding methodology may be extended to allow the determination of S-parameters of arbitrary two-port junctions. The measurement technique proposed should prove most useful above 325 GHz where there is a lack of measurement standards.

What is the climate system able to do ‘on its own’?

The climate of the Earth, like planetary climates in general, is broadly controlled by solar irradiation, planetary albedo and emissivity as well as its rotation rate and distribution of land (with its orography) and oceans. However, the majority of climate fluctuations that affect mankind are internal modes of the general circulation of the atmosphere and the oceans. Some of these modes, such as El Nino-Southern Oscillation (ENSO), are quasi-regular and have some longer-term predictive skill; others like the Arctic and Antarctic Oscillation are chaotic and generally unpredictable beyond a few weeks. Studies using general circulation models indicate that internal processes dominate the regional climate and that some like ENSO events have even distinct global signatures. This is one of the reasons why it is so difficult to separate internal climate processes from external ones caused, for example, by changes in greenhouse gases and solar irradiation. However, the accumulation of the warmest seasons during the latest two decades is lending strong support to the forcing of the greenhouse gases. As models are getting more comprehensive, they show a gradually broader range of internal processes including those on longer time scales, challenging the interpretation of the causes of past and present climate events further.

Some numerical experiments on the effect of the variation of static stability in two-layer quasi-geostrophic models

A method to solve a quasi-geostrophic two-layer model including the variation of static stability is presented. The divergent part of the wind is incorporated by means of an iterative procedure. The procedure is rather fast and the time of computation is only 60–70% longer than for the usual two-layer model. The method of solution is justified by the conservation of the difference between the gross static stability and the kinetic energy. To eliminate the side-boundary conditions the experiments have been performed on a zonal channel model. The investigation falls mainly into three parts: The first part (section 5) contains a discussion of the significance of some physically inconsistent approximations. It is shown that physical inconsistencies are rather serious and for these inconsistent models which were studied the total kinetic energy increased faster than the gross static stability. In the next part (section 6) we are studying the effect of a Jacobian difference operator which conserves the total kinetic energy. The use of this operator in two-layer models will give a slight improvement but probably does not have any practical use in short periodic forecasts. It is also shown that the energy-conservative operator will change the wave-speed in an erroneous way if the wave-number or the grid-length is large in the meridional direction. In the final part (section 7) we investigate the behaviour of baroclinic waves for some different initial states and for two energy-consistent models, one with constant and one with variable static stability. According to the linear theory the waves adjust rather rapidly in such a way that the temperature wave will lag behind the pressure wave independent of the initial configuration. Thus, both models give rise to a baroclinic development even if the initial state is quasi-barotropic. The effect of the variation of static stability is very small, qualitative differences in the development are only observed during the first 12 hours. For an amplifying wave we will get a stabilization over the troughs and an instabilization over the ridges.