Growth rate and vertical propagation of the initial error in baroclinic models

The present study investigates the growth of error in baroclinic waves. It is found that stable or neutral waves are particularly sensitive to errors in the initial condition. Short stable waves are mainly sensitive to phase errors and the ultra long waves to amplitude errors. Analysis simulation experiments have indicated that the amplitudes of the very long waves become usually too small in the free atmosphere, due to the sparse and very irregular distribution of upper air observations. This also applies to the four-dimensional data assimilation experiments, since the amplitudes of the very long waves are usually underpredicted. The numerical experiments reported here show that if the very long waves have these kinds of amplitude errors in the upper troposphere or lower stratosphere the error is rapidly propagated (within a day or two) to the surface and to the lower troposphere.

Tissue culture propagation alters plant-microbe interactions in tobacco rhizosphere

We have compared properties of roots from different lines (genotypes) of tobacco raised either in tissue culture or grown from seed. The different lines included unmodified plants and plants modified to express reduced activity of the enzyme cinnamoyl-CoA reductase, which has a pivotal role in lignin biosynthesis. The size and structure of the rhizosphere microbial community, characterized by adenosine triphosphate and phospholipid fatty acid analyses, were related to root chemistry (specifically the soluble carbohydrate concentration) and decomposition rate of the roots. The root material from unmodified plants decomposed faster following tissue culture compared with seed culture, and the faster decomposing material had significantly higher soluble carbohydrate concentrations. These observations are linked to the larger microbial biomass and greater diversity of the rhizosphere communities of tissue culture propagated plants.

Tissue culture propagation alters plant-microbe interactions in tobacco rhizosphere

We have compared properties of roots from different lines (genotypes) of tobacco raised either in tissue culture or grown from seed. The different lines included unmodified plants and plants modified to express reduced activity of the enzyme cinnamoyl-CoA reductase, which has a pivotal role in lignin biosynthesis. The size and structure of the rhizosphere microbial community, characterized by adenosine triphosphate and phospholipid fatty acid analyses, were related to root chemistry (specifically the soluble carbohydrate concentration) and decomposition rate of the roots. The root material from unmodified plants decomposed faster following tissue culture compared with seed culture, and the faster decomposing material had significantly higher soluble carbohydrate concentrations. These observations are linked to the larger microbial biomass and greater diversity of the rhizosphere communities of tissue culture propagated plants.

A block coprocessor for user data rate improvements to GPRS coding scheme 4

The general packet radio service (GPRS) has been developed to allow packet data to be transported efficiently over an existing circuit-switched radio network, such as GSM. The main application of GPRS are in transporting Internet protocol (IP) datagrams from web servers (for telemetry or for mobile Internet browsers). Four GPRS baseband coding schemes are defined to offer a trade-off in requested data rates versus propagation channel conditions. However, data rates in the order of > 100 kbits/s are only achievable if the simplest coding scheme is used (CS-4) which offers little error detection and correction (EDC) (requiring excellent SNR) and the receiver hardware is capable of full duplex which is not currently available in the consumer market. A simple EDC scheme to improve the GPRS block error rate (BLER) performance is presented, particularly for CS-4, however gains in other coding schemes are seen. For every GPRS radio block that is corrected by the EDC scheme, the block does not need to be retransmitted releasing bandwidth in the channel and improving the user's application data rate. As GPRS requires intensive processing in the baseband, a viable field programmable gate array (FPGA) solution is presented in this paper.

Multispacecraft observation of magnetic cloud erosion by magnetic reconnection during propagation

During propagation, Magnetic Clouds (MC) interact with their environment and, in particular, may reconnect with the solar wind around it, eroding away part of its initial magnetic flux. Here we quantitatively analyze such an interaction using combined, multipoint observations of the same MC flux rope by STEREO A, B, ACE, WIND and THEMIS on November 19–20, 2007. Observation of azimuthal magnetic flux imbalance inside a MC flux rope has been argued to stem from erosion due to magnetic reconnection at its front boundary. The present study adds to such analysis a large set of signatures expected from this erosion process. (1) Comparison of azimuthal flux imbalance for the same MC at widely separated points precludes the crossing of the MC leg as a source of bias in flux imbalance estimates. (2) The use of different methods, associated errors and parametric analyses show that only an unexpectedly large error in MC axis orientation could explain the azimuthal flux imbalance. (3) Reconnection signatures are observed at the MC front at all spacecraft, consistent with an ongoing erosion process. (4) Signatures in suprathermal electrons suggest that the trailing part of the MC has a different large-scale magnetic topology, as expected. The azimuthal magnetic flux erosion estimated at ACE and STEREO A corresponds respectively to 44% and 49% of the inferred initial azimuthal magnetic flux before MC erosion upon propagation. The corresponding average reconnection rate during transit is estimated to be in the range 0.12–0.22 mV/m, suggesting most of the erosion occurs in the inner parts of the heliosphere. Future studies ought to quantify the influence of such an erosion process on geo-effectiveness.

The counter-propagating Rossby-wave perspective on baroclinic instability. I: Mathematical basis

It is shown that Bretherton's view of baroclinic instability as the interaction of two counter-propagating Rossby waves (CRWs) can be extended to a general zonal flow and to a general dynamical system based on material conservation of potential vorticity (PV). The two CRWs have zero tilt with both altitude and latitude and are constructed from a pair of growing and decaying normal modes. One CRW has generally large amplitude in regions of positive meridional PV gradient and propagates westwards relative to the flow in such regions. Conversely, the other CRW has large amplitude in regions of negative PV gradient and propagates eastward relative to the zonal flow there. Two methods of construction are described. In the first, more heuristic, method a ‘home-base’ is chosen for each CRW and the other CRW is defined to have zero PV there. Consideration of the PV equation at the two home-bases gives ‘CRW equations’ quantifying the evolution of the amplitudes and phases of both CRWs. They involve only three coefficients describing the mutual interaction of the waves and their self-propagation speeds. These coefficients relate to PV anomalies formed by meridional fluid displacements and the wind induced by these anomalies at the home-bases. In the second method, the CRWs are defined by orthogonality constraints with respect to wave activity and energy growth, avoiding the subjective choice of home-bases. Using these constraints, the same form of CRW equations are obtained from global integrals of the PV equation, but the three coefficients are global integrals that are not so readily described by ‘PV-thinking’ arguments. Each CRW could not continue to exist alone, but together they can describe the time development of any flow whose initial conditions can be described by the pair of growing and decaying normal modes, including the possibility of a super-modal growth rate for a short period. A phase-locking configuration (and normal-mode growth) is possible only if the PV gradient takes opposite signs and the mean zonal wind and the PV gradient are positively correlated in the two distinct regions where the wave activity of each CRW is concentrated. These are easily interpreted local versions of the integral conditions for instability given by Charney and Stern and by Fjørtoft.

The counter-propagating Rossby-wave perspective on baroclinic instability. II: Application to the Charney model

The constant-density Charney model describes the simplest unstable basic state with a planetary-vorticity gradient, which is uniform and positive, and baroclinicity that is manifest as a negative contribution to the potential-vorticity (PV) gradient at the ground and positive vertical wind shear. Together, these ingredients satisfy the necessary conditions for baroclinic instability. In Part I it was shown how baroclinic growth on a general zonal basic state can be viewed as the interaction of pairs of ‘counter-propagating Rossby waves’ (CRWs) that can be constructed from a growing normal mode and its decaying complex conjugate. In this paper the normal-mode solutions for the Charney model are studied from the CRW perspective. Clear parallels can be drawn between the most unstable modes of the Charney model and the Eady model, in which the CRWs can be derived independently of the normal modes. However, the dispersion curves for the two models are very different; the Eady model has a short-wave cut-off, while the Charney model is unstable at short wavelengths. Beyond its maximum growth rate the Charney model has a neutral point at finite wavelength (r=1). Thereafter follows a succession of unstable branches, each with weaker growth than the last, separated by neutral points at integer r—the so-called ‘Green branches’. A separate branch of westward-propagating neutral modes also originates from each neutral point. By approximating the lower CRW as a Rossby edge wave and the upper CRW structure as a single PV peak with a spread proportional to the Rossby scale height, the main features of the ‘Charney branch’ (0propagation mechanism and the CRW interaction. The behaviour of the Charney modes and the first neutral branch, which rely on tropospheric PV gradients, are arguably more applicable to the atmosphere than modes of the Eady model where the positive PV gradient exists only at the tropopause

A tale of two elements: P1ncP1 and RTO

The and RT0 finite element schemes are among the most promising low order elements for use in unstructured mesh marine and lake models. They are both free of spurious elevation modes, have good dispersive properties and have a relatively low computational cost. In this paper, we derive both finite element schemes in the same unified framework and discuss their respective qualities in terms of conservation, consistency, propagation factor and convergence rate. We also highlight the impact that the local variables placement can have on the model solution. The main conclusion that we can draw is that the choice between elements is highly application dependent. We suggest that the element is better suited to purely hydrodynamical applications while the RT0 element might perform better for hydrological applications that require scalar transport calculations.

Linear amplification of marginally neutral baroclinic waves

Baroclinic wave development is investigated for unstable parallel shear flows in the limit of vanishing normal-mode growth rate. This development is described in terms of the propagation and interaction mechanisms of two coherent structures, called counter-propagating Rossby waves (CRWs). It is shown that, in this limit of vanishing normal-mode growth rate, arbitrary initial conditions produce sustained linear amplification of the marginally neutral normal mode (mNM). This linear excitation of the mNM is subsequently interpreted in terms of a resonance phenomenon. Moreover, while the mathematical character of the normal-mode problem changes abruptly as the bifurcation point in the dispersion diagram is encountered and crossed, it is shown that from an initial-value viewpoint, this transition is smooth. Consequently, the resonance interpretation remains relevant (albeit for a finite time) for wavenumbers slightly different from the ones defining cut-off points. The results are further applied to a two-layer version of the classic Eady model in which the upper rigid lid has been replaced by a simple stratosphere.

The influence of bottom topography on the decay of modeled Agulhas rings

The influence of a large meridional submarine ridge on the decay of Agulhas rings is investigated with a 1 and 2-layer setup of the isopycnic primitive-equation ocean model MICOM. In the single-layer case we show that the SSH decay of the ring is primarily governed by bottom friction and secondly by the radiation of Rossby waves. When a topographic ridge is present, the effect of the ridge on SSH decay and loss of tracer from the ring is negligible. However, the barotropic ring cannot pass the ridge due to energy and vorticity constraints. In the case of a two-layer ring the initial SSH decay is governed by a mixed barotropic–baroclinic instability of the ring. Again, radiation of barotropic Rossby waves is present. When the ring passes the topographic ridge, it shows a small but significant stagnation of SSH decay, agreeing with satellite altimetry observations. This is found to be due to a reduction of the growth rate of the m = 2 instability, to conversions of kinetic energy to the upper layer, and to a decrease in Rossby-wave radiation. The energy transfer is related to the fact that coherent structures in the lower layer cannot pass the steep ridge due to energy constraints. Furthermore, the loss of tracer from the ring through filamentation is less than for a ring moving over a flat bottom, related to a decrease in propagation speed of the ring. We conclude that ridges like the Walvis Ridge tend to stabilize a multi-layer ring and reduce its decay.

Evolving graphs: dynamical models, inverse problems and propagation

Applications such as neuroscience, telecommunication, online social networking, transport and retail trading give rise to connectivity patterns that change over time. In this work, we address the resulting need for network models and computational algorithms that deal with dynamic links. We introduce a new class of evolving range-dependent random graphs that gives a tractable framework for modelling and simulation. We develop a spectral algorithm for calibrating a set of edge ranges from a sequence of network snapshots and give a proof of principle illustration on some neuroscience data. We also show how the model can be used computationally and analytically to investigate the scenario where an evolutionary process, such as an epidemic, takes place on an evolving network. This allows us to study the cumulative effect of two distinct types of dynamics.