Modelling the effects of gravity waves on stratocumulus clouds observed during VOCALS-UK

During the VOCALS campaign spaceborne satellite observations showed that travelling gravity wave packets, generated by geostrophic adjustment, resulted in perturbations to marine boundary layer (MBL) clouds over the south-east Pacific Ocean (SEP). Often, these perturbations were reversible in that passage of the wave resulted in the clouds becoming brighter (in the wave crest), then darker (in the wave trough) and subsequently recovering their properties after the passage of the wave. However, occasionally the wave packets triggered irreversible changes to the clouds, which transformed from closed mesoscale cellular convection to open form. In this paper we use large eddy simulation (LES) to examine the physical mechanisms that cause this transition. Specifically, we examine whether the clearing of the cloud is due to (i) the wave causing additional cloud-top entrainment of warm, dry air or (ii) whether the additional condensation of liquid water onto the existing drops and the subsequent formation of drizzle are the important mechanisms. We find that, although the wave does cause additional drizzle formation, this is not the reason for the persistent clearing of the cloud; rather it is the additional entrainment of warm, dry air into the cloud followed by a reduction in longwave cooling, although this only has a significant effect when the cloud is starting to decouple from the boundary layer. The result in this case is a change from a stratocumulus to a more patchy cloud regime. For the simulations presented here, cloud condensation nuclei (CCN) scavenging did not play an important role in the clearing of the cloud. The results have implications for understanding transitions between the different cellular regimes in marine boundary layer (MBL) clouds.

The Madden-Julian Oscillation and the diurnal cycle over the Maritime Continent: scale interactions and modelling

The Maritime Continent archipelago, situated on the equator at 95-165E, has the strongest land-based precipitation on Earth. The latent heat release associated with the rainfall affects the atmospheric circulation throughout the tropics and into the extra-tropics. The greatest source of variability in precipitation is the diurnal cycle. The archipelago is within the convective region of the Madden-Julian Oscillation (MJO), which provides the greatest variability on intra-seasonal time scales: large-scale (∼10^7 km^2) active and suppressed convective envelopes propagate slowly (∼5 m s^-1) eastwards between the Indian and Pacific Oceans. High-resolution satellite data show that a strong diurnal cycle is triggered to the east of the advancing MJO envelope, leading the active MJO by one-eighth of an MJO cycle (∼6 days). Where the diurnal cycle is strong its modulation accounts for 81% of the variability in MJO precipitation. Over land this determines the structure of the diagnosed MJO. This is consistent with the equatorial wave dynamics in existing theories of MJO propagation. The MJO also affects the speed of gravity waves propagating offshore from the Maritime Continent islands. This is largely consistent with changes in static stability during the MJO cycle. The MJO and its interaction with the diurnal cycle are investigated in HiGEM, a high-resolution coupled model. Unlike many models, HiGEM represents the MJO well with eastward-propagating variability on intra-seasonal time scales at the correct zonal wavenumber, although the inter-tropical convergence zone's precipitation peaks strongly at the wrong time, interrupting the MJO's spatial structure. However, the modelled diurnal cycle is too weak and its phase is too early over land. The modulation of the diurnal amplitude by the MJO is also too weak and accounts for only 51% of the variability in MJO precipitation. Implications for forecasting and possible causes of the model errors are discussed, and further modelling studies are proposed.

Effects of a mid-latitude solar eclipse on the thermosphere and ionosphere: a modelling study

A modelling study is presented which investigates in-situ generated changes of the thermosphere and ionosphere during a solar eclipse. Neutral temperatures are expected to drop by up to 40 degrees K at 240 km height in the totality footprint, with neutral winds of up to 26 m/s responding to the change of pressure. Both temperatures and winds are found to respond with a time lag of 30 min after the passing of the Moon's shadow. A gravity wave is generated in the neutral atmosphere and propagates into the opposite hemisphere at around 300 m/s. The combined effects of thermal cooling and downwelling lead to an overall increase in [O], while [N(2)] initially rises and then for several hours after the eclipse is below the "steady state" level. An enhancement of [NmF2] is found and explained by the atmosphere's contraction during, and the reduced [O]/[N(2)] ratio after the eclipse.

Body-centric modelling, identification, and acceleration tracking control of a quadrotor UAV

This paper presents the mathematical development of a body-centric nonlinear dynamic model of a quadrotor UAV that is suitable for the development of biologically inspired navigation strategies. Analytical approximations are used to find an initial guess of the parameters of the nonlinear model, then parameter estimation methods are used to refine the model parameters using the data obtained from onboard sensors during flight. Due to the unstable nature of the quadrotor model, the identification process is performed with the system in closed-loop control of attitude angles. The obtained model parameters are validated using real unseen experimental data. Based on the identified model, a Linear-Quadratic (LQ) optimal tracker is designed to stabilize the quadrotor and facilitate its translational control by tracking body accelerations. The LQ tracker is tested on an experimental quadrotor UAV and the obtained results are a further means to validate the quality of the estimated model. The unique formulation of the control problem in the body frame makes the controller better suited for bio-inspired navigation and guidance strategies than conventional attitude or position based control systems that can be found in the existing literature.

Infrared and millimetre-wave scintillometry in the suburban environment – Part 2: Large-area sensible and latent heat fluxes

A millimetre-wave scintillometer was paired with an infrared scintillometer, enabling estimation of large-area evapotranspiration across northern Swindon, a suburban area in the UK. Both sensible and latent heat fluxes can be obtained using this "two-wavelength" technique, as it is able to provide both temperature and humidity structure parameters, offering a major advantage over conventional single-wavelength scintillometry. The first paper of this two-part series presented the measurement theory and structure parameters. In this second paper, heat fluxes are obtained and analysed. These fluxes, estimated using two-wavelength scintillometry over an urban area, are the first of their kind. Source area modelling suggests the scintillometric fluxes are representative of 5–10 km2. For comparison, local-scale (0.05–0.5 km2) fluxes were measured by an eddy covariance station. Similar responses to seasonal changes are evident at the different scales but the energy partitioning varies between source areas. The response to moisture availability is explored using data from 2 consecutive years with contrasting rainfall patterns (2011–2012). This extensive data set offers insight into urban surface-atmosphere interactions and demonstrates the potential for two-wavelength scintillometry to deliver fluxes over mixed land cover, typically representative of an area 1–2 orders of magnitude greater than for eddy covariance measurements. Fluxes at this scale are extremely valuable for hydro-meteorological model evaluation and assessment of satellite data products

Plane wave discontinuous Galerkin methods: exponential convergence of the hp-version

We consider the two-dimensional Helmholtz equation with constant coefficients on a domain with piecewise analytic boundary, modelling the scattering of acoustic waves at a sound-soft obstacle. Our discretisation relies on the Trefftz-discontinuous Galerkin approach with plane wave basis functions on meshes with very general element shapes, geometrically graded towards domain corners. We prove exponential convergence of the discrete solution in terms of number of unknowns.

On mathematical and physical principles of transformations of the coherent radar backscatter matrix

The congruential rule advanced by Graves for polarization basis transformation of the radar backscatter matrix is now often misinterpreted as an example of consimilarity transformation. However, consimilarity transformations imply a physically unrealistic antilinear time-reversal operation. This is just one of the approaches found in literature to the description of transformations where the role of conjugation has been misunderstood. In this paper, the different approaches are examined in particular in respect to the role of conjugation. In order to justify and correctly derive the congruential rule for polarization basis transformation and properly place the role of conjugation, the origin of the problem is traced back to the derivation of the antenna height from the transmitted field. In fact, careful consideration of the role played by the Green’s dyadic operator relating the antenna height to the transmitted field shows that, under general unitary basis transformation, it is not justified to assume a scalar relationship between them. Invariance of the voltage equation shows that antenna states and wave states must in fact lie in dual spaces, a distinction not captured in conventional Jones vector formalism. Introducing spinor formalism, and with the use of an alternate spin frame for the transmitted field a mathematically consistent implementation of the directional wave formalism is obtained. Examples are given comparing the wider generality of the congruential rule in both active and passive transformations with the consimilarity rule.

SHIMMER (1.0): a novel mathematical model for microbial and biogeochemical dynamics in glacier forefield ecosystems

SHIMMER (Soil biogeocHemIcal Model for Microbial Ecosystem Response) is a new numerical modelling framework designed to simulate microbial dynamics and biogeochemical cycling during initial ecosystem development in glacier forefield soils. However, it is also transferable to other extreme ecosystem types (such as desert soils or the surface of glaciers). The rationale for model development arises from decades of empirical observations in glacier forefields, and enables a quantitative and process focussed approach. Here, we provide a detailed description of SHIMMER, test its performance in two case study forefields: the Damma Glacier (Switzerland) and the Athabasca Glacier (Canada) and analyse sensitivity to identify the most sensitive and unconstrained model parameters. Results show that the accumulation of microbial biomass is highly dependent on variation in microbial growth and death rate constants, Q10 values, the active fraction of microbial biomass and the reactivity of organic matter. The model correctly predicts the rapid accumulation of microbial biomass observed during the initial stages of succession in the forefields of both the case study systems. Primary production is responsible for the initial build-up of labile substrate that subsequently supports heterotrophic growth. However, allochthonous contributions of organic matter, and nitrogen fixation, are important in sustaining this productivity. The development and application of SHIMMER also highlights aspects of these systems that require further empirical research: quantifying nutrient budgets and biogeochemical rates, exploring seasonality and microbial growth and cell death. This will lead to increased understanding of how glacier forefields contribute to global biogeochemical cycling and climate under future ice retreat.

DAMPED WAVE EQUATIONS WITH FAST GROWING DISSIPATIVE NONLINEARITIES

Let a > 0, Omega subset of R(N) be a bounded smooth domain and - A denotes the Laplace operator with Dirichlet boundary condition in L(2)(Omega). We study the damped wave problem {u(tt) + au(t) + Au - f(u), t > 0, u(0) = u(0) is an element of H(0)(1)(Omega), u(t)(0) = v(0) is an element of L(2)(Omega), where f : R -> R is a continuously differentiable function satisfying the growth condition vertical bar f(s) - f (t)vertical bar <= C vertical bar s - t vertical bar(1 + vertical bar s vertical bar(rho-1) + vertical bar t vertical bar(rho-1)), 1 < rho < (N - 2)/(N + 2), (N >= 3), and the dissipativeness condition limsup(vertical bar s vertical bar ->infinity) s/f(s) < lambda(1) with lambda(1) being the first eigenvalue of A. We construct the global weak solutions of this problem as the limits as eta -> 0(+) of the solutions of wave equations involving the strong damping term 2 eta A(1/2)u with eta > 0. We define a subclass LS subset of C ([0, infinity), L(2)(Omega) x H(-1)(Omega)) boolean AND L(infinity)([0, infinity), H(0)(1)(Omega) x L(2)(Omega)) of the `limit` solutions such that through each initial condition from H(0)(1)(Omega) x L(2)(Omega) passes at least one solution of the class LS. We show that the class LS has bounded dissipativeness property in H(0)(1)(Omega) x L(2)(Omega) and we construct a closed bounded invariant subset A of H(0)(1)(Omega) x L(2)(Omega), which is weakly compact in H(0)(1)(Omega) x L(2)(Omega) and compact in H({I})(s)(Omega) x H(s-1)(Omega), s is an element of [0, 1). Furthermore A attracts bounded subsets of H(0)(1)(Omega) x L(2)(Omega) in H({I})(s)(Omega) x H(s-1)(Omega), for each s is an element of [0, 1). For N = 3, 4, 5 we also prove a local uniqueness result for the case of smooth initial data.

Regularity of solutions on the global attractor for a semilinear damped wave equation

We consider attractors A(eta), eta epsilon [0, 1], corresponding to a singularly perturbed damped wave equation u(tt) + 2 eta A(1/2)u(t) + au(t) + Au = f (u) in H-0(1)(Omega) x L-2 (Omega), where Omega is a bounded smooth domain in R-3. For dissipative nonlinearity f epsilon C-2(R, R) satisfying vertical bar f ``(s)vertical bar <= c(1 + vertical bar s vertical bar) with some c > 0, we prove that the family of attractors {A(eta), eta >= 0} is upper semicontinuous at eta = 0 in H1+s (Omega) x H-s (Omega) for any s epsilon (0, 1). For dissipative f epsilon C-3 (R, R) satisfying lim(vertical bar s vertical bar) (->) (infinity) f ``(s)/s = 0 we prove that the attractor A(0) for the damped wave equation u(tt) + au(t) + Au = f (u) (case eta = 0) is bounded in H-4(Omega) x H-3(Omega) and thus is compact in the Holder spaces C2+mu ((Omega) over bar) x C1+mu((Omega) over bar) for every mu epsilon (0, 1/2). As a consequence of the uniform bounds we obtain that the family of attractors {A(eta), eta epsilon [0, 1]} is upper and lower semicontinuous in C2+mu ((Omega) over bar) x C1+mu ((Omega) over bar) for every mu epsilon (0, 1/2). (c) 2007 Elsevier Inc. All rights reserved.

Low-dimensional chaos and wave turbulence in plasmas

We investigated drift-wave turbulence in the plasma edge of a small tokamak by considering solutions of the Hasegawa-Mima equation involving three interacting modes in Fourier space. The resulting low-dimensional dynamics presented periodic as well as chaotic evolution of the Fourier-mode amplitudes, and we performed the control of chaotic behaviour through the application of a fourth resonant wave of small amplitude.

Granularity and disaggregation in compositional modelling with applications to ecological systems

In the past decade, compositional modelling (CM) has established itself as the predominant knowledge-based approach to construct mathematical (simulation) models automatically. Although it is mainly applied to physical systems, there is a growing interest in applying CM to other domains, such as ecological and socio-economic systems. Inspired by this observation, this paper presents a method for extending the conventional CM techniques to suit systems that are fundamentally presented by interacting populations of individuals instead of physical components or processes. The work supports building model repositories for such systems, especially in addressing the most critical outstanding issues of granularity and disaggregation in ecological systems modelling.

On Compositional Modelling

Many solutions to AI problems require the task to be represented in one of a multitude of rigorous mathematical formalisms. The construction of such mathematical models forms a difficult problem which is often left to the user of the problem solver. This void between problem solvers and the problems is studied by the eclectic field of automated modelling. Within this field, compositional modelling, a knowledge-based methodology for system modelling, has established itself as a leading approach. In general, a compositional modeller organises knowledge in a structure of composable fragments that relate to particular system components or processes. Its embedded inference mechanism chooses the appropriate fragments with respect to a given problem, instantiates and assembles them into a consistent system model. Many different types of compositional modeller exist, however, with significant differences in their knowledge representation and approach to inference. This paper examines compositional modelling. It presents a general framework for building and analysing compositional modellers. Based on this framework, a number of influential compositional modellers are examined and compared. The paper also identifies the strengths and weaknesses of compositional modelling and discusses some typical applications.

Modelling the effect of the physical and chemical characteristics of the materials used as casing layers on the production parameters of Agaricus bisporus

The aim of this research was to show the mathematical data obtained through the correlations found between the physical and chemical characteristics of casing layers and the final mushrooms' properties. For this purpose, 8 casing layers were used: soil, soil + peat moss, soil + black peat, soil + composted pine bark, soil + coconut fibre pith, soil + wood fibre, soil + composted vine shoots and, finally, the casing of La Rioja subjected to the ruffling practice. The conclusion that interplays in the fructification process with only the physical and chemical characteristics of casing are complicated was drawn. The mathematical data obtained in earliness could be explained in non-ruffled cultivation. The variability observed for the mushroom weight and the mushroom diameter variables could be explained in both ruffled and non-ruffled cultivations. Finally, the properties of the final quality of mushrooms were established by regression analysis.

A contribution for thermoeconomic modelling: A methodology proposal

This work presents a thermoeconomic optimization methodology for the analysis and design of energy systems. This methodology involves economic aspects related to the exergy conception, in order to develop a tool to assist the equipment selection, operation mode choice as well as to optimize the thermal plants design. It also presents the concepts related to exergy in a general scope and in thermoeconomics which combines the thermal sciences principles (thermodynamics, heat transfer, and fluid mechanics) and the economic engineering in order to rationalize energy systems investment decisions, development and operation. Even in this paper, it develops a thermoeconomic methodology through the use of a simple mathematical model, involving thermodynamics parameters and costs evaluation, also defining the objective function as the exergetic production cost. The optimization problem evaluation is developed for two energy systems. First is applied to a steam compression refrigeration system and then to a cogeneration system using backpressure steam turbine. (C) 2010 Elsevier Ltd. All rights reserved.