Perturbation Of Boundary Conditions Research Articles

Hydro-meteorological evaluation of a convection-permitting ensemble prediction system for Mediterranean heavy precipitating events

Abstract. An assessment of the performance of different convection-permitting ensemble prediction systems (EPSs) is performed, with a focus on Heavy Precipitating Events (HPEs). The convective-scale EPS configuration includes perturbations of lateral boundary conditions (LBCs) by using a global ensemble to provide LBCs, initial conditions (ICs) through an ensemble data assimilation technique and perturbations of microphysical parameterisations to account for part of model errors. A probabilistic evaluation is conducted over an 18-day period. A clear improvement is found when uncertainties on LBCs and ICs are considered together, but the chosen microphysical perturbations have no significant impact on probabilistic scores. Innovative evaluation processes for three HPE case studies are implemented. First, maxima diagrams provide a multi-scale analysis of intense rainfall. Second, an hydrological evaluation is performed through the computation of discharge forecasts using hourly ensemble precipitation forecasts as an input. All ensembles behave similarly, but differences are found highlighting the impact of microphysical perturbations on HPEs forecasts, especially for cases involving complex small-scale processes.

Optimal inflow boundary condition perturbations in steady stenotic flow

AbstractWe determine optimal inflow boundary perturbations to steady flow through a straight inflexible tube with a smooth axisymmetric stenosis at a bulk-flow Reynolds number $\mathit{Re}= 400$, for which the flow is asymptotically stable. The perturbations computed produce an optimal gain, i.e. kinetic energy in the domain at a given time horizon normalized by a measure of time-integrated energy on the inflow boundary segment. We demonstrate that similarly to the optimal initial condition problem, the gain can be interpreted as the leading singular value of the forward linearized operator that evolves the boundary conditions to the final state at a fixed time. In this investigation we restrict our attention to problems where the temporal profile of the perturbations examined is a product of a Gaussian bell and a sinusoid, whose frequency is selected to excite axial wavelengths similar to those of the optimal initial perturbations in the same geometry. Comparison of the final state induced by the optimal boundary perturbation with that induced by the optimal initial condition demonstrates a close agreement for the selected problem. Previous works dealing with optimal boundary perturbation considered a prescribed spatial structure and computed an optimal temporal variation of a wall-normal velocity component, whereas in this paper we consider the problem of a prescribed temporal structure and compute the optimal spatial variation of velocity boundary conditions over a one-dimensional inflow boundary segment. The methodology is capable of optimizing boundary perturbations in general non-parallel two- and three-dimensional flows.

Oceanic controls on the primary production of the northwest European continental shelf: model experiments under recent past conditions and a potential future scenario

Abstract. In this paper we clearly demonstrate that changes in oceanic nutrients are a first order factor in determining changes in the primary production of the northwest European continental shelf on time scales of 5–10 yr. We present a series of coupled hydrodynamic ecosystem modelling simulations, using the POLCOMS-ERSEM system. These are forced by both reanalysis data and a single example of a coupled ocean-atmosphere general circulation model (OA-GCM) representative of possible conditions in 2080–2100 under an SRES A1B emissions scenario, along with the corresponding present day control. The OA-GCM forced simulations show a substantial reduction in surface nutrients in the open-ocean regions of the model domain, comparing future and present day time-slices. This arises from a large increase in oceanic stratification. Tracer transport experiments identify a substantial fraction of on-shelf water originates from the open-ocean region to the south of the domain, where this increase is largest, and indeed the on-shelf nutrient and primary production are reduced as this water is transported on-shelf. This relationship is confirmed quantitatively by comparing changes in winter nitrate with total annual nitrate uptake. The reduction in primary production by the reduced nutrient transport is mitigated by on-shelf processes relating to temperature, stratification (length of growing season) and recycling. Regions less exposed to ocean-shelf exchange in this model (Celtic Sea, Irish Sea, English Channel, and Southern North Sea) show a modest increase in primary production (of 5–10%) compared with a decrease of 0–20% in the outer shelf, Central and Northern North Sea. These findings are backed up by a boundary condition perturbation experiment and a simple mixing model.

Topology of tokamak plasma equilibria with toroidal current reversal

Some general principles about scalar functions with critical points are used to rigorously ascertain that magnetic equilibria with both toroidal current reversal and nested magnetic surfaces are atypical solutions and highly unstable to arbitrary perturbations of boundary conditions and other parameters. The cause for such is shown to lie in the condition of nested magnetic surfaces and not in the possibility of current reversal and consequent vanishing of the poloidal field inside the plasma. Rather than supporting the claim that instability against experimentally driven perturbations forbids configurations with toroidal current reversal, it is argued that these can be attained if an axisymmetric island system is allowed for in order to break the condition of nested magnetic surfaces. A number of results previously reported in the literature are discussed and reinterpreted under the proposed framework, providing some physical insight on the nature of equilibria with toroidal current reversal.

Improved Computation of Propagation Losses in Waveguide Structures Using Perturbation of Boundary Conditions

In this letter, a method for the improved consideration of propagation losses in metallic waveguide structures is presented. The method relies on the perturbation of the boundary conditions on the metallic walls of the waveguides. Following this advanced technique, we are able to compute a complex modal propagation constant, thus avoiding the drawbacks of the classical power-loss method where losses associated to evanescent modes were not taken into account. A Computer Aided Design (CAD) software package based on such a modal analysis tool has been applied to predict the propagation loss effects in a Ka-Band rectangular waveguide filter.

Asymptotic approximations for solutions to quasilinear and linear parabolic problems with different perturbed boundary conditions in perforated domains

We consider quasilinear and linear parabolic problems with rapidly oscillating coefficients in a domain Ω e that is e-periodically perforated by small holes of order . The holes are divided into three e-periodical sets depending on boundary conditions. The homogeneous Dirichlet boundary conditions are imposed for holes of one set, whereas, for holes in the remaining sets, different inhomogeneous Neumann and nonlinear Robin boundary conditions involving additional perturbation parameters are imposed. For a solution to the quasilinear problem we find the leading terms of the asymptotic expansion and prove asymptotic estimates that show the influence of perturbation parameters. In the linear case, we construct and justify a complete asymptotic expansion of the solution by using the two-scale asymptotic expansion method. Bibliography: 25 titles. Illustrations: 1 figure.

Variational–hemivariational inequalities with small perturbations of nonhomogeneous Neumann boundary conditions

In this paper variational–hemivariational inequalities with nonhomogeneous Neumann boundary conditions are investigated. Under an appropriate oscillating behavior of the nonlinear term, the existence of infinitely many solutions to this type of problems, even under small perturbations of nonhomogeneous Neumann boundary conditions, is established.

Strong stability and uniform decay of solutions to a wave equation with semilinear porous acoustic boundary conditions

We consider a wave equation with semilinear porous acoustic boundary conditions. This is a coupled system of second and first order in time partial differential equations, with possibly semilinear boundary conditions on the interface. The results obtained are (i) strong stability for the linear model, (ii) exponential decay rates for the energy of the linear model, and (iii) local exponential decay rates for the energy of the semilinear model. This work builds on a previous result showing generation of a well-posed dynamical system. The main tools used in the proofs are (i) the Stability Theorem of Arendt–Batty, (ii) energy methods used in the study of a wave equation with boundary damping, and (iii) an abstract result of I. Lasiecka applicable to hyperbolic-like systems with nonlinearly perturbed boundary conditions.

Assimilating remote sensing and in situ observations into a coastal model of northern South China Sea using ensemble Kalman filter

Major forecast errors on the background error covariance from initial conditions, atmospheric forcing, model open boundary conditions, and the river discharges are examined in a coastal model of northern South China Sea. The analysis of background error covariance matrix produced by model ensemble shows that the perturbations of the initial conditions and atmospheric forcing play major roles in producing and maintaining the amplitude of ensemble spread except for the sea surface height (SSH) field. The perturbation of model open boundary conditions can influence ensemble spread of all variables and covariance between temperature and velocity or between temperature and SSH. The perturbation of river discharge mainly affects the covariance of salinity in river estuary. A data assimilation experiment of northern South China Sea is conducted using ensemble Kalman filter (EnKF) in the Princeton Ocean Model. In the experiment the ensemble model forecasts are made by perturbing the above mentioned four major model inputs. The assimilated data include sea-surface temperature (SST) and conductive–temperature–depth (CTD) observations. The assimilation experiment suggests that assimilating SST and CTD data can effectively improve the model simulation that has a shallower thermocline and weaker plume comparing to the observations. Moreover, consistent with these improvements of temperature and salinity, the along-shore velocity, cross-shore velocity, and characters of water mass are also corrected, respectively.

Asymptotic approximations for solutions to quasilinear and linear elliptic problems with different perturbed boundary conditions in perforated domains

Asymptotic approximations for solutions to quasilinear and linear elliptic problems with different perturbed boundary conditions in perforated domains

Sensing small changes in a wave chaotic scattering system

Classical analogs of the quantum mechanical concepts of the Loschmidt Echo and quantum fidelity are developed with the goal of detecting small perturbations in a closed wave chaotic region. Sensing techniques that employ a one-recording-channel time-reversal-mirror, which in turn relies on time reversal invariance and spatial reciprocity of the classical wave equation, are introduced. In analogy with quantum fidelity, we employ scattering fidelity techniques which work by comparing response signals of the scattering region, by means of cross correlation and mutual information of signals. The performance of the sensing techniques is compared for various perturbations induced experimentally in an acoustic resonant cavity. The acoustic signals are parametrically processed to mitigate the effect of dissipation and to vary the spatial diversity of the sensing schemes. In addition to static boundary condition perturbations at specified locations, perturbations to the medium of wave propagation are shown to be detectable, opening up various real world sensing applications in which a false negative cannot be tolerated.

Implications of initial conditions and ice–ocean coupling for grounding-line evolution

Ice-sheet grounding lines are sensitive to initial conditions and to small perturbations in boundary conditions, based on new model results coupling ocean and ice flow. To study ice–ocean dynamics near ice-stream grounding lines, we couple an ocean-plume model that simulates ice-shelf basal melting with a two-dimensional, isothermal model of ice-stream and ice-shelf flow. The notable results of the coupled model experiments are to reveal grounding-line migration sensitivities to i) specific aspects of modeling-derived and history-dependent initial conditions, ii) to the overall melt magnitude, and iii) to a positive feedback between focused melting and local slopes of basal ice that is eventually stabilized by buttressing for lengthening ice shelves. These interactions can lead to multiple steady states for ice flow over a bed that shallows in the along-flow direction and have an important bearing on the effects of bedrock bumps. When in the vicinity of bedrock highs, grounding lines tend to rapidly advance or retreat towards the basal asperity. A significant delay or cessation of (de)glaciation occurs once the grounding line reaches the leeward side of the bedrock crest. However, while bedrock bumps can offer stability in the grounding zone, minor changes in ocean conditions can easily offset their effect through basal melting feedbacks.

Family of equilibria in a population kinetics model and its collapse

The system of nonlinear parabolic equations that models the dynamics of three populations is studied. The strong nonuniqueness in the form of continuous cosymmetric family of steady states is detected for some parameter values. Collapse of the family of equilibria under perturbation of boundary conditions is analyzed numerically.

Remote Sensing of Layered Media: Perturbative Scattering Models

In this paper, we present a new comprehensive model for the bistatic electromagnetic scattering from 3D multilayered structure with rough boundaries, which is based on the boundary condition perturbation theory. The obtained compact closed-form solution turns out to be fully polarimetric and exhibits a direct functional dependence on the structure parameters, so that it can be widely applied in remote sensing applications scenario. A particular effort has been devoted to set the presented general model in an organized formal framework, highlighting the connections with all the previously existing simplified perturbative models.

Ensemble perturbation smoother for optimizing tidal boundary conditions by assimilation of High-Frequency radar surface currents – application to the German Bight

Abstract. High-Frequency (HF) radars measure the ocean surface currents at various spatial and temporal scales. These include tidal currents, wind-driven circulation, density-driven circulation and Stokes drift. Sequential assimilation methods updating the model state have been proven successful to correct the density-driven currents by assimilation of observations such as sea surface height, sea surface temperature and in-situ profiles. However, the situation is different for tides in coastal models since these are not generated within the domain, but are rather propagated inside the domain through the boundary conditions. For improving the modeled tidal variability it is therefore not sufficient to update the model state via data assimilation without updating the boundary conditions. The optimization of boundary conditions to match observations inside the domain is traditionally achieved through variational assimilation methods. In this work we present an ensemble smoother to improve the tidal boundary values so that the model represents more closely the observed currents. To create an ensemble of dynamically realistic boundary conditions, a cost function is formulated which is directly related to the probability of each boundary condition perturbation. This cost function ensures that the boundary condition perturbations are spatially smooth and that the structure of the perturbations satisfies approximately the harmonic linearized shallow water equations. Based on those perturbations an ensemble simulation is carried out using the full three-dimensional General Estuarine Ocean Model (GETM). Optimized boundary values are obtained by assimilating all observations using the covariances of the ensemble simulation.

Aeroelastic simulations using gridless boundary condition and small perturbation techniques

This paper examines the use of stationary Cartesian mesh for non-linear flutter computations involving complex geometries. The surface boundary conditions are implemented using reflected points which are determined via a gridless approach. The method uses a cloud of nodes in the vicinity of the surface to get a weighted-average of the flow properties using radial basis functions. To ensure computational efficiency and for local grid refinements, multigrid computations within an embedded grids framework are used. As the displacements of moving surfaces from their original position are typically small for flutter problems, a small perturbation boundary condition method is used to account for the moving surfaces. The method therefore does not require repeated grid re-generation for the deforming surfaces. The overall method is both accurate and robust. Computations of the well-known Onera M6 wing, RAE wing-body configuration, the AGARD 445.6 wing flutter test case show good accuracy and efficiencies. Simulations of the aeroelastic behavior of a complete fighter-type aircraft with wing tip missiles at high transonic speeds further demonstrate the practical usefulness of the present boundary conditions technique.

ON THE INFLUENCE OF FLUCTUATIONS OF THE DIRECTION OF AN EXTERNAL MAGNETIC FIELD ON PHASE AND AMPLITUDE CORRELATION FUNCTIONS OF SCATTERED RADIATION BY MAGNETIZED PLASMA SLAB

Statistical characteristics of scattered electromagnetic waves by turbulent magnetized plasma slab with electron density and magnetic fleld ∞uctuations are considered via the perturbation method and boundary conditions. Magnetic fleld ∞uctuates both in magnitude and direction. Analytical expressions for the component of scattered electric fleld, correlation functions of the amplitude and phase ∞uctuations, and also the phase structure function for arbitrary correlation functions of ∞uctuating plasma parameters are derived. The obtained results are valid for near and far zones. Under equal conditions, at strong magnetic flelds, electron density ∞uctuations play the important role and in this case the imposed magnetic fleld decreases ∞uctuation intensity of the ordinary and extraordinary waves. Numerical calculations of statistical characteristics of scattered radiation were carried out for anisotropic Gaussian correlation function

Solution of Cauchy problem to stationary heat conduction equation by modified method of elementary balances with interpolation of the solution in physical plane

This article presents a solution of stationary direct and inverse problems (Cauchy problem) of cooling a circular ring with the modified method of elementary balances. The idea of the method itself relies on the division of the considered range into elements and interpolation of the solution within the elements with the help of linear combination of base functions. In the vicinity of every mesh node, the control regions are created in which the energy is balanced. The regions include or interpenetrate with each other. The numerical calculation has been carried out with the use of a quadrilateral mesh with four nodes and a triangular mesh with six nodes. The presented solution to the inverse problem with randomly perturbed boundary conditions of the flux and temperature at the outer boundary of the ring with maximal error reaching up to 10% gave very good results. The solution of the inverse problem has been obtained in the sense of singular value decomposition algorithm.

Perturbations of a critical point of the energy functional of a two-phase elastic medium I. Perturbation of the contact problem in a Sobolev space

We study perturbations of the solution to the equations of a two-phase elastic medium under small perturbations of force fields, boundary conditions, and temperature. Bibliography: 10 titles.

Dynamically constrained ensemble perturbations – application to tides on the West Florida Shelf

Abstract. A method is presented to create an ensemble of perturbations that satisfies linear dynamical constraints. A cost function is formulated defining the probability of each perturbation. It is shown that the perturbations created with this approach take the land-sea mask into account in a similar way as variational analysis techniques. The impact of the land-sea mask is illustrated with an idealized configuration of a barrier island. Perturbations with a spatially variable correlation length can be also created by this approach. The method is applied to a realistic configuration of the West Florida Shelf to create perturbations of the M2 tidal parameters for elevation and depth-averaged currents. The perturbations are weakly constrained to satisfy the linear shallow-water equations. Despite that the constraint is derived from an idealized assumption, it is shown that this approach is applicable to a non-linear and baroclinic model. The amplitude of spurious transient motions created by constrained perturbations of initial and boundary conditions is significantly lower compared to perturbing the variables independently or to using only the momentum equation to compute the velocity perturbations from the elevation.