952 resultados para Numerical example
Resumo:
In this article we describe recent progress on the design, analysis and implementation of hybrid numerical-asymptotic boundary integral methods for boundary value problems for the Helmholtz equation that model time harmonic acoustic wave scattering in domains exterior to impenetrable obstacles. These hybrid methods combine conventional piecewise polynomial approximations with high-frequency asymptotics to build basis functions suitable for representing the oscillatory solutions. They have the potential to solve scattering problems accurately in a computation time that is (almost) independent of frequency and this has been realized for many model problems. The design and analysis of this class of methods requires new results on the analysis and numerical analysis of highly oscillatory boundary integral operators and on the high-frequency asymptotics of scattering problems. The implementation requires the development of appropriate quadrature rules for highly oscillatory integrals. This article contains a historical account of the development of this currently very active field, a detailed account of recent progress and, in addition, a number of original research results on the design, analysis and implementation of these methods.
Resumo:
Where joint forest management has been introduced into Tanzania, ‘volunteer’ patrollers take responsibility for enforcing restrictions over the harvesting of forest resources, often receiving as an incentive a share of the collected fine revenue. Using an optimal enforcement model, we explore how that share, and whether villagers have alternative sources of forest products, determines the effort patrollers put into enforcement and whether they choose to take a bribe rather than honestly reporting the illegal collection of forest resources. Without funds for paying and monitoring patrollers, policy makers face tradeoffs over illegal extraction, forest protection and revenue generation through fine collection.
Resumo:
This dissertation deals with aspects of sequential data assimilation (in particular ensemble Kalman filtering) and numerical weather forecasting. In the first part, the recently formulated Ensemble Kalman-Bucy (EnKBF) filter is revisited. It is shown that the previously used numerical integration scheme fails when the magnitude of the background error covariance grows beyond that of the observational error covariance in the forecast window. Therefore, we present a suitable integration scheme that handles the stiffening of the differential equations involved and doesn’t represent further computational expense. Moreover, a transform-based alternative to the EnKBF is developed: under this scheme, the operations are performed in the ensemble space instead of in the state space. Advantages of this formulation are explained. For the first time, the EnKBF is implemented in an atmospheric model. The second part of this work deals with ensemble clustering, a phenomenon that arises when performing data assimilation using of deterministic ensemble square root filters in highly nonlinear forecast models. Namely, an M-member ensemble detaches into an outlier and a cluster of M-1 members. Previous works may suggest that this issue represents a failure of EnSRFs; this work dispels that notion. It is shown that ensemble clustering can be reverted also due to nonlinear processes, in particular the alternation between nonlinear expansion and compression of the ensemble for different regions of the attractor. Some EnSRFs that use random rotations have been developed to overcome this issue; these formulations are analyzed and their advantages and disadvantages with respect to common EnSRFs are discussed. The third and last part contains the implementation of the Robert-Asselin-Williams (RAW) filter in an atmospheric model. The RAW filter is an improvement to the widely popular Robert-Asselin filter that successfully suppresses spurious computational waves while avoiding any distortion in the mean value of the function. Using statistical significance tests both at the local and field level, it is shown that the climatology of the SPEEDY model is not modified by the changed time stepping scheme; hence, no retuning of the parameterizations is required. It is found the accuracy of the medium-term forecasts is increased by using the RAW filter.
Resumo:
Metrics are often used to compare the climate impacts of emissions from various sources, sectors or nations. These are usually based on global-mean input, and so there is the potential that important information on smaller scales is lost. Assuming a non-linear dependence of the climate impact on local surface temperature change, we explore the loss of information about regional variability that results from using global-mean input in the specific case of heterogeneous changes in ozone, methane and aerosol concentrations resulting from emissions from road traffic, aviation and shipping. Results from equilibrium simulations with two general circulation models are used. An alternative metric for capturing the regional climate impacts is investigated. We find that the application of a metric that is first calculated locally and then averaged globally captures a more complete and informative signal of climate impact than one that uses global-mean input. The loss of information when heterogeneity is ignored is largest in the case of aviation. Further investigation of the spatial distribution of temperature change indicates that although the pattern of temperature response does not closely match the pattern of the forcing, the forcing pattern still influences the response pattern on a hemispheric scale. When the short-lived transport forcing is superimposed on present-day anthropogenic CO2 forcing, the heterogeneity in the temperature response to CO2 dominates. This suggests that the importance of including regional climate impacts in global metrics depends on whether small sectors are considered in isolation or as part of the overall climate change.
Resumo:
El Chichón volcano, Chiapas, Mexico, erupted explosively on March 29th, 1982, after a repose period of about 550 years. Amongst ten eruptive episodes documented between March 29th and April 4th, only the three that occurred on March 29th and April 4th produced significant pyroclastic tephra deposits. Here we use analytical (HAZMAP) and numerical (FALL3D) tephra transport models to reconstruct the deposits and the atmospheric plume dispersal associated with the three main fallout units of the 1982 eruption. On the basis of such a reconstruction, we produce hazard maps of tephra fallout associated to a Plinian eruption and discuss the implications of such a severe eruption scenario.
Resumo:
An ensemble forecast is a collection of runs of a numerical dynamical model, initialized with perturbed initial conditions. In modern weather prediction for example, ensembles are used to retrieve probabilistic information about future weather conditions. In this contribution, we are concerned with ensemble forecasts of a scalar quantity (say, the temperature at a specific location). We consider the event that the verification is smaller than the smallest, or larger than the largest ensemble member. We call these events outliers. If a K-member ensemble accurately reflected the variability of the verification, outliers should occur with a base rate of 2/(K + 1). In operational forecast ensembles though, this frequency is often found to be higher. We study the predictability of outliers and find that, exploiting information available from the ensemble, forecast probabilities for outlier events can be calculated which are more skilful than the unconditional base rate. We prove this analytically for statistically consistent forecast ensembles. Further, the analytical results are compared to the predictability of outliers in an operational forecast ensemble by means of model output statistics. We find the analytical and empirical results to agree both qualitatively and quantitatively.
Resumo:
Common approaches to the simulation of borehole heat exchangers (BHEs) assume heat transfer in circulating fluid and grout to be in a quasi-steady state and ignore fluctuations in fluid temperature due to transport of the fluid around the loop. However, in domestic ground source heat pump (GSHP) systems, the heat pump and circulating pumps switch on and off during a given hour; therefore, the effect of the thermal mass of the circulating fluid and the dynamics of fluid transport through the loop has important implications for system design. This may also be important in commercial systems that are used intermittently. This article presents transient simulation of a domestic GSHP system with a single BHE using a dynamic three-dimensional (3D) numerical BHE model. The results show that delayed response associated with the transit of fluid along the pipe loop is of some significance in moderating swings in temperature during heat pump operation. In addition, when 3D effects are considered, a lower heat transfer rate is predicted during steady operations. These effects could be important when considering heat exchanger design and system control. The results will be used to develop refined two-dimensional models.
Resumo:
Data assimilation algorithms are a crucial part of operational systems in numerical weather prediction, hydrology and climate science, but are also important for dynamical reconstruction in medical applications and quality control for manufacturing processes. Usually, a variety of diverse measurement data are employed to determine the state of the atmosphere or to a wider system including land and oceans. Modern data assimilation systems use more and more remote sensing data, in particular radiances measured by satellites, radar data and integrated water vapor measurements via GPS/GNSS signals. The inversion of some of these measurements are ill-posed in the classical sense, i.e. the inverse of the operator H which maps the state onto the data is unbounded. In this case, the use of such data can lead to significant instabilities of data assimilation algorithms. The goal of this work is to provide a rigorous mathematical analysis of the instability of well-known data assimilation methods. Here, we will restrict our attention to particular linear systems, in which the instability can be explicitly analyzed. We investigate the three-dimensional variational assimilation and four-dimensional variational assimilation. A theory for the instability is developed using the classical theory of ill-posed problems in a Banach space framework. Further, we demonstrate by numerical examples that instabilities can and will occur, including an example from dynamic magnetic tomography.
Resumo:
In this paper, numerical analyses of the thermal performance of an indirect evaporative air cooler incorporating a M-cycle cross-flow heat exchanger has been carried out. The numerical model was established from solving the coupled governing equations for heat and mass transfer between the product and working air, using the finite-element method. The model was developed using the EES (Engineering Equation Solver) environment and validated by published experimental data. Correlation between the cooling (wet-bulb) effectiveness, system COP and a number of air flow/exchanger parameters was developed. It is found that lower channel air velocity, lower inlet air relative humidity, and higher working-to-product air ratio yielded higher cooling effectiveness. The recommended average air velocities in dry and wet channels should not be greater than 1.77 m/s and 0.7 m/s, respectively. The optimum flow ratio of working-to-product air for this cooler is 50%. The channel geometric sizes, i.e. channel length and height, also impose significant impact to system performance. Longer channel length and smaller channel height contribute to increase of the system cooling effectiveness but lead to reduced system COP. The recommend channel height is 4 mm and the dimensionless channel length, i.e., ratio of the channel length to height, should be in the range 100 to 300. Numerical study results indicated that this new type of M-cycle heat and mass exchanger can achieve 16.7% higher cooling effectiveness compared with the conventional cross-flow heat and mass exchanger for the indirect evaporative cooler. The model of this kind is new and not yet reported in literatures. The results of the study help with design and performance analyses of such a new type of indirect evaporative air cooler, and in further, help increasing market rating of the technology within building air conditioning sector, which is currently dominated by the conventional compression refrigeration technology.