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The efficiency of current adjoint-based observations targeting strategies in variational data assimilation is closely determined
by the underlying assumption of a linear propagation of initial condition errors into the model forecasts. A novel targeting
strategy is proposed in the context of four-dimensional variational data assimilation (4D-Var) to account for nonlinear error
growth as the forecast lead time increases. A quadratic error growth model is shown to maintain the accuracy in tracking the
nonlinear evolution of initial condition perturbations, as compared to the first-order approximation. A second-order adjoint
model is used to provide the derivative information that is necessary in the higher-order Taylor series approximation. The
observation targeting approach relies on the dominant eigenvectors of the Hessian matrix associated with a specific forecast
error aspect as an indicator of the directions of largest quadratic error growth. A comparative qualitative analysis between
observation targeting based on first- and second-order adjoint information is presented in idealized 4D-Var experiments with
a two-dimensional global shallow-water model. The results indicate that accounting for the quadratic error growth in the targeting
strategy is of particular benefit as the forecast lead time increases. 相似文献
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Humberto C. Godinez Esteban Rougier Dave Osthus Zhou Lei Earl Knight Gowri Srinivasan 《国际地质力学数值与分析法杂志》2019,43(1):30-44
Fracture propagation plays a key role for a number of applications of interest to the scientific community, from dynamic fracture processes like spallation and fragmentation in metals to failure of ceramics, airplane wings, etc. Simulations of material deformation and fracture propagation rely on accurate knowledge of material characteristics such as material strength and the amount of energy being dissipated during the fracture process. Within the combined finite-discrete element method (FDEM) framework material fracture behavior is typically described through a parametrized softening curve, which defines a stress-strain relationship unique to each material. We apply the Fourier amplitude sensitivity test to explore how each of these parameters influences the simulated damage processes and to determine the key input parameters that have the most impact on the model response. We present several sensitivity numerical experiments for the simulation of a split Hopkinson pressure bar (SHPB) test for weathered granite samples using different combinations of model parameters. We validate the obtained results against SHPB experimental data. The experiments show that the model is mostly sensitive to parameters related to tensile and shear strengths, even in the presence of other parameter perturbations. The results suggest that the specification of tensile and shear strengths at the interfaces dominate the stress-time history of the FDEM simulation of SHPB test. 相似文献
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San Martin Tuxtla Volcano, the largest and highest edifice in the Tuxtla Volcanic Field, had explosive eruptions in 1664 and
1793. This volcano poses the highest hazard for the growing population centers surrounding it. The impacts and deposits of
the 1793 eruption have been studied recently, and some of its characteristics, such as eruptive mass, grain-size distribution
of the products and plume height, have been estimated. These data, together with daily data on wind velocities taken in the
nearby city of Veracruz, have been used to conduct numerical modeling of ash distribution from an eruptive column comparable
to that estimated during the 1793 event. Using wind velocities of randomly chosen days, we constructed probability maps of
areas likely to receive, at least 1, 5, or 10 cm of ash. Our results indicate that an area about 1.3 × 104 km2 has a 12% probability of being covered by an ash fall more than 1 cm thick, if a mass of 1014 g was erupted and deposited from a 10-km-high eruptive plume. The results presented in this paper serve as a scientific basis
to estimate volcano risk in the area from a possible eruption, consisting of one or several large explosive events, at San
Martin Tuxtla volcano. 相似文献
4.
We present a method of using classical wavelet-based multiresolution analysis to separate scales in model and observations during data assimilation with the ensemble Kalman filter. In many applications, the underlying physics of a phenomena involve the interaction of features at multiple scales. Blending of observational and model error across scales can result in large forecast inaccuracies since large errors at one scale are interpreted as inexact data at all scales due to the misrepresentation of observational error. Our method uses a partitioning of the range of the observation operator into separate observation scales. This naturally induces a transformation of the observation covariance and we put forward several algorithms to efficiently compute the transformed covariance. Another advantage of our multiresolution ensemble Kalman filter is that scales can be weighted independently to adjust each scale’s affect on the forecast. To demonstrate feasibility, we present applications to a one-dimensional Kuramoto-Sivashinsky (K–S) model with scale-dependent observation noise and an application involving the forecasting of solar photospheric flux. The solar flux application uses the Air Force Data Assimilative Photospheric Transport (ADAPT) model which has model and observation error exhibiting strong scale dependence. Results using our multiresolution ensemble Kalman filter show significant improvement in solar forecast error compared to traditional ensemble Kalman filtering. 相似文献
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Espíndola Juan Manuel De Lourdes Godinez Maria Espindola Victor Hugo 《Natural Hazards》2004,31(1):191-207
Popocatepetl volcano in Central Mexico entered its latest stage of activity in late 1994. Due to the nature of its eruptive history and its location in a heavily populated area, it constitutes the highest risk in the cuntry. For this reason the volcano is currently under continuous surveillance; yet the interpretation of the information is carried out mostly on empirical basis and an integrating working model is lacking, at the present. In this paper, models of elastic deformation and mass erupted are developed to estimate the mass erupted according to the observed deformation patterns. We present results obtained from input based upon a gravimetric model of the volcano's internal structure and reasonable physical parameters of the volcanic system. These results are helpful in the planning of deformation and gravimetric observations aimed to forecast a major eruption. 相似文献
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In this work, we present an efficient matrix-free ensemble Kalman filter (EnKF) algorithm for the assimilation of large data
sets. The EnKF has increasingly become an essential tool for data assimilation of numerical models. It is an attractive assimilation
method because it can evolve the model covariance matrix for a non-linear model, through the use of an ensemble of model states,
and it is easy to implement for any numerical model. Nevertheless, the computational cost of the EnKF can increase significantly
for cases involving the assimilation of large data sets. As more data become available for assimilation, a potential bottleneck
in most EnKF algorithms involves the operation of the Kalman gain matrix. To reduce the complexity and cost of assimilating
large data sets, a matrix-free EnKF algorithm is proposed. The algorithm uses an efficient matrix-free linear solver, based
on the Sherman–Morrison formulas, to solve the implicit linear system within the Kalman gain matrix and compute the analysis.
Numerical experiments with a two-dimensional shallow water model on the sphere are presented, where results show the matrix-free
implementation outperforming an singular value decomposition-based implementation in computational time. 相似文献
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