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35
A comparison study of data assimilation algorithms for ozone forecasts
 J. Geophys. Res
, 2008
"... The objective of this report is to evaluate the performances of different data assimilation schemes with the aim of designing suitable assimilation algorithms for shortrange ozone forecasts in realistic applications. The underlying atmospheric chemistrytransport models are stiff but stable systems ..."
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Cited by 27 (9 self)
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The objective of this report is to evaluate the performances of different data assimilation schemes with the aim of designing suitable assimilation algorithms for shortrange ozone forecasts in realistic applications. The underlying atmospheric chemistrytransport models are stiff but stable systems with high uncertainties (e.g., over 20 % for ozone daily peaks, Hanna et al. [1998]; Mallet and Sportisse [2006b], and much more for other pollutants like aerosols). Therefore the main difficulty of the ozone data assimilation problem is how to account for the strong model uncertainties. In this report, the model uncertainties are either parameterized with homogeneous error correlations of the model state or estimated by perturbing some sources of the uncertainties, e.g. the model uncertain parameters. Four assimilation methods have been considered, namely optimal interpolation, reducedrank square root Kalman filter, ensemble Kalman filter, and fourdimensional variational assimilation. These assimilation algorithms are compared under the same experimental settings. It is found that the assimilations significantly improve the oneday ozone forecasts. The comparison results reveal the limitations and the potentials of each assimilation algorithm. In our fourdimensional variational method, the low dependency of model simulations on initial conditions leads to moderate performances. In our sequential methods, the optimal interpolation algorithm has the best performance during assimilation periods. Our ensemble Kalman filter algorithm perturbs the uncertain parameters to approximate model uncertainties and has better forecasts than the optimal interpolation algorithm during prediction periods. This could partially be explained by the low dependency on the uncertainties in initial conditions. The sensitivity analysis on the algorithmic parameters is also conducted for the design of suitable assimilation algorithms for ozone forecasts. 1
Uncertainty in a chemistrytransport model due to physical parameterizations and numerical approximations: An ensemble approach applied to ozone modeling,
 J. Geophys. Res.,
, 2006
"... Abstract. This paper estimates the uncertainty in the outputs of a chemistrytransport model due to physical parameterizations and numerical approximations. An ensemble of twenty simulations is generated from a reference simulation in which one key parameterization (chemical mechanism, dry depositi ..."
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Cited by 22 (8 self)
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Abstract. This paper estimates the uncertainty in the outputs of a chemistrytransport model due to physical parameterizations and numerical approximations. An ensemble of twenty simulations is generated from a reference simulation in which one key parameterization (chemical mechanism, dry deposition parameterization, turbulent closure, etc.) or one numerical approximation (grid size, splitting method, etc.) is changed at a time. Intercomparisons of the simulations and comparisons with observations allow us to assess the impact of each parameterization and numerical approximation, and the robustness of the model. An ensemble of sixteen simulations is also generated with multiple changes in the reference simulation in order to estimate the overall uncertainty. The case study is a fourmonth simulation of ozone concentrations over Europe in 2001 performed using the modeling system Polyphemus. It is shown that there is a high uncertainty due to the physical parameterizations (notably the turbulence closure and the chemical mechanism). The low robustness suggests that ensemble approaches are necessary in most applications.
Approximate factorization for timedependent partial differential equations. Journal of Computational and Applied Mathematics, 128(12):447–466, 2001. A LIRK methods The coefficients of the LIRK3 method [8]: γ 0 γ 1+γ 1−γ 2 γ 1 0 b2 b3 γ 0 b2 b3 γ γ γ 0 1
 a32 a32 0 1 0 1− a43 a43 0 0 b2 b3 γ , where b2 = − 3γ2 2 + 4γ − 4 and b3 = 3γ2 2 − 5γ + 4 . And the choice for the free parameter is γ = 0.435866521508459 and a32 = 0.35. The coefficients of the LIRK4 method [8]: − 34 0 − 1120 0 50 − − 12 0 1360 − 1 0 25
"... and their applications. SMC is sponsored by the Netherlands Organization for Scientific Research (NWO). CWI is a member of ..."
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Cited by 9 (1 self)
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and their applications. SMC is sponsored by the Netherlands Organization for Scientific Research (NWO). CWI is a member of
Adaptive stiff solvers at low accuracy and complexity.
 J. Comp. Appl. 146 Math.,
, 2006
"... Abstract This paper is concerned with adaptive stiff solvers at low accuracy and complexity for systems of ordinary differential equations. The considered stiff solvers are: two second order Rosenbrock methods with low complexity, and the BDF method of the same order. For the adaptive algorithm we ..."
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Cited by 8 (6 self)
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Abstract This paper is concerned with adaptive stiff solvers at low accuracy and complexity for systems of ordinary differential equations. The considered stiff solvers are: two second order Rosenbrock methods with low complexity, and the BDF method of the same order. For the adaptive algorithm we propose to use a monitor function defined by comparing a measure of the local variability of the solution times the used step size and the order of magnitude of the solution instead of the classical approach based on some local error estimation. This simple stepsize selection procedure is implemented in order to control the behavior of the numerical solution. It is easily used to automatically adjust the step size, as the calculation progresses, until userspecified tolerance bounds for the introduced monitor function are fulfilled. This leads to important advantages in accuracy, efficiency and general easeofuse. At the end of the paper we present two numerical tests which show the performance of the implementation of the stiff solvers, with the proposed adaptive procedure.
A zooming technique for wind transport of air pollution
 Finite Volumes for Complex Applications
, 1999
"... www.cwi.nl [berkvens, botchev, walter, janv] @ cwi.nl In air pollution dispersion models, typically systems of millions of equations that describe wind transport, chemistry and vertical mixing have to be integrated in time. To have more accurate results over specific fixed areas of interest—usually ..."
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Cited by 7 (1 self)
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www.cwi.nl [berkvens, botchev, walter, janv] @ cwi.nl In air pollution dispersion models, typically systems of millions of equations that describe wind transport, chemistry and vertical mixing have to be integrated in time. To have more accurate results over specific fixed areas of interest—usually highly polluted areas with intensive emissions—a local grid refinement or zoom is often required. For the wind transport part of the models, i.e. for finite volume discretizations of the transport equation, we propose a zoom technique that is positive, massconservative and allows to use smaller time steps as enforced by the CFL restriction in the zoom regions only.
Solving Vertical Transport and Chemistry in Air Pollution Models
 PROC. OF IMA WORKSHOP ON &QUOT;ATMOSPHERIC MODELING
, 2000
"... For the time integration of stiff transportchemistry problems from air pollution modelling, standard ODE solvers are not feasible due to the large number of species and the 3D nature. The popular alternative, standard operator splitting, introduces artificial transients for shortlived species. T ..."
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Cited by 6 (6 self)
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For the time integration of stiff transportchemistry problems from air pollution modelling, standard ODE solvers are not feasible due to the large number of species and the 3D nature. The popular alternative, standard operator splitting, introduces artificial transients for shortlived species. This complicates the chemistry solution, easily causing large errors for such species. In the framework of an operational global air pollution model, we focus on the problem formed by chemistry and vertical transport, which is based on diffusion, cloudrelated vertical winds, and wet deposition. Its specific nature leads to full Jacobian matrices, ruling out standard implicit integration. We compare Strang operator splitting with two alternatives: source splitting and an (unsplit) Rosenbrock method with approximate matrix factorization, all having equal computational cost. The comparison is performed with real data. All methods are applied with halfhour time steps, and give good accur...
A filtering technique for system of reaction diffusion equations,” Int
 J. for Numerical Methods in Fluids
, 2006
"... We present here a fast parallel solver designed for a system of reaction convection diffusion equations. Typical applications are large scale computing of air quality models or numerical simulation of population models where several colonies compete. ReactionDiffusion systems can be integrated in t ..."
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Cited by 6 (2 self)
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We present here a fast parallel solver designed for a system of reaction convection diffusion equations. Typical applications are large scale computing of air quality models or numerical simulation of population models where several colonies compete. ReactionDiffusion systems can be integrated in time by pointwise Newton iteration when all space dependent terms are explicit in the time integration. Such methods are easy to code and have scalable parallelism, but are numerically inefficient. An alternative method is to use operator splitting, decoupling the time integration of reaction from convectiondiffusion. However, such methods may not be time accurate thanks to the stiffness of the reaction term and are complex to parallelize with good scalability. A second alternative is to use matrix free NewtonKrylov methods. These techniques are particularly efficient provided that a good parallel preconditioner is customized to the application. The method is then not trivial to implement. We propose here a new family of fast, easy to code and numerically efficient reactiondiffusion solvers based on a filtering technique that stabilizes the explicit treatment of the diffusion terms. The scheme is completely explicit with respect to space, and the postprocessing to stabilize time stepping uses a simple FFT. We demonstrate the potential of this numerical scheme with two examples in air quality models and have compared our solution to classical
A new approximate matrix factorization for implicit time integration in air pollution modeling
, 2003
"... Implicit time stepping typically requires solution of one or several linear systems with a matrix I − τJ per time step where J is the Jacobian matrix. If solution of these systems is expensive, replacing I −τJ with its approximate matrix factorization (AMF) (I − τR)(I − τV), R + V = J, often leads t ..."
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Cited by 5 (2 self)
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Implicit time stepping typically requires solution of one or several linear systems with a matrix I − τJ per time step where J is the Jacobian matrix. If solution of these systems is expensive, replacing I −τJ with its approximate matrix factorization (AMF) (I − τR)(I − τV), R + V = J, often leads to a good compromise between stability and accuracy of the time integration on the one hand and its efficiency on the other hand. For example, in air pollution modeling, AMF has been successfully used in the framework of Rosenbrock schemes. The standard AMF gives an approximation to I − τJ with the error τ 2 RV, which can be significant in norm. In this paper we propose a new AMF. In assumption that −V is an Mmatrix, the error of the new AMF can be shown to have an upper bound τ‖R‖, while still being asymptotically O(τ 2). This new AMF, called AMF+, is equal in costs to standard AMF and, as both analysis and numerical experiments reveal, provides a better accuracy. We also report on our experience with another, cheaper AMF and with AMFpreconditioned GMRES.
ImplicitExplicit Time Stepping with Spatial Discontinuous Finite Elements
"... In this paper a combination of discontinuous, piecewise linear, finite elements with BDF2 implicitexplicit time stepping is considered for convectionreaction equations. Combined with low order quadrature rules, this leads to convenient schemes. We shall consider the effect of such low order quadra ..."
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In this paper a combination of discontinuous, piecewise linear, finite elements with BDF2 implicitexplicit time stepping is considered for convectionreaction equations. Combined with low order quadrature rules, this leads to convenient schemes. We shall consider the effect of such low order quadrature rules on accuracy and stability for onedimensional problems. Furthermore, attention will be given to the stability and TVD properties of the explicit BDF2type formula used for convection in the implicitexplicit time stepping.