Adrian Sandu

The kinetic preprocessor KPP*/a software environment for solving chemical kinetics

Abstract The kinetic preprocessor (KPP) is a software tool that assists the computer simulation of chemical kinetic systems. The concentrations of a chemical system evolve in time according to the differential law of mass action kinetics. A computer simulation requires the implementation of the differential system and its numerical integration in time. KPP translates a specification of the chemical mechanism into fortran or c simulation code that implement the concentration time derivative function and its Jacobian, together with a suitable numerical integration scheme. Sparsity in Jacobian is carefully exploited in order to obtain computational efficiency. KPP incorporates a library with several widely used atmospheric chemistry mechanisms and users can add their own chemical mechanisms to the library. KPP also includes a comprehensive suite of stiff numerical integrators. The KPP development environment is designed in a modular fashion and allows for rapid prototyping of new chemical kinetic schemes as well as new numerical integration methods.

Benchmarking stiff ODE solvers for atmospheric chemistry problems II: Rosenbrock solvers

Abstract In the numerical simulation of atmospheric transport-chemistry processes, a major task is the integration of the stiff systems of ordinary differential equations describing the chemical transformations. It is therefore of interest to systematically search for stiff solvers which can be identified as close to optimal for atmospheric applications. In this paper we continue our investigation from Sandu et al. (1996, CWI Report NM-R9603 and Report in Comput. Math., No. 85) and compare eight solvers on a set of seven box-models used in present day models. The focus is on Rosenbrock solvers. These turn out to be very well suited for our application when they are provided with highly efficient sparse matrix techniques to economize on the linear algebra. Two of the Rosenbrock solvers tested are from the literature, viz. rodas and Ros 4, and two are new and specially developed for air quality applications, viz. rodas 3 and ros 3.

Benchmarking stiff ode solvers for atmospheric chemistry problems-I. implicit vs explicit

Abstract In many applications of atmospheric transport-chemistry problems, a major task is the numerical integration of the stiff systems of ordinary differential equations describing the chemical transformations. This paper presents a comprehensive numerical comparison between five dedicated explicit and four implicit solvers for a set of seven benchmark problems from actual applications. The implicit solvers use sparse matrix techniques to economize on the numerical linear algebra overhead. As a result they are often more efficient than the dedicated explicit ones, particularly when approximately two or more figures of accuracy are required. In most test cases, sparse RODAs, a Rosenbrock solver, came out as most competitive in the 1% error region. Of the dedicated explicit solvers, TWOSTEP came out as best. When less than 1% accuracy is aimed at, this solver performs very efficiently for tropospheric gas-phase problems. However, like all other dedicated explicit solvers, it cannot efficiently deal with gas-liquid phase chemistry. The results presented may constitute a guide for atmospheric modelers to select a suitable integrator based on the type and dimension of their chemical mechanism and on the desired level of accuracy. Furthermore, we would like to consider this paper an open invitation for other groups to add new representative test problems to those described here and to benchmark their numerical algorithms in our standard computational environment.

Predicting air quality: Improvements through advanced methods to integrate models and measurements

Air quality prediction plays an important role in the management of our environment. Computational power and efficiencies have advanced to the point where chemical transport models can predict pollution in an urban air shed with spatial resolution less than a kilometer, and cover the globe with a horizontal resolution of less than 50km. Predicting air quality remains a challenge due to the complexity of the governing processes and the strong coupling across scales. While air quality prediction is closely aligned with weather prediction, there are important differences, including the role of pollution emissions and their associated large uncertainties. Improvements in air quality prediction require a close integration of observations. As more atmospheric chemical observations become available chemical data assimilation is expected to play an essential role in air quality forecasting. In this paper advances in air quality forecasting are discussed with an emphasis on data assimilation. Applications of the four-dimensional variational method (4D-Var) and the ensemble Kalman filter (EnKF) approach are presented and the computation challenges are discussed.

Three-dimensional simulations of inorganic aerosol distributions in east Asia during spring 2001

In this paper, aerosol composition and size distributions in east Asia are simulated using a comprehensive chemical transport model. Three-dimensional aerosol simulations for the TRACE-P and ACE-Asia periods are performed and used to help interpret actual observations. The regional chemical transport model, STEM-2K3, which includes the on-line gas-aerosol thermodynamic module SCAPE II, and explicitly considers chemical aging of dust, is used in the analysis. The model is found to represent many of the important observed features. The Asian outflow during March and April of 2001 is heavily polluted with high aerosol loadings. Under conditions of low dust loading, SO_2 condensation and gas phase ammonia distribution determine the nitrate size and gas-aerosol distributions along air mass trajectories, a situation that is analyzed in detail for two TRACE-P flights. Dust is predicted to alter the partitioning of the semivolatile components between the gas and aerosol phases as well as the size distributions of the secondary aerosol constituents. Calcium in the dust affects the gas-aerosol equilibrium by shifting the equilibrium balance to an anion-limited status, which benefits the uptake of sulfate and nitrate, but reduces the amount of aerosol ammonium. Surface reactions on dust provide an additional mechanism to produce aerosol nitrate and sulfate. The size distribution of dust is shown to be a critical factor in determining the size distribution of secondary aerosols. As much of the dust mass is found in the supermicron mode (70–90%), appreciable amounts of sulfate and nitrate are found in the supermicron particles. For sulfate the observations and the analysis indicate that 10–30% of sulfate is in the supermicron fraction during dust events; in the case of nitrate, more than 80% is found in the supermicron fraction.

Multirate Timestepping Methods for Hyperbolic Conservation Laws

Abstract This paper constructs multirate time discretizations for hyperbolic conservation laws that allow different timesteps to be used in different parts of the spatial domain. The proposed family of discretizations is second order accurate in time and has conservation and linear and nonlinear stability properties under local CFL conditions. Multirate timestepping avoids the necessity to take small global timesteps (restricted by the largest value of the Courant number on the grid) and therefore results in more efficient algorithms. Numerical results obtained for the advection and Burgers’ equations confirm the theoretical findings.

Sensitivity analysis for atmospheric chemistry models via automatic differentiation

Abstract Automatic differentiation techniques are introduced and applied in the sensitivity analysis of atmospheric chemistry studies. Specifically, ADIFOR software is used to calculate the sensitivity of ozone with respect to all initial concentrations (of 84 species) and all reaction rate constants (178 chemical reactions, for six different chemical regimes, varying from the marine boundary layer to continental boundary layers with and without isoprene, to the upper troposphere, including plumes with and without non-methane hydrocarbons. Numerical aspects of the application of ADIFOR are also presented. Automatic differentiation is shown to be a powerful tool for the application of sensitivity analysis to atmospheric chemistry problems.

Multiscale simulations of tropospheric chemistry in the eastern Pacific and on the U.S. West Coast during spring 2002

[ 1] Regional modeling analysis for the Intercontinental Transport and Chemical Transformation 2002 (ITCT 2K2) experiment over the eastern Pacific and U. S. West Coast is performed using a multiscale modeling system, including the regional tracer model Chemical Weather Forecasting System (CFORS), the Sulfur Transport and Emissions Model 2003 (STEM-2K3) regional chemical transport model, and an off-line coupling with the Model of Ozone and Related Chemical Tracers ( MOZART) global chemical transport model. CO regional tracers calculated online in the CFORS model are used to identify aircraft measurement periods with Asian influences. Asian-influenced air masses measured by the National Oceanic and Atmospheric Administration (NOAA) WP-3 aircraft in this experiment are found to have lower DeltaAcetone/DeltaCO, DeltaMethanol/DeltaCO, and DeltaPropane/DeltaEthyne ratios than air masses influenced by U. S. emissions, reflecting differences in regional emission signals. The Asian air masses in the eastern Pacific are found to usually be well aged (> 5 days), to be highly diffused, and to have low NOy levels. Chemical budget analysis is performed for two flights, and the O-3 net chemical budgets are found to be negative ( net destructive) in the places dominated by Asian influences or clear sites and positive in polluted American air masses. During the trans-Pacific transport, part of gaseous HNO3 was converted to nitrate particle, and this conversion was attributed to NOy decline. Without the aerosol consideration, the model tends to overestimate HNO3 background concentration along the coast region. At the measurement site of Trinidad Head, northern California, high-concentration pollutants are usually associated with calm wind scenarios, implying that the accumulation of local pollutants leads to the high concentration. Seasonal variations are also discussed from April to May for this site. A high-resolution nesting simulation with 12-km horizontal resolution is used to study the WP-3 flight over Los Angeles and surrounding areas. This nested simulation significantly improved the predictions for emitted and secondary generated species. The difference of photochemical behavior between the coarse (60-km) and nesting simulations is discussed and compared with the observation.

A Polynomial Chaos-Based Kalman Filter Approach for Parameter Estimation of Mechanical Systems

Background. Mechanical systems operate under parametric and external excitation uncertainties. The polynomial chaos approach has been shown to be more efficient than Monte Carlo for quantifying the effects of such uncertainties on the system response. Many uncertain parameters cannot be measured accurately, especially in real time applications. Information about them is obtained via parameter estimation techniques. Parameter estimation for large systems is a difficult problem, and the solution approaches are computationally expensive. Method of Approach. This paper proposes a new computational approach for parameter estimation based on the Extended Kalman Filter (EKF) and the polynomial chaos theory for parameter estimation. The error covariances needed by EKF are computed from polynomial chaos expansions, and the EKF is used to update the polynomial chaos representation of the uncertain states and the uncertain parameters. The proposed method is applied to a nonlinear four degree of freedom roll plane model of a vehicle, in which an uncertain mass with an uncertain position is added on the roll bar. Results. The main advantages of this method are an accurate representation of uncertainties via polynomial chaoses, a computationally efficient update formula based on EKF, and the ability to provide aposteriori probability densities of the estimated parameters. The method is able to deal with non-Gaussian parametric uncertainties. The paper identifies and theoretically explains a possible weakness of the EKF with approximate covariances: numerical errors due to the truncation in the polynomial chaos expansions can accumulate quickly when measurements are taken at a fast sampling rate. To prevent filter divergence we propose to lower the sampling rate, and to take a smoother approach where a set of time-distributed observations are all processed at once. Conclusions. We propose a parameter estimation approach that uses polynomial chaoses to propagate uncertainties and estimate error covariances in the EKF framework. Parameter estimates are obtained in the form of a polynomial chaos expansion which carries information about the aposteriori probability density function. The method is illustrated on a roll plane vehicle model.

Comparison of POD reduced order strategies for the nonlinear 2D shallow water equations

SUMMARY This paper introduces tensorial calculus techniques in the framework of POD to reduce the computational complexity of the reduced nonlinear terms. The resulting method, named tensorial POD, can be applied to polynomial nonlinearities of any degree p. Such nonlinear terms have an online complexity of O(kp+1), where k is the dimension of POD basis and therefore is independent of full space dimension. However, it is efficient only for quadratic nonlinear terms because for higher nonlinearities, POD model proves to be less time consuming once the POD basis dimension k is increased. Numerical experiments are carried out with a two-dimensional SWE test problem to compare the performance of tensorial POD, POD, and POD/discrete empirical interpolation method (DEIM). Numerical results show that tensorial POD decreases by 76× the computational cost of the online stage of POD model for configurations using more than 300,000 model variables. The tensorial POD SWE model was only 2 to 8× slower than the POD/DEIM SWE model but the implementation effort is considerably increased. Tensorial calculus was again employed to construct a new algorithm allowing POD/DEIM SWE model to compute its offline stage faster than POD and tensorial POD approaches. Copyright