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The task of providing an optimal analysis of the state of the atmosphere requires the development of dynamic data-driven systems (DDDAS) that efficiently integrate the observational data and the models. Data assimilation, the dynamic incorporation of additional data into an executing application, is an essential DDDAS concept with wide applicability. In this paper we discuss practical aspects of nonlinear ensemble Kalman data assimilation applied to atmospheric chemical transport models. We highlight the challenges encountered in this approach such as filter divergence and spurious corrections, and propose solutions to overcome them, such as background covariance inflation and filter localization. The predictability is further improved by including model parameters in the assimilation process. Results for a large scale simulation of air pollution in North-East United States illustrate the potential of nonlinear ensemble techniques to assimilate chemical observations.

In this paper we discuss variational data assimilation using the STEM atmospheric Chemical Transport Model. STEM is a multiscale model and can perform air quality simulations and predictions over spatial and temporal scales of different orders of magnitude. To improve the accuracy of model predictions we construct a dynamic data driven application system (DDDAS) by integrating data assimilation techniques with STEM. We illustrate the improvements in STEM field predictions before and after data assimilation. We also compare three popular optimization methods for data assimilation and conclude that L-BFGS method is the best for our model because it requires fewer model runs to recover optimal initial conditions.

Recent studies have shown that exposure to particulate black carbon (BC) has significant adverse health effects and may be more detrimental to human health than exposure to PM2.5 as a whole. Mobile source BC emission controls, mostly on diesel-burning vehicles, have successfully decreased mobile source BC emissions to less than half of what they were 30 years ago. Quantification of the benefits of previous emissions controls conveys the value of these regulatory actions and provides a method by which future control alternatives could be evaluated. In this study we use the adjoint of the Community Multiscale Air Quality (CMAQ) model to estimate highly-resolved spatial distributions of benefits related to emission reductions for six urban regions within the continental US. Emissions from outside each of the six chosen regions account for between 7% and 27% of the premature deaths attributed to exposure to BC within the region. While we estimate that nonroad mobile and onroad diesel emissions account for the largest number of premature deaths attributable to exposure to BC, onroad gasoline is shown to have more than double the benefit per unit emission relative to that of nonroad mobile and onroad diesel. Within the region encompassing New York City and Philadelphia, reductions in emissions from large industrial combustion sources that are not classified as EGUs (i.e., non-EGU) are estimated to have up to triple the benefits per unit emission relative to reductions to onroad diesel sectors, and provide similar benefits per unit emission to that of onroad gasoline emissions in the region. While onroad mobile emissions have been decreasing in the past 30 years and a majority of vehicle emission controls that regulate PM focus on diesel emissions, our analysis shows the most efficient target for stricter controls is actually onroad gasoline emissions.

Purpose: To test the accuracy and reproducibility of both translational and rotational movements for a couch with six degrees of freedom (6DoF) using a novel phantom design Methods: An end-to-end test was carried out using two different phantoms. A 6 cm3 cube with a central fiducial BB (WL-QA Sun Nuclear) and a custom fabricated rectangular prism (31 cm x 8 cm x 8 cm), placed on a baseplate with known angular offsets for pitch, roll and yaw with a central fiducial BB and unique surface structures for registration purposes, were used. The end-to-end test included an initial CT simulation for a reference study, setup to an offset mark on each phantom, registration of the reference CT to the acquired cone-beam CT, and final Winston-Lutz delivery at four cardinal gantry angles. Results for both translational and rotational movements were recorded and compared for both phantoms. Results: Translational and rotational measurements were performed with a PerfectPitch (Varian) couch for 10 trials for both phantoms. Distinct translational shifts were [−5.372±0.384mm, −10.183±0.137mm, 14.028±0.155mm] for the cube and [7.520±0.159mm, −9.117±0.101mm, 16.273±0.115mm] for the prototype phantom for lateral, longitudinal, and vertical shifts, respectively. Distinct rotational adjustments were [1.121±0.102o, −1.067±0.235o, −2.662±0.380o] for the cube and [2.534±0.059o, 1.994±0.025o, 2.094±0.076o] for the prototype for pitch, roll, and yaw, respectively. Winston-Lutz test results performed after 6DoF couch correction from each cardinal gantry angle ranged from 0.26–0.72mm for the cube and 0.55–0.86mm for the prototype. Conclusion: The prototype phantom is more precise for both translational and rotational adjustments compared to a commercial phantom. The design of the prototype phantom allows for a more discernible visual confirmation of correct translational and rotational adjustments with the prototype phantom. Winston-Lutz results are more accurate for the commercial phantom but are still within tolerance for the prototype phantom.

An application of the adjoint method in air quality management is demonstrated. We use a continental scale chemical transport model (STEM) to calculate the sensitivities of a nationwide U.S. ozone national ambient air quality standard (NAAQS) nonattainment metric to precursor emissions for the period July 1 to August 15, 2004. The model shows low bias and error (−4 and 24%, respectively), particularly for areas with high ozone concentrations. The nonattainment metric accounts for both 1-h and 8-h ozone standards, but is dominated by the 8-h exceedances (97% of the combined metric). Largest values of sensitivities are found to be with respect to emissions in the south and southeast U.S., Ohio River Valley, and California. When nonattainment sensitivities are integrated over the entire U.S., NOx emissions account for the largest contribution (62% of the total), followed by biogenic and anthropogenic VOCs (24% and 14%, respectively). For NO_x emissions, point/area and mobile sources account for 54% and 46% of the total sensitivities, respectively. We also provide a state-by-state comparison for the nonattainment magnitude, nonattainment sensitivity, and emission magnitudes to explore the influence of interstate transport of ozone and its precursors, and policy implications of the results. Our analysis of the nationwide ozone nonattainment metric suggests that simple cap-and-trade programs may prove inadequate in achieving sought-after air quality objectives.

[1] In this paper, the four-dimensional variational (4D-Var) technique is applied to assimilate aircraft measurements during the Transport and Chemical Evolution over the Pacific (TRACE-P) field experiment into a chemical transport model, Sulfur Transport Eulerian Model, version 2K1 (STEM-2K1). Whether data assimilation would produce better analyzed fields is examined. It is found that assimilating ozone observations from one of two independent flights improves model prediction of the other flight ozone measurements, which are withheld as validation data. The adjusted initial fields after only assimilating the total reactive nitrogen (NOy) observations lead to better predictions of NO, NO2, and PAN, based on their agreement with the withheld measurements. One experiment simultaneously assimilating the observations of O3, NO, NO2, HNO3, PAN, and RNO3 demonstrates that the model is able to match those measurements well by changing the initial fields. In addition, the model predictions of NOy improve significantly after assimilating the aforementioned multiple observation species, which are independent of the withheld NOy measurements. In the paper, we also show that the key species whose initial mixing ratios would significantly affect the agreement between model and measurements can be identified using adjoint sensitivity analysis. Such information can be used to reduce the number of control variables in the 4D-Var data assimilation. To speed up the optimization process in the 4D-Var, we enforce the concentration upper bounds through the limited memory–Broyden-Fletcher-Goldfarb-Shanno-B (L-BFGS-B) algorithm, and this proves to be effective.

This paper presents the new version 2.1 of the Kinetic PreProcessor (KPP). Taking a set of chemical reactions and their rate coefficients as input, KPP generates Fortran90, Fortran77, Matlab, or C code for the temporal integration of the kinetic system. Efficiency is obtained by carefully exploiting the sparsity structures of the Jacobian and of the Hessian. A comprehensive suite of stiff numerical integrators is also provided. Moreover, KPP can be used to generate the tangent linear model, as well as the continuous and discrete adjoint models of the chemical system.

This paper presents the new stiff solvers of the new version 2.2 of the Kinetic PreProcessor (KPP). Taking a set of chemical reactions and their rate coefficients as input, KPP generates Fortran90, Fortran77, Matlab, or C code for the temporal integration of the kinetic system. Efficiency is obtained by carefully exploiting the sparsity structures of the Jacobian and of the Hessian. A set of integration methods was added to the comprehensive suite of stiff numerical integrators. Moreover, KPP is now ready do be used to generate the tangent linear model, as well as the continuous and discrete adjoint models of the chemical system to do sensitivity analysis.

In this paper we analyze the consistency and stability properties of Runge-Kutta discrete adjoints. Discrete adjoints are very popular in optimization and control since they can be constructed automatically by reverse mode automatic differentiation. The consistency analysis uses the concept of elementary differentials and reveals that the discrete Runge-Kutta adjoint method has the same order of accuracy as the original, forward method. A singular perturbation analysis reveals that discrete adjoints of stiff Runge-Kutta methods are well suited for stiff problems.

One fundamental difficulty in understanding the physics of the off-road traction and in predicting vehicle performance is the variability of the terrain profile and soil parameters. These operating conditions are uniquely defined at a given spatial location and a given time. It is not practically feasible, however, to measure them at a sufficiently large number of points to be able to accurately represent the terrain in models. This renders traditional analysis tools insufficient when dealing with rough deformable terrain. We employ stochastic analysis to capture the uncertain nature of this running support and the corresponding vehicle response. From a finite number of observations the terrain profile and soil properties can be modeled as random processes, with the actual operating conditions viewed as a particular realization of these processes. Soil parameters vary substantially from one type of soil to another. Moreover, for the same soil type, the parameters change with environmental conditions difficult to predict, for example the moisture content. Such uncertain soil parameters are modeled in this study as uniform or normal distributed random variables.

[1] An adjoint model is used for inverse modeling of black carbon during the Asian Pacific Regional Aerosol Characterization Experiment (ACE-Asia). We use the four-dimensional variational data assimilation (4D-Var) approach to optimally recover spatially resolved anthropogenic and biomass-burning emissions and initial and boundary conditions of black carbon. Boundary conditions and biomass-burning emissions are assigned daily scaling factors. Anthropogenic emissions are scaled by a combination of daily and monthly scaling factors. Simulation results are compared to various observations of black carbon concentrations during the campaign. Measurements at five islands and on board the research vessel Ronald H. Brown are used for inverse modeling. Different levels of constraints are examined for inversion, and a case with 62% reduction in the total square errors is chosen. The assimilated results are compared with the observations on board the Twin Otter aircraft that were not used for assimilation. Among the scaled variables, anthropogenic emissions are the most significant, followed by the boundary conditions. The domain-wide emissions inventory does not change significantly as a result of the assimilation, but sizable changes occur on the subregional level. Most noticeably, anthropogenic emissions over southeastern China are reduced while those in northeast China and Japan are increased.

This paper discusses an implementation of an adaptive resolution system for modeling regional air pollution based on the chemical transport model STEM. The grid adaptivity is implemented using the generic tool Paramesh. The computational algorithm uses a decomposition of the domain, with the solution in different sub-domains computed at different spatial resolutions. We analyze the parallel computational performance versus the accuracy of long time simulations.

This paper discusses several aspects related to the consistency and stability of the discrete adjoints of upwind numerical schemes. First and third order upwind discretizations of the one-dimensional advection equation are considered in both the finite difference and finite volume formulations. We show that the discrete adjoints may lose consistency and stability near the points where upwinding is changed, and near inflow boundaries where the numerical scheme is changed. The impact of adjoint inconsistency and instability on data assimilation is analyzed.

This paper presents the mathematical development of and simulation results for a full vehicle model with parametric uncertainties operating over unprepared terrain. The vehicle is modeled as a rigid multi-body dynamic system, consisting of chassis and four suspension and tire subsystems. The vehicle parameters considered uncertain are the suspension damping and the tire stiffness. The terrain profile is also modeled as a stochastic function. The uncertainties are explicitly represented using polynomial chaos decompositions. The computational technique presented in this study is more efficient than the traditional Monte Carlo approach, in modeling nonlinear multi-body dynamic systems with uncertainties. The numerical results presented here are very promising. The general computational tools discussed in this paper can be applied directly to any area that involves multi-body dynamic models, e.g., robotics, autonomous mechanical systems, actuator dynamics, and automatic control of systems with uncertainties.Copyright © 2005 by ASME

The task of providing an optimal analysis of the state of the atmosphere requires the development of dynamic data-driven systems (d3as) that efficiently integrate the observational data and the models. In this paper we discuss fundamental aspects of nonlinear ensemble data assimilation applied to atmospheric chemical transport models. We formulate autoregressive models for the background errors and show how these models are capable of capturing flow dependent correlations. Total energy singular vectors describe the directions of maximum errors growth and are used to initialize the ensembles. We highlight the challenges encountered in the computation of singular vectors in the presence of stiff chemistry and propose solutions to overcome them. Results for a large scale simulation of air pollution in East Asia illustrate the potential of nonlinear ensemble techniques to assimilate chemical observations.

The feasibility of inverse modeling a multicomponent, size-resolved aerosol evolving by condensation/evaporation is investigated. The adjoint method is applied to the multicomponent aerosol dynamic equation in a box model (zero-dimensional) framework. Both continuous and discrete formulations of the model (the forward equation) and the adjoint are considered. A test example is studied in which the initial aerosol size composition distribution and the pure component vapor concentrations (i.e., vapor pressures) are estimated on the basis of measurements of all species, or a subset of the species, and the entire size distribution, or a portion of the size distribution. It is found that the adjoint method can successfully retrieve the initial size distribution and the pure component vapor concentrations even when only a subset of the species or a portion of the size distribution is observed, although this success is shown to depend upon the form of the initial estimates, the nature of the observations, and the length of the assimilation period. The results presented here provide a basis for the inverse modeling of aerosols in three-dimensional atmospheric chemical transport models.

[ 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.

We discuss an adaptive resolution system for modeling regional air pollution based on the chemical transport model Stem. The grid adaptivity is implemented using the generic tool Paramesh, which enables the grid management operations while harnessing the power of parallel computers. The computational algorithm is based on a decomposition of the domain, with the solution in different sub-domains being solved at different spatial resolutions. Numerical experiments confirm that adaptive resolution leads to the decrease in spatial error with an acceptable increase in computational time. Advantages and shortcomings of the present approach are also discussed.

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.

In this paper we discuss the algorithmic tools needed for data assimilation for aerosol dynamics. Continuous and discrete adjoints of the aerosol dynamic equation are considered, as well as sensitivity coefficients with respect to the coagulation kernel, the growth rate, and emission and deposition coefficients. Numerical experiments performed in the twin experiment framework for a single component model problem show that initial distributions and the dynamic parameters can be recovered from time series of observations of particle size distributions.

This study investigates a control methodology for dynamic systems based on representing all possible system responses under all possible values of the control variables. The underlying idea is to extend the system along the “control dimension” and explicitly account for the dependence of the system state on control variables. A spectral discretization along the “control dimension” is employed. The optimal control values are chosen to obtain the desired system response. Numerical studies for the control of linear and nonlinear quarter car models riding on various terrain profiles show promising results.Copyright © 2004 by ASME

This paper presents a discretization technique for particle dynamics equation based on the B-spline interpolation of the solution. The method is developed in the general framework recently proposed by the authors. Numerical tests include the coagulation-growth of the exponential distribution and of a cosine hill in logarithmic coordinates.

When performing dynamic analysis of a constrained mechanical system, a set of index 3 Differential-Algebraic Equations (DAE) describes the time evolution of the system. The paper presents a state-space based method for the numerical solution of the resulting DAE. A subset of so called independent generalized coordinates, equal in number to the number of degrees of freedom of the mechanical system, is used to express the time evolution of the mechanical system. The second order statespace ordinary differential equations (SSODE) that describe the time variation of independent coordinates are numerically integrated using a Rosenbrock type formula. For stiff mechanical systems, the proposed algorithm is shown to significantly reduce simulation times when compared to state of the art existent algorithms. The better efficiency is due to the use of an L-stable integrator and a rigorous and general approach to providing analytical derivatives required by it.Copyright © 2003 by ASME

The task of providing aa optimal analysis of the state of the atmosphere requires the development of novel computational tools that facilitate an efficient integeration of observational data into models. In this paper we discuss some of the computational tools developed for the assimilation of chemical data imo atmospheric models. We perform a theoretical analysis of discrete and cominuous adjoints for stiff differential equation solvers. Software tools particularly tailored for direct and adjoint sensitivity analysis of chemical systems are presented. The adjoint of the state-of-the-art model STEM-III is discussed, together with ozone assimilation results for a realistic test problem.

This paper presents an application of adjoint sensitivity calculation to retrieve the initial distribution of the aerosol population from measurements at later times. A general framework is given for the discretization of particle dynamics equation by projection methods. The adjoint of the discrete model is constructed. Adjoint modeling successfully retrieves the initial distribution, even is the measurements are restricted to only specific size bins.

When performing dynamic analysis of a constrained mechanical system, a set of index 3 Differential-Algebraic Equations (DAE) describes the time evolution of the system model. The paper presents a state-space based method for the numerical solution of the resulting DAE.

Data assimilation obtains improved estimates of the state of a physical system by combining imperfect model results with sparse and noisy observations of reality. Not all observations used in data assimilation are equally valuable. The ability to characterize the usefulness of different observation locations is important for analyzing the effectiveness of the assimilation system, for data pruning, and for the design of future sensor systems. This paper proposes a new approach to characterizes the usefulness of different observation in four dimensional variational (4D-Var) data assimilation. Metrics from information theory are used to quantify the contribution of observations to decreasing uncertainty with which the system state is known. We derive ensemble based, computationally feasible procedures to estimate the information content of various observations.

This paper presents a new ‘Parareal-algorithm’ to solve time-dependent ODEs parallel in time. The algorithm approximates the solutions later in time simultaneously with the solutions earlier in time. To approximate the solutions simultaneously, an optimization problem is constructed and solved using gradient based techniques. The accurate gradients are evaluated using adjoints. Promising results are obtained when the interval of interest is split into suffciently small subintervals.

Adaptivity in space and time is ubiquitous in modern numerical simulations. The large number of unknowns associated with today's typical inverse problem may run in the millions, or more. To capture small scale phenomena in regions of interest, adaptive mesh and temporal step refinements are required, since uniform refinements quickly make the problem computationally intractable. To date, there is still a considerable gap between the state–of–the–art techniques used in direct (forward) simulations, and those employed in the solution of inverse problems, which have traditionally relied on fixed meshes and time steps. This paper describes a framework for building a space-time consistent adjoint discretization for a general discrete forward problem, in the context of adaptive mesh, adaptive time step models. The discretize–then–di_erentiate approach to optimization is a very attractive approach in practice, because the adjoint model code may be generated using automatic di_erentiation (AD). However, several challenges are introduced when using an adaptive forward solver. First, one may have consistency problems with the adjoint of the forward numerical scheme. Similarly, intergrid transfer operators may reduce the accuracy of the discrete adjoint sensitivities. The optimization algorithm may need to be specifically tailored to handle variations in the state and gradient vector sizes. This work shows that several of these potential issues can be avoided when using the Runge–Kutta discontinuous Galerkin (DG) method, an excellent candidate method for h=p-adaptive parallel simulations. Selective application of automatic di_erentiation on individual numerical algorithms may simplify considerably the adjoint code development. A numerical data assimilation example illustrates the e_ectiveness of the primal/dual RK–DG methods when used in inverse simulations.

Implicit-explicit time stepping methods have proved useful for effciently solving problems with both still and nonstill components. IMEX Runge-Kutta methods and IMEX multistep methods have been studied in the literature. But there are no available IMEX general linear methods (IMEX-GLMs). In this paper, we construct IMEX schemes based on diagonally-implicit multi-stage integration methods. The new algorithms have great potential for practical use. Numerical results indicate the observed order of accuracy matches the theoretical order.

The aim of this paper is to address computational aspects of the total energy singular vector analysis of atmospheric chemical transport models. We discuss the symmetry of the tangent-linear/adjoint operator for stiff systems. Results for a 3D simulation with real data reveal that the total energy singular vectors depend on the target domain, simulation window, chemical reactions, and meteorological data.