Adjoint Algorithm Research Articles

NCAR Auto-Nowcast System

The Auto-Nowcast System (ANC), a software system that produces time- and space-specific, routine (every 5 min) short-term (0‐1 h) nowcasts of storm location, is presented. A primary component of ANC is its ability to identify and characterize boundary layer convergence lines. Boundary layer information is used along with storm and cloud characteristics to augment extrapolation with nowcasts of storm initiation, growth, and dissipation. A fuzzy logic routine is used to combine predictor fields that are based on observations (radar, satellite, sounding, mesonet, and profiler), a numerical boundary layer model and its adjoint, forecaster input, and feature detection algorithms. The ANC methodology is illustrated using nowcasts of storm initiation, growth, and dissipation. Statistical verification shows that ANC is able to routinely improve over extrapolation and persistence.

Adjoint and Generalized Adjoint Flux Calculations Using the Collision Probability Technique

Computation of adjoint and generalized adjoint fluxes may present some difficulties, especially when relying on the collision probability technique in transport theory. This paper proposes a simple method to compute those adjoint flux and generalized adjoint fluxes associated with homogenized and condensed cross sections. By defining a pseudo adjoint flux, one can apply an algorithm, similar to that required for the evaluation of the direct neutron flux, to adjoint flux calculations. Because of the presence of the scattering source, a multigroup iterative procedure is used in DRAGON for the direct flux solution. We show that this procedure can be easily modified in such a way that the performance of the solution algorithm is preserved for the adjoint problem. Finally, a generic adjoint algorithm is presented to deal with generalized adjoint fluxes’ computation.

Optical tomography using the time-independent equation of radiative transfer—Part 2: inverse model

Optical tomography is a novel imaging modality that is employed to reconstruct cross-sectional images of the optical properties of highly scattering media given measurements performed on the surface of the medium. Recent advances in this field have mainly been driven by biomedical applications in which near-infrared light is used for transillumination and reflectance measurements of highly scattering biological tissues. Many of the reconstruction algorithms currently utilized for optical tomography make use of model-based iterative image reconstruction (MOBIIR) schemes. The imaging problem is formulated as an optimization problem, in which an objective function is minimized. In the simplest case the objective function is a normalized-squared error between measured and predicted data. The predicted data are obtained by using a forward model that describes light propagation in the scattering medium given a certain distribution of optical properties. In part I of this two-part study, we presented a forward model that is based on the time-independent equation of radiative transfer. Using experimental data we showed that this transport-theory-based forward model can accurately predict light propagation in highly scattering media that contain void-like inclusions. In part II we focus on the details of our image reconstruction scheme (inverse model). A crucial component of this scheme involves the efficient and accurate determination of the gradient of the objective function with respect to all optical properties. This calculation is performed using an adjoint differentiation algorithm that allows for fast calculation of this gradient. Having calculated this gradient, we minimize the objective function with a gradient-based optimization method, which results in the reconstruction of the spatial distribution of scattering and absorption coefficients inside the medium. In addition to presenting the mathematical and numerical background of our code, we present reconstruction results based on experimentally obtained data from highly scattering media that contain void-like regions. These types of media play an important role in optical tomographic imaging of the human brain and joints.

Variational data assimilation for tropospheric chemistry modeling

The method of variational adjoint data assimilation has been applied to assimilate chemistry observations into a comprehensive tropospheric gas phase model. The rationale of this method is to find the correct initial values for a subsequent atmospheric chemistry model run when observations scattered in time are available. The variational adjoint technique is esteemed to be a promising tool for future advanced meteorological forecasting. The stimulating experience gained with the application of four‐dimensional variational data assimilation in this research area has motivated the attempt to apply the technique to air quality modeling and analysis of the chemical state of the atmosphere. The present study describes the development and application of the adjoint of the second‐generation regional acid deposition model gas phase mechanism, which is used in the European air pollution dispersion model system. Performance results of the assimilation scheme using both model‐generated data and real observations are presented for tropospheric conditions. In the former case it is demonstrated that time series of only few or even one measured key species convey sufficient information to improve considerably the analysis of unobserved species which are directly coupled with the observed species. In the latter case a Lagrangian approach is adopted where trajectory calculations between two comprehensively furnished measurement sites are carried out. The method allows us to analyze initial data for air pollution modeling even when only sparse observations are available. Besides remarkable improvements of the model performance by properly analyzed initial concentrations, it is shown that the adjoint algorithm offers the feasibility to estimate the sensitivity of ozone concentrations relative to its precursors.

Optimized numerical models for semiconductor devices: Part I

This article presents some results from a study concerned with the trade-off between efficiency of numerical computation and accuracy of numerical models for semiconductor devices. The approach taken in this study was to use nonuniform grids in the finite difference equations approximating the semiconductor partial differential equations. A constrained minimization problem was formulated which analytically optimizes the numerical models. Several performance functions were found useful in optimizing the numerical models; the one presented here matches computed and "exact" terminal current responses. An example is presented to illustrate the results obtained with this performance function. The example model optimization shows that the optimized grids should have their greatest density in the space-charge region near the junction. An interesting side result is that when one performance function is optimized, apparently other desired features are optimized for numerical models for semiconductor devices. The Fletcher-Powell optimization algorithm was used with an adjoint gradient algorithm specifically developed for this study, without which the use of nonuniform grids would not have been practical.