Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “adjoint problem”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

444 records · Page 25
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Drag reduction at a plane wall

The objective is to determine by analytical means how drag on a plane wall may be modified favorably using a minimal amount of flow information - preferably only information at the wall. What quantities should be measured? How should that information be assimilated in order to arrive at effective control? As a prototypical problem, incompressible, viscous flow, governed by the Navier-Stokes equations, past a plane wall at which the no-slip condition was modified was considered. The streamwise and spanwise velocity components are required to be zero, but the normal component is to be specified according to some control law. The challenge is to choose the wall-normal velocity component based on flow conditions at the wall so that the mean drag is as small as possible. There can be no net mass flux through the wall, and the total available control energy is constrained. A turbulent flow is highly unsteady and has detailed spatial structure. The mean drag on the wall is the integral over the wall of the local shear forces exerted by the fluid, which is then averaged in time; it is a 'macroscopic' property of the flow. It is not obvious how unsteady boundary control is to be applied in order to modify the mean flow most effectively, especially in view of the non- self-adjoint nature of the governing equations. An approximate analytical solution to the suboptimal scheme is pursued.

Hill, D. C.↗
DOE OSTI2020

Online adaptive basis refinement and compression for reduced-order models via vector-space sieving

In many applications, projection-based reduced-order models (ROMs) have demonstrated the ability to provide rapid approximate solutions to high-fidelity full-order models (FOMs). However, there is no a priori assurance that these approximate solutions are accurate; their accuracy depends on the ability of the low-dimensional trial basis to represent the FOM solution. As a result, ROMs can generate inaccurate approximate solutions, e.g., when the FOM solution at the online prediction point is not well represented by training data used to construct the trial basis. To address this fundamental deficiency of standard model-reduction approaches, this work proposes a novel online-adaptive mechanism for efficiently enriching the trial basis in a manner that ensures convergence of the ROM to the FOM, yet does not incur any FOM solves. The mechanism is based on the previously proposed adaptive $h$-refinement method for ROMs, but improves upon this work in two crucial ways. First, the proposed method enables basis refinement with respect to any orthogonal basis (not just the Kronecker basis), thereby generalizing the refinement mechanism and enabling it to be tailored to the physics characterizing the problem at hand. Second, the proposed method provides a fast online algorithm for periodically compressing the enriched basis via an efficient proper orthogonal decomposition (POD) method, which does not incur any operations that scale with the FOM dimension. We report these two features allow the proposed method to serve as (1) a failsafe mechanism for ROMs, as the method enables the ROM to satisfy any prescribed error tolerance online (even in the case of inadequate training), and (2) an efficient online basis-adaptation mechanism, as the combination of basis enrichment and compression enables the basis to adapt online while controlling its dimension.

42 ENGINEERING↗
DOE OSTI2017

An Immersed Boundary method with divergence-free velocity interpolation and force spreading

The Immersed Boundary (IB) method is a mathematical framework for constructing robust numerical methods to study fluid–structure interaction in problems involving an elastic structure immersed in a viscous fluid. The IB formulation uses an Eulerian representation of the fluid and a Lagrangian representation of the structure. The Lagrangian and Eulerian frames are coupled by integral transforms with delta function kernels. The discretized IB equations use approximations to these transforms with regularized delta function kernels to interpolate the fluid velocity to the structure, and to spread structural forces to the fluid. It is well-known that the conventional IB method can suffer from poor volume conservation since the interpolated Lagrangian velocity field is not generally divergence-free, and so this can cause spurious volume changes. In practice, the lack of volume conservation is especially pronounced for cases where there are large pressure differences across thin structural boundaries. The aim of this paper is to greatly reduce the volume error of the IB method by introducing velocity-interpolation and force-spreading schemes with the properties that the interpolated velocity field in which the structure moves is at least $\mathscr{C}$ 1 and satisfies a continuous divergence-free condition, and that the force-spreading operator is the adjoint of the velocity-interpolation operator. We confirm through numerical experiments in two and three spatial dimensions that this new IB method is able to achieve substantial improvement in volume conservation compared to other existing IB methods, at the expense of a modest increase in the computational cost. Further, the new method provides smoother Lagrangian forces (tractions) than traditional IB methods. Finally, the method presented here is restricted to periodic computational domains. Its generalization to non-periodic domains is important future work.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Elastic full-waveform inversion and parameterization analysis applied to walk-away vertical seismic profile data for unconventional (heavy oil) reservoir characterization

We report seismic full-waveform inversion (FWI) methods hold strong potential to recover multiple subsurface elastic properties for hydrocarbon reservoir characterization. Simultaneously updating multiple physical parameters introduces the problem of interparameter tradeoff, arising from the covariance between different physical parameters, which increases nonlinearity and uncertainty of multiparameter FWI. The coupling effects of different physical parameters are significantly influenced by model parameterization and acquisition arrangement. An appropriate choice of model parameterization is critical to successful field data applications of multiparameter FWI. The objective of this paper is to examine the performance of various model parameterizations in isotropic-elastic FWI with walk-away vertical seismic profile (W-VSP) dataset for unconventional heavy oil reservoir characterization. Six model parameterizations are considered: velocity-density (α, β and ρ'), modulus-density (κ, μ and ρ), Lamé-density (λ, μ' and ρ'''), impedance-density (IP, IS and ρ''), velocity-impedance-I (α', β' and I' P ), and velocity-impedance-II (α'', β'' and I'S). We begin analyzing the interparameter tradeoff by making use of scattering radiation patterns, which is a common strategy for qualitative parameter resolution analysis. In this paper, we discuss the advantages and limitations of the scattering radiation patterns and recommend that interparameter tradeoffs be evaluated using interparameter contamination kernels, which provide quantitative, second-order measurements of the interparameter contaminations and can be constructed efficiently with an adjoint-state approach. Synthetic W-VSP isotropic-elastic FWI experiments in the time domain verify our conclusions about interparameter tradeoffs for various model parameterizations. Density profiles are most strongly influenced by the interparameter contaminations; depending on model parameterization, the inverted density profile can be over-estimated, under-estimated or spatially distorted. Among the six cases, only the velocity-density parameterization provides stable and informative density features not included in the starting model. Field data applications of multicomponent W-VSP isotropic-elastic FWI in the time domain were also carried out. Finally, the heavy oil reservoir target zone, characterized by low α-to-β ratios and low Poisson’s ratios, can be identified clearly with the inverted isotropic-elastic parameters.

58 GEOSCIENCES↗
NASA NTRS1996

Variational Methods in Sensitivity Analysis and Optimization for Aerodynamic Applications

Variational methods (VM) sensitivity analysis, which is the continuous alternative to the discrete sensitivity analysis, is employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The determination of the sensitivity derivatives of the performance index or functional entails the coupled solutions of the state and costate equations. As the stable and converged numerical solution of the costate equations with their boundary conditions are a priori unknown, numerical stability analysis is performed on both the state and costate equations. Thereafter, based on the amplification factors obtained by solving the generalized eigenvalue equations, the stability behavior of the costate equations is discussed and compared with the state (Euler) equations. The stability analysis of the costate equations suggests that the converged and stable solution of the costate equation is possible only if the computational domain of the costate equations is transformed to take into account the reverse flow nature of the costate equations. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Ibrahim, A. H.↗
NASA NTRS2017

Reconfigurable Model Execution in the OpenMDAO Framework

NASA's OpenMDAO framework facilitates constructing complex models and computing their derivatives for multidisciplinary design optimization. Decomposing a model into components that follow a prescribed interface enables OpenMDAO to assemble multidisciplinary derivatives from the component derivatives using what amounts to the adjoint method, direct method, chain rule, global sensitivity equations, or any combination thereof, using the MAUD architecture. OpenMDAO also handles the distribution of processors among the disciplines by hierarchically grouping the components, and it automates the data transfer between components that are on different processors. These features have made OpenMDAO useful for applications in aircraft design, satellite design, wind turbine design, and aircraft engine design, among others. This paper presents new algorithms for OpenMDAO that enable reconfigurable model execution. This concept refers to dynamically changing, during execution, one or more of: the variable sizes, solution algorithm, parallel load balancing, or set of variables-i.e., adding and removing components, perhaps to switch to a higher-fidelity sub-model. Any component can reconfigure at any point, even when running in parallel with other components, and the reconfiguration algorithm presented here performs the synchronized updates to all other components that are affected. A reconfigurable software framework for multidisciplinary design optimization enables new adaptive solvers, adaptive parallelization, and new applications such as gradient-based optimization with overset flow solvers and adaptive mesh refinement. Benchmarking results demonstrate the time savings for reconfiguration compared to setting up the model again from scratch, which can be significant in large-scale problems. Additionally, the new reconfigurability feature is applied to a mission profile optimization problem for commercial aircraft where both the parametrization of the mission profile and the time discretization are adaptively refined, resulting in computational savings of roughly 10% and the elimination of oscillations in the optimized altitude profile.

Hwang, John T.↗
DOE OSTI2016

Assessment of Multi-Step CADIS Parameter Sensitivity to Neutron Flux Spectrum in Shutdown Dose Rate Calculations

Shutdown dose rate (SDDR) analysis requires (a) a neutron transport calculation to estimate neutron flux fields, (b) an activation calculation to compute radionuclide inventories and associated photon sources, and (c) a photon transport calculation to estimate final dose rate. In some applications, accurate full-scale Monte Carlo (MC) SDDR simulations are needed for very large systems with massive amounts of shielding materials. For example, SDDR assessments are required throughout the biological shield (bio-shield) of the ITER experimental facility to evaluate the required waiting period after the shutdown of ITER and to identify the locations where human accessibility should be prohibited. The bio-shield is a large cylindrical concrete structure (30 m tall and 34 m in diameter) surrounding the very complex tokamak machine. Determining the effects on SDDR of important factors, such as the cross talk (interactions) between the different ports of ITER, is possible only through full-scale simulations that involve all the complex inner details of the ITER tokamak machine. These simulations are impractical because calculation of space- and energy-dependent neutron fluxes throughout the structural materials is needed to estimate the distribution of radioisotopes causing the SDDR. Determining a good importance function that can be used in biasing a neutron MC calculation for SDDR is complicated because it is difficult to explicitly express the SDDR response function, which depends on subsequent computational steps. The Multi-Step Consistent Adjoint Driven Importance Sampling (MS-CADIS) hybrid MC/deterministic method was developed to speed up the SDDR MC neutron transport calculation using an importance function that represents the neutron importance to the final SDDR. The MS-CADIS method uses the CADIS method, which has been Notice: This manuscript has been authored by UT-Battelle, LLC, under Contract No. DE-AC0500OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for the United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan). successfully used for more than a decade in radiation shielding applications to generate consistent source biasing and weight window (WW) variance reduction parameters to accelerate continuous-energy MC simulations. However, because MS-CADIS focuses on multi-step shielding calculations such as SDDR calculations, it develops an importance function for the initial radiation transport calculation (e.g., the neutron calculations in SDDR simulations) that represents the importance of particles to the final response of the overall simulation. To develop this importance function, the MS-CADIS method uses an adjoint calculation with a specific neutron adjoint source that represents the neutron's contribution to the final SDDR. Brute force calculation of the MS-CADIS neutron adjoint source requires a deterministic neutron transport calculation coupled with activation calculations in each element of the deterministic mesh. These calculations are needed to determine the MS-CADIS parameter for the neutron interactions that produce radioisotopes contributing to the SDDR. The MS-CADIS parameter is the microscopic cross section of the radioisotope-producing interaction, multiplied by the mass of this radioisotope existing at the end of the irradiation and decay scenario, and divided by the steady-state rate of the interaction. Because the activation calculations are performed for each radionuclide in each mesh element, implementation of the MS-CADIS method can be computationally expensive. However, these neutron transport and activation calculations are not needed if we assume that the radioisotopes are created due to single neutron interactions and their concentrations do not change as a result of burnup by neutron irradiation. The use of this approximation, which renders the MS-CADIS parameter independent of the neutron flux, seems reasonable in calculating the MS-CADIS importance function because this function is needed only to speed up the MC calculation, not to calculate the final SDDR. In this work, we investigate the validity of this approximation by investigating the behavior of the MS-CADIS parameter as a function of the neutron flux spectra in the Fusion Evaluated Nuclear Data Library (FENDL) Neutronics and Shielding Benchmark problem that contains representative isotopes and flux environments of fusion energy systems. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2020

TurboRVB: A many-body toolkit for ab initio electronic simulations by quantum Monte Carlo

TurboRVB is a computational package for ab initio Quantum Monte Carlo (QMC) simulations of both molecular and bulk electronic systems. The code implements two types of well established QMC algorithms: Variational Monte Carlo (VMC) and diffusion Monte Carlo in its robust and efficient lattice regularized variant. A key feature of the code is the possibility of using strongly correlated many-body wave functions (WFs), capable of describing several materials with very high accuracy, even when standard mean-field approaches [e.g., density functional theory (DFT)] fail. The electronic WF is obtained by applying a Jastrow factor, which takes into account dynamical correlations, to the most general mean-field ground state, written either as an antisymmetrized geminal power with spin-singlet pairing or as a Pfaffian, including both singlet and triplet correlations. This WF can be viewed as an efficient implementation of the so-called resonating valence bond (RVB) Ansatz, first proposed by Pauling and Anderson in quantum chemistry [L. Pauling, The Nature of the Chemical Bond (Cornell University Press, 1960)] and condensed matter physics [P.W. Anderson, Mat. Res. Bull 8, 153 (1973)], respectively. The RVB Ansatz implemented in TurboRVB has a large variational freedom, including the Jastrow correlated Slater determinant as its simplest, but nontrivial case. Moreover, it has the remarkable advantage of remaining with an affordable computational cost, proportional to the one spent for the evaluation of a single Slater determinant. Therefore, its application to large systems is computationally feasible. The WF is expanded in a localized basis set. Several basis set functions are implemented, such as Gaussian, Slater, and mixed types, with no restriction on the choice of their contraction. The code implements the adjoint algorithmic differentiation that enables a very efficient evaluation of energy derivatives, comprising the ionic forces. Thus, one can perform structural optimizations and molecular dynamics in the canonical NVT ensemble at the VMC level. For the electronic part, a full WF optimization (Jastrow and antisymmetric parts together) is made possible, thanks to state-of-the-art stochastic algorithms for energy minimization. In the optimization procedure, the first guess can be obtained at the mean-field level by a built-in DFT driver. The code was efficiently parallelized by using a hybrid MPI-OpenMP protocol, which is also an ideal environment for exploiting the computational power of modern Graphics Processing Unit accelerators.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Bi-orthogonal approach to non-Hermitian Hamiltonians with the oscillator spectrum: Generalized coherent states for nonlinear algebras

A set of Hamiltonians that are not self-adjoint but have the spectrum of the harmonic oscillator is studied. The eigenvectors of these operators and those of their Hermitian conjugates form a bi-orthogonal system that provides a mathematical procedure to satisfy the superposition principle. In this form the non-Hermitian oscillators can be studied in much the same way as in the Hermitian approaches. Two different nonlinear algebras generated by properly constructed ladder operators are found and the corresponding generalized coherent states are obtained. The non-Hermitian oscillators can be steered to the conventional one by the appropriate selection of parameters. In such limit, the generators of the nonlinear algebras converge to generalized ladder operators that would represent either intensity-dependent interactions or multi-photon processes if the oscillator is associated with single mode photon fields in nonlinear media.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Group Structure Optimization Using the PyGroup Code

Group constants are used as coefficients in the energy domain discretized Linear Boltzmann Equation (LBE), in which the Continuous-Energy (CE) fluxes are also integrated over energy bins and transformed into group fluxes. This procedure, based on the Multi-Group (MG) theory, is widely applied in radiation transport and diffusion simulations Careful preparation of MG cross section data, or group constants, is thus a prerequisite for success in acquiring high-fidelity LBE solutions. Generation of MG cross section data itself is a complicated multi-step task, since group constants are indispensably coupled with the solution of the LBE, i.e. the flux spectrum in the problem to be solved. Theoretically, a MG cross section library is only valid for the problem that it is built upon. Nevertheless, in practice MG cross section libraries are prepared for similar type of problems, such as thermal reactors, fast reactors, etc., to facilitate the neutronic simulations. Generally, CE point-wise cross section data set, generated by both theoretical models and experimental data, is first converted to Fine-Group (FG) libraries using a pre-defined or precalculated flux spectra, then, Broad-Group (BG) libraries are collapsed from the fine-group libraries using problem-dependent flux spectra. Proper treatments of energy and spatial self-shielding and resonance cross section are required in the CE-to-MG converting process Previously, we have developed a computer code, YGROUP, for fine-to-broad group cross section collapsing. To maintain high accuracy of the resulting BG libraries, YGROUP provides users several options on collapsing strategies and weighting schemes for group binning and evaluation of BG cross section data in users' specific problems.. An approach based on Particle Swarm Optimization was applied to automatically determine the optimal group structure. We also developed a hybrid weighting scheme to further improve BG library performance for Special Nuclear Materials (SNM) detection applications. In this work, a new computer code, PyGroup, has been developed to implement the PSO approach with an improved simulation-driven fitness function design that includes both response and forward/adjoint flux errors. Together with YGROUP, and deterministic transport code TITAN/PENMSHXP, the PyGroup code package is tested on a Dual Range Coincident Counter (DRCC) model. In this paper, we demonstrated the capability of the PyGroup code for group structure optimization using the DRCC detector model. In the future, an iteration scheme can be implemented to determine the number of broad groups based on a user-defined tolerance. we will also apply PyGroup to more complicated reactor models, and investigate physics-based fitness function designs to further reduce computational cost. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2007

Simulation of a Periodic Jet in a Crossflow with a RANS Solver Using an Unstructured Grid

A second-order unstructured-grid code, developed and used primarily for steady aerodynamic simulations, is applied to the synthetic jet in a cross flow. The code, FUN3D, is a vertex-centered finite-volume method originally developed by Anderson[1, 2], and is currently supported by members of the Fast Adaptive Aerospace Tools team at NASA Langley. Used primarily for design[3] and analysis[4] of steady aerodynamic configurations, FUN3D incorporates a discrete adjoint capability, and supports parallel computations using MPI. A detailed description of the FUN3D code can be found in the references given above. The code is under continuous development and contains a variety of flux splitting algorithms for the inviscid terms, two methods for computing gradients, several turbulence models, and several solution methodologies; all in varying states of development. Only the most robust and reliable components, based on experiences with steady aerodynamic simulations, were employed in this work. As applied in this work, FUN3D solves the Reynolds averaged Navier-Stokes equations using the one equation turbulence model of Spalart and Allmaras[5]. The spatial discretization is formed on unstructured meshes using a vertex-centered approach. The inviscid terms are evaluated by a flux-difference splitting formulation using least-squares reconstruction and Roe-type approximate Riemann fluxes. Green-Gauss gradient evaluations are used for viscous and turbulence modeling terms. The discrete spatial operator is combined with a backward time operator which is then solved iteratively using point or line Gauss-Seidel and local time stepping in a pseudo time. For steady flows, the physical time step is set to infinity and the pseudo time step is ramped up with the iteration count. A second-order backward in time operator is used for time accurate flows with 20 to 50 steps in the pseudo time applied at each physical time step. For this effort, FUN3D was modified to support spatially varying boundary and initial conditions, and unsteady boundary conditions. Also, a specialized in/out flow boundary condition was implemented to model the action of the diaphragm. This boundary condition is described below in more detail. The grids were generated using the internally developed codes GridEX[6] for meshing the surfaces and inviscid regions of the domain, and for CAD access; and MesherX[7] for meshing the viscous regions. Grid spacing in on the surfaces and in the inviscid regions are indirectly controlled by specifying sources. The viscous layers are generated using an advancing layer technique. MeshersX allows the user to control the spatial variation of the first step off the surface, growth rates, and the termination criterion by providing small problem dependent subroutines.

Atkins, H. L.↗
NASA NTRSDate not supplied

Understanding and Utilizing PBL Height Data from Multiple Observing Systems in the GEOS System

The accuracy of PBL height simulation is a key issue in many applications including forecasting near surface meteorology and air quality, however, it is a very challenging problem due to the lack of not only comprehensive, global Planetary Boundary Layer (PBL) observations but also a strategy and infrastructure to utilize PBL height data from a variety of sensors. Following the designation of PBL as an incubation class observable in the 2017 Decadal Survey, the PBL Incubation Study Team Report [14] made clear that “a future global PBL observing system requires modeling and data assimilation as essential components.” There is an urgent need for global modeling development in order to utilize Program of Record (POR) observations, assess their impacts, and identify gaps to be filled by future PBL missions. Our overall objective is to develop PBL data assimilation capabilities in the NASA Global Earth Observing System (GEOS), focusing on PBL height from multiple observing systems, to support the assessment and use of future PBL observations. The NASA GEOS system is composed of the GEOS global atmospheric general circulation model (AGCM) and the atmospheric data assimilation system (ADAS). The PBL parameterizations include the “Lock” K-profile scheme driven by surface and cloud-top buoyancy fluxes ([4]), and the “Louis” local scheme for stable conditions based on the Richardson number ([5]). Above the mixed layer defined by the Lock surface plume, shallow cumulus convection is represented by the mass flux scheme of [9]. Additional parameterizations are summarized in [1]. The ADAS employs the hybrid 4D Ensemble- Variational (EnVar) configuration ([15]), with the ensemble providing flow-dependent background error covariance information. The resultant analysis increments are fed back to the forecast model through the 4D incremental analysis update (IAU) approach ([11]). In this study, PBL height data are being or have been generated from radiosondes, GNSS RO, satellite (CATS, CALIPSO and ICESat-2) and ground-based (MPLNET) lidars, and wind profiler. Investigations have been conducted to specify quality marks for PBL height retrievals for the data assimilation purpose. These PBL height data have different strengths and weaknesses ([2], [3], [6], [7], [8], [10]), and the satellite PBL height data provide better global coverage and complement in-situ PBL height data. Radiosondes offer high accuracy and in situ measurement of temperature and humidity profiles, but with poor spatio-temporal sampling. The in-situ observing systems like MPLNET and wind profiler provide long history of PBL height records at each station. The GNSS RO based PBL height is retrieved based on the sharp gradients in refractivity profile that represent the fine vertical structure of temperature and moisture changes above the PBL. However, not all RO refractivity profiles reach the surface depending on location and regime, and RO refractivity retrievals can be negatively biased below 2km. The PBL height data from satellite lidars provide high resolution along track PBL height retrievals, but over land they are affected by previous day convective PBL aerosol and strongly associated with mixing layer and retrievals cannot be made below thick, attenuating clouds. A successful assimilation of PBL height data requires a thorough understanding of the observing method and the retrieval algorithm for each observing system in order to use the PBL height data from multiple observing systems properly. Due to the sensitivity of PBL height data to the observing method and choice of algorithm, it is important to use a model definition appropriate for each observation type to compute differences between PBL height data and model PBL height (OmFs). The GEOS model currently includes two PBL height definitions suitable for direct comparison with observed PBL height, and additional definitions are being added in this study. Evaluation of different model PBL height definitions is underway. Meanwhile, efforts have been made in the GEOS data assimilation system to develop PBL height data assimilation capability. PBL height data can be assimilated using two different approaches. The traditional approach is to construct an observation operator and its tangent linear and adjoint, which link control variables to PBL height data from each observing system. This observation operator can be very complicated, e.g., the lidar-based PBL height observation operator includes the backscatter lidar forward observation operator, the algorithm to derive PBL height from attenuated total backscatter, interpolation, and calculations handling the mismatch between observed and model scales. The other approach is to augment PBL height to the control variable vector, and it is adopted in this study. The latter approach was also used in previous studies, e.g., the assimilation of PBL height data from radiosonde and aircraft in the Real Time Mesoscale Analysis (RTMA) system for a dispersion modelling study ([13]); the PBL height assimilation study using lidar PBL height data at Greensburg, Kansas for a field campaign ([12]). The PBL height assimilation from multiple observing systems in this study allows us to take advantage of the diverse PBL height data that provide much better global coverage collectively under different meteorological conditions and with different temporal and spatial scales. As all the PBL heights are tightly coupled with the PBL thermodynamic variables, the strong correlations, which are provided by the 4D ensemble forecast, enable PBL height data from various sources to interact and combine coherently and provide additional information for PBL temperature and moisture fields. The results of comparisons among PBL height data from different sources and the evaluation of the model PBL height definitions with the PBL height data will be presented, and the PBL height data synergy strategies and preliminary results will also be discussed at the conference.

Y. Zhu↗