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Generating Global Leaf Area Index from Landsat: Algorithm Formulation and Demonstration

This paper summarizes the implementation of a physically based algorithm for the retrieval of vegetation green Leaf Area Index (LAI) from Landsat surface reflectance data. The algorithm is based on the canopy spectral invariants theory and provides a computationally efficient way of parameterizing the Bidirectional Reflectance Factor (BRF) as a function of spatial resolution and wavelength. LAI retrievals from the application of this algorithm to aggregated Landsat surface reflectances are consistent with those of MODIS for homogeneous sites represented by different herbaceous and forest cover types. Example results illustrating the physics and performance of the algorithm suggest three key factors that influence the LAI retrieval process: 1) the atmospheric correction procedures to estimate surface reflectances; 2) the proximity of Landsatobserved surface reflectance and corresponding reflectances as characterized by the model simulation; and 3) the quality of the input land cover type in accurately delineating pure vegetated components as opposed to mixed pixels. Accounting for these factors, a pilot implementation of the LAI retrieval algorithm was demonstrated for the state of California utilizing the Global Land Survey (GLS) 2005 Landsat data archive. In a separate exercise, the performance of the LAI algorithm over California was evaluated by using the short-wave infrared band in addition to the red and near-infrared bands. Results show that the algorithm, while ingesting the short-wave infrared band, has the ability to delineate open canopies with understory effects and may provide useful information compared to a more traditional two-band retrieval. Future research will involve implementation of this algorithm at continental scales and a validation exercise will be performed in evaluating the accuracy of the 30-m LAI products at several field sites. ©

Landsat

A Corrected Formulation of the Multilayer Model (MLM) for Inferring Gaseous Dry Deposition to Vegetated Surfaces

The Multilayer Model (MLM) has been used for many years to infer dry deposition fluxes from measured trace species concentrations and standard meteorological measurements for national networks in the U.S., including the U.S. Environmental Protection Agency's Clean Air Status and Trends Network (CASTNet). MLM utilizes a resistance analogy to calculate deposition velocities appropriate for whole vegetative canopies, while employing a multilayer integration to account for vertically varying meteorology, canopy morphology and radiative transfer within the canopy. However, the MLM formulation, as it was originally presented and as it has been subsequently employed, contains a non-physical representation related to the leaf-level quasi-laminar boundary layer resistance that affects the calculation of the total canopy resistance. In this note, the non-physical representation of the canopy resistance as originally formulated in MLM is discussed and a revised, physically consistent, formulation is suggested as a replacement. The revised canopy resistance formulation reduces estimates of HNO3 deposition velocities by as much as 38% during mid-day as compared to values generated by the original formulation. Inferred deposition velocities for SO2 and O3 are not significantly altered by the change in formulation (less than 3%). Inferred deposition loadings of oxidized and total nitrogen from CASTNet data may be reduced by 10-20% and 5-10%, respectively, for the Eastern U. S. when employing the revised formulation of MLM as compared to the original formulation.

vegetated surfaces

Aerodynamic shape optimization of wing and wing-body configurations using control theory

This paper describes the implementation of optimization techniques based on control theory for wing and wing-body design. In previous studies it was shown that control theory could be used to devise an effective optimization procedure for airfoils and wings in which the shape and the surrounding body-fitted mesh are both generated analytically, and the control is the mapping function. Recently, the method has been implemented for both potential flows and flows governed by the Euler equations using an alternative formulation which employs numerically generated grids, so that it can more easily be extended to treat general configurations. Here results are presented both for the optimization of a swept wing using an analytic mapping, and for the optimization of wing and wing-body configurations using a general mesh.

Reuther, James

A New Recycling Method to Generate Turbulent Inflow Profiles

The accuracy of the scale-resolving simulations for practical geometries strongly depends on the inflow boundary conditions. Imposing experimentally observed turbulent inflow profiles for the numerical simulations is a major challenge. Existing methods available in the literature assume self-similar behavior, which is not true for most of the experiments. In the present work, we formulate the turbulent inflow profile generation technique as an optimization problem. An adjoint technique is exploited to evaluate the sensitivities of multiple input parameters for the present problem. The present formulation is then tested to generate a laminar boundary layer profile, turbulent boundary layer profile, and turbulent jet profile.

Garai, Anirban

Numerical Study of Boundary Layer Interaction with Shocks: Method Improvement and Test Computation

The objective is the development of a high-order and high-resolution method for the direct numerical simulation of shock turbulent-boundary-layer interaction. Details concerning the spatial discretization of the convective terms can be found in Adams and Shariff (1995). The computer code based on this method as introduced in Adams (1994) was formulated in Cartesian coordinates and thus has been limited to simple rectangular domains. For more general two-dimensional geometries, as a compression corner, an extension to generalized coordinates is necessary. To keep the requirements or limitations for grid generation low, the extended formulation should allow for non-orthogonal grids. Still, for simplicity and cost efficiency, periodicity can be assumed in one cross-flow direction. For easy vectorization, the compact-ENO coupling algorithm as used in Adams (1994) treated whole planes normal to the derivative direction with the ENO scheme whenever at least one point of this plane satisfied the detection criterion. This is apparently too restrictive for more general geometries and more complex shock patterns. Here we introduce a localized compact-ENO coupling algorithm, which is efficient as long as the overall number of grid points treated by the ENO scheme is small compared to the total number of grid points. Validation and test computations with the final code are performed to assess the efficiency and suitability of the computer code for the problems of interest. We define a set of parameters where a direct numerical simulation of a turbulent boundary layer along a compression corner with reasonably fine resolution is affordable.

Adams, N. A.

On the Ice Nucleation Spectrum

This work presents a novel formulation of the ice nucleation spectrum, i.e. the function relating the ice crystal concentration to cloud formation conditions and aerosol properties. The new formulation is physically-based and explicitly accounts for the dependency of the ice crystal concentration on temperature, supersaturation, cooling rate, and particle size, surface area and composition. This is achieved by introducing the concepts of ice nucleation coefficient (the number of ice germs present in a particle) and nucleation probability dispersion function (the distribution of ice nucleation coefficients within the aerosol population). The new formulation is used to generate ice nucleation parameterizations for the homogeneous freezing of cloud droplets and the heterogeneous deposition ice nucleation on dust and soot ice nuclei. For homogeneous freezing, it was found that by increasing the dispersion in the droplet volume distribution the fraction of supercooled droplets in the population increases. For heterogeneous ice nucleation the new formulation consistently describes singular and stochastic behavior within a single framework. Using a fundamentally stochastic approach, both cooling rate independence and constancy of the ice nucleation fraction over time, features typically associated with singular behavior, were reproduced. Analysis of the temporal dependency of the ice nucleation spectrum suggested that experimental methods that measure the ice nucleation fraction over few seconds would tend to underestimate the ice nuclei concentration. It is shown that inferring the aerosol heterogeneous ice nucleation properties from measurements of the onset supersaturation and temperature may carry significant error as the variability in ice nucleation properties within the aerosol population is not accounted for. This work provides a simple and rigorous ice nucleation framework where theoretical predictions, laboratory measurements and field campaign data can be reconciled, and that is suitable for application in atmospheric modeling studies.

Barahona, D.

Mixed-Integer Linear Programming Formulation with Embedded Machine Learning Surrogates for the Design of Chemical Process Families

In previous work, we introduced process family design. The main idea is to design a platform of common elements, and, allowing us to capture additional cost savings, simultaneously design a family of processes, and reducing both engineering and deployment timelines. We formulate this as an optimization problem, specifically a nonlinear generalized disjunctive program (GDP). We have proposed two approaches for reformulating and solving this problem: one based on full-discretization of the design space and one that uses Machine Learning (ML) surrogates to replace the nonlinear process models. Using ML surrogates to predict required system costs and performance indicators allows us to reformulate the nonlinearities in the GDP generate an efficient MILP formulation. In this work, we apply the ML surrogate approach to two case studies. One case study involves designing a family of carbon capture systems to cover a set of different flue gas flow rates and inlet CO 2 concentrations, where we consider the absorber and stripper as common unit module types. The second case study focuses on a water-desalination process, where we design a family of these processes for a variety of salt concentrations and flow rates. In both of these case studies, we demonstrate a scalable optimization approach that enables the design of multiple processes simultaneously, reducing the time-to-market and overall costs by maximizing the cost savings due to both economies of scale and economies of numbers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Frequency-Nadir-Constrained Unit Commitment for Low-Inertia, High-IBR Island Power Systems [Slides]

The process of energy decarbonization in island power systems is accelerated due to the swift integration of inverter-based renewable energy resources (IBRs). The unique features of such systems, including rapid frequency changes resulting from potential generation outages or imbalances due to the unpredictability of renewable power, pose a significant challenge in maintaining the frequency nadir without external support. This paper presents a unit commitment (UC) model with data-driven frequency nadir constraints, including either frequency nadir or minimum inertia requirements, helping to limit frequency deviations after significant generator outages. The constraints are formulated using a linear regression model that takes advantage of real-world, year-long generation scheduling and dynamic simulation data. The efficacy of the proposed UC model is verified through a year-long simulation in an actual island power system using historical weather data. The alternative minimum inertia constraint, derived from actual system operation assumptions, is also evaluated. Findings demonstrate that the proposed frequency nadir constraint notably improves the system's frequency nadir under high photovoltaic (PV) penetration levels, albeit with a slight increase in generation costs, when compared to the alternative minimum inertia constraint.

14 SOLAR ENERGY

Hyperbolic Methods for Surface and Field Grid Generation

This chapter describes the use of hyperbolic partial differential equation methods for structured surface grid generation and field grid generation. While the surface grid generation equations are inherently three dimensional, the field grid generation equations can be formulated in two or three dimensions. The governing equations are derived from orthogonality relations and cell area/volume constraints; and are solved numerically by marching from an initial curve or surface. The marching step size and marching distance can be prescribedly the user. Exact specifications of the side and outer boundaries are not possible with a one sweep marching scheme but limited control is achievable. Excellent orthogonality and grid clustering characteristics are provided by hyperbolic methods with one to two orders of magnitude savings in time over typical elliptic methods. Since hyperbolic grid generation methods do not require the exact specifications of the side and outer boundaries of a grid, these methods are particularly well suited for the overlapping grid approach for solving problems on complex configurations. Grid generation software based on hyperbolic methods and their applications on several complex configurations will be described.

Chan, William M.

Spline methods for approximating quantile functions and generating random samples

Two cubic spline formulations are presented for representing the quantile function (inverse cumulative distribution function) of a random sample of data. Both B-spline and rational spline approximations are compared with analytic representations of the quantile function. It is also shown how these representations can be used to generate random samples for use in simulation studies. Comparisons are made on samples generated from known distributions and a sample of experimental data. The spline representations are more accurate for multimodal and skewed samples and to require much less time to generate samples than the analytic representation.

Schiess, J. R.

Water recovery and solid waste processing for aerospace and domestic applications

The work is described accomplished in compiling information needed to establish the current water supply and waste water processing requirements for dwellings, and for developing a preliminary design for a waste water to potable water management system. Data generated was used in formulation of design criteria for the preliminary design of the waste water to potable water recycling system. The system as defined was sized for a group of 500 dwelling units. Study tasks summarized include: water consumption, nature of domestic water, consumer appliances for low water consumption, water quality monitoring, baseline concept, and current and projected costs.

Murawczyk, C.

A study of Space Shuttle approach and landing navigation with conventional navaids

Four candidate navigation systems for the Space Shuttle Orbiter approach and landing phase are evaluated in detail. These include three conventional navaid systems and a single-station one-way Doppler system. In each case a Kalman filter is assumed to be mechanized in the onboard computer, blending the navaid data with IMU and altimeter data. Filter state dimensions ranging from 6 to 24 are involved in the candidate systems. Comprehensive truth models with state dimensions ranging from 63 to 82 are formulated and used to generate detailed performance projections. The detailed results are summarized, compared, and interpreted, the filter designs are reviewed, and suggestions are made concerning possible software improvements.

Crawford, B. S.

Space shuttle entry and landing navigation analysis

A navigation system for the entry phase of a Space Shuttle mission which is an aided-inertial system which uses a Kalman filter to mix IMU data with data derived from external navigation aids is evaluated. A drag pseudo-measurement used during radio blackout is treated as an additional external aid. A comprehensive truth model with 101 states is formulated and used to generate detailed error budgets at several significant time points -- end-of-blackout, start of final approach, over runway threshold, and touchdown. Sensitivity curves illustrating the effect of variations in the size of individual error sources on navigation accuracy are presented. The sensitivity of the navigation system performance to filter modifications is analyzed. The projected overall performance is shown in the form of time histories of position and velocity error components. The detailed results are summarized and interpreted, and suggestions are made concerning possible software improvements.

Jones, H. L.

Space shuttle post-entry and landing analysis. Volume 2: Appendices

Four candidate navigation systems for the space shuttle orbiter approach and landing phase are evaluated in detail. These include three conventional navaid systems and a single-station one-way Doppler system. In each case, a Kalman filter is assumed to be mechanized in the onboard computer, blending the navaid data with IMU and altimeter data. Filter state dimensions ranging from 6 to 24 are involved in the candidate systems. Comprehensive truth models with state dimensions ranging from 63 to 82 are formulated and used to generate detailed error budgets and sensitivity curves illustrating the effect of variations in the size of individual error sources on touchdown accuracy. The projected overall performance of each system is shown in the form of time histories of position and velocity error components.

Crawford, B. S.

Analytical redundancy and the design of robust failure detection systems

The Failure Detection and Identification (FDI) process is viewed as consisting of two stages: residual generation and decision making. It is argued that a robust FDI system can be achieved by designing a robust residual generation process. Analytical redundancy, the basis for residual generation, is characterized in terms of a parity space. Using the concept of parity relations, residuals can be generated in a number of ways and the design of a robust residual generation process can be formulated as a minimax optimization problem. An example is included to illustrate this design methodology. Previously announcedd in STAR as N83-20653

Chow, E. Y.

Measurement of damping of graphite epoxy composite materials and structural joints

The damping capacity of graphite epoxy materials and structural joints was evaluated. The damping ratio of different composite specimens and bonded joints were systematically evaluated under normal atmospheric conditions and in a vacuum environment. Free and forced vibration test methods were employed for measuring the damping ratios. The effect of edge support conditions on the damping value of a composite tube specimen was studied by using a series of experiments performed on the specimen with different edge supports. It was found that simulating a free-free boundary conditions by having no constraints at the ends gives the lowest value of the material damping of the composite. The accuracy of the estimation of the damping ratio value was improved by using a curve-fitting technique on the response data obtained through measurement. The effect of outgassing (moisture desorption) on the damping capacity was determined by measuring the damping ratio of the tube specimen in a vacuum environment before and after outgassing had occurred. The effects of high and low temperatures on the damping was also investigated by using a series of experiments on tube and beam specimens. An analytical model to study the vibrations of a bonded lap joint system was formulated. Numerical results were generated for different overlap ratios of the system. These were compared with experimental results. In order to determine the influence of bonded joints on the material damping capacity, experiments were conducted on bonded lap-jointed and double-butt-jointed specimens. These experimental results were compared with simple beam specimens with no joints.

Crocker, Malcolm J.

A new Lagrangian method for real gases at supersonic speed

With the renewed interest in high speed flights, the real gas effect is of theoretical as well as practical importance. In the past decade, upwind splittings or Godunov-type Riemann solutions have received tremendous attention and as a result significant progress has been made both in the ideal and non-ideal gas. In this paper, we propose a new approach that is formulated using the Lagrangian description, for the calculation of supersonic/hypersonic real gas inviscid flows. This new formulation avoids the grid generation step which is automatically obtained as the solution procedure marches in the 'time-like' direction. As a result, no remapping is required and the accuracy is faithfully maintained in the Lagrangian level. In this paper, we give numerical results for a variety of real gas problems consisting of essential elements in high speed flows, such as shock waves, expansion waves, slip surfaces and their interactions. Finally, calculations for flows in a generic inlet and nozzle are presented.

Loh, C. Y.

Applications of automatic differentiation in computational fluid dynamics

Automatic differentiation (AD) is a powerful computational method that provides for computing exact sensitivity derivatives (SD) from existing computer programs for multidisciplinary design optimization (MDO) or in sensitivity analysis. A pre-compiler AD tool for FORTRAN programs called ADIFOR has been developed. The ADIFOR tool has been easily and quickly applied by NASA Langley researchers to assess the feasibility and computational impact of AD in MDO with several different FORTRAN programs. These include a state-of-the-art three dimensional multigrid Navier-Stokes flow solver for wings or aircraft configurations in transonic turbulent flow. With ADIFOR the user specifies sets of independent and dependent variables with an existing computer code. ADIFOR then traces the dependency path throughout the code, applies the chain rule to formulate derivative expressions, and generates new code to compute the required SD matrix. The resulting codes have been verified to compute exact non-geometric and geometric SD for a variety of cases. in less time than is required to compute the SD matrix using centered divided differences.

Green, Lawrence L.