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An Open-Source Tool for Energy Storage Sizing and Placement in Electric Grids
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Cloud cover estimation: Use of GOES imagery in development of cloud cover data base for insolation assessment
The potential of using digital satellite data to establish a cloud cover data base for the United States, one that would provide detailed information on the temporal and spatial variability of cloud development are studied. Key elements include: (1) interfacing GOES data from the University of Wisconsin Meteorological Data Facility with the Jet Propulsion Laboratory's VICAR image processing system and IBIS geographic information system; (2) creation of a registered multitemporal GOES data base; (3) development of a simple normalization model to compensate for sun angle; (4) creation of a variable size georeference grid that provides detailed cloud information in selected areas and summarized information in other areas; and (5) development of a cloud/shadow model which details the percentage of each grid cell that is cloud and shadow covered, and the percentage of cloud or shadow opacity. In addition, comparison of model calculations of insolation with measured values at selected test sites was accomplished, as well as development of preliminary requirements for a large scale data base of cloud cover statistics.
Finite element computation on nearest neighbor connected machines
Research aimed at faster, more cost effective parallel machines and algorithms for improving designer productivity with finite element computations is discussed. A set of 8 boards, containing 4 nearest neighbor connected arrays of commercially available floating point chips and substantial memory, are inserted into a commercially available machine. One-tenth Mflop (64 bit operation) processors provide an 89% efficiency when solving the equations arising in a finite element problem for a single variable regular grid of size 40 by 40 by 40. This is approximately 15 to 20 times faster than a much more expensive machine such as a VAX 11/780 used in double precision. The efficiency falls off as faster or more processors are envisaged because communication times become dominant. A novel successive overrelaxation algorithm which uses cyclic reduction in order to permit data transfer and computation to overlap in time is proposed.
Solution of elliptic partial differential equations by fast Poisson solvers using a local relaxation factor. 1: One-step method
An algorithm for solving a large class of two- and three-dimensional nonseparable elliptic partial differential equations (PDE's) is developed and tested. It uses a modified D'Yakanov-Gunn iterative procedure in which the relaxation factor is grid-point dependent. It is easy to implement and applicable to a variety of boundary conditions. It is also computationally efficient, as indicated by the results of numerical comparisons with other established methods. Furthermore, the current algorithm has the advantage of possessing two important properties which the traditional iterative methods lack; that is: (1) the convergence rate is relatively insensitive to grid-cell size and aspect ratio, and (2) the convergence rate can be easily estimated by using the coefficient of the PDE being solved.
Solution of elliptic PDEs by fast Poisson solvers using a local relaxation factor
A large class of two- and three-dimensional, nonseparable elliptic partial differential equations (PDEs) is presently solved by means of novel one-step (D'Yakanov-Gunn) and two-step (accelerated one-step) iterative procedures, using a local, discrete Fourier analysis. In addition to being easily implemented and applicable to a variety of boundary conditions, these procedures are found to be computationally efficient on the basis of the results of numerical comparison with other established methods, which lack the present one's: (1) insensitivity to grid cell size and aspect ratio, and (2) ease of convergence rate estimation by means of the coefficient of the PDE being solved. The two-step procedure is numerically demonstrated to outperform the one-step procedure in the case of PDEs with variable coefficients.
Evapotranspiration from nonuniform surfaces - A first approach for short-term numerical weather prediction
Observations of surface heterogeneity of soil moisture from scales of meters to hundreds of kilometers are discussed, and a relationship between grid element size and soil moisture variability is presented. An evapotranspiration model is presented which accounts for the variability of soil moisture, standing surface water, and vegetation internal and stomatal resistance to moisture flow from the soil. The mean values and standard deviations of these parameters are required as input to the model. Tests of this model against field observations are reported, and extensive sensitivity tests are presented which explore the importance of including subgrid-scale variability in an evapotranspiration model.
A zonal flow analysis method for two-dimensional airfoils
A closed-loop, overlapped, velocity-coupling procedure has been utilized to combine a two-dimensional potential flow panel code and a Navier-Stokes code. The fully coupled, two-zone code has been used to compute the flow past a NACA 0012 airfoil. For this case, the zonal method has shown that the grid domain size can be reduced to 0.14 chord lengths with less than 1 percent loss in accuracy. Further, the required computation time is reduced by a factor of approximately four.
Mach number validation of a new zonal CFD method (ZAP2D) for airfoil simulations
A closed-loop overlapped velocity coupling procedure has been utilized to combine a two-dimensional potential-flow panel code and a Navier-Stokes code. The fully coupled two-zone code (ZAP2D) has been used to compute the flow past a NACA 0012 airfoil at Mach numbers ranging from 0.3 to 0.84 near the two-dimensional airfoil C(lmax) point for a Reynolds number of 3 million. For these cases, the grid domain size can be reduced to 3 chord lengths with less than 3-percent loss in accuracy for freestream Mach numbers through 0.8. Earlier validation work with ZAP2D has demonstrated a reduction in the required Navier-Stokes computation time by a factor of 4 for subsonic Mach numbers. For this more challenging condition of high lift and Mach number, the saving in CPU time is reduced to a factor of 2.
Flowfield simulation about the SOFIA Airborne Observatory
The Reynolds averaged Navier-Stokes equations have been applied to Stratospheric Observatory For Infrared Astronomy (SOFIA) configurations. Comparisons between numerical and experimental results are made in two-dimensions for free shear layers and a rectangular cavity, and in three-dimensions for simplified SOFIA geometries. Dominant acoustic behaviour of the cavity flows compare well with experiment. The sensitivity of the solutions to changes in grid cell size and artificial dissipation levels are shown. Furthermore, optical path distortion due to the flow field is modelled using geometrical constructs. The results demonstrate the viability and usefulness of the present computational methods for this class unsteady applications.
Analysis of multigrid methods on massively parallel computers: Architectural implications
We study the potential performance of multigrid algorithms running on massively parallel computers with the intent of discovering whether presently envisioned machines will provide an efficient platform for such algorithms. We consider the domain parallel version of the standard V cycle algorithm on model problems, discretized using finite difference techniques in two and three dimensions on block structured grids of size 10(exp 6) and 10(exp 9), respectively. Our models of parallel computation were developed to reflect the computing characteristics of the current generation of massively parallel multicomputers. These models are based on an interconnection network of 256 to 16,384 message passing, 'workstation size' processors executing in an SPMD mode. The first model accomplishes interprocessor communications through a multistage permutation network. The communication cost is a logarithmic function which is similar to the costs in a variety of different topologies. The second model allows single stage communication costs only. Both models were designed with information provided by machine developers and utilize implementation derived parameters. With the medium grain parallelism of the current generation and the high fixed cost of an interprocessor communication, our analysis suggests an efficient implementation requires the machine to support the efficient transmission of long messages, (up to 1000 words) or the high initiation cost of a communication must be significantly reduced through an alternative optimization technique. Furthermore, with variable length message capability, our analysis suggests the low diameter multistage networks provide little or no advantage over a simple single stage communications network.
Time-accurate Navier-Stokes calculations with multigrid acceleration
A numerical scheme to solve the unsteady Navier-Stokes equations is described. The scheme is implemented by modifying the multigrid-multiblock version of the steady Navier-Stokes equations solver, TLNS3D. The scheme is fully implicit in time and uses TLNS3D to iteratively invert the equations at each physical time step. The design objective of the scheme is unconditional stability (at least for first- and second-order discretizations of the physical time derivatives). With unconditional stability, the choice of the time step is based on the physical phenomena to be resolved rather than limited by numerical stability which is especially important for high Reynolds number viscous flows, where the spatial variation of grid cell size can be as much as six orders of magnitude. An analysis of the iterative procedure and the implementation of this procedure in TLNS3D are discussed. Numerical results are presented to show both the capabilities of the scheme and its speed up relative to the use of global minimum time stepping. Reductions in computational times of an order of magnitude are demonstrated.
Multigrid Acceleration of Time-Accurate Navier-Stokes Calculations
A numerical scheme to solve the unsteady Navier-Stokes equations is described. The scheme is fully implicit in time and is unconditionally stable (at least for first- and second-order discretizations of the physical time derivatives). With unconditional stability, the choice of the time step is based on the physical phenomena to be resolved rather than limited by numerical stability. This is especially important for high Reynolds number viscous flows, where the spatial variation of grid cell size can be as much as six orders of magnitude. A multigrid-multiblock, steady-state, three-dimensional Navier-Stokes solver, TLNS3D, was modified to iteratively invert the equations at each physical time step. The implementation of this procedure in TLNS3D is discussed. The implications of applying several popular turbulence models to unsteady flow are also considered. Numerical results are presented to show the application of the scheme to various two-dimensional turbulent flows. The results of a three-dimensional laminar flow calculation are also given.
Low-Dispersion Scheme for Nonlinear Acoustic Waves in Nonuniform Flow
The linear dispersion-relation-preserving scheme and its boundary conditions have been extended to the nonlinear Euler equations. This allowed computing, a nonuniform flowfield and a nonlinear acoustic wave propagation in such a medium, by the same scheme. By casting all the equations, boundary conditions, and the solution scheme in generalized curvilinear coordinates, the solutions were made possible for non-Cartesian domains and, for the better deployment of the grid points, nonuniform grid step sizes could be used. It has been tested for a number of simple initial-value and periodic-source problems. A simple demonstration of the difference between a linear and nonlinear propagation was conducted. The wall boundary condition, derived from the momentum equations and implemented through a pressure at a ghost point, and the radiation boundary condition, derived from the asymptotic solution to the Euler equations, have proven to be effective for the nonlinear equations and nonuniform flows. The nonreflective characteristic boundary conditions also have shown success but limited to the nonlinear waves in no mean flow, and failed for nonlinear waves in nonuniform flow.
BOREAS AFM-12 1-km AVHRR Seasonal Land Cover Classification
The Boreal Ecosystem-Atmosphere Study (BOREAS) Airborne Fluxes and Meteorology (AFM)-12 team's efforts focused on regional scale Surface Vegetation and Atmosphere (SVAT) modeling to improve parameterization of the heterogeneous BOREAS landscape for use in larger scale Global Circulation Models (GCMs). This regional land cover data set was developed as part of a multitemporal one-kilometer Advanced Very High Resolution Radiometer (AVHRR) land cover analysis approach that was used as the basis for regional land cover mapping, fire disturbance-regeneration, and multiresolution land cover scaling studies in the boreal forest ecosystem of central Canada. This land cover classification was derived by using regional field observations from ground and low-level aircraft transits to analyze spectral-temporal clusters that were derived from an unsupervised cluster analysis of monthly Normalized Difference Vegetation Index (NDVI) image composites (April-September 1992). This regional data set was developed for use by BOREAS investigators, especially those involved in simulation modeling, remote sensing algorithm development, and aircraft flux studies. Based on regional field data verification, this multitemporal one-kilometer AVHRR land cover mapping approach was effective in characterizing the biome-level land cover structure, embedded spatially heterogeneous landscape patterns, and other types of key land cover information of interest to BOREAS modelers.The land cover mosaics in this classification include: (1) wet conifer mosaic (low, medium, and high tree stand density), (2) mixed coniferous-deciduous forest (80% coniferous, codominant, and 80% deciduous), (3) recent visible bum, vegetation regeneration, or rock outcrops-bare ground-sparsely vegetated slow regeneration bum (four classes), (4) open water and grassland marshes, and (5) general agricultural land use/ grasslands (three classes). This land cover mapping approach did not detect small subpixel-scale landscape features such as fens, bogs, and small water bodies. Field observations and comparisons with Landsat Thematic Mapper (TM) suggest a minimum effective resolution of these land cover classes in the range of three to four kilometers, in part, because of the daily to monthly compositing process. In general, potential accuracy limitations are mitigated by the use of conservative parameterization rules such as aggregation of predominant land cover classes within minimum horizontal grid cell sizes of ten kilometers. The AFM-12 one-kilometer AVHRR seasonal land cover classification data are available from the Earth Observing System Data and Information System (EOSDIS) Oak Ridge National Laboratory (ORNL) Distributed Active Archive Center (DAAC). The data files are available on a CD-ROM (see document number 20010000884).
Combustion Of Moving Droplets And Of Droplets Suspended Within A Convective Environment: Transient Numerical Results
The problem considered is that of a single-component liquid fuel (n-heptane) droplet undergoing evaporation and combustion in a hot, convective, low pressure, zero-gravity environment of infinite expanse. For a moving droplet, the relative velocity (U(sub infinity)) between the droplet and freestream is subject to change due to the influence of the drag force on the droplet. For a suspended droplet, the relative velocity is kept constant. The governing equations for the gas-phase and the liquid-phase consist of the unsteady, axisymmetric equations of mass, momentum, species (gas-phase only) and energy conservation. Interfacial conservation equations are employed to couple the two phases. Variable properties are used in the gas- and liquid-phase. Multicomponent diffusion in the gas-phase is accounted for by solving the Stefan-Maxwell equations for the species diffusion velocities. A one-step overall reaction is used to model the combustion. The governing equations are discretized using the finite volume and SIMPLEC methods. A colocated grid is adopted. Hyperbolic tangent stretching functions are used to concentrate grid points near the fore and aft lines of symmetry and at the droplet surface in both the gas- and liquid-phase. The discretization equations are solved using the ADI method with the TDMA used on each line of the two alternating directions. Iterations are performed within each time-step until convergence is achieved. The grid spacing, size of the computational domain and time-step were tested to ensure that all solutions are independent of these parameters. A detailed discussion of the numerical model is given.
Retraction Note: A 10 per cent increase in global land evapotranspiration from 2003 to 2019
In this article, we calculated global land evapotranspiration for 2003 to 2019 using a massbalance approach. To do this, we calculated evapotranspiration as the residual of the water balance, using an ensemble of datasets for precipitation, discharge and total water storage change. We made an error in calculating the global mean precipitation: we used arithmetic averaging to calculate the mean, instead of calculating a spatially weighted mean to account for the changing grid box size with latitude. As a result, the magnitudes of the global mean precipitation time series were underestimated. This impacted the subsequent calculation of global mean evapotranspiration, resulting in the mean evapotranspiration values being underestimated and altering some results. We are therefore retracting this article. We thank Ning Ma and others for bringing this error to our attention.
3D Cloud Tomography and Droplet Size Retrieval from Multi-Angle Polarimetric Imaging of Scattered Sunlight from Above
Tomography aims to recover a three-dimensional (3D) density map of a medium or an object. In medical imaging,it is extensively used for diagnostics via X-ray computed tomography (CT). We define and derive a tomographyof cloud droplet distributions via passive remote sensing. We use multi-view polarimetric images to fit a 3Dpolarized radiative transfer (RT) forward model. Our motivation is 3D volumetric probing of vertically-developedconvectively-driven clouds that are ill-served by current methods in operational passive remote sensing. Currenttechniques are indeed based on strictly 1D RT modeling and applied to a single cloudy pixel, where cloud geometrydefaults to that of a plane-parallel slab. Incident unpolarized sunlight, once scattered by cloud droplets, changesits polarization state according to droplet size. Therefore, polarimetric measurements in the rainbow and gloryangular regions can be used to infer the droplet size distribution. This work defines and derives a framework for afull 3D tomography of cloud droplets for both their mass concentration in space and their distribution across arange of sizes. This gridded 3D retrieval of key microphysical properties is made tractable by our novel approachthat involves a restructuring and partial linearization of an open-source polarized 3D RT code to accommodate aspecial two-step iterative optimization technique. Physically-realistic synthetic clouds are used to demonstrate themethodology with rigorous uncertainty quantification, while a real-world cloud imaged by AirMSPI is processedto illustrate the new remote sensing capability