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At least 19 records

Are grid cells used for navigation? On local metrics, subjective spaces, and black holes

The symmetric, lattice-like spatial pattern of grid-cell activity is thought to provide a neuronal global metric for space. This view is compatible with grid cells recorded in empty boxes but inconsistent with data from more naturalistic settings. Here, we review evidence arguing against the global-metric notion, including the distortion and disintegration of the grid pattern in complex and three-dimensional environments. We argue that deviations from lattice symmetry are key for understanding grid-cell function. We propose three possible functions for grid cells, which treat real-world grid distortions as a feature rather than a bug. First, grid cells may constitute a local metric for proximal space rather than a global metric for all space. Second, grid cells could form a metric for subjective action-relevant space rather than physical space. Third, distortions may represent salient locations. Finally, we discuss mechanisms that can underlie these functions. These ideas may transform our thinking about grid cells.

59 BASIC BIOLOGICAL SCIENCES↗

Convergence acceleration of implicit schemes in the presence of high aspect ratio grid cells

The performance of Navier-Stokes codes are influenced by several phenomena. For example, the robustness of the code may be compromised by the lack of grid resolution, by a need for more precise initial conditions or because all or part of the flowfield lies outside the flow regime in which the algorithm converges efficiently. A primary example of the latter effect is the presence of extended low Mach number and/or low Reynolds number regions which cause convergence deterioration of time marching algorithms. Recent research into this problem by several workers including the present authors has largely negated this difficulty through the introduction of time-derivative preconditioning. In the present paper, we employ the preconditioned algorithm to address convergence difficulties arising from sensitivity to grid stretching and high aspect ratio grid cells. Strong grid stretching is particularly characteristic of turbulent flow calculations where the grid must be refined very tightly in the dimension normal to the wall, without a similar refinement in the tangential direction. High aspect ratio grid cells also arise in problems that involve high aspect ratio domains such as combustor coolant channels. In both situations, the high aspect ratio cells can lead to extreme deterioration in convergence. It is the purpose of the present paper to address the reasons for this adverse response to grid stretching and to suggest methods for enhancing convergence under such circumstances. Numerical algorithms typically possess a maximum allowable or optimum value for the time step size, expressed in non-dimensional terms as a CFL number or vonNeumann number (VNN). In the presence of high aspect ratio cells, the smallest dimension of the grid cell controls the time step size causing it to be extremely small, which in turn results in the deterioration of convergence behavior. For explicit schemes, this time step limitation cannot be exceeded without violating stability restrictions of the scheme. On the other hand, for implicit schemes, which are typically unconditionally stable, there appears to be room for improvement through careful tailoring of the time step definition based on results of linear stability analyses. In the present paper, we focus on the central-differenced alternating direction implicit (ADI) scheme. The understanding garnered from this analyses can then be applied to other implicit schemes. In order to systematically study the effects of aspect ratio and the methods of mitigating the associated problems, we use a two pronged approach. We use stability analyses as a tool for predicting numerical convergence behavior and numerical experiments on simple model problems to verify predicted trends. Based on these analyses, we determine that efficient convergence may be obtained at all aspect ratios by getting a combination of things right. Primary among these are the proper definition of the time step size, proper selection of viscous preconditioner and the precise treatment of boundary conditions. These algorithmic improvements are then applied to a variety of test cases to demonstrate uniform convergence at all aspect ratios.

Buelow, B. E. O.↗

Multi-Grid-Cell Validation of Satellite Aerosol Property Retrievals in INTEX/ITCT/ICARTT 2004

Aerosol transport off the US Northeast coast during the Summer 2004 International Consortium for Atmospheric Research on Transport and Transformation (ICARTT) Intercontinental Chemical Transport Experiment (INTEX) and Intercontinental Transport and Chemical Transformation (ITCT) experiments produced a wide range of aerosol types and aerosol optical depth (AOD) values, often with strong horizontal AOD gradients. In these conditions we flew the 14-channel NASA Ames Airborne Tracking Sun photometer (AATS) on a Jetstream 31 (J31) aircraft. Legs flown at low altitude (usually less than 100 m ASL) provided comparisons of AATS AOD spectra to retrievals for 90 grid cells of the satellite radiometers MODIS-Terra, MODIS-Aqua, and MISR, all over the ocean. Characterization of the retrieval environment was aided by using vertical profiles by the J31 (showing aerosol vertical structure) and, on occasion, shipboard measurements of light scattering and absorption. AATS provides AOD at 13 wavelengths lambda from 354 to 2138 nm, spanning the range of aerosol retrieval wavelengths for MODIS over ocean (466-2119 nm) and MISR (446-866 nm). Midvisible AOD on low-altitude J31 legs in satellite grid cells ranged from 0.05 to 0.9, with horizontal gradients often in the range 0.05 to 0.13 per 10 km. When possible, we used ship measurements of humidified aerosol scattering and absorption to estimate AOD below the J31. In these cases, which had J31 altitudes 60-110 m ASL (typical of J31 low-altitude transects), estimated midvisible AOD below the J31 ranged from 0.003 to 0.013, with mean 0.009 and standard deviation 0.003. These values averaged 6 percent of AOD above the 53 1. MISR-AATS comparisons on 29 July 2004 in 8 grid cells (each -17.6 km x 17.6 km) show that MISR versions 15 and 16 captured the AATS-measured AOD gradient (correlation coefficient R2 = 0.87 to 0.92), but the MISR gradient was somewhat weaker than the AATS gradient. The large AOD (midvisible values up to -0.9) and differing gradients in this case produced root-mean-square (RMS) MISR-AATS AOD differences of 0.03 to 0.21 (9 to 31%). MISR V15 Angstrom exponent alpha (= -dlnAOD/dln lambda) was closer to AATS than was MISR V16. MODIS-AATS AOD comparisons on 8 overpasses using 61 grid cells (each nominally 10 km x 10 km) had R2 approximately 0.97, with RMS AOD difference approximately 0.03 (approximately 20%). About 87% of the MODIS AOD retrievals differed from AATS values by less than the predicted MODIS over-ocean uncertainty, Delta tau = plus/minus 0.03 plus/minus 0.05 tau. In contrast to the small MODIS-AATS differences in AOD, MODIS-AATS differences in Angstrom exponent alpha were large: RMS differences for alpha (553, 855 nm) were 0.28 for MODIS-Terra and 0.64 for MODIS-Aqua; RMS differences for alpha (855, 2119 nm) were larger still, 0.61 for MODIS-Terra and 1.14 for MODIS-Aqua. The largest MODIS-AATS Angstrom exponent differences were associated with small AOD values, for which MODIS AOD relative uncertainty is large. Excluding cases with AOD(855 nm) less than 0.1 reduced MODIS-AATS alpha differences substantially. In one grid cell on 21 July 2004, smoke over cloud appeared to impair the MODIS-Aqua cloud mask, resulting in retrieved AODs that significantly exceeded AATS values. Experiments with extending MODIS retrievals into the glint mask yielded MODIS AODs consistently less than AATS AODs, especially at long wavelength, indicating that the current MODIS glint mask limits should not be reduced to the extent tried here. The sign of the AOD differences within the glint mask (MODIS AOD less than AATS AOD) is consistent with ship-measured wind speeds there.

Russell, P. B.↗

Infrared and visible satellite rain estimation. I - A grid cell approach. II - A cloud definition approach

This study explores the relationships between satellite-viewed cloudy grid cells and the variability of the precipitation contained therein, together with the relationships between the satellite-IR clouds and rainfall and the IR-thresholded visible clouds and rainfall. In the grid cell approach, IR, visible, and radar data for five days of the Florida Area Cumulus Experiment were examined using a 32-km grid and 30-min interval; the results of this experiment indicated that useful, accurate rainfall estimates beyond rain/no rain discrimination are unlikely. In the cloud definition approach, it was found that the cloud IR area was highly correlated with the rain area and with the volume rain rate across the entire spectrum of cloud sizes. It was poorly correlated with mean cloud rain rate.

Negri, Andrew J.↗

Optimizing solar-cell grid geometry

Trade-off analysis and mathematical expressions calculate optimum grid geometry in terms of various cell parameters. Determination of the grid geometry provides proper balance between grid resistance and cell output to optimize the energy conversion process.

Crossley, A. P.↗

Development of inter-grid-cell lateral unsaturated and saturated flow model in the E3SM Land Model (v2.0)

Abstract. The lateral transport of water in the subsurface is important in modulating terrestrial water energy distribution. Although a few land surface models have recently included lateral saturated flow within and across grid cells, it is not a default configuration in the Climate Model Intercomparison Project version 6 experiments. In this work, we developed the lateral subsurface flow model within both unsaturated and saturated zones in the Energy Exascale Earth System Model (E3SM) Land Model version 2 (ELMv2.0). The new model, called ELMlat, was benchmarked against PFLOTRAN, a 3D subsurface flow and transport model, for three idealized hillslopes that included a convergent hillslope, divergent hillslope, and tilted V-shaped hillslope with variably saturated initial conditions. ELMlat showed comparable performance against PFLOTRAN in terms of capturing the dynamics of soil moisture and groundwater table for the three benchmark hillslope problems. Specifically, the mean absolute errors (MAEs) of the soil moisture in the top 10 layers between ELMlat and PFLOTRAN were within 1 %±3 %, and the MAEs of water table depth were within ±0.2 m. Next, ELMlat was applied to the Little Washita experimental watershed to assess its prediction of groundwater table, soil moisture, and soil temperature. The spatial pattern of simulated groundwater table depth agreed well with the global groundwater table benchmark dataset generated from a global model calibrated with long-term observations. The effects of lateral groundwater flow on the energy flux partitioning were more prominent in lowland areas with shallower groundwater tables, where the difference in simulated annual surface soil temperature could reach 0.3–0.4 ∘C between ELMv2.0 and ELMlat. Incorporating lateral subsurface flow in ELM improves the representation of the subsurface hydrology, which will provide a good basis for future large-scale applications.

58 GEOSCIENCES↗

Solar cell grid patterns

A grid pattern is described for a solar cell of the type which includes a semiconductive layer doped to a first polarity and a top counter-doped layer. The grid pattern comprises a plurality of concentric conductive grids of selected geometric shapes which are centered about the center of the exposed active surface of the counter-doped layer. Connected to the grids is one or more conductors which extend to the cell's periphery. For the pattern area, the grids and conductors are arranged in the pattern to minimize the maximum distance which any injected majority carriers have to travel to reach any of the grids or conductors. The pattern has a multiaxes symmetry with respect to the cell center to minimize the maximum temperature differentials between points on the cell surface and to provide a more uniform temperature distribution across the cell face.

Yasui, R. K.↗

Investigation of the effects of external current systems on the MAGSAT data utilizing grid cell modeling techniques

The feasibility of modeling magnetic fields due to certain electrical currents flowing in the Earth's ionosphere and magnetosphere was studied. Initial efforts were devoted to reading MAGSAT data tapes in preparation for further analysis of the MAGSAT data. Further efforts concern a modeling procedure developed to compute the magnetic field at satellite orbit due to hypothesized current distributions in the ionosphere and magnetosphere. This technique utilizes a linear current element representation of the large scale space current system.

Klumpar, D. M.↗

Investigation of the effects of external current systems on the MAGSAT data utilizing grid cell modeling techniques

Efforts devoted to reading MAGSAT data tapes in preparation for further analysis of the MAGSAT data are discussed. A modeling procedure developed to compute the magnetic fields at satellite orbit due to hypothesized current distributions in the ionosphere and magnetosphere is described. This technique utilizes a linear current element representation of the large-scale space-current system. Several examples of the model field perturbations computed along hypothetical satellite orbits are shown.

Klumpar, D. M.↗

Investigation of the effects of external current systems on the MAGSAT data utilizing grid cell modeling techniques

Refinements to the modeling procedure developed to compute the magnetic fields at satellite orbit due to current distributions in the ionosphere and magnetosphere are described. The modeling technique utilizes a linear current element representation of the large scale space current system. A model polar current system is presented and magnetic field perturbations resulting from this system are computed along two hypothetical satellite orbits.

Klumpar, D. M.↗

Investigation of the effects of external current systems on the MAGSAT data utilizing grid cell modeling techniques

Efforts in support of the development of a model of the magnetic fields due to ionospheric and magnetospheric electrical currents are discussed. Specifically, progress made in reading MAGSAT tapes and plotting the deviation of the measured magnetic field components with respect to a spherical harmonic model of the main geomagnetic field is reported. Initial tests of the modeling procedure developed to compute the ionosphere/magnetosphere-induced fields at satellite orbit are also described. The modeling technique utilizes a liner current element representation of the large scale current system.

Klumpar, D. M.↗

Investigation of the effects of external current systems on the MAGSAT data utilizing grid cell modeling techniques

Progress made in reducing MAGSAT data and displaying magnetic field perturbations caused primarily by external currents is reported. A periodic and repeatable perturbation pattern is described that arises from external current effects but appears as unique signatures associated with upper middle latitudes on the Earth's surface. Initial testing of the modeling procedure that was developed to compute the magnetic fields at satellite orbit due to current distributions in the ionosphere and magnetosphere is also discussed. The modeling technique utilizes a linear current element representation of the large scale space current system.

Klumpar, D. M.↗

Investigation of the effects of external current systems on the MAGSAT data utilizing grid cell modeling techniques

The feasibility of modeling magnetic fields due to certain electrical currents flowing in the Earth's ionosphere and magnetosphere was investigated. A method was devised to carry out forward modeling of the magnetic perturbations that arise from space currents. The procedure utilizes a linear current element representation of the distributed electrical currents. The finite thickness elements are combined into loops which are in turn combined into cells having their base in the ionosphere. In addition to the extensive field modeling, additional software was developed for the reduction and analysis of the MAGSAT data in terms of the external current effects. Direct comparisons between the models and the MAGSAT data are possible.

Klumpar, D. M.↗

Regional climates in the GISS general circulation model: Surface air temperature

One of the more viable research techniques into global climate change for the purpose of understanding the consequent environmental impacts is based on the use of general circulation models (GCMs). However, GCMs are currently unable to reliably predict the regional climate change resulting from global warming, and it is at the regional scale that predictions are required for understanding human and environmental responses. Regional climates in the extratropics are in large part governed by the synoptic-scale circulation and the feasibility of using this interscale relationship is explored to provide a way of moving to grid cell and sub-grid cell scales in the model. The relationships between the daily circulation systems and surface air temperature for points across the continental United States are first developed in a quantitative form using a multivariate index based on principal components analysis (PCA) of the surface circulation. These relationships are then validated by predicting daily temperature using observed circulation and comparing the predicted values with the observed temperatures. The relationships predict surface temperature accurately over the major portion of the country in winter, and for half the country in summer. These relationships are then applied to the surface synoptic circulation of the Goddard Institute for Space Studies (GISS) GCM control run, and a set of surface grid cell temperatures are generated. These temperatures, based on the larger-scale validated circulation, may now be used with greater confidence at the regional scale. The generated temperatures are compared to those of the model and show that the model has regional errors of up to 10 C in individual grid cells.

Hewitson, Bruce↗