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At least 181 records · Page 10

Hyperbolic string vertices

The string vertices of closed string field theory are subsets of the moduli spaces of punctured Riemann surfaces that satisfy a geometric version of the Batalin-Vilkovisky master equation. We present a homological proof of existence of string vertices and their uniqueness up to canonical transformations. Using hyperbolic metrics on surfaces with geodesic boundaries we give an exact construction of string vertices as sets of surfaces with systole greater than or equal to L with L ≤ 2 arcsinh 1. Intrinsic hyperbolic collars prevent the appearance of short geodesics upon sewing. The surfaces generated by Feynman diagrams are naturally endowed with Thurston metrics: hyperbolic on the vertices and flat on the propagators. For the classical theory the length L is arbitrary and, as L → ∞hyperbolic vertices become the minimal-area vertices of closed string theory

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Effect of Vertical Strut Arrangements on Compression Characteristics of 3D Printed Polymer Lattice Structures: Experimental and Computational Study

This paper discusses the behavior of the three-dimensional (3D) printed polymer lattice core structures during compressive deformation, by both physical testing and computer modeling. Four lattice configurations based on the body-centered cubic (BCC) unit cell were selected to investigate the effect of vertical strut arrangements on stiffness, failure load, and energy absorption per unit mass or the specific energy absorption (SEA). The basic BCC unit cell consists of struts connecting the body center to the corners of the cube. Three variations in the BCC configuration considered in this study are (1) BCCV, with vertical members connecting all nodes of the lattice, (2) BCCA, with vertical members in alternating layers of the lattice, and (3) BCCG, with a gradient in the number of vertical members increasing from none at the top layer to all vertical members at the bottom layer. The unit cell dimensions were 5 mm × 5 mm × 5 mm with strut diameter of 1 mm. The lattice was assembled with 5 cells in the x and y directions and 4 cells in the z direction. Specimens were first made by 3D printing by using a fused deposition modeling printer with acrylonitrile–butadiene–styrene thermoplastic. Specimens were then tested under compression in the z direction under quasi-static conditions. Finite element analysis was used to model the compressive behavior of the different lattice structures. Results from both experiments and finite element models show that the strength of the lattice structures is greater when vertical members are present, and the SEA depends on the lattice geometry and not its mass.

36 MATERIALS SCIENCE↗

Structural, optical and gas sensing properties of vertically well-aligned ZnO nanowires grown on graphene/Si substrate by thermal evaporation method

Highlights: • Vertically well-aligned ZnO NW arrays with high aspect ratio and extremely large-surface-volume ratio were synthesized on graphene/Si substrate without the aid of metal catalyst by a simple thermal evaporation. • The gas sensor based on the vertical ZnO NW arrays-graphene structure exhibited high sensitivity and rapid response/recovery characteristics to NO{sub 2} gas at 200oC, and could be used to detect NO{sub 2} gas at very low levels (2, 6, 10 ppm). • The excellent sensing performance is mainly because of the large specific surface area and the presence of oxygen-vacancies at the surface of ZnO NWs, together with the creation of p-n heterojunctions between n-type ZnO NW and p-type graphene. • The common defects and optical properties of the ZnO NW arrays-graphene structure were studied in detail. • The possible growth mechanism of vertically well-aligned ZnO NWs on graphene and the gas-sensing mechanism of sensors were proposed. - Abstract: We report catalyst-free vertical growth of high-density ZnO nanowire (NW) arrays on Si substrate with a graphene buffer layer by thermal evaporation method. Structural, surface morphology, chemical composition and optical properties of ZnO NWs were studied by Field emission scanning electron microscopy (FE-SEM), High-resolution transmission electron microscopy (HR-TEM), X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), Fourier transform infrared spectroscopy (FTIR), photoluminescence (PL) and Raman spectroscopy. The results indicate that the grown ZnO NWs are single-crystalline and exhibit the hexagonal wurtzite crystal structure with a preferred orientation along the [0001] direction; all of the ZnO NWs vertically grow on the graphene/Si substrate. The majority of the as-grown NWs have diameters in the range of 250–300 nm and length up to several tens of micrometers, whereas a small portion of NWs have a diameter of approximately of 9–12 nm. Room temperature PL spectrum of the ZnO NWs exhibits a sharp and strong ultraviolet emission at 380 nm and a weak visible emission at around 516 nm. The role of graphene buffer layer in the vertical-aligned ZnO NW arrays growth and its improved optical properties is demonstrated. Importantly, the gas sensor based on these ZnO NWs exhibits high sensitivity and rapid response/recovery characteristics to NO{sub 2} gas at 200 °C, and can detect NO{sub 2} concentration as low as 2, 6 and 10 ppm. The excellent sensing performance is mainly due to the combination of the large specific surface area and the presence of oxygen-vacancies at the surface of ZnO NWs, together with the creation of p-n heterojunctions between n-type ZnO NW and p-type graphene. Such a ZnO NW/graphene structure is very promising for various applications, such as photonic, optoelectronic and sensor devices. In addition, the possible growth mechanism and the NO{sub 2} sensing gas mechanism of the ZnO NWs-graphene structure have been discussed.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Sub-grid drag model for immersed vertical cylinders in fluidized beds

Immersed vertical cylinders are often used as heat exchanger in gas-solid fluidized beds. Computational Fluid Dynamics (CFD) simulations are computationally expensive for large scale systems with bundles of cylinders. Therefore sub-grid models are required to facilitate simulations on a coarse grid, where internal cylinders are treated as a porous medium. The influence of cylinders on the gas-solid flow tends to enhance segregation and affect the gas-solid drag. A correction to gas-solid drag must be modeled using a suitable sub-grid constitutive relationship. In the past, Sarkar et al. have developed a sub-grid drag model for horizontal cylinder arrays based on 2D simulations. However, the effect of a vertical cylinder arrangement was not considered due to computational complexities. In this study, highly resolved 3D simulations with vertical cylinders were performed in small periodic domains. These simulations were filtered to construct a sub-grid drag model which can then be implemented in coarse-grid simulations. Gas-solid drag was filtered for different solids fractions and a significant reduction in drag was identified when compared with simulation without cylinders and simulation with horizontal cylinders. Slip velocities significantly increase when vertical cylinders are present. Lastly, vertical suspension drag due to vertical cylinders is insignificant however substantial horizontal suspension drag is observed which is consistent to the finding for horizontal cylinders.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Ultra-Fast Vertical Ordering of Lamellar Block Copolymer Films on Unmodified Substrates

To utilize the full potential of block copolymer (BCP) thin films for use in technological devices ranging from ion conduction membranes, transistors to nanowire array antennas, rapid self- assembly of lamellar block copolymers (l-BCPs) with vertically oriented lamellar domains on a variety of unmodified substrates is needed. l-BCPs have an inherently larger interfacial area for transport compared to their cylindrical counterpart. Our observations demonstrate that the as-cast weakly ordered vertically oriented state of l-BCP films of polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) from directional evaporation of select solvents, act as “seed templates” for their ultra-fast evolution (~30 s) into well-ordered vertically oriented nanostructures, using a thermal gradient-based Cold Zone Annealing (CZA) technique. Furthermore, vertical lamellae are obtained on unmodified substrates, Quartz and Kapton, and the kinetics of l-BCP ordering is much faster by CZA as compared to the isotropic oven annealing. The rapid ordering kinetics of vertical l-BCPs is tested and found applicable to different molecular weights and film thicknesses ranging from 20 nm to 480 nm, which ultimately flip over to their equilibrium parallel morphology at upper limits of annealing times. This rapid ordering strategy for vertical orientation of l-BCPs using roll-to-roll compatible CZA would be highly relevant for fundamental studies of interfacial transport as well as for industrial applications from membranes to nanowires.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The Energy Exascale Earth System Model Simulations With High Vertical Resolution in the Lower Troposphere

Abstract General circulation models (GCMs) are typically run with coarse vertical resolution. For example, the Energy Exascale Earth System Model (E3SM) has a vertical resolution of about 200 m in the boundary layer, which is far too coarse to resolve sharp gradients often found in the thermodynamic fields capping subtropical marine stratocumulus. In this article, we present a series of multiyear atmosphere only simulations of E3SM version 1 where we progressively increase the vertical resolution in the lower troposphere to scales approaching those often used in large eddy simulation (LES). We report marginal impacts in regards to the simulation of boundary layer clouds when vertical resolution is moderately increased, yet find significant positive impacts when the vertical resolution approaches that typically used in LES (∼10 m). In these experiments, there is a marked change in the simulated turbulence and thermodynamics which leads to more abundant marine stratocumulus. However, these simulations are burdened with excessive computational cost. They are also subject to degradations in overall climate metrics due to time step sensitivities and because some processes and parameterizations are sensitive to changes in the vertical resolution.

54 ENVIRONMENTAL SCIENCES↗

Regime-specific Cloud Vertical Overlap Characteristics from Radar and Lidar Observations at the ARM sites

Climate and numerical weather prediction models require assumptions to represent the vertical distribution of subgrid-scale clouds, which have radiative transfer implications. In this study, nearly 25 years of ground-based radar and lidar observations of vertical cloud profiles at the Atmospheric Radiation Measurement Program (ARM) Southern Great Plains (SGP) site are utilized to derive cloud vertical overlap characteristics from the Cloud Type (CLDTYPE) data product. Here, the cloud vertical overlap characteristics are further separated by cloud regime by considering seven cloud types (i.e., low cloud, congestus, deep convection, altocumulus, altostratus, cirrostratus, and cirrus) as well as periods of shallow cumulus. The decorrelation length scale (i.e., exponential transition from maximum to random overlap with layer separation) is found to vary by cloud regime, ranging between 0.04 km for cirrostratus paired with cirrus to 4.58 km for low cloud paired with cirrus at SGP. Cloud vertical overlap characteristics are also considered for other ARM sites including the Tropical Western Pacific (TWP), North Slope of Alaska (NSA), and Eastern North Atlantic (ENA) sites amongst other shorter term ARM deployments globally. The decorrelation length scale ranged globally from 1.03 km in the Arctic Ocean to 3.06 km in Manacapuru, Brazil. Globally, the decorrelation length scale by cloud regime exhibited similarities (e.g., for cirrus paired with cirrus) and differences (e.g., congestus paired with cirrus). The results could help inform development of cloud vertical overlap assumptions within operational numerical weather prediction models and potentially improve prediction of radiative fluxes for weather, climate, and renewable energy forecasting.

54 ENVIRONMENTAL SCIENCES↗

Suppression of vertical instability in elongated current-carrying plasmas by applying stellarator rotational transform

The passive stability of vertically elongated current-carrying toroidal plasmas has been investigated in the Compact Toroidal Hybrid, a stellarator/tokamak hybrid device. In this experiment, the fractional transform f, defined as the ratio of the imposed external rotational transform from stellarator coils to the total rotational transform, was varied from 0.04 to 0.50, and the elongation κ was varied from 1.4 to 2.2. Plasmas that were vertically unstable were evidenced by motion of the plasma in the vertical direction. Vertical drifts are measured with a set of poloidal field pickup coils. A three chord horizontally viewing interferometer and a soft X-ray diode array confirmed the drifts. Plasmas with low fractional transform and high elongation are the most susceptible to vertical instability, consistent with analytic predictions that the vertical mode in elongated plasmas can be stabilized by the poloidal field of a relatively weak stellarator equilibrium.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Energy harvesting from coherent resonance of horizontal vibration of beam excited by vertical base motion

This letter investigates the energy harvesting from the horizontal coherent resonance of a vertical cantilever beam subjected to the vertical base excitation. The potential energy of the system has two symmetric potential wells. So, under vertical excitation, the system can jump between two potential wells, which will lead to the large vibration in horizontal direction. Two piezoelectric patches are pasted to harvest the energy. From experiment, it is found that the vertical excitation can make the beam turn to be bistable. The system can transform vertical vibration into horizontal vibration of low frequency when excited by harmonic motion. The horizontal coherence resonance can be observed when excited by a vertical white noise. The corresponding output voltages of piezoelectric films reach high values.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

The vertical-velocity skewness in the atmospheric boundary layer without buoyancy and Coriolis effects

One of the main features of near-neutral atmospheric boundary layer (ABL) turbulence is the positive vertical velocity skewness $Sk_w$ above the roughness sublayer or the buffer region in smooth-walls. The $Sk_w$ variations are receiving renewed interest in many climate-related parameterizations of the ABL given their significance to cloud formation and to testing sub-grid schemes for Large Eddy Simulations (LES). The vertical variations of $Sk_w$ are explored here using wind tunnel and flume experiments collected above smooth, rough, and permeable-walls in the absence of buoyancy and Coriolis effects. These laboratory experiments form a necessary starting point to probe the canonical structure of $Sk_w$ as they deal with a key limiting case (i.e., near-neutral conditions). Diagnostic models based on cumulant expansions, realizability constraints, and constant mass flux approach routinely employed in the convective boundary layer as well as prognostic models based on third-order budgets are used to explain variations in $Sk_w$ for the idealized laboratory conditions. The failure of flux-gradient relations to model $Sk_w$ from the gradients of the vertical velocity variance σ$_w^2$ are explained and corrections based on models of energy transport offered. Novel links between the diagnostic and prognostic models are also featured, especially for the inertial term in the third-order budget of the vertical velocity fluctuation. The co-spectral properties of w′/σ w vs w′ 2 /σ$_w^2$ are also presented for the first time to assess the dominant scales governing $Sk_w$ in the inner and outer layers, where w′ is the fluctuating vertical velocity and σ w is the vertical velocity standard deviation.>

Boundary layer flow↗

Demonstration of tokamak vertical stability control based on non-inductive Faraday-effect polarimetry measurements

Long-pulse or steady-state fusion reactors are envisioned to control vertical stability based on non-inductive measurements, i.e. that do not rely on temporal change of magnetic field. For the first time, vertical stability control using non-inductive Faraday-effect polarimetry measurements has been demonstrated. The Radial Interferometer-Polarimeter system on DIII-D is capable of microsecond resolution and was used to absolutely determine the vertical position of the plasma magnetic axis Z 0 . A vertical stability controller was developed to robustly stabilize diverted plasmas using Faraday-based measurements. The system was able to stabilize against vertical displacement events with growth rates up to 350 s -1 in elongated and elliptical plasma shapes, and instabilities with even higher growth rates are likely to be controllable with further improvements to controller tuning. Tests show that the Faraday-based controller remains effective and is capable of recovering from loss of control even when the plasma vertical position is far from the region where the linear model used to calculate Z 0 is most valid. Faraday control has also been activated during plasma ramp-up, demonstrating the robustness of the technique to larger systematic diagnostic uncertainty at low electron density.

Faraday-effect polarimetry↗

A Vertically Resolved Analysis of Radiative Feedbacks on Moist Static Energy Variance in Tropical Cyclones

Abstract A vertically resolved moist static energy (MSE) variance budget framework is used to diagnose processes associated with the development of tropical cyclones (TCs) in a general circulation model (GCM) under realistic boundary conditions. Previous studies have shown that interactions between radiation and MSE promote TC development. Here, we examine the vertical contributions of radiation and its interactions with MSE by performing several mechanism-denial experiments in which synoptic-scale radiative interactions are suppressed either in the boundary layer or in the free troposphere. Partly suppressing radiative interactions results in a reduction in global TC frequency. However, the magnitude of reduction and structure of the feedback depend on the intensity and structure of the TCs in these mechanism-denial experiments, indicating that both the magnitude and the vertical location of radiative interactions can impact global TC frequency. Using instantaneous 6-hourly outputs, an explicit computation reveals distinct spatial patterns of the advection term: the vertical component is positive in the mid- to upper troposphere, which reflects an upward transport of MSE by deep convection, whereas the horizontal component is positive in the boundary layer. These results illustrate the impact of the vertical distribution of radiative interactions and vertically varied contribution of the advection term in the development of TCs.

Meteorology & Atmospheric Sciences↗

Project Title: Adaptive Vertical Grid Enhancement for E3SM (Final Technical Report)

During the first phase of the project (2018/05-2021/05), we proved the hypothesis that, without tuning, high vertical resolution improves the representation of unresolved, parameterized low altitude clouds such as stratocumulus clouds in global climate models. We evaluated the effectiveness of the newly developed computational framework, Framework for Improvement by Vertical Enhancement (FIVE) by implementing it into E3SM. FIVE aims to improve representation of the target cloud, low level cloud for this project, with use of a locally high vertical resolution for computation of selected processes. FIVE was assessed via direct comparison among E3SM, E3SM-FIVE, and satellite data as well as a newly developed ensemble artificial neural network methodology. We demonstrated that E3SM-FIVE remarkably improves marine stratocumulus representation. To advance the FIVE methodology, we took a first step toward the adaptive vertical grid in the FIVE method by modifying the E3SM single column model. For future application of FIVE to the global storm resolving model with a few km horizontal grid resolution, we developed the vertical-meridional two-dimensional (2D) Hadley circulation model, which allows one to run simulations with much higher vertical resolution and significantly longer duration than current three-dimensional global storm resolving model. During the second phase of the project (2021/05-2023/11; period for this technical report), we sought a way to appropriately transform FIVE to a regionalized version of FIVE, which allows one to select locations with/without FIVE. In parallel, we demonstrated that E3SM-FIVE with a 25-km mesh significantly reduced the bias associated with coastal stratocumulus. Furthermore, we showed that the same improvement was able to be obtained with the use of both the Regional Refined Model (RRM) targeted to one of the stratocumulus regions with 25-km resolution and FIVE. We explored a new implementation strategy of FIVE with our 2D Hadley circulation model. In parallel we applied the 2D Hadley circulation model to study the double intertropical convergence zone bias with storm resolving model resolution and aerosol-cloud interactions within the Hadley circulation with near large eddy simulation resolution. Last, we have been investigating Arctic mixed-phase stratocumulus clouds with large eddy simulations in order to improve their representation in global models. During the course of the entire project, 6 journal articles were published, and 3 manuscripts are currently in preparation. We gave a total of 30 presentations at various domestic and international conferences. In addition we gave 6 seminar talks at universities and a national laboratory. E3SM- FIVE is available as a branch of E3SM.

54 ENVIRONMENTAL SCIENCES↗

Aerosol-induced changes in the vertical structure of precipitation: a perspective of TRMM precipitation radar

Our knowledge is still poor regarding the response of the precipitation vertical structure to aerosols, partly due to the ignorance of precipitation occurring at different spatial scales. A total of 6 years of collocated ground-based PM 10 and satellite-based (Tropical Rainfall Measuring Mission, TRMM) radar data, along with ERA-Interim reanalysis, are used in this study to investigate the aerosol effects on three localized rain regimes (shallow, stratiform, and convective rain) over the Pearl River Delta region of China. A subjective analysis method is proposed to discriminate between the localized and synoptic-scale precipitations based on weather composite charts where daily averaged wind field at 850 hPa is overlaid with the geopotential height at 500 hPa. In general, average rain rate tends to be greater under polluted conditions than under clean conditions. But such potential aerosol effects are regime dependent: as the atmosphere becomes slightly polluted (PM 10 ≤38 µg m -3 ), the top 1 % radar reflectivity (Z) for all regimes initially increases, followed by continued increases and weak decreases for convective and stratiform/shallow rain regimes, respectively. As the atmosphere becomes much more polluted, such regime dependences of aerosol effects are more significant. From a perspective of the vertical Z structure, comparisons between polluted conditions (days with the highest third of PM 10 concentration) and clean conditions (days with the lowest third of PM 10 concentration) show that the convective rain regime exhibits a deeper and stronger Z pattern, whereas a much shallower and weaker Z pattern is observed for stratiform and shallow precipitation regimes. In particular, the top height of the 30 dBZ rain echo increases by ~29 % (~1.27 km) for the convective regime, but decreases by ~10.8 % (~0.47 km) for the stratiform regime. However, no noticeable changes are observed for the shallow precipitation regime. Impacts of meteorological factors are further studied on both rain top height (RTH) and the center of gravity of Z, including vertical velocity, vertical wind shear, convection available potential energy, and vertically integrated moisture flux divergence (MFD). The possible invigoration effect on convective precipitation seems dependent on wind shear, in good agreement with previous findings. Overall, the observed dependence of the precipitation vertical structure on ground-based PM 10 supports the notion of aerosol invigoration or suppression effect on cold or warm rain and adds new insights into the nature of the complex interactions between aerosol and various localized precipitation regimes.

54 ENVIRONMENTAL SCIENCES↗

Observations of mesoscale vertical velocities around frontal zones

Vertical velocity and reflectivity data obtained with a VHF Doppler radar over a 15-day period in October and November of 1981 are analyzed. Standard radiosonde data and surface observations were used to locate two occluded fronts, two warm fronts, and a cold front that passed the radar site. These fronts are also evident in the radar reflectivity data. Most studies of the vertical circulation patterns associated with mososcale systems have used precipitation and cloud formations as tracers. Unlike other observational techniques, the VHF radar permits the continuous measurement of the three-dimensional air velocity vector in time and height from a fixed location. With the beam in a vertically pointing position, signals are scattered from turbulent variations in the refractive index with half the scale of the radar wavelength and by regions with sudden changes in the refractive index associated with horizontally stratified layers. Generally, the strongest echoes occur at the maximum in the vertical gradient of refractivity, usually at the base of a temperature inversion, such as the tropopause. VHF radars can also be used to locate atmospheric fronts, which are characterized by static stability, large horizontal temperature gradients, large vorticities, and vertical wind shears. These radars can provide the velocity field data needed to study wave motions associated with fronts and compare the actual vertical circulation to theoretical predictions.

Dennis, T. S.↗

GPS vertical axis performance enhancement for helicopter precision landing approach

Several areas were investigated for improving vertical accuracy for a rotorcraft using the differential Global Positioning System (GPS) during a landing approach. Continuous deltaranging was studied and the potential improvement achieved by estimating acceleration was studied by comparing the performance on a constant acceleration turn and a rough landing profile of several filters: a position-velocity (PV) filter, a position-velocity-constant acceleration (PVAC) filter, and a position-velocity-turning acceleration (PVAT) filter. In overall statistics, the PVAC filter was found to be most efficient with the more complex PVAT performing equally well. Vertical performance was not significantly different among the filters. Satellite selection algorithms based on vertical errors only (vertical dilution of precision or VDOP) and even-weighted cross-track and vertical errors (XVDOP) were tested. The inclusion of an altimeter was studied by modifying the PVAC filter to include a baro bias estimate. Improved vertical accuracy during degraded DOP conditions resulted. Flight test results for raw differential results excluding filter effects indicated that the differential performance significantly improved overall navigation accuracy. A landing glidepath steering algorithm was devised which exploits the flexibility of GPS in determining precise relative position. A method for propagating the steering command over the GPS update interval was implemented.

Denaro, Robert P.↗

Numerical experiments on consistent horizontal and vertical resolution for atmospheric models and observing systems

Simple numerical experiments are performed in order to determine the effects of inconsistent combinations of horizontal and vertical resolution in both atmospheric models and observing systems. In both cases, we find that inconsistent spatial resolution is associated with enhanced noise generation. A rather fine horizontal resolution in a satellite data observing system seems to be excessive when combined with the usually available relatively coarse vertical resolution. Using different strength horizontal filters, adjusted in such a way as to render the effective horizontal resolution more consistent with vertical resolution for the observing system, may result in improvement of the analysis accuracy. However, the increase of vertical resolution for a satellite data observing system is desirable. For the conventional data observing system with better vertically resolved data, the results are different in that little or no horizontal filtering is needed to make spatial resolution more consistent for the system. The obtained experimental estimates of consistent vertical and effective horizontal resolution are in a general agreement with consistent resolution estimates previously derived theoretically by the authors.

Fox-Rabinovitz, Michael S.↗

Numerical experiments on consistent horizontal and vertical resolution for atmospheric models and observing systems

Simple numerical experiments are performed in order to determine the effects of inconsistent combinations of horizontal and vertical resolution in both atmospheric models and observing systems. In both cases, we find that inconsistent spatial resolution is associated with enhanced noise generation. A rather fine horizontal resolution in a satellite-data observing system seems to be excessive when combined with the usually available relatively coarse vertical resolution. Using horizontal filters of different strengths, adjusted in such a way as to render the effective horizontal resolution more consistent with vertical resolution for the observing system, may result in improvement of the analysis accuracy. The increase of vertical resolution for a satellite data observing system with better vertically resolved data, the results are different in that little or no horizontal filtering is needed to make spatial resolution more consistent for the system. The obtained experimental estimates of consistent vertical and effective horizontal resolution are in a general agreement with consistent resolution estimates previously derived theoretically by the authors.

Fox-Rabinovitz, Michael S.↗