I Smolyar’s research while affiliated with National Oceanic and Atmospheric Administration and other places

In our previous work, we introduced an empirical model (EM) of arbitrary binary images and three morphological characteristics: disorder of layer structure (DStr), disorder of layer size (DSize), and pattern complexity (PCom). The basic concept of the EM is that forms of lines play no role as a morphological factor in any narrow area of an arbitrary binary image; instead, the basic factor is the type of line connectivity, i.e., isotropic/anisotropic connections. The goal of the present work is to justify the possibility of making the EM applicable for the processing of grayscale arbitrary images. One of the possible ways to reach this goal is to assess the influence of image binarization on the robustness of DStr and DSize. Images that exhibit high and low edge gradient are used for this experimental study. The robustness of DStr and DSize against the binarization procedure is described in absolute (deviation from average) and relative (Pearson’s coefficient correlation) terms. Images with low edge gradient are converted into binary contour maps by applying the watershed algorithm, and DStr and DSize are then calculated for these maps. The robustness of DStr and DSize were assessed against the image threshold for images with high edge gradient and against the grid size of contour maps and Gaussian blur smoothing for images with low edge gradient. Experiments with grayscale arbitrary patterns, such as the surface of Earth and Mars, tidal sand ripples, turbulent flow, a melanoma, and cloud images, are presented to illustrate the spectrum of problems that may be possible to solve by applying the EM. The majority of our experiments show a high level of robustness for DStr and DSize.

Patterns found among both living systems, such as fish scales, bones, and tree rings, and non-living systems, such as terrestrial and extraterrestrial dunes, microstructures of alloys, and geological seismic profiles, are comprised of anisotropic layers of different thicknesses and lengths. These layered patterns form a record of internal and external factors that regulate pattern formation in their various systems, making it potentially possible to recognize events in the formation history of these systems. In our previous work, we developed an empirical model (EM) of anisotropic layered patterns using an N-partite graph, denoted as G(N), and a Boolean function to formalize the layer structure. The concept of isotropic and anisotropic layers was presented and described in terms of the G(N) and Boolean function. The central element of the present work is the justification that arbitrary binary patterns are made up of such layers. It has been shown that within the frame of the proposed model, it is the isotropic and anisotropic layers themselves that are the building blocks of binary layered and arbitrary patterns; pixels play no role. This is why the EM can be used to describe the morphological characteristics of such patterns. We present the parameters disorder of layer structure, disorder of layer size, and pattern complexity to describe the degree of deviation of the structure and size of an arbitrary anisotropic pattern being studied from the structure and size of a layered isotropic analog. Experiments with arbitrary patterns, such as regular geometric figures, convex and concave polygons, contour maps, the shape of island coastlines, river meanders, historic texts, and artistic drawings are presented to illustrate the spectrum of problems that it may be possible to solve by applying the EM. The differences and similarities between the proposed and existing morphological characteristics of patterns has been discussed, as well as the pros and cons of the suggested method.

Various natural patterns—such as terrestrial sand dune ripples, lamellae in vertebrate bones, growth increments in fish scales and corals, aortas and lamellar corpuscles in humans and animals—comprise layers of different thicknesses and lengths. Microstructures in manmade materials—such as alloys, perlite steels, polymers, ceramics, and ripples induced by laser on the surface of graphen—also exhibit layered structures. These layered patterns form a record of internal and external factors regulating pattern formation in their various systems, making it potentially possible to recognize and identify in their incremental sequences trends, periodicities, and events in the formation history of these systems. The morphology of layered systems plays a vital role in developing new materials and in biomimetic research. The structures and sizes of these two-dimensional (2D) patterns are characteristically anisotropic: That is, the number of layers and their absolute thicknesses vary significantly in different directions. The present work develops a method to quantify the morphological characteristics of 2D layered patterns that accounts for anisotropy in the object of study. To reach this goal, we use Boolean functions and an N -partite graph to formalize layer structure and thickness across a 2D plane and to construct charts of (1) “layer thickness vs. layer number” and (2) “layer area vs. layer number.” We present a parameter disorder of layer structure (DStr) to describe the deviation of a study object’s anisotropic structure from an isotropic analog and illustrate that charts and DStr could be used as local and global morphological characteristics describing various layered systems such as images of, for example, geological, atmospheric, medical, materials, forensic, plants, and animals. Suggested future experiments could lead to new insights into layered pattern formation.

This atlas consists of a description of data analysis procedures and horizontal maps of climatological distribution fields of temperature at selected standard depth levels of the World Ocean on one-degree and quarter-degree latitude-longitude grids. The aim of the maps is to illustrate large-scale characteristics of the distribution of ocean temperature. The fields used to generate these climatological maps were computed by objective analysis of all scientifically quality-controlled historical temperature data in the World Ocean Database 2018. Maps are presented for climatological composite periods (annual, seasonal, monthly, seasonal and monthly difference fields from the annual mean field, and the number of observations) at 102 standard depths.

This document describes the World Ocean Atlas 2018 (WOA18) statistical and objectively analyzed field data files. This description includes the types of statistical fields available, the oceanographic variables analyzed, and at which standard depth levels, time spans, time periods and grid resolutions they were analyzed. This description also includes the naming convention for the files, as well as the structure and format for the files. For a description of the data used, and the procedures for calculating WOA statistical fields, see https://www.nodc.noaa.gov/OC5/woa18/pubwoa18.html

This atlas consists of a description of data analysis procedures and horizontal maps of climatological distribution fields of dissolved inorganic nutrients (phosphate, nitrate and nitrate+nitrite, and silicate) at selected standard depth levels of the World Ocean on a one-degree latitude-longitude grid. The aim of the maps is to illustrate large-scale characteristics of the distribution of these nutrients. The oceanographic data fields used to generate these climatological maps were computed by objective analysis of all scientifically quality-controlled historical nutrient data in the World Ocean Database 2018. Maps are presented for climatological composite periods (annual, seasonal, monthly, seasonal and monthly difference fields from the annual mean field, and the number of observations) at 102 standard depths. We also provide estimates of the basin-scale uncertainty of the WOA18 nutrient objectively analyzed annual fields.

This atlas consists of a description of data analysis procedures and horizontal maps of climatological distribution fields of salinity at selected standard depth levels of the World Ocean on a one-degree and quarter-degree latitude-longitude grids. The aim of the maps is to illustrate large-scale characteristics of the distribution of ocean salinity. The fields used to generate these climatological maps were computed by objective analysis of all scientifically quality-controlled historical salinity data in the World Ocean Database 2018. Maps are presented for climatological composite periods (annual, seasonal, monthly, seasonal and monthly difference fields from the annual mean field, and the number of observations) at 102 standard depths.

This atlas consists of a description of data analysis procedures and horizontal maps of climatological distribution fields of dissolved oxygen (O2), apparent oxygen utilization (AOU), and dissolved oxygen saturation ( ) at selected standard depth levels of the world ocean on a one-degree latitude-longitude grid. The aim is to illustrate large-scale characteristics of the distribution of dissolved oxygen. The oceanographic data fields used to generate these climatological maps were computed by objective analysis of scientifically quality-controlled historical dissolved oxygen data in the World Ocean Database 2018. Distribution concentration maps are presented for climatological composite periods (annual, seasonal, monthly, seasonal and monthly difference fields from the annual mean field, and the number of observations) at 102 standard depths. We also provide estimates of the basin-scale uncertainty of the WOA18 O2 objectively analyzed annual fields.

Various natural patterns—such as terrestrial sand dune ripples, lamellae in vertebrate bones, growth increments in fish scales and corals, aorta and lamellar corpuscle of humans and animals—comprise layers of different thicknesses and lengths. Microstructures in manmade materials—such as alloys, perlite steels, polymers, ceramics, and ripples induced by laser on the surface of graphen—also exhibit layered structures. These layered patterns form a record of internal and external factors regulating pattern formation in their various systems, making it potentially possible to recognize and identify in their incremental sequences trends, periodicities, and events in the formation history of these systems. The morphology of layered systems plays a vital role in developing new materials and in biomimetic research. The structures and sizes of these two-dimensional (2-D) patterns are characteristically anisotropic: That is, the number of layers and their absolute thicknesses vary significantly in different directions. The present work develops a method to quantify the morphological characteristics of layered patterns that accounts for anisotropy in the object of study. To reach this goal, we use Boolean functions and an N-partite graph to formalize layer structure and thickness across a 2-D plane and to construct charts of 1) “layer thickness vs. layer number” and 2) “layer area vs. layer number.” We present a parameter for structural disorder in a layered pattern (DStr) to describe the deviation of a study object’s anisotropic structure from an isotropic analog and illustrate that charts and DStr could be used as local and global morphological characteristics describing various layered systems such as images of, for example, geological, atmospheric, medical, materials, forensic, plants, and animals. Suggested future experiments could lead to new insights into layered pattern formation.

Various natural patterns—such as terrestrial sand dune ripples, lamellae in vertebrate bones, growth increments in fish scales and corals, aorta and lamellar corpuscle of humans and animals—comprise layers of different thicknesses and lengths. Microstructures in manmade materials—such as alloys, perlite steels, polymers, ceramics, and ripples induced by laser on the surface of graphen—also exhibit layered structures. These layered patterns form a record of internal and external factors regulating pattern formation in their various systems, making it potentially possible to recognize and identify in their incremental sequences trends, periodicities, and events in the formation history of these systems. The morphology of layered systems plays a vital role in developing new materials and in biomimetic research. The structures and sizes of these two-dimensional (2-D) patterns are characteristically anisotropic: That is, the number of layers and their absolute thicknesses vary significantly in different directions. The present work develops a method to quantify the morphological characteristics of layered patterns that accounts for anisotropy in the object of study. To reach this goal, we use Boolean functions and an N-partite graph to formalize layer structure and thickness across a 2-D plane and to construct charts of 1) “layer thickness vs. layer number” and 2) “layer area vs. layer number.” We present a parameter for structural disorder in a layered pattern (DStr) to describe the deviation of a study object’s anisotropic structure from an isotropic analog and illustrate that charts and DStr could be used as local and global morphological characteristics describing various layered systems such as images of, for example, geological, atmospheric, medical, materials, forensic, plants, and animals. Suggested future experiments could lead to new insights into layered pattern formation.