Fractals in Geoscience and Remote Sensing

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Recognizing the Shape and Size of Tundra Lakes in Synthetic Aperture Radar (SAR) Images Using Deep Learning Segmentation

Permafrost tundra contains more than twice as much carbon as is currently in the atmosphere, and it is warming six times as fast as the global mean. Tundra lakes dynamics is a robust indicator of global climate processes, and is still not well understood. Satellite data, particularly, from synthetic aperture radar (SAR) is a suitable tool for tundra lakes recognition and monitoring of their changes. However, manual analysis of lake boundaries can be slow and inefficient; therefore, reliable automated algorithms are required. To address this issue, we propose a two-stage approach, comprising instance deep-learning-based segmentation by U-Net, followed by semantic segmentation based on a watershed algorithm for separating touching and overlapping lakes. Implementation of this concept is essential for accurate sizes and shapes estimation of an individual lake. Here, we evaluated the performance of the proposed approach on lakes, manually extracted from tens of C-band SAR images from Sentinel-1, which were collected in the Yamal Peninsula and Alaska areas in the summer months of 2015–2022. An accuracy of 0.73, in terms of the Jaccard similarity index, was achieved. The lake’s perimeter, area and fractal sizes were estimated, based on the algorithm framework output from hundreds of SAR images. It was recognized as lognormal distributed. The evaluation of the results indicated the efficiency of the proposed approach for accurate automatic estimation of tundra lake shapes and sizes, and its potential to be used for further studies on tundra lake dynamics, in the context of global climate change, aimed at revealing new factors that could cause the planet to warm or cool

Topics in environmental and physical geodesy

A compilation of mathematical techniques and physical basic knowledge in order to prepare the post graduate students of the subjects of physical geodesy, environmental physics and the visiting students of Erasmus-Socrates projects of the Mediterranean Institute of Oceanography of Toulon and the Campus Universitari de la Mediterrania in Vilanova i la Geltru, Barcelona.Postprint (published version

Turbulent structure in environmental flows: effects of stratification and rotation

Several series of experiments in stratified and in rotating/stratified decaying flows after a grid is used to stir the two layer stable fluid brine and fresh water set up. We measure by comparing the gained potential energy with the available kinetic energy AKE, the relative efficiency of mixing. The experiments in stratified rotating flows with grid driven turbulence were both periodic (quasi stationary) and non-monotonic (decaying) forcing. This thesis compares experimental, numerical and field observations on the structure and Topology of the Stratified Rotating Flows as well as their decay, the horizontal spectra changes appreciable with slopes from 1.1 to 5, but vorticity and local circulation, and also the initial topology and forcing of the flow. A detailed study of the vorticity decay and vortex and energy structure has been performed, the new results show that neither stratified nor rotating flows exhibit pure 2D structures. The work parameterizes the role of the Richardson number and the Rossby number, both in the experiments and in the ocean visualizations is very important. The conditions of vortex decay show the effects of the internal waves in the decay turbulent conditions both for stratified and rotating flows. The parameter space (Re,Ri,Ro) has been used to interpret many previously disconnected explanations of the 2D-3D turbulent behaviour. The comparison of numerical simulations with experiments has allowed implementing new theoretical aspects of the interaction between waves and vortices finding the surprising and very interesting result that these interactions depend on the level of enstrophy. This also leads to new ways of using multifractal analysis ad intermittency in ocean environmental observations. A large collection of SAR images obtained from three European coastal areas were used for routine satellite analysis by SAR and other sensors, which seem very important to build seasonal databases of the dynamic conditions of ocean mixing. The topology of the basic flow is very important and in particular the topology of the vortices and their decay which depends on ambient factors such as wave activity, wind and currents. We find more realistic estimates of the spatial/temporal non-homogeneities (and intermittency obtained as spatial correlations of the turbulent dissipation); these values are used to parameterize the sea surface turbulence, as well as a laboratory experiments at a variety of scales. Using multi-fractal geometry as well, we can establish now a theoretical pattern for the turbulence behaviour that is reflected in the different descriptors. Vorticity evolution is smoother and different than that of scalar or tracer density. The correlation between the local Ri and the fractal dimension detected from energy or entropy is good. Using multi-fractal geometry we can also establish certain regions of higher local activity used to establish the geometry of the turbulence mixing that needs to be studied in detail when interpreting the complex balance between the direct 3D Kolmogorov type cascade and the Inverse 2D Kraichnan type cascade

Exploiting the multiscale synergy among ocean variables : application to the improvement of remote sensing salinity maps

Les imatges de teledetecció de la superfície oceànica proporcionen una vista sinòptica de la complexa geometria de la circulació oceànica, dominada per la variabilitat de mesoescala. Estructures com filaments i vòrtex són presents en els diferents escalars advectats pel flux oceànic. L’origen més probable d’aquestes estructures és el caràcter turbulent dels corrents, aquestes estructures són persistents amb el temps i compatibles amb la dinàmica mesoscalar oceànica. A escales espacials de quilòmetres o més, la turbulència és principalment 2D, i una complexa geometria, plena de filaments i remolins de mides diferents, emergeix en les imatges superficials de teledetecció de concentració de clorofil·la-a, salinitat superficial, així com en altres escalars més coneguts com són la temperatura superficial i la topografia dinàmica. L’objectiu d’aquesta tesi és explorar i aplicar metodologies de mapatge que permeten millorar la qualitat de mapes de teledetecció oceànica en general, i en particular de la salinitat superficial del mar (SSS). Les diferents metodologies emprades en aquesta tesi han estat aplicades amb l’objectiu específic de millorar els mapes de teledetecció de salinitat superficial del mar proveïts per la missió SMOS de l’Agència Espaial Europea. SMOS és el primer satèl·lit capaç de mesurar la humitat del sol i salinitat oceànica des de l’espai a escala global. La primera part d’aquesta tesi se centra a analitzar les característiques dels productes de nivell 2 (L2) de salinitat de SMOS i produir mapes de nivell 3 (L3) de salinitat utilitzant aproximacions clàssiques: millora del filtratge, mitjana ponderada i Interpolació Òptima. En el curs de la nostra recerca obtenim un conjunt de recomanacions de com processar les dades de SMOS començant des del nivell L2. Aquesta tesi també presenta una nova tècnica de fusió de dades que permet explotar les estructures turbulentes comunes entre diferents variables oceàniques, representant un pas endavant en la cadena de processat per generar mapes de nivell 4 (L4). Aquesta tècnica de fusió es basa teòricament en les propietats geomètriques dels traçadors advectats per la dinàmica oceànica (Turiel et al., 2005a). Degut a l’efecte de forta cissalla als fluits turbulents, l’estructura espacial d’un traçador oceànic hereta algunes propietats del flux subjacent, i en particular el seu arranjament geomètric. Com a conseqüència, les diferents variables oceàniques mostren propietats d’escala similars a la cascada d’energia turbulenta (Seuront and Schmitt, 2005; Nieves et al., 2007; Nieves and Turiel, 2009; Isern-Fontanet et al., 2007). El mètode de fusió agafa un senyal de menor qualitat (afectat per soroll, forats de dades i/o de resolució més baixa) i en millora la seva qualitat. A més d’això, el mètode de fusió és capaç d’extrapolar les dades de forma geofísicament coherent. Aquesta millora del senyal s’aconsegueix utilitzant una altra variable oceànica adquirida amb major qualitat, cobertura espacial més gran i/o millor resolució. Un punt clau d’aquesta aproximació és la suposició de l’existència d’una estructura multifractal de les imatges de teledetecció oceànica (Lovejoy et al., 2001b), i que les línies de singularitat de les diferents variables de l’oceà coincideixen. Sota aquestes premises, els gradients de les dues variables a fusionar estan relacionats per una matriu suau. Com a primera i simple aproximació, s’assumeix que aquesta matriu és proporcional a la identitat; això porta a un esquema de regressió lineal local. Aquesta tesi mostra que aquesta aproximació senzilla permet reduir l’error i millorar la cobertura del producte de nivell 4 resultant. D’altra banda, s’obté informació sobre la relació estadística entre les dues variables fusionades, ja que la dependència funcional entre elles es determina per cada punt de la imatge.Remote sensing imagery of the ocean surface provides a synoptic view of the complex geometry of ocean circulation, which is dominated by mesoscale variability. The signature of filaments and vortices is present in different ocean scalars advected by the oceanic flow. The most probable origin of the observed structures is the turbulent character of ocean currents, and those signatures are persistent over time scales compatible with ocean mesoscale dynamics. At spatial scales of kilometers or more, turbulence is mainly 2D, and a complex geometry, full of filaments and eddies of different sizes, emerges in remote sensing images of surface chlorophyll-a concentration and surface salinity, as well as in other scalars acquired with higher quality such as surface temperature and absolute dynamic topography. The aim of this thesis is to explore and apply mapping methodologies to improve the quality of remote sensing maps in general, but focusing in the case of remotely sensed sea surface salinity (SSS) data. The different methodologies studied in this thesis have been applied with the specific goal of improving surface salinity maps generated from data acquired by the European Space Agency's mission SMOS, the first satellite able to measure soil moisture and ocean salinity from space at a global scale. The first part of this thesis will introduce the characteristics of the operational SMOS Level 2 (L2) SSS products and the classical approaches to produce the best possible SSS maps at Level 3 (L3), namely data filtering, weighted average and Optimal Interpolation. In the course of our research we will obtain a set of recommendations about how to process SMOS data starting from L2 data. A fusion technique designed to exploit the common turbulent signatures between different ocean variables is also explored in this thesis, in what represents a step forward from L3 to Level 4 (L4). This fusion technique is theoretically based on the geometrical properties of advected tracers. Due to the effect of the strong shear in turbulent flows, the spatial structure of tracers inherit some properties of the underlying flow and, in particular, its geometrical arrangement. As a consequence, different ocean variables exhibit scaling properties, similar to the turbulent energy cascade. The fusion method takes a signal affected by noise, data gaps and/or low resolution, and improves it in a geophysically meaningful way. This signal improvement is achieved by using an appropriate data, which is another ocean variable acquired with higher quality, greater spatial coverage and/or finer resolution. A key point in this approach is the assumption of the existence of a multifractal structure in ocean images, and that singularity lines of the different ocean variables coincide. Under these assumptions, the horizontal gradients of both variables, signal and template, can be related by a smooth matrix. The first, simplest approach to exploit such an hypothesis assumes that the relating matrix is proportional to the identity, leading to a local regression scheme. As shown in the thesis, this simple approach allows reducing the error and improving the coverage of the resulting Level 4 product; Moreover, information about the statistical relationship between the two fields is obtained since the functional dependence between signal and template is determined at each point

Quantitative Estimation of Surface Soil Moisture in Agricultural Landscapes using Spaceborne Synthetic Aperture Radar Imaging at Different Frequencies and Polarizations

Soil moisture and its distribution in space and time plays an important role in the surface energy balance at the soil-atmosphere interface. It is a key variable influencing the partitioning of solar energy into latent and sensible heat flux as well as the partitioning of precipitation into runoff and percolation. Due to their large spatial variability, estimation of spatial patterns of soil moisture from field measurements is difficult and not feasible for large scale analyses. In the past decades, Synthetic Aperture Radar (SAR) remote sensing has proven its potential to quantitatively estimate near surface soil moisture at high spatial resolutions. Since the knowledge of the basic SAR concepts is important to understand the impact of different natural terrain features on the quantitative estimation of soil moisture and other surface parameters, the fundamental principles of synthetic aperture radar imaging are discussed. Also the two spaceborne SAR missions whose data was used in this study, the ENVISAT of the European Space Agency (ESA) and the ALOS of the Japanese Aerospace Exploration Agency (JAXA), are introduced. Subsequently, the two essential surface properties in the field of radar remote sensing, surface soil moisture and surface roughness are defined, and the established methods of their measurement are described. The in situ data used in this study, as well as the research area, the River Rur catchment, with the individual test sites where the data was collected between 2007 and 2010, are specified. On this basis, the important scattering theories in radar polarimetry are discussed and their application is demonstrated using novel polarimetric ALOS/PALSAR data. A critical review of different classical approaches to invert soil moisture from SAR imaging is provided. Five prevalent models have been chosen with the aim to provide an overview of the evolution of ideas and techniques in the field of soil moisture estimation from active microwave data. As the core of this work, a new semi-empirical model for the inversion of surface soil moisture from dual polarimetric L-band SAR data is introduced. This novel approach utilizes advanced polarimetric decomposition techniques to correct for the disturbing effects from surface roughness and vegetation on the soil moisture retrieval without the use of a priori knowledge. The land use specific algorithms for bare soil, grassland, sugar beet, and winter wheat allow quantitative estimations with accuracies in the order of 4 Vol.-%. Application of remotely sensed soil moisture patterns is demonstrated on the basis of mesoscale SAR data by investigating the variability of soil moisture patterns at different spatial scales ranging from field scale to catchment scale. The results show that the variability of surface soil moisture decreases with increasing wetness states at all scales. Finally, the conclusions from this dissertational research are summarized and future perspectives on how to extend the proposed model by means of improved ground based measurements and upcoming advances in sensor technology are discussed. The results obtained in this thesis lead to the conclusion that state-of-the-art spaceborne dual polarimetric L-band SAR systems are not only suitable to accurately retrieve surface soil moisture contents of bare as well as of vegetated agricultural fields and grassland, but for the first time also allow investigating within-field spatial heterogeneities from space

Advanced Geoscience Remote Sensing

Nowadays, advanced remote sensing technology plays tremendous roles to build a quantitative and comprehensive understanding of how the Earth system operates. The advanced remote sensing technology is also used widely to monitor and survey the natural disasters and man-made pollution. Besides, telecommunication is considered as precise advanced remote sensing technology tool. Indeed precise usages of remote sensing and telecommunication without a comprehensive understanding of mathematics and physics. This book has three parts (i) microwave remote sensing applications, (ii) nuclear, geophysics and telecommunication; and (iii) environment remote sensing investigations

Fractal analyses of some natural systems

Fractal dimensions are estimated by the box-counting method for real world data sets and for mathematical models of three natural systems. 1 he natural systems are nearshore sea wave profiles, the topography of Shei-pa National Park in Taiwan, and the normalised difference vegetation index (NDV1) image of a fresh fern. I he mathematical models which represent the natural systems utilise multi-frequency sinusoids for the sea waves, a synthetic digital elevation model constructed by the mid-point displacement method for the topography and the Iterated Function System (IFS) codes for the fern leaf. The results show that similar fractal dimensions are obtained for discrete sub-sections of the real and synthetic one-dimensional wave data, whilst different fractal dimensions are obtained for discrete sections of the real and synthetic topographical and fern data. The similarities and differences are interpreted in the context of system evolution which was introduced by Mandelbrot (1977). Finally, the results for the fern images show that use of fractal dimensions can successfully separate void and filled elements of the two-dimensional series

Small-scale deformation of an Arctic sea ice floe detected by GPS and satellite imagery

Small-scale (~100 to 200 m) deformations of an Arctic sea ice floe were detected from multiple GPS-equipped buoys that were deployed on the same ice floe. Over a nine-month period three deformation events were recorded. At each case the event was of limited duration, each lasting less than a day. The events were highly compressive in nature with the area occupied by the buoy array decreasing by over half of the original area. The strain rate during the deformation, of the order of 10−5 s−1, is about three orders of magnitude larger than previous estimates for brittle fracturing for cracks of about 100 m in length. On the 2-day time scale, the strain rate became too small and none of the deformation events could be detected. This suggests that satellite data with longer time scales may significantly underestimate the amount of intermittent, small-scale brittle failure of total deformation. Taken as a whole, our results show the influence that large-scale wind stress can have on small-scale deformation. However, it is important to note that the impact of large-scale wind stress is also dependent on the properties of sea ice as well as on the spatial and temporal evolution of the underlying forces that influence the fracturing proces

Spacelab Science Results Study

Beginning with OSTA-1 in November 1981 and ending with Neurolab in March 1998, a total of 36 Shuttle missions carried various Spacelab components such as the Spacelab module, pallet, instrument pointing system, or mission peculiar experiment support structure. The experiments carried out during these flights included astrophysics, solar physics, plasma physics, atmospheric science, Earth observations, and a wide range of microgravity experiments in life sciences, biotechnology, materials science, and fluid physics which includes combustion and critical point phenomena. In all, some 764 experiments were conducted by investigators from the U.S., Europe, and Japan. The purpose of this Spacelab Science Results Study is to document the contributions made in each of the major research areas by giving a brief synopsis of the more significant experiments and an extensive list of the publications that were produced. We have also endeavored to show how these results impacted the existing body of knowledge, where they have spawned new fields, and if appropriate, where the knowledge they produced has been applied