Nonequilibrium Phase Transitions in Directed Small-World Networks

Many social, biological, and economic systems can be approached by complex networks of interacting units. The behaviour of several models on small-world networks has recently been studied. These models are expected to capture the essential features of the complex processes taking place on real networks like disease spreading, formation of public opinion, distribution of wealth, etc. In many of these systems relations are directed, in the sense that links only act in one direction (outwards or inwards). We investigate the effect of directed links on the behaviour of a simple spin-like model evolving on a small-world network. We show that directed networks may lead to a highly nontrivial phase diagram including first and second-order phase transitions out of equilibrium.Comment: 4 pages, RevTeX format, 4 postscript figs, uses eps

A Review of Crop Height Retrieval Using InSAR Strategies: Techniques and Challenges

This article compares the performance of four different interferometric synthetic aperture radar (SAR) techniques for the estimation of rice crop height by means of bistatic TanDEM-X data. Methods based on the interferometric phase alone, on the coherence amplitude alone, on the complex coherence value, and on polarimetric SAR interferometry (PolInSAR) are analyzed. Validation is conducted with reference data acquired over rice fields in Spain during the Science Phase of the TanDEM-X mission. Single- and dual-polarized data are exploited to also provide further insights into the polarization influence on these approaches. Vegetation height estimates from methodologies based on the interferometric phase show a general underestimation for the HH channel (with a bias that reaches around 25 cm in mid-July for some fields), whereas the VV channel is strongly influenced by noisy phases, especially at large incidences [root-mean-square error (RMSE) = 31 cm]. Results show that these approaches perform better at shallower incidences than the methodologies based on coherence amplitude and on PolInSAR, which obtain the most suitable results at steep incidences, with RMSE values of 17 and 23 cm. On the contrary, at shallower incidences, they are highly affected by very low input coherence levels. Hence, they tend to overestimate vegetation height.This work was supported by the Spanish Ministry of Science and Innovation, in part by the State Agency of Research, and in part by the European Funds for Regional Development under Project TEC2017-85244-C2-1-P. The work of Noelia Romero-Puig was supported in part by the Generalitat Valenciana and in part by the European Social Fund under Grant ACIF/2018/204

Multi-Annual Evaluation of Time Series of Sentinel-1 Interferometric Coherence as a Tool for Crop Monitoring

Interferometric coherence from SAR data is a tool used in a variety of Earth observation applications. In the context of crop monitoring, vegetation indices are commonly used to describe crop dynamics. The most frequently used vegetation indices based on radar data are constructed using the backscattered intensity at different polarimetric channels. As coherence is sensitive to the changes in the scene caused by vegetation and its evolution, it may potentially be used as an alternative tool in this context. The objective of this work is to evaluate the potential of using Sentinel-1 interferometric coherence for this purpose. The study area is an agricultural region in Sevilla, Spain, mainly covered by 18 different crops. Time series of different backscatter-based radar vegetation indices and the coherence amplitude for both VV and VH channels from Sentinel-1 were compared to the NDVI derived from Sentinel-2 imagery for a 5-year period, from 2017 to 2021. The correlations between the series were studied both during and outside the growing season of the crops. Additionally, the use of the ratio of the two coherences measured at both polarimetric channels was explored. The results show that the coherence is generally well correlated with the NDVI across all seasons. The ratio between coherences at each channel is a potential alternative to the separate channels when the analysis is not restricted to the growing season of the crop, as its year-long temporal evolution more closely resembles that of the NDVI. Coherence and backscatter can be used as complementary sources of information, as backscatter-based indices describe the evolution of certain crops better than coherence.This research work was supported by the the European Space Agency under Project SEOM-S14SCI-Land (SInCohMap), and by the Spanish Ministry of Science and Innovation (State Agency of Research, AEI) and the European Funds for Regional Development (Project PID2020-117303GB-C22)

Spatial Adaptive Speckle Filtering Driven by Temporal Polarimetric Statistics and Its Application to PSI

Persistent scatterer (PS) interferometry (PSI) techniques are designed to measure ground deformations using satellite synthetic aperture radar (SAR) data. They rely on the identification of pixels not severely affected by spatial or temporal decorrelation, which, in general, correspond to pointlike PSs commonly found in urban areas. However, in urban areas, we can find not only PSs but also distributed scatterers (DSs) whose phase information may be exploited for PSI applications. Estimation of DS parameters requires speckle filtering to be applied to the complex SAR data, but conventional speckle filtering approaches tend to mask PS information due to spatial averaging. In the context of single-polarization PSI, adaptive speckle filtering strategies based on the exploitation of amplitude temporal statistics have been proposed, which seek to avoid spatial filtering on nonhomogeneous areas. Given the growing interest on polarimetric PSI techniques, i.e., those using polarimetric diversity to increase performance over conventional single-polarization PSI, in this paper, we propose an adaptive spatial filter driven by polarimetric temporal statistics, rather than single-polarization amplitudes. The proposed approach is able to filter DS while preserving PS information. In addition, a new methodology for the joint processing of PS and DS in the context of PSI is introduced. The technique has been tested for two different urban data sets: 41 dual-polarization TerraSAR-X images of Murcia (Spain) and 31 full-polarization Radarsat-2 images of Barcelona (Spain). Results show an important improvement in terms of number of pixels with valid deformation information, hence denser area coverage.This work was supported in part by the Spanish Ministerio de Economía y Competitividad and in part by the European Union FEDER funds under Project TEC2011-28201-C02-02

Model-Based Decomposition of Dual-Pol SAR Data: Application to Sentinel-1

In this study, we advance a new family of model-based decompositions adapted for dual-pol synthetic aperture radar data. These are formulated using the Stokes vector formalism, coupled to mappings from full quad-pol decomposition theory. A generalized model-based decomposition is developed, which allows separation of an arbitrary Stokes vector into partially polarized and polarized wave components. We employ the widely used random dipole cloud as a volume model but, in general, non-dipole options can be used. The cross-polarized phase δ, and the α angle, which is a function of the ratio between wave components, measure the transformation of polarization state on reflection. We apply the decomposition to dual-pol data provided by Sentinel-1 covering different scenarios, such as agricultural, forest, urban and glacial land-ice. We show that the polarized term of received polarization state is not usually the same as the transmitted one, and can therefore be used for key applications, e.g., classification and geo-physical parameter estimation. We show that, for vegetated terrain, depolarization is not the only influencing factor to Sentinel-1 backscattered intensities and, in the case of vertical crops (e.g., rice), this allows the crop orientation effects to be decoupled from volume scattering in the canopy. We demonstrate that coherent dual-pol systems show strong phase signatures over glaciers, where the polarized contribution significantly affects the backscattered state, resulting in elliptical polarization on receive. This is a key result for Sentinel-1, for which dual-pol phase analysis coupled to dense time series offer great opportunities for land-ice monitoring.This work was funded by the Spanish Ministry of Science and Innovation, the State Agency of Research (AEI) and the European Funds for Regional Development (EFRD) under Projects TEC2017-85244-C2-1-P and PID2020-117303GB-C22, and by the University of Alicante under grant VIGROB-114

Evaluation of PolInSAR Observables for Crop-Type Mapping Using Bistatic TanDEM-X Data

The contribution of Polarimetric SAR Interferometry (PolInSAR) observables to crop-type classification is investigated in this letter. The focus is set on characteristic parameters of the Coherence Region (CoRe), i.e. the representation in the polar plot of the PolInSAR data. For this purpose, time series of dual-pol HH-VV single-pass TanDEM-X bistatic data acquired over an agricultural area in Spain are exploited. In the experiment, up to 13 different crop types are evaluated. Crop classification is performed by means of the well-known Random Forest algorithm. The retrieved accuracy metrics highlight the potential of the evaluated PolInSAR descriptors for this application. Some PolInSAR features have proven to be enough representative of the scene, such as the Trace Coherence, which yields a classification accuracy of 75% and 87% at pixel and field level, respectively, on its own. Using all the PolInSAR parameters jointly as input features, classification reaches around 90% and 94% accuracy at pixel and field level, respectively. However, there are some PolInSAR feature subsets, e.g. the coherence measured at the Pauli channels or the foci of the ellipse which represents the CoRe, which yield accuracy levels very close to these maxima. These results demonstrate the suitability of the PolInSAR parameters for crop-type classification. Results are further improved when both polarimetric and PolInSAR features are combined, reaching 94% and 96% accuracy at pixel and field level, respectively.This work was supported by the Spanish Ministry of Science and Innovation, the State Agency of Research (AEI) and the European Funds for Regional Development (EFRD) under Project PID2020-117303GB-C22. Mario Busquier received a grant from the University of Alicante [UAFPU20-08]

Optimal Grid-Based Filtering for Crop Phenology Estimation with Sentinel-1 SAR Data

In the last decade, suboptimal Bayesian filtering (BF) techniques, such as Extended Kalman Filtering (EKF) and Particle Filtering (PF), have led to great interest for crop phenology monitoring with Synthetic Aperture Radar (SAR) data. In this study, a novel approach, based on the Grid-Based Filter (GBF), is proposed to estimate crop phenology. Here, phenological scales, which consist of a finite number of discrete stages, represent the one-dimensional state space, and hence GBF provides the optimal phenology estimates. Accordingly, contrarily to literature studies based on EKF and PF, no constraints are imposed on the models and the statistical distributions involved. The prediction model is defined by the transition matrix, while Kernel Density Estimation (KDE) is employed to define the observation model. The approach is applied on dense time series of dual-polarization Sentinel-1 (S1) SAR images, collected in four different years, to estimate the BBCH stages of rice crops. Results show that 0.94 ≤ R2 ≤ 0.98, 5.37 ≤ RMSE ≤ 7.9 and 20 ≤ MAE ≤ 33.This research was funded in part by the Spanish Ministry of Science and Innovation (State Agency of Research, AEI) and the European Funds for Regional Development (EFRD) under Projects TEC2017-85244-C2-1-P and PID2020-117303GB-C22, and in part by the University of Alicante (ref. VIGROB-114)

Analysis of the performance of polarimetric PSI over distributed scatterers with Sentinel-1 data

Sentinel−1 (S1) data enables effective monitoring of displacements using persistent scatterer interferometry (PSI). S1 includes VV and VH polarization channels, allowing us to apply polarimetric techniques to PSI. In short, polarimetric PSI (PolPSI) exploits the available polarization channels to enhance the identification and processing of measurement points including persistent scatterers (PS) and distributed scatterers (DS). Previous works have shown the benefits of using PolPSI for PS points with S1 data, but the corresponding analysis for DS is missing. DS points are processed by finding a neighborhood of statistically homogeneous pixels (SHP) and averaging the phase within that neighborhood. In this work we show how dual-polarimetric data are stricter on the selection of the SHP group than single-polarimetric data. Thanks to the information added by the second channel, different land covers are not mixed in the SHP group. As a result, the number of points in the SHP groups is generally smaller than with VV alone, but they are more reliable. The impact of this strategy on the resulting deformation estimates is also investigated in this work, showing that the deformation areas are fully preserved and the influence of nearby pixels associated with other scene elements is avoided.This work was supported in part by the European Funds for Regional Development and by the Spanish Ministry of Science and Innovation (Agencia Estatal de Investigación, AEI) with Project PID2020-117303GB-C22/AEI/10.13039/501100011033, and in part by the Generalitat Valenciana, Conselleria de Innovacion, Universidades, Ciencia y Sociedad Digital with Project CIAICO/2021/335. The research was also partially performed in the ESA-MOST China DRAGON-5 project ref. 59339

A new polarimetric change detector in radar imagery

In modern society, the anthropogenic influences on ecosystems are central points to understand the evolution of our planet. A polarimetric SAR (synthetic aperture radar) may have a significant contribution in tackling problems concerning land use change, since such data are available with any-weather conditions. Additionally, the discrimination capability can be enhanced by the polarimetric analysis. Recently, an algorithm able to identify targets scattering an electromagnetic wave with any degree of polarization has been developed, which makes use of a vector rearrangement of the elements of the coherency matrix. In the present work, this target detector is modified in order to perform change detection between two polarimetric acquisitions, for land use monitoring purposes. Regarding the selection of the detector parameters, a physical rationale is followed, developing a new parameterization of the algebraic space where the detector is defined. As it will be illustrated in the following, this space is 6 dimensional complex with restrictions due to the physical feasibility of the vectors. Specifically, a link between the detector parameters and the angle differences of the eigenvector model is obtained. Moreover, a dual polarimetric version of the change detector is developed, in case that quad-polarimetric data are not available. With the purpose of testing the methodology, a variety of datasets were exploited: quad-polarimetric airborne data at L-band (E-SAR), quad-polarimetric satellite data at C-band (Radarsat-2), and dual-polarimetric satellite data at X-band (TerraSAR-X). The algorithm results show agreement with the available information about land changes. Moreover, a comparison with a known change detector based on the maximum likelihood ratio is presented, providing improvements in some conditions. The two methodologies differ in the analysis of the total amplitude of the backscattering, where the proposed algorithm does not take this into consideration