Linear global instability of non-orthogonal incompressible swept attachment-line boundary layer flow

Instability of the orthogonal swept attachment line boundary layer has received attention by local1, 2 and global3–5 analysis methods over several decades, owing to the significance of this model to transition to turbulence on the surface of swept wings. However, substantially less attention has been paid to the problem of laminar flow instability in the non-orthogonal swept attachment-line boundary layer; only a local analysis framework has been employed to-date.6 The present contribution addresses this issue from a linear global (BiGlobal) instability analysis point of view in the incompressible regime. Direct numerical simulations have also been performed in order to verify the analysis results and unravel the limits of validity of the Dorrepaal basic flow7 model analyzed. Cross-validated results document the effect of the angle _ on the critical conditions identified by Hall et al.1 and show linear destabilization of the flow with decreasing AoA, up to a limit at which the assumptions of the Dorrepaal model become questionable. Finally, a simple extension of the extended G¨ortler-H¨ammerlin ODE-based polynomial model proposed by Theofilis et al.4 is presented for the non-orthogonal flow. In this model, the symmetries of the three-dimensional disturbances are broken by the non-orthogonal flow conditions. Temporal and spatial one-dimensional linear eigenvalue codes were developed, obtaining consistent results with BiGlobal stability analysis and DNS. Beyond the computational advantages presented by the ODE-based model, it allows us to understand the functional dependence of the three-dimensional disturbances in the non-orthogonal case as well as their connections with the disturbances of the orthogonal stability problem.

Efficient local unfolding with ancestor stacks for full prolog

The integration of powerful partial evaluation methods into practical compilers for logic programs is still far from reality. This is related both to 1) efficiency issues and to 2) the complications of dealing with practical programs. Regarding efnciency, the most successful unfolding rules used nowadays are based on structural orders applied over (covering) ancestors, i.e., a subsequence of the atoms selected during a derivation. Unfortunately, maintaining the structure of the ancestor relation during unfolding introduces significant overhead. We propose an efficient, practical local unfolding rule based on the notion of covering ancestors which can be used in combination with any structural order and allows a stack-based implementation without losing any opportunities for specialization. Regarding the second issue, we propose assertion-based techniques which allow our approach to deal with real programs that include (Prolog) built-ins and external predicates in a very extensible manner. Finally, we report on our implementation of these techniques in a practical partial evaluator, embedded in a state of the art compiler which uses global analysis extensively (the Ciao compiler and, specifically, its preprocessor CiaoPP). The performance analysis of the resulting system shows that our techniques, in addition to dealing with practical programs, are also significantly more efficient in time and somewhat more efficient in memory than traditional tree-based implementations.

Effectiveness of global analysis in strict independence-based automatic program parallelization

This paper presents a study of the effectiveness of global analysis in the parallelization of logic programs using strict independence. A number of well-known approximation domains are selected and tlieir usefulness for the application in hand is explained. Also, methods for using the information provided by such domains to improve parallelization are proposed. Local and global analyses are built using these domains and such analyses are embedded in a complete parallelizing compiler. Then, the performance of the domains (and the system in general) is assessed for this application through a number of experiments. We argüe that the results offer significant insight into the characteristics of these domains, the demands of the application, and the tradeoffs involved.

Evaluación y análisis de la trazabilidad metrológica en redes para la verificación y calibración de instrumental GNSS (Global Navigation Satellite System)

Los estudios realizados hasta el momento para la determinación de la calidad de medida del instrumental geodésico han estado dirigidos, fundamentalmente, a las medidas angulares y de distancias. Sin embargo, en los últimos años se ha impuesto la tendencia generalizada de utilizar equipos GNSS (Global Navigation Satellite System) en el campo de las aplicaciones geomáticas sin que se haya establecido una metodología que permita obtener la corrección de calibración y su incertidumbre para estos equipos. La finalidad de esta Tesis es establecer los requisitos que debe satisfacer una red para ser considerada Red Patrón con trazabilidad metrológica, así como la metodología para la verificación y calibración de instrumental GNSS en redes patrón. Para ello, se ha diseñado y elaborado un procedimiento técnico de calibración de equipos GNSS en el que se han definido las contribuciones a la incertidumbre de medida. El procedimiento, que se ha aplicado en diferentes redes para distintos equipos, ha permitido obtener la incertidumbre expandida de dichos equipos siguiendo las recomendaciones de la Guide to the Expression of Uncertainty in Measurement del Joint Committee for Guides in Metrology. Asimismo, se han determinado mediante técnicas de observación por satélite las coordenadas tridimensionales de las bases que conforman las redes consideradas en la investigación, y se han desarrollado simulaciones en función de diversos valores de las desviaciones típicas experimentales de los puntos fijos que se han utilizado en el ajuste mínimo cuadrático de los vectores o líneas base. Los resultados obtenidos han puesto de manifiesto la importancia que tiene el conocimiento de las desviaciones típicas experimentales en el cálculo de incertidumbres de las coordenadas tridimensionales de las bases. Basándose en estudios y observaciones de gran calidad técnica, llevados a cabo en estas redes con anterioridad, se ha realizado un exhaustivo análisis que ha permitido determinar las condiciones que debe satisfacer una red patrón. Además, se han diseñado procedimientos técnicos de calibración que permiten calcular la incertidumbre expandida de medida de los instrumentos geodésicos que proporcionan ángulos y distancias obtenidas por métodos electromagnéticos, ya que dichos instrumentos son los que van a permitir la diseminación de la trazabilidad metrológica a las redes patrón para la verificación y calibración de los equipos GNSS. De este modo, ha sido posible la determinación de las correcciones de calibración local de equipos GNSS de alta exactitud en las redes patrón. En esta Tesis se ha obtenido la incertidumbre de la corrección de calibración mediante dos metodologías diferentes; en la primera se ha aplicado la propagación de incertidumbres, mientras que en la segunda se ha aplicado el método de Monte Carlo de simulación de variables aleatorias. El análisis de los resultados obtenidos confirma la validez de ambas metodologías para la determinación de la incertidumbre de calibración de instrumental GNSS. ABSTRACT The studies carried out so far for the determination of the quality of measurement of geodetic instruments have been aimed, primarily, to measure angles and distances. However, in recent years it has been accepted to use GNSS (Global Navigation Satellite System) equipment in the field of Geomatic applications, for data capture, without establishing a methodology that allows obtaining the calibration correction and its uncertainty. The purpose of this Thesis is to establish the requirements that a network must meet to be considered a StandardNetwork with metrological traceability, as well as the methodology for the verification and calibration of GNSS instrumental in those standard networks. To do this, a technical calibration procedure has been designed, developed and defined for GNSS equipment determining the contributions to the uncertainty of measurement. The procedure, which has been applied in different networks for different equipment, has alloweddetermining the expanded uncertainty of such equipment following the recommendations of the Guide to the Expression of Uncertainty in Measurement of the Joint Committee for Guides in Metrology. In addition, the three-dimensional coordinates of the bases which constitute the networks considered in the investigationhave been determined by satellite-based techniques. There have been several developed simulations based on different values of experimental standard deviations of the fixed points that have been used in the least squares vectors or base lines calculations. The results have shown the importance that the knowledge of experimental standard deviations has in the calculation of uncertainties of the three-dimensional coordinates of the bases. Based on high technical quality studies and observations carried out in these networks previously, it has been possible to make an exhaustive analysis that has allowed determining the requirements that a standard network must meet. In addition, technical calibration procedures have been developed to allow the uncertainty estimation of measurement carried outby geodetic instruments that provide angles and distances obtained by electromagnetic methods. These instruments provide the metrological traceability to standard networks used for verification and calibration of GNSS equipment. As a result, it has been possible the estimation of local calibration corrections for high accuracy GNSS equipment in standardnetworks. In this Thesis, the uncertainty of calibration correction has been calculated using two different methodologies: the first one by applying the law of propagation of uncertainty, while the second has applied the propagation of distributions using the Monte Carlo method. The analysis of the obtained results confirms the validity of both methodologies for estimating the calibration uncertainty of GNSS equipment.

Dimensional synthesis of a spherical parallel manipulator based on the evaluation of global performance indexes

In this work, the dimensional synthesis of a spherical Parallel Manipulator (PM) with a -1S kinematic chain is presented. The goal of the synthesis is to find a set of parameters that defines the PM with the best performance in terms of workspace capabilities, dexterity and isotropy. The PM is parametrized in terms of a reference element, and a non-directed search of these parameters is carried out. First, the inverse kinematics and instantaneous kinematics of the mechanism are presented. The latter is found using the screw theory formulation. An algorithm that explores a bounded set of parameters and determines the corresponding value of global indexes is presented. The concepts of a novel global performance index and a compound index are introduced. Simulation results are shown and discussed. The best PMs found in terms of each performance index evaluated are locally analyzed in terms of its workspace and local dexterity. The relationship between the performance of the PM and its parameters is discussed, and a prototype with the best performance in terms of the compound index is presented and analyzed.

Order 10 4 speedup in global linear instability analysis using matrix formation

A unified solution framework is presented for one-, two- or three-dimensional complex non-symmetric eigenvalue problems, respectively governing linear modal instability of incompressible fluid flows in rectangular domains having two, one or no homogeneous spatial directions. The solution algorithm is based on subspace iteration in which the spatial discretization matrix is formed, stored and inverted serially. Results delivered by spectral collocation based on the Chebyshev-Gauss-Lobatto (CGL) points and a suite of high-order finite-difference methods comprising the previously employed for this type of work Dispersion-Relation-Preserving (DRP) and Padé finite-difference schemes, as well as the Summationby- parts (SBP) and the new high-order finite-difference scheme of order q (FD-q) have been compared from the point of view of accuracy and efficiency in standard validation cases of temporal local and BiGlobal linear instability. The FD-q method has been found to significantly outperform all other finite difference schemes in solving classic linear local, BiGlobal, and TriGlobal eigenvalue problems, as regards both memory and CPU time requirements. Results shown in the present study disprove the paradigm that spectral methods are superior to finite difference methods in terms of computational cost, at equal accuracy, FD-q spatial discretization delivering a speedup of ð (10 4). Consequently, accurate solutions of the three-dimensional (TriGlobal) eigenvalue problems may be solved on typical desktop computers with modest computational effort.

Estimation of daily global solar radiation from measured temperatures at Cañada de Luque, Córdoba, Argentina

Solar radiation is the most important source of renewable energy in the planet; it's important to solar engineers, designers and architects, and it's also fundamental for efficiently determining irrigation water needs and potential yield of crops, among others. Complete and accurate solar radiation data at a specific region are indispensable. For locations where measured values are not available, several models have been developed to estimate solar radiation. The objective of this paper was to calibrate, validate and compare five representative models to predict global solar radiation, adjusting the empirical coefficients to increase the local applicability and to develop a linear model. All models were based on easily available meteorological variables, without sunshine hours as input, and were used to estimate the daily solar radiation at Cañada de Luque (Córdoba, Argentina). As validation, measured and estimated solar radiation data were analyzed using several statistic coefficients. The results showed that all the analyzed models were robust and accurate (R2 and RMSE values between 0.87 to 0.89 and 2.05 to 2.14, respectively), so global radiation can be estimated properly with easily available meteorological variables when only temperature data are available. Hargreaves-Samani, Allen and Bristow-Campbell models could be used with typical values to estimate solar radiation while Samani and Almorox models should be applied with calibrated coefficients. Although a new linear model presented the smallest R2 value (R2 = 0.87), it could be considered useful for its easy application. The daily global solar radiation values produced for these models can be used to estimate missing daily values, when only temperature data are available, and in hydrologic or agricultural applications.

Seismic Risk Scenarios in Puerto Principe (Haiti). A Tool for Reconstruction and Emergency Planning

The 12 January 2010, an earthquake hit the city of Port-au-Prince, capital of Haiti. The earthquake reached a magnitude Mw 7.0 and the epicenter was located near the town of Léogâne, approximately 25 km west of the capital. The earthquake occurred in the boundary region separating the Caribbean plate and the North American plate. This plate boundary is dominated by left-lateral strike slip motion and compression, and accommodates about 20 mm/y slip, with the Caribbean plate moving eastward with respect to the North American plate (DeMets et al., 2000). Initially the location and focal mechanism of the earthquake seemed to involve straightforward accommodation of oblique relative motion between the Caribbean and North American plates along the Enriquillo-Plantain Garden fault system (EPGFZ), however Hayes et al., (2010) combined seismological observations, geologic field data and space geodetic measurements to show that, instead, the rupture process involved slip on multiple faults. Besides, the authors showed that remaining shallow shear strain will be released in future surface-rupturing earthquakes on the EPGFZ. In December 2010, a Spanish cooperation project financed by the Politechnical University of Madrid started with a clear objective: Evaluation of seismic hazard and risk in Haiti and its application to the seismic design, urban planning, emergency and resource management. One of the tasks of the project was devoted to vulnerability assessment of the current building stock and the estimation of seismic risk scenarios. The study was carried out by following the capacity spectrum method as implemented in the software SELENA (Molina et al., 2010). The method requires a detailed classification of the building stock in predominant building typologies (according to the materials in the structure and walls, number of stories and age of construction) and the use of the building (residential, commercial, etc.). Later, the knowledge of the soil characteristics of the city and the simulation of a scenario earthquake will provide the seismic risk scenarios (damaged buildings). The initial results of the study show that one of the highest sources of uncertainties comes from the difficulty of achieving a precise building typologies classification due to the craft construction without any regulations. Also it is observed that although the occurrence of big earthquakes usually helps to decrease the vulnerability of the cities due to the collapse of low quality buildings and the reconstruction of seismically designed buildings, in the case of Port-au-Prince the seismic risk in most of the districts remains high, showing very vulnerable areas. Therefore the local authorities have to drive their efforts towards the quality control of the new buildings, the reinforcement of the existing building stock, the establishment of seismic normatives and the development of emergency planning also through the education of the population.

Spatial linear global instability analysis of the HIFiRE-5 elliptic cone model flow

The linear instability of the three-dimensional boundary-layer over the HIFiRE-5 flight test geometry, i.e. a rounded-tip 2:1 elliptic cone, at Mach 7, has been analyzed through spatial BiGlobal analysis, in a effort to understand transition and accurately predict local heat loads on next-generation ight vehicles. The results at an intermediate axial section of the cone, Re x = 8x10 5, show three different families of spatially amplied linear global modes, the attachment-line and cross- ow modes known from earlier analyses, and a new global mode, peaking in the vicinity of the minor axis of the cone, termed \center-line mode". We discover that a sequence of symmetric and anti-symmetric centerline modes exist and, for the basic ow at hand, are maximally amplied around F* = 130kHz. The wavenumbers and spatial distribution of amplitude functions of the centerline modes are documented

Application of global numerical procedures to the analysis of shells

Examples of global solutions of the shell equations are presented, such as the ones based on the well known Levy series expansion. Also discussed are some natural extensions of the Levy method as well as the inherent limitations of these methods concerning the shell model assumptions, boundary conditions and geometric regularity. Finally, some open additional design questions are noted mainly related to the simultaneous use in analysis of these global techniques and the local methods (like the finite elements) to finding the optimal shell shape, and to determining the reinforcement layout.

On a competitive system under chemotactic effects with non-local terms

In this paper, we study a system of partial differential equations describing the evolution of a population under chemotactic effects with non-local reaction terms. We consider an external application of chemoattractant in the system and study the cases of one and two populations in competition. By introducing global competitive/cooperative factors in terms of the total mass of the populations, weobtain, forarangeofparameters, thatanysolutionwithpositive and bounded initial data converges to a spatially homogeneous state with positive components. The proofs rely on the maximum principle for spatially homogeneous sub- and super-solutions.

Towards mitigation of greenhouse gases by small changes in farming practices: understanding local barriers in Spain.

Small changes in agricultural practices have a large potential for reducing greenhouse gas emissions. However, the implementation of such practices at the local level is often limited by a range of barriers. Understanding the barriers is essential for defining effective measures, the actual mitigation potential of the measures, and the policy needs to ensure implementation. Here we evaluate behavioural, cultural, and policy barriers for implementation of mitigation practices at the local level that imply small changes to farmers. The choice of potential mitigation practices relevant to the case study is based on a literature review of previous empirical studies. Two methods that include the stakeholders? involvement (experts and farmers) are undertaken for the prioritization of these potential practices: (a) Multi-criteria analysis (MCA) of the choices of an expert panel and (b) Analysis of barriers to implementation based on a survey of farmers. The MCA considers two future climate scenarios ? current climate and a drier and warmer climate scenario. Results suggest that all potential selected practices are suitable for mitigation considering multiple criteria in both scenarios. Nevertheless, if all the barriers for implementation had the same influence, the preferred mitigation practices in the case study would be changes in fertilization management and use of cover crops. The identification of barriers for the implementation of the practices is based on the econometric analysis of surveys given to farmers. Results show that farmers? environmental concerns, financial incentives and access to technical advice are the main factors that define their barriers to implementation. These results may contribute to develop effective mitigation policy to be included in the 2020 review of the European Union Common Agricultural Policy.

La caliad social de la educación como instrumento facilitador del desarrollo rural/local. Propuesta de acción conjunta.

El desarrollo rural/local requiere personas capaces de asumir la gestión de sus actividades integrándolas con una visión global de desarrollo del territorio que habitan. La escuela constituye su primer ámbito de formación y por tanto es el elemento clave en el desarrollo futuro de las personas. Ésta ha perdido terreno como constructora de significados en los últimos años; ha asistido a la sistemática destitución de sus condiciones de generar capacidades de simbolización, lo que provoca una anomia constante en su conjunto. La realidad se le presenta de manera fragmentada y no es capaz de reconstituir un orden lógico y simbólico que contenga y retenga al alumnado ni tampoco se encuentra con capacidad para estructurar el cambio, factor fundamental del desarrollo rural/local. Se presenta propuesta de acción conjunta aplicable a la Provincia de Buenos Aires (Argentina), con un instrumento integrador: el huerto familiar. Con ella se pretende dar un salto cualitativo a las dificultades diagnosticadas y aportar elementos para la reconstrucción de una representación compartida de la realidad basada en una educación que a su vez sea emancipadora y productora de conocimientos que preparen para el protagonismo activo del individuo.

El Parque Agrario: estructura de preservación de los espacios agrarios en entornos urbanos en un contexto de cambio global

La propuesta del análisis de la figura de Parque Agrario en el ámbito español surge ante la constatación de que un nuevo paradigma está aconteciendo a escala estatal. Diversos focos se encuentran trabajando en paralelo, y de forma participada, en pos de la reformulación de las políticas públicas relacionadas con la agricultura periurbana. Estos focos ven en la figura de Parque Agrario un instrumento territorial que permite mejorar la sostenibilidad y cohesión territorial a través de la defensa de la gobernanza alimentaria local, sin olvidar la necesidad de conservación de los recursos naturales y el patrimonio paisajístico, junto a la prestación de múltiples servicios de los ecosistemas de estos ámbitos a la ciudadanía. Complementariamente, se empieza a vislumbrar el papel que esta figura puede desempeñar como herramienta de desarrollo territorial de los sistemas agrarios periurbanos, clave ante los efectos de carácter local que la globalización ejerce en estos territorios. La figura de Parque Agrario es una estructura que actúa bloqueando la base territorial, favoreciendo el desarrollo de la actividad agraria. Su mayor potencial es el de convertir el factor “proximidad urbana” de una amenaza a una oportunidad de desarrollo local endógeno que permita la continuidad de la agricultura, de los agricultores y del espacio agrario. La peculiaridad del Parque Agrario es que no es una figura al uso, estructurada y reglada por una legislación, sino que se trata de una iniciativa ad hoc, específica para cada caso, orientada a cumplir determinados objetivos de dinamización agraria, protección urbanística y valorización territorial. A pesar de la existencia de diversas definiciones y aportaciones sobre diferentes aspectos de la figura, no existe un análisis complejo de la misma en todas sus dimensiones, ni una tentativa de descripción de un modelo global y unitario del caso español y de sus potenciales resultados. Tampoco se han analizado en profundidad sus “invariantes” que se muestran como los elementos estructurantes del proyecto, capaces desarrollarse de forma diversa, de alcanzar diferentes niveles de complejidad, y de materializarse en función a las posibilidades que permita el marco normativo y legal. Por tanto, se plantea como objetivo principal de la tesis la definición de un modelo conceptual de Parque Agrario español, capaz de ser articulado e institucionalizado mediante un proceso de gobernanza, y que, como condición sine qua non sea duradero en el tiempo. Para poder llegar a describir un modelo colectivo se realiza, en primer lugar, un análisis genealógico que permita analizar sistemáticamente las propuestas desarrolladas en el ámbito español y los casos para establecer la existencia de una continuidad en la idea de Parque Agrario en las propuestas desarrolladas durante los últimos 25 años—sus invariantes—, y analice todos aquellos elementos que han ido enriqueciendo la figura en cada experiencia —sus variantes. Este análisis, además, ofrece como aportaciones el árbol genealógico y los mapas de dispersión de la figura y el primer catálogo de propuestas de Parque Agrario materializadas en proyecto. El resultado de la inducción de los datos obtenidos en el análisis genealógico es el modelo conceptual de Parque Agrario, que se define como una estructura orgánica de planificación-gestión-gobierno del territorio capaz de adaptarse a las necesidades específicas de todo sistema agrario periurbano que requiera la articulación-institucionalización de esta figura en él. Una vez descrito el modelo, se contrasta su fiabilidad mediante su aplicación como metodología de caracterización y evaluación de dos estudios de casos: uno exitoso, el Parque Agrario del Baix Llobregat, y uno frustrado, la propuesta de Parque Agrario de la Vega de Granada. ------------------------------------------------------ ABSTRACT -------------------------------------------------------------------- The proposed analysis of the figure of Agrarian Park in the Spanish sphere arises from the awareness that a new paradigm is happening at the state level. Different focuses are working in parallel, under participated programs, after the reformulation of public policies related to urban agriculture. These areas understand the figure of Agrarian Park as a territorial instrument for improving sustainability and territorial cohesion through the defense of local food governance, considering the need for conservation of natural resources and landscape heritage together with the multiple ecosystem services provided by these areas to the public. Additionally, the role that this figure can play as a tool for territorial development of peri-urban agrarian systems, which are key to the local effects that globalization has on these territories, is staring to be envisioned. The figure of Agrarian Park is a structure that works by blocking the territorial base to encourage the development of agrarian activity. Its greatest potential is to convert the threat of "urban proximity" into an opportunity for an endogenous local development that allows the persistence of agriculture, farmers and the agrarian space. The uniqueness of the Agrarian Park is that it is not a standard figure, structured and regulated by legislation, but rather an ad hoc initiative, specific to each case, designed to meet certain objectives of agrarian revitalization, urban protection and territorial enhance. Despite the existence of several definitions and contributions on different aspects of the figure, there is a lack of a complex analysis of it in all its dimensions, missing any attempt to describe a global and unitary model of the Spanish case and its potential outcomes. Its "invariants” have neither been evaluated in depth, shown as the structural elements of the project able to be developed in different ways, to achieve numerous levels of complexity, and to be materialized according to the possibilities allowed by the regulatory and legal framework. Therefore, the definition of a conceptual model of Spanish Agrarian Park able to be articulated and institutionalized through a process of governance, and durable over time as a sine qua non requisite, it is proposed as the main aim of the thesis. To get to describe a collective model, a genealogical analysis that systematically analyzes the proposals and cases developed in the Spanish field is undertaken to verify the existence of a continuity of the idea of Agrarian Park on the proposals developed during the past 25 years -invariants-, and evaluate all the elements that have enriched this figure in each experience - variants. This analysis also provides as inputs a family tree, maps of dispersion of the figure and the first catalog of Agrarian Park proposals materialized into projects. The result of inducting the data obtained in the genealogical analysis is the Conceptual Model of Agrarian Park, defined as an organic planning-management-government structure of the territory able to adapt to the specific needs of all peri-urban agrarian systems that require the articulation-institutionalization of this figure in it. Having described the model, its reliability is tested by applying it as a methodology for characterization and evaluation of two case studies, one successful, the Baix Llobregat Agrarian Park, and one frustrated, the proposed Agrarian Park de la Vega of Granada.

Local optimal scale in a hierarchical segmentation method for satellite image: an OBIA approach for the agricultural landscape

Overrecentdecades,remotesensinghasemergedasaneffectivetoolforimprov- ing agriculture productivity. In particular, many works have dealt with the problem of identifying characteristics or phenomena of crops and orchards on different scales using remote sensed images. Since the natural processes are scale dependent and most of them are hierarchically structured, the determination of optimal study scales is mandatory in understanding these processes and their interactions. The concept of multi-scale/multi- resolution inherent to OBIA methodologies allows the scale problem to be dealt with. But for that multi-scale and hierarchical segmentation algorithms are required. The question that remains unsolved is to determine the suitable scale segmentation that allows different objects and phenomena to be characterized in a single image. In this work, an adaptation of the Simple Linear Iterative Clustering (SLIC) algorithm to perform a multi-scale hierarchi- cal segmentation of satellite images is proposed. The selection of the optimal multi-scale segmentation for different regions of the image is carried out by evaluating the intra- variability and inter-heterogeneity of the regions obtained on each scale with respect to the parent-regions defined by the coarsest scale. To achieve this goal, an objective function, that combines weighted variance and the global Moran index, has been used. Two different kinds of experiment have been carried out, generating the number of regions on each scale through linear and dyadic approaches. This methodology has allowed, on the one hand, the detection of objects on different scales and, on the other hand, to represent them all in a sin- gle image. Altogether, the procedure provides the user with a better comprehension of the land cover, the objects on it and the phenomena occurring.