Estimación del riesgo sísmico en puerto príncipe (Haití)

Tras el devastador terremoto del 12 de enero de 2010 en Puerto Príncipe, Haití, las autoridades locales, numerosas ONGs y organismos nacionales e internacionales están trabajando en el desarrollo de estrategias para minimizar el elevado riesgo sísmico existente en el país. Para ello es necesario, en primer lugar, estimar dicho riesgo asociado a eventuales terremotos futuros que puedan producirse, evaluando el grado de pérdidas que podrían generar, para dimensionar la catástrofe y actuar en consecuencia, tanto en lo referente a medidas preventivas como a adopción de planes de emergencia. En ese sentido, este Trabajo Fin de Master aporta un análisis detallado del riesgo sísmico asociado a un futuro terremoto que podría producirse con probabilidad razonable, causando importantes daños en Puerto Príncipe. Se propone para ello una metodología de cálculo del riesgo adaptada a los condicionantes de la zona, con modelos calibrados empleando datos del sismo de 2010. Se ha desarrollado en el marco del proyecto de cooperación Sismo-Haití, financiado por la Universidad Politécnica de Madrid, que comenzó diez meses después del terremoto de 2010 como respuesta a una petición de ayuda del gobierno haitiano. El cálculo del riesgo requiere la consideración de dos inputs: la amenaza sísmica o movimiento esperado por el escenario definido (sismo de cierta magnitud y localización) y los elementos expuestos a esta amenaza (una clasificación del parque inmobiliario en diferentes tipologías constructivas, así como su vulnerabilidad). La vulnerabilidad de estas tipologías se describe por medio de funciones de daño: espectros de capacidad, que representan su comportamiento ante las fuerzas horizontales motivadas por los sismos, y curvas de fragilidad, que representan la probabilidad de que las estructuras sufran daños al alcanzar el máximo desplazamiento horizontal entre plantas debido a la mencionada fuerza horizontal. La metodología que se propone especifica determinadas pautas y criterios para estimar el movimiento, asignar la vulnerabilidad y evaluar el daño, cubriendo los tres estados del proceso. Por una parte, se consideran diferentes modelos de movimiento fuerte incluyendo el efecto local, y se identifican los que mejor ajustan a las observaciones de 2010. Por otra se clasifica el parque inmobiliario en diferentes tipologías constructivas, en base a la información extraída en una campaña de campo y utilizando además una base de datos aportada por el Ministerio de Obras Públicas de Haití. Ésta contiene información relevante de todos los edificios de la ciudad, resultando un total de 6 tipologías. Finalmente, para la estimación del daño se aplica el método capacidad-demanda implementado en el programa SELENA (Molina et al., 2010). En primer lugar, utilizado los datos de daño del terremoto de 2010, se ha calibrado el modelo propuesto de cálculo de riesgo sísmico: cuatro modelos de movimiento fuerte, tres modelos de tipo de suelo y un conjunto de funciones de daño. Finalmente, con el modelo calibrado, se ha simulado un escenario sísmico determinista correspondiente a un posible terremoto con epicentro próximo a Puerto Príncipe. Los resultados muestran que los daños estructurales serán considerables y podrán llevar a pérdidas económicas y humanas que causen un gran impacto en el país, lo que pone de manifiesto la alta vulnerabilidad estructural existente. Este resultado será facilitado a las autoridades locales, constituyendo una base sólida para toma de decisiones y adopción de políticas de prevención y mitigación del riesgo. Se recomienda dirigir esfuerzos hacia la reducción de la vulnerabilidad estructural - mediante refuerzo de edificios vulnerables y adopción de una normativa sismorresistente- y hacia el desarrollo de planes de emergencia. Abstract After the devastating 12 January 2010 earthquake that hit the city of Port-au-Prince, Haiti, strategies to minimize the high seismic risk are being developed by local authorities, NGOs, and national and international institutions. Two important tasks to reach this objective are, on the one hand, the evaluation of the seismic risk associated to possible future earthquakes in order to know the dimensions of the catastrophe; on the other hand, the design of preventive measures and emergency plans to minimize the consequences of such events. In this sense, this Master Thesis provides a detailed estimation of the damage that a possible future earthquake will cause in Port-au-Prince. A methodology to calculate the seismic risk is proposed, adapted to the study area conditions. This methodology has been calibrated using data from the 2010 earthquake. It has been conducted in the frame of the Sismo-Haiti cooperative project, supported by the Technical University of Madrid, which started ten months after the 2010 earthquake as an answer to an aid call of the Haitian government. The seismic risk calculation requires two inputs: the seismic hazard (expected ground motion due to a scenario earthquake given by magnitude and location) and the elements exposed to the hazard (classification of the building stock into building typologies, as well as their vulnerability). This vulnerability is described through the damage functions: capacity curves, which represent the structure performance against the horizontal forces caused by the seisms; and fragility curves, which represent the probability of damage as the structure reaches the maximum spectral displacement due to the horizontal force. The proposed methodology specifies certain guidelines and criteria to estimate the ground motion, assign the vulnerability, and evaluate the damage, covering the whole process. Firstly, different ground motion prediction equations including the local effect are considered, and the ones that have the best correlation with the observations of the 2010 earthquake, are identified. Secondly, the classification of building typologies is made by using the information collected during a field campaign, as well as a data base provided by the Ministry of Public Works of Haiti. This data base contains relevant information about all the buildings in the city, leading to a total of 6 different typologies. Finally, the damage is estimated using the capacity-spectrum method as implemented in the software SELENA (Molina et al., 2010). Data about the damage caused by the 2010 earthquake have been used to calibrate the proposed calculation model: different choices of ground motion relationships, soil models, and damage functions. Then, with the calibrated model, a deterministic scenario corresponding to an epicenter close to Port-au-Prince has been simulated. The results show high structural damage, and therefore, they point out the high structural vulnerability in the city. Besides, the economic and human losses associated to the damage would cause a great impact in the country. This result will be provided to the Haitian Government, constituting a scientific base for decision making and for the adoption of measures to prevent and mitigate the seismic risk. It is highly recommended to drive efforts towards the quality control of the new buildings -through reinforcement and construction according to a seismic code- and the development of emergency planning.

Comparison and Assessment of Two Emission inventories for the Madrid Region

Emission inventories are databases that aim to describe the polluting activities that occur across a certain geographic domain. According to the spatial scale, the availability of information will vary as well as the applied assumptions, which will strongly influence its quality, accuracy and representativeness. This study compared and contrasted two emission inventories describing the Greater Madrid Region (GMR) under an air quality simulation approach. The chosen inventories were the National Emissions Inventory (NEI) and the Regional Emissions Inventory of the Greater Madrid Region (REI). Both of them were used to feed air quality simulations with the CMAQ modelling system, and the results were compared with observations from the air quality monitoring network in the modelled domain. Through the application of statistical tools, the analysis of emissions at cell level and cell – expansion procedures, it was observed that the National Inventory showed better results for describing on – road traffic activities and agriculture, SNAP07 and SNAP10. The accurate description of activities, the good characterization of the vehicle fleet and the correct use of traffic emission factors were the main causes of such a good correlation. On the other hand, the Regional Inventory showed better descriptions for non – industrial combustion (SNAP02) and industrial activities (SNAP03). It incorporated realistic emission factors, a reasonable fuel mix and it drew upon local information sources to describe these activities, while NEI relied on surrogation and national datasets which leaded to a poorer representation. Off – road transportation (SNAP08) was similarly described by both inventories, while the rest of the SNAP activities showed a marginal contribution to the overall emissions.

Seismic Hazard and Risk in Central America

1999 Seismic Hazard In Guatemala 2001 Post-Event Mision 2006 Resis Ii Project Norad 2007 Workshop Seismic Hazard 2010 Book Amenaza Sísmica En América Central 2011 Cooperation Haití, República Dominicana, Puerto Rico

Metodología para medir beneficios de la ciudad Puerto de Valparaíso Chile, con relación a la actividad marítima portuaria

La presente tesis propone una metodología para medir variables de impacto socio económico en la ciudad Puerto de Valparaíso, como una alternativa que permite evaluar la asignación del uso y explotación del borde costero. La ciudad de Valparaíso se formó al alero de la actividad marítima portuaria, en sus comienzos esta actividad fue el motor de desarrollo económico de la ciudad, sus habitantes mantenían una alta dependencia de ésta actividad, formando una identidad y cultura portuaria. Con la decadencia de la actividad portuaria, producto principalmente a la construcción del canal de Panamá y a la modernización de los buques de transporte aumentando su distancia franqueable1, la ciudad fue dejando su dependencia de esta actividad. Hoy en día casi la totalidad del borde costero de la ciudad está asignado a las actividades portuarias con escasa participación laboral de los habitantes de la ciudad y una alta demanda urbana por el uso del borde costero. Por otra parte, la ciudad ha presentado en la última década altos niveles de cesantía, cuestionándose la verdadera utilidad de mantener un puerto en la ciudad. La investigación de la tesis permitió dimensionar la cantidad de firmas y actividades económicas que se desarrollaban en torno a la actividad marítima portuaria en la ciudad, cuantificando los empleos que éstas otorgaban a la ciudad, los niveles de remuneraciones, los tributos a la municipalidad de la ciudad, el aporte al comercio local, entre otros. Descubriéndose hallazgos que permiten reflexionar sobre la importancia del la actividad en el desarrollo económico actual y futuro de la ciudad. También los antecedentes obtenidos permiten contribuir a la evaluación de proyectos alternativos para el uso y explotación del borde costero. La metodología utilizada también puede ser adaptada para medir los beneficios de otras ciudades puertos en el mundo. Los resultados obtenidos fueron expuestos a las autoridades gubernamentales locales, presentados en seminarios y congresos nacionales e internacionales, como en la prensa local; los más destacados son: la actividad otorga 12.727 empleos directos e indirectos que corresponden al 12% de la fuerza laboral ocupada; la actividad representa el 19% del Producto Interno Bruto de la ciudad; la actividad aporta un 21% al presupuesto municipal por concepto de recaudación de tributos y representan un 11% del presupuesto total asignado al municipio por el Estado de Chile. El sector industrial marítimo-portuario de la ciudad sigue siendo la actividad industrial más relevante en la ciudad y demanda el desarrollo de una planificación estratégica que permita vincular la actividad turística de la ciudad vecina de Viña del Mar con la actividad portuaria de Valparaíso. Para lograr tal objetivo es necesario realizar cambios en los atributos de las operaciones portuarias que permitan ofrecer productos asociados al turismo. This thesis proposes a methodology to measure the socio economic variables in the port city of Valparaiso, as an alternative to evaluate the allocation of the usage and exploitation of the coastline. The city of Valparaiso was formed to advance the port maritime activity and in the beginning this activity was the engine of economic development of the city. Its inhabitants remained highly dependent on it and formed a port identity and culture. With the decline of port activity, mainly due to the construction of the Panama Canal and the modernization of the transport vessels increasing distances, the city lost its dependence on this activity. Today almost all of the coastline of the city is assigned to port activities with very little labor participation of the inhabitants of the city and a high demand for the use of urban waterfront. Moreover, the city has shown high levels of unemployment in the past decade, questioning the true value of maintaining a port in the city. The research of this thesis provides insights into the number of firms and economic activities that were developed around the port maritime activity in the city, quantifying the jobs they gave to the city, the levels of pay, taxes to the municipality of city and the contribution to local commerce, among others. The findings discovered allow reflexions on the importance of the activity in the current and future economic development of the city. The data obtained also allows a contribution of the evaluation of alternative projects for the use and exploitation of the coastline. The methodology can also be adapted to measure the benefits of other port cities in the world. The results were presented to local government authorities, at seminars and national and international conferences, and in the local press. The most important finding are: the activity maritime port activity provides 12,727 direct and indirect jobs that are 12% of the employed labor force; activity represents which is 19% of the GDP of the city, the activity contributes 21% to the municipal budget by way of the collection of taxes and represents 11% of the total budget allocated to the municipality by the Republic of Chile. The industrial maritime port sector of the city remains the most important industrial activity in the city and demands the development of strategic planning to link the tourism in the neighboring city of Viña del Mar and to the Valparaiso port activity. To achieve this goal it is necessary to make changes to the attributes of port operations that allow the offering of products associated with tourism.

Estudio geológico-geotécnico para las instalaciones pesqueras de un puerto en el sur de España

El objetivo de este proyecto es realizar el estudio geológico-geotécnico para la construcción de un muelle pesquero. Para caracterizar el terreno se ha realizado una campaña geotécnica compuesta por 4 sondeos y diversos ensayos “in situ”; así mismo se obtuvieron muestras inalteradas, con las que se realizaron ensayos de laboratorio. Entre los trabajos desarrollados se han realizado cortes geológicos-geotécnicos; cuyos resultados han servido para caracterizar los niveles geotécnicos. Posteriormente para definir las soluciones y procesar los datos se utilizó el software GeoSlope, con el que se estudió dos distintas alternativas posibles para realizar la cimentación del muelle: muelle vertical sin columnas de grava y muelle vertical con columnas de grava. Finalmente, los resultados obtenidos demostraron que la alternativa óptima sería una pantalla de columnas de grava considerando diversos factores técnicos, estructurales y económicos. ABSTRACT The objective of this project is to develop a geological and geotechnical study for the construction of a fishing quay. To characterize the field it has been done a geotechnical campaign with 4 drills and various "in situ" assays, likewise undisturbed samples were obtained, on which laboratory tests were performed. Among all the performed works, geological-geotechnical profiles were made, whose results have been used to characterize the geotechnical levels. Subsequently to define solutions and to process all the data, GeoSlope software was used, with which two different options for the quay foundation were studied: vertical quay without gravel columns and vertical quay with gravel columns. Finally, the results showed that the best alternative would be a gravel screen columns considering various technical, structural and economic factors.

Pollutant concentrations and Meteorological data classification by Neural Networks

This paper present an environmental contingency forecasting tool based on Neural Networks (NN). Forecasting tool analyzes every hour and daily Sulphur Dioxide (SO2) concentrations and Meteorological data time series. Pollutant concentrations and meteorological variables are self-organized applying a Self-organizing Map (SOM) NN in different classes. Classes are used in training phase of a General Regression Neural Network (GRNN) classifier to provide an air quality forecast. In this case a time series set obtained from Environmental Monitoring Network (EMN) of the city of Salamanca, Guanajuato, México is used. Results verify the potential of this method versus other statistical classification methods and also variables correlation is solved.

Development of mathematical models to elaborate strategies, to select alternatives and the development of plans for the adaptation of communities to climate change in different geographical areas including costs to implement it

Climate change is on the policy agenda at the global level, with the aim of understanding and reducing its causes and to mitigate its consequences. In most of the countries and international organisms UNO, OECD, EC, etc … the efforts and debates have been directed to know the possible causes, to predict the future evolution of some variable conditioners, and trying to make studies to fight against the effects or to delay the negative evolution of such. Nevertheless, the elaboration of a global model was not boarded that can help to choose the best alternative between the feasible ones, to elaborate the strategies and to evaluate the costs. As in all natural, technological and social changes, the best-prepared countries will have the best bear and the more rapid recover. In all the geographic areas the alternative will not be the same one, but the model should help us to make the appropriated decision. It is essential to know those areas that are more sensitive to the negative effects of climate change, the parameters to take into account for its evaluation, and comprehensive plans to deal with it. The objective of this paper is to elaborate a mathematical model support of decisions, that will allow to develop and to evaluate alternatives of adaptation to the climatic change of different communities in Europe and Latin-America, mainly, in vulnerable areas to the climatic change, considering in them all the intervening factors. The models will take into consideration criteria of physical type (meteorological, edaphic, water resources), of use of the ground (agriculturist, forest, mining, industrial, urban, tourist, cattle dealer), economic (income, costs, benefits, infrastructures), social (population), politician (implementation, legislation), educative (Educational programs, diffusion), sanitary and environmental, at the present moment and the future.

ANN and Fuzzy c-Means applied to environmental pollution prediction

Salamanca, situated in center of Mexico is among the cities which suffer most from the air pollution in Mexico. The vehicular park and the industry, as well as orography and climatic characteristics have propitiated the increment in pollutant concentration of Sulphur Dioxide (SO2). In this work, a Multilayer Perceptron Neural Network has been used to make the prediction of an hour ahead of pollutant concentration. A database used to train the Neural Network corresponds to historical time series of meteorological variables and air pollutant concentrations of SO2. Before the prediction, Fuzzy c-Means and K-means clustering algorithms have been implemented in order to find relationship among pollutant and meteorological variables. Our experiments with the proposed system show the importance of this set of meteorological variables on the prediction of SO2 pollutant concentrations and the neural network efficiency. The performance estimation is determined using the Root Mean Square Error (RMSE) and Mean Absolute Error (MAE). The results showed that the information obtained in the clustering step allows a prediction of an hour ahead, with data from past 2 hours.

Vulnerabilidad sísmica en Puerto Príncipe, Haití. Escala Macrosísmica Haitiana.

Haití, es un país claramente prioritario como receptor de cooperación para el desarrollo. Tras el terremoto del 12 de enero de 2010, se ha desarrollado un Proyecto de Cooperación Interuniversitaria entre la Universidad del Estado de Haití y la Universidad Politécnica de Madrid, financiado por la Agencia Española de Cooperación Internacional para el Desarrollo.El proyecto consiste en la formación y capacitación de los técnicos Haitianos para reconstruir su país. Se está trabajando en la creación de una escala macrosísmica Haitiana, partiendo como base de la Escala Macrosísmica Europea 1998. En este sentido, se hace un análisis exhaustivo de toda la documentación técnica y científica existente hasta la fecha sobre tipos de edificios, clases de vulnerabilidad y grados de daños dependiendo del tipo de edificio. Como caso de estudio se aplica en la ciudad de Puerto Príncipe.En primer lugar se ha clasificado el parque inmobiliario de Puerto Príncipe en diferentes tipologías constructivas, tras un trabajo de campo y teniendo en cuenta las guías de auto-construcción y reparación de edificios publicadas por el Ministerio de Obras Públicas, Transporte y Comunicaciones de Haití. (MTPTC).En el estudio de la vulnerabilidad, además del tipo de estructura de los edificios, se tiene en cuenta la habitabilidad básica que debe tener todo asentamiento humano, analizando no sólo el edificio, sino todo el entorno externo de espacios públicos, infraestructuras, dotaciones y servicios que, en conjunto,conforman el núcleo de cada población y permiten el funcionamiento eficiente del sistema de asentamientos del territorio habitado; pues, en última instancia, dicho territorio construido es el que mejor acota los riesgos ante la vulnerabilidad material y más garantiza la vida saludable de las personas. Los parámetros estudiados son: urbanísticos (anchos de vías, dimensiones de manzanas, trazado, infraestructuras,...), geológicos (estudios del efecto local e identificación de las fallas activas respecto a la edificación) y topográficos (implantación del edificio en zonas llanas, en laderas...). En último lugar, con todos estos datos y los daños registrados en el terremoto de enero de 2010, se hace una escala de intensidades macrosísmica y un plano de ordenación de la vulnerabilidad en Puerto Príncipe, que sirva de base a las autoridades haitianas para la planificación urbanística y la reconstrucción, mitigando de esta manera el riesgo símico. SUMMARY Haiti is a clear priority country as a recipient of development cooperation. After the earthquake of January 12, 2010, an Inter-University Cooperation Project has been developed between the State University of Haiti and the Polytechnic University of Madrid, funded by the Spanish Agency for International Development.The project consists of training and qualifying Haitian technicians to rebuild their country. We are currently working on the creation of a Haitian Macroseismic Scale,based on the European Macroseismic Scale 1998.For the accomplishment of this goal, a comprehensive (deep) analysis is being held, going through all the scientific and technical documentation to date, related to building types, kinds of vulnerability and degrees/ levels of damage depending on the type of building. As a case study, this has been applied to the city of Port-au-Prince.First of all, we have classified the housing typology of Port-au-Prince in different construction types, after carrying on field work in this area and keeping in mind the guidelines for self-construction and repairment of buildings published by the Ministry of Work, Transport and Communications of Haiti. (MTPTC).Regarding the study of vulnerability, besides the type of structure of the buildings, we take into account the basic habitability every human settlement should have, analyzing not only the building, but all the external environment of public spaces,infrastructures, amenities and services, which, as a whole, shape the core of each population and allow the efficient functioning of the settlement system on the inhabited territory. It is this territory,ultimately, the one that better narrows the risks when facing material vulnerability and that better ensures a healthy life for people. The studied parameters are: urban (lane width, block dimensions, layout, infrastructure...), geological (studies focusing on local effects and identification of the active faults in relation to the building) and topographical (implementation of the building on flat areas, slopes...)Finally, with all this data (information) and the registered damages related to the earthquake occurred in 2010, we create a Macroseismic Intensity Scale and a Management Plan of the vulnerability in Port-au-Prince. They will serve as a guideline for Haitians authorities in the urban planning and reconstruction, thus reducing seismic risk.

Mapa preliminar de períodos predominantes del suelo en Puerto Príncipe (Haití) a partir de medidas de ruido ambiental.

The 2010 Haiti earthquake, occurred on January 12th at 16:53:09 local time (21:53:09 UTC) with epicentral distance of 15 km from the capital Port au Prince, MW 7.0 and 13 km hypocenter deep, was the strongest event in the area since happened in 1770. The maximum macroseismic intensity was estimated as X (MMI scale). The aim of this research is to obtain a preliminary zonation of Port-au-Prince in terms of predominant resonance periods of ground. A total of 36 short-period ambient noise records have been carried out on a grid of about 500x500m. H/V spectral ratio method (HVSR) has been applied to determine the predominant period at each point. The lowest values (<0.2s) predominate in the southern part of the city, composed by Miocene conglomerates, while highest values (> 0.45s) correspond to the center and western parts, composed of Pleistocene-Holocene alluvial deposits and anthropogenic land reclaimed from the sea. We have determined the ground VS30 structure inside National Palace garden, using simultaneous ambient noise measurements. An array made up of 6 sensors were used, with 5 of them uniformly distributed along a circumference and a sixth one placed in its centre. The records were analyzed by using the spatial autocorrelation method (SPAC). The VS 30 value obtained was 331m/sec, in good agreement with the average values obtained for this area by other authors, using prospecting techniques.

An experimental and theoretical study of unsteady flow (gust) effects on structures

The gust wind tunnel at IDR, Universidad Politécnica de Madrid (UPM), has been enhanced and the impact of the modification has been characterized. Several flow quality configurations have been tested. The problems in measuring gusty winds with Pitot tubes have been considered. Experimental results have been obtained and compared with theoretically calculated results (based on potential flow theory). A theoretical correction term has been proposed for unsteady flow measurements obtained with Pitot tubes. The effect of unsteady flow on structures and laying bodies on the ground has been also considered. A theoretical model has been proposed for a semi-circular cylinder and experimental tests have been performed to study the unsteady flow effects, which can help in clarifying the phenomenon.

Reconstructing the Timing and Dispersion Routes of HIV-1 Subtype B Epidemics in The Caribbean and Central America: A Phylogenetic Story.

The Caribbean and Central America are among the regions with highest HIV-1B prevalence worldwide. Despite of this high virus burden, little is known about the timing and the migration patterns of HIV-1B in these regions. Migration is one of the major processes shaping the genetic structure of virus populations. Thus, reconstruction of epidemiological network may contribute to understand HIV-1B evolution and reduce virus prevalence. We have investigated the spatio-temporal dynamics of the HIV-1B epidemic in The Caribbean and Central America using 1,610 HIV-1B partial pol sequences from 13 Caribbean and 5 Central American countries. Timing of HIV-1B introduction and virus evolutionary rates, as well as the spatial genetic structure of the HIV-1B populations and the virus migration patterns were inferred. Results revealed that in The Caribbean and Central America most of the HIV-1B variability was generated since the 80 s. At odds with previous data suggesting that Haiti was the origin of the epidemic in The Caribbean, our reconstruction indicated that the virus could have been disseminated from Puerto Rico and Antigua. These two countries connected two distinguishable migration areas corresponding to the (mainly Spanish-colonized) Easter and (mainly British-colonized) Western islands, which indicates that virus migration patterns are determined by geographical barriers and by the movement of human populations among culturally related countries. Similar factors shaped the migration of HIV-1B in Central America. The HIV-1B population was significantly structured according to the country of origin, and the genetic diversity in each country was associated with the virus prevalence in both regions, which suggests that virus populations evolve mainly through genetic drift. Thus, our work contributes to the understanding of HIV-1B evolution and dispersion pattern in the Americas, and its relationship with the geography of the area and the movements of human populations.

Port planning for the Port of Vigo using port and city integration criteria

Project planning and architectural management of a port area should include many variables, it must be in harmony with its environment and its historical development as the key to successful integration. This article explains the elements which should be taken into account when doing such planning by describing the proposal presented on the ?Concurso public internacional de ideas para proyectar la ordenación urbanística y arquitectónica del área central del puerto de Vigo?, with the aim of sharing comprehensive applied design philosofy, it will inspire and help future designers. Creative imagination is great added value to engineering creations, but should not overwhelm functionality and sustainability, but to be in harmony with them. The maximum aesthetic expression in engineering is achieved as the product of the conceptual elegance of the functionality of the structures.

Determinación de un modelo de geoide gravimétrico para Puerto Rico como sistema de referencia para las altitudes ortométricas

El geoide, definido como la superficie equipotencial que mejor se ajusta (en el sentido de los mínimos cuadrados) al nivel medio del mar en una determinada época, es la superficie que utilizamos como referencia para determinar las altitudes ortométricas. Si disponemos de una superficie equipotencial de referencia como dátum altimétrico preciso o geoide local, podemos entonces determinar las altitudes ortométricas de forma eficiente a partir de las altitudes elipsoidales proporcionadas por el Sistema Global de Navegación por Satélite (Global Navigation Satellite System, GNSS ). Como es sabido uno de los problemas no resueltos de la geodesia (quizás el más importante de los mismos en la actualidad) es la carencia de un dátum altimétrico global (Sjoberg, 2011) con las precisiones adecuadas. Al no existir un dátum altimétrico global que nos permita obtener los valores absolutos de la ondulación del geoide con la precisión requerida, es necesario emplear modelos geopotenciales como alternativa. Recientemente fue publicado el modelo EGM2008 en el que ha habido una notable mejoría de sus tres fuentes de datos, por lo que este modelo contiene coeficientes adicionales hasta el grado 2190 y orden 2159 y supone una sustancial mejora en la precisión (Pavlis et al., 2008). Cuando en una región determinada se dispone de valores de gravedad y Modelos Digitales del Terreno (MDT) de calidad, es posible obtener modelos de superficies geopotenciales más precisos y de mayor resolución que los modelos globales. Si bien es cierto que el Servicio Nacional Geodésico de los Estados Unidos de América (National Geodetic Survey, NGS) ha estado desarrollando modelos del geoide para la región de los Estados Unidos de América continentales y todos sus territorios desde la década de los noventa, también es cierto que las zonas de Puerto Rico y las Islas Vírgenes Estadounidenses han quedado un poco rezagadas al momento de poder aplicar y obtener resultados de mayor precisión con estos modelos regionales del geoide. En la actualidad, el modelo geopotencial regional vigente para la zona de Puerto Rico y las Islas Vírgenes Estadounidenses es el GEOID12A (Roman y Weston, 2012). Dada la necesidad y ante la incertidumbre de saber cuál sería el comportamiento de un modelo del geoide desarrollado única y exclusivamente con datos de gravedad locales, nos hemos dado a la tarea de desarrollar un modelo de geoide gravimétrico como sistema de referencia para las altitudes ortométricas. Para desarrollar un modelo del geoide gravimétrico en la isla de Puerto Rico, fue necesario implementar una metodología que nos permitiera analizar y validar los datos de gravedad terrestre existentes. Utilizando validación por altimetría con sistemas de información geográfica y validación matemática por colocación con el programa Gravsoft (Tscherning et al., 1994) en su modalidad en Python (Nielsen et al., 2012), fue posible validar 1673 datos de anomalías aire libre de un total de 1894 observaciones obtenidas de la base de datos del Bureau Gravimétrico Internacional (BGI). El aplicar estas metodologías nos permitió obtener una base de datos anomalías de la gravedad fiable la cual puede ser utilizada para una gran cantidad de aplicaciones en ciencia e ingeniería. Ante la poca densidad de datos de gravedad existentes, fue necesario emplear un método alternativo para densificar los valores de anomalías aire libre existentes. Empleando una metodología propuesta por Jekeli et al. (2009b) se procedió a determinar anomalías aire libre a partir de los datos de un MDT. Estas anomalías fueron ajustadas utilizando las anomalías aire libre validadas y tras aplicar un ajuste de mínimos cuadrados por zonas geográficas, fue posible obtener una malla de datos de anomalías aire libre uniforme a partir de un MDT. Tras realizar las correcciones topográficas, determinar el efecto indirecto de la topografía del terreno y la contribución del modelo geopotencial EGM2008, se obtuvo una malla de anomalías residuales. Estas anomalías residuales fueron utilizadas para determinar el geoide gravimétrico utilizando varias técnicas entre las que se encuentran la aproximación plana de la función de Stokes y las modificaciones al núcleo de Stokes, propuestas por Wong y Gore (1969), Vanicek y Kleusberg (1987) y Featherstone et al. (1998). Ya determinados los distintos modelos del geoide gravimétrico, fue necesario validar los mismos y para eso se utilizaron una serie de estaciones permanentes de la red de nivelación del Datum Vertical de Puerto Rico de 2002 (Puerto Rico Vertical Datum 2002, PRVD02 ), las cuales tenían publicados sus valores de altitud elipsoidal y elevación. Ante la ausencia de altitudes ortométricas en las estaciones permanentes de la red de nivelación, se utilizaron las elevaciones obtenidas a partir de nivelación de primer orden para determinar los valores de la ondulación del geoide geométrico (Roman et al., 2013). Tras establecer un total de 990 líneas base, se realizaron dos análisis para determinar la 'precisión' de los modelos del geoide. En el primer análisis, que consistió en analizar las diferencias entre los incrementos de la ondulación del geoide geométrico y los incrementos de la ondulación del geoide de los distintos modelos (modelos gravimétricos, EGM2008 y GEOID12A) en función de las distancias entre las estaciones de validación, se encontró que el modelo con la modificación del núcleo de Stokes propuesta por Wong y Gore presentó la mejor 'precisión' en un 91,1% de los tramos analizados. En un segundo análisis, en el que se consideraron las 990 líneas base, se determinaron las diferencias entre los incrementos de la ondulación del geoide geométrico y los incrementos de la ondulación del geoide de los distintos modelos (modelos gravimétricos, EGM2008 y GEOID12A), encontrando que el modelo que presenta la mayor 'precisión' también era el geoide con la modificación del núcleo de Stokes propuesta por Wong y Gore. En este análisis, el modelo del geoide gravimétrico de Wong y Gore presento una 'precisión' de 0,027 metros en comparación con la 'precisión' del modelo EGM2008 que fue de 0,031 metros mientras que la 'precisión' del modelo regional GEOID12A fue de 0,057 metros. Finalmente podemos decir que la metodología aquí presentada es una adecuada ya que fue posible obtener un modelo del geoide gravimétrico que presenta una mayor 'precisión' que los modelos geopotenciales disponibles, incluso superando la precisión del modelo geopotencial global EGM2008. ABSTRACT The geoid, defined as the equipotential surface that best fits (in the least squares sense) to the mean sea level at a particular time, is the surface used as a reference to determine the orthometric heights. If we have an equipotential reference surface or a precise local geoid, we can then determine the orthometric heights efficiently from the ellipsoidal heights, provided by the Global Navigation Satellite System (GNSS). One of the most common and important an unsolved problem in geodesy is the lack of a global altimetric datum (Sjoberg, 2011)) with the appropriate precision. In the absence of one which allows us to obtain the absolute values of the geoid undulation with the required precision, it is necessary to use alternative geopotential models. The EGM2008 was recently published, in which there has been a marked improvement of its three data sources, so this model contains additional coefficients of degree up to 2190 and order 2159, and there is a substantial improvement in accuracy (Pavlis et al., 2008). When a given region has gravity values and high quality digital terrain models (DTM), it is possible to obtain more accurate regional geopotential models, with a higher resolution and precision, than global geopotential models. It is true that the National Geodetic Survey of the United States of America (NGS) has been developing geoid models for the region of the continental United States of America and its territories from the nineties, but which is also true is that areas such as Puerto Rico and the U.S. Virgin Islands have lagged behind when to apply and get more accurate results with these regional geopotential models. Right now, the available geopotential model for Puerto Rico and the U.S. Virgin Islands is the GEOID12A (Roman y Weston, 2012). Given this need and given the uncertainty of knowing the behavior of a regional geoid model developed exclusively with data from local gravity, we have taken on the task of developing a gravimetric geoid model to use as a reference system for orthometric heights. To develop a gravimetric geoid model in the island of Puerto Rico, implementing a methodology that allows us to analyze and validate the existing terrestrial gravity data is a must. Using altimetry validation with GIS and mathematical validation by collocation with the Gravsoft suite programs (Tscherning et al., 1994) in its Python version (Nielsen et al., 2012), it was possible to validate 1673 observations with gravity anomalies values out of a total of 1894 observations obtained from the International Bureau Gravimetric (BGI ) database. Applying these methodologies allowed us to obtain a database of reliable gravity anomalies, which can be used for many applications in science and engineering. Given the low density of existing gravity data, it was necessary to employ an alternative method for densifying the existing gravity anomalies set. Employing the methodology proposed by Jekeli et al. (2009b) we proceeded to determine gravity anomaly data from a DTM. These anomalies were adjusted by using the validated free-air gravity anomalies and, after that, applying the best fit in the least-square sense by geographical area, it was possible to obtain a uniform grid of free-air anomalies obtained from a DTM. After applying the topographic corrections, determining the indirect effect of topography and the contribution of the global geopotential model EGM2008, a grid of residual anomalies was obtained. These residual anomalies were used to determine the gravimetric geoid by using various techniques, among which are the planar approximation of the Stokes function and the modifications of the Stokes kernel, proposed by Wong y Gore (1969), Vanicek y Kleusberg (1987) and Featherstone et al. (1998). After determining the different gravimetric geoid models, it was necessary to validate them by using a series of stations of the Puerto Rico Vertical Datum of 2002 (PRVD02) leveling network. These stations had published its values of ellipsoidal height and elevation, and in the absence of orthometric heights, we use the elevations obtained from first - order leveling to determine the geometric geoid undulation (Roman et al., 2013). After determine a total of 990 baselines, two analyzes were performed to determine the ' accuracy ' of the geoid models. The first analysis was to analyze the differences between the increments of the geometric geoid undulation with the increments of the geoid undulation of the different geoid models (gravimetric models, EGM2008 and GEOID12A) in function of the distance between the validation stations. Through this analysis, it was determined that the model with the modified Stokes kernel given by Wong and Gore had the best 'accuracy' in 91,1% for the analyzed baselines. In the second analysis, in which we considered the 990 baselines, we analyze the differences between the increments of the geometric geoid undulation with the increments of the geoid undulation of the different geoid models (gravimetric models, EGM2008 and GEOID12A) finding that the model with the highest 'accuracy' was also the model with modifying Stokes kernel given by Wong and Gore. In this analysis, the Wong and Gore gravimetric geoid model presented an 'accuracy' of 0,027 meters in comparison with the 'accuracy' of global geopotential model EGM2008, which gave us an 'accuracy' of 0,031 meters, while the 'accuracy ' of the GEOID12A regional model was 0,057 meters. Finally we can say that the methodology presented here is adequate as it was possible to obtain a gravimetric geoid model that has a greater 'accuracy' than the geopotential models available, even surpassing the accuracy of global geopotential model EGM2008.