Algoritmos para mineria de datos con redes de neuronas

Este trabajo propone una serie de algoritmos con el objetivo de extraer información de conjuntos de datos con redes de neuronas. Se estudian dichos algoritmos con redes de neuronas Enhenced Neural Networks (ENN), debido a que esta arquitectura tiene algunas ventajas cuando se aproximan funciones mediante redes neuronales. En la red ENN los pesos de la matriz principal varián con cada patrón, por lo que se comete un error menor en la aproximación. Las redes de neuronas ENN reúnen la información en los pesos de su red auxiliar, se propone un método para obtener información de la red a través de dichos pesos en formas de reglas y asignando un factor de certeza de dichas reglas. La red ENN obtiene un error cuadrático medio menor que el error teórico de una aproximación matemática por ejemplo mediante polinomios de Taylor. Se muestra como una red ENN, entrenada a partir un conjunto de patrones obtenido de una función de variables reales, sus pesos asociados tienen unas relaciones similares a las que se veri_can con las variables independientes con dicha función de variables reales. Las redes de neuronas ENN aproximan polinomios, se extrae conocimiento de un conjunto de datos de forma similar a la regresión estadística, resolviendo de forma más adecuada el problema de multicolionalidad en caso de existir. Las relaciones a partir de los pesos asociados de la matriz de la red auxiliar se obtienen similares a los coeficientes de una regresión para el mismo conjunto numérico. Una red ENN entrenada a partir de un conjunto de datos de una función boolena extrae el conocimiento a partir de los pesos asociados, y la influencia de las variables de la regla lógica de la función booleana, queda reejada en esos pesos asociados a la red auxiliar de la red ENN. Se plantea una red de base radial (RBF) para la clasificación y predicción en problemas forestales y agrícolas, obteniendo mejores resultados que con el modelo de regresión y otros métodos. Los resultados con una red RBF mejoran al método de regresión si existe colinealidad entre los datos que se dispone y no son muy numerosos. También se detecta que variables tienen más importancia en virtud de la variable pronóstico. Obteniendo el error cuadrático medio con redes RBF menor que con otros métodos, en particular que con el modelo de regresión. Abstract A series of algorithms is proposed in this study aiming at the goal of producing information about data groups with a neural network. These algorithms are studied with Enheced Neural Networks (ENN), owing to the fact that this structure shows sever advantages when the functions are approximated by neural networks. Main matrix weights in th ENN vary on each pattern; so, a smaller error is produced when approximating. The neural network ENN joins the weight information contained in their auxiliary network. Thus, a method to obtain information on the network through those weights is proposed by means of rules adding a certainty factor. The net ENN obtains a mean squared error smaller than the theorical one emerging from a mathematical aproximation such as, for example, by means of Taylor's polynomials. This study also shows how in a neural network ENN trained from a set of patterns obtained through a function of real variables, its associated weights have relationships similar to those ones tested by means of the independent variables connected with such functions of real variables. The neural network ENN approximates polynomials through it information about a set of data may be obtained in a similar way than through statistical regression, solving in this way possible problems of multicollinearity in a more suitable way. Relationships emerging from the associated weights in the auxiliary network matrix obtained are similar to the coeficients corresponding to a regression for the same numerical set. A net ENN trained from a boolean function data set obtains its information from its associated weights. The inuence of the variables of the boolean function logical rule are reected on those weights associated to the net auxiliar of the ENN. A radial basis neural networks (RBF) for the classification and prediction of forest and agricultural problems is proposed. This scheme obtains better results than the ones obtained by means of regression and other methods. The outputs with a net RBF better the regression method if the collineality with the available data and their amount is not very large. Detection of which variables are more important basing on the forecast variable can also be achieved, obtaining a mean squared error smaller that the ones obtained through other methods, in special the one produced by the regression pattern.

Statistical models for short-term wind power ramp forecasting

La predicción de energía eólica ha desempeñado en la última década un papel fundamental en el aprovechamiento de este recurso renovable, ya que permite reducir el impacto que tiene la naturaleza fluctuante del viento en la actividad de diversos agentes implicados en su integración, tales como el operador del sistema o los agentes del mercado eléctrico. Los altos niveles de penetración eólica alcanzados recientemente por algunos países han puesto de manifiesto la necesidad de mejorar las predicciones durante eventos en los que se experimenta una variación importante de la potencia generada por un parque o un conjunto de ellos en un tiempo relativamente corto (del orden de unas pocas horas). Estos eventos, conocidos como rampas, no tienen una única causa, ya que pueden estar motivados por procesos meteorológicos que se dan en muy diferentes escalas espacio-temporales, desde el paso de grandes frentes en la macroescala a procesos convectivos locales como tormentas. Además, el propio proceso de conversión del viento en energía eléctrica juega un papel relevante en la ocurrencia de rampas debido, entre otros factores, a la relación no lineal que impone la curva de potencia del aerogenerador, la desalineación de la máquina con respecto al viento y la interacción aerodinámica entre aerogeneradores. En este trabajo se aborda la aplicación de modelos estadísticos a la predicción de rampas a muy corto plazo. Además, se investiga la relación de este tipo de eventos con procesos atmosféricos en la macroescala. Los modelos se emplean para generar predicciones de punto a partir del modelado estocástico de una serie temporal de potencia generada por un parque eólico. Los horizontes de predicción considerados van de una a seis horas. Como primer paso, se ha elaborado una metodología para caracterizar rampas en series temporales. La denominada función-rampa está basada en la transformada wavelet y proporciona un índice en cada paso temporal. Este índice caracteriza la intensidad de rampa en base a los gradientes de potencia experimentados en un rango determinado de escalas temporales. Se han implementado tres tipos de modelos predictivos de cara a evaluar el papel que juega la complejidad de un modelo en su desempeño: modelos lineales autorregresivos (AR), modelos de coeficientes variables (VCMs) y modelos basado en redes neuronales (ANNs). Los modelos se han entrenado en base a la minimización del error cuadrático medio y la configuración de cada uno de ellos se ha determinado mediante validación cruzada. De cara a analizar la contribución del estado macroescalar de la atmósfera en la predicción de rampas, se ha propuesto una metodología que permite extraer, a partir de las salidas de modelos meteorológicos, información relevante para explicar la ocurrencia de estos eventos. La metodología se basa en el análisis de componentes principales (PCA) para la síntesis de la datos de la atmósfera y en el uso de la información mutua (MI) para estimar la dependencia no lineal entre dos señales. Esta metodología se ha aplicado a datos de reanálisis generados con un modelo de circulación general (GCM) de cara a generar variables exógenas que posteriormente se han introducido en los modelos predictivos. Los casos de estudio considerados corresponden a dos parques eólicos ubicados en España. Los resultados muestran que el modelado de la serie de potencias permitió una mejora notable con respecto al modelo predictivo de referencia (la persistencia) y que al añadir información de la macroescala se obtuvieron mejoras adicionales del mismo orden. Estas mejoras resultaron mayores para el caso de rampas de bajada. Los resultados también indican distintos grados de conexión entre la macroescala y la ocurrencia de rampas en los dos parques considerados. Abstract One of the main drawbacks of wind energy is that it exhibits intermittent generation greatly depending on environmental conditions. Wind power forecasting has proven to be an effective tool for facilitating wind power integration from both the technical and the economical perspective. Indeed, system operators and energy traders benefit from the use of forecasting techniques, because the reduction of the inherent uncertainty of wind power allows them the adoption of optimal decisions. Wind power integration imposes new challenges as higher wind penetration levels are attained. Wind power ramp forecasting is an example of such a recent topic of interest. The term ramp makes reference to a large and rapid variation (1-4 hours) observed in the wind power output of a wind farm or portfolio. Ramp events can be motivated by a broad number of meteorological processes that occur at different time/spatial scales, from the passage of large-scale frontal systems to local processes such as thunderstorms and thermally-driven flows. Ramp events may also be conditioned by features related to the wind-to-power conversion process, such as yaw misalignment, the wind turbine shut-down and the aerodynamic interaction between wind turbines of a wind farm (wake effect). This work is devoted to wind power ramp forecasting, with special focus on the connection between the global scale and ramp events observed at the wind farm level. The framework of this study is the point-forecasting approach. Time series based models were implemented for very short-term prediction, this being characterised by prediction horizons up to six hours ahead. As a first step, a methodology to characterise ramps within a wind power time series was proposed. The so-called ramp function is based on the wavelet transform and it provides a continuous index related to the ramp intensity at each time step. The underlying idea is that ramps are characterised by high power output gradients evaluated under different time scales. A number of state-of-the-art time series based models were considered, namely linear autoregressive (AR) models, varying-coefficient models (VCMs) and artificial neural networks (ANNs). This allowed us to gain insights into how the complexity of the model contributes to the accuracy of the wind power time series modelling. The models were trained in base of a mean squared error criterion and the final set-up of each model was determined through cross-validation techniques. In order to investigate the contribution of the global scale into wind power ramp forecasting, a methodological proposal to identify features in atmospheric raw data that are relevant for explaining wind power ramp events was presented. The proposed methodology is based on two techniques: principal component analysis (PCA) for atmospheric data compression and mutual information (MI) for assessing non-linear dependence between variables. The methodology was applied to reanalysis data generated with a general circulation model (GCM). This allowed for the elaboration of explanatory variables meaningful for ramp forecasting that were utilized as exogenous variables by the forecasting models. The study covered two wind farms located in Spain. All the models outperformed the reference model (the persistence) during both ramp and non-ramp situations. Adding atmospheric information had a noticeable impact on the forecasting performance, specially during ramp-down events. Results also suggested different levels of connection between the ramp occurrence at the wind farm level and the global scale.

Comparison of Airborne Laser Scanning Methods for Estimating Forest Structure Indicators Based on Lorenz Curves

The purpose of this study was to compare a number of state-of-the-art methods in airborne laser scan- ning (ALS) remote sensing with regards to their capacity to describe tree size inequality and other indi- cators related to forest structure. The indicators chosen were based on the analysis of the Lorenz curve: Gini coefficient ( GC ), Lorenz asymmetry ( LA ), the proportions of basal area ( BALM ) and stem density ( NSLM ) stocked above the mean quadratic diameter. Each method belonged to one of these estimation strategies: (A) estimating indicators directly; (B) estimating the whole Lorenz curve; or (C) estimating a complete tree list. Across these strategies, the most popular statistical methods for area-based approach (ABA) were used: regression, random forest (RF), and nearest neighbour imputation. The latter included distance metrics based on either RF (NN–RF) or most similar neighbour (MSN). In the case of tree list esti- mation, methods based on individual tree detection (ITD) and semi-ITD, both combined with MSN impu- tation, were also studied. The most accurate method was direct estimation by best subset regression, which obtained the lowest cross-validated coefficients of variation of their root mean squared error CV(RMSE) for most indicators: GC (16.80%), LA (8.76%), BALM (8.80%) and NSLM (14.60%). Similar figures [CV(RMSE) 16.09%, 10.49%, 10.93% and 14.07%, respectively] were obtained by MSN imputation of tree lists by ABA, a method that also showed a number of additional advantages, such as better distributing the residual variance along the predictive range. In light of our results, ITD approaches may be clearly inferior to ABA with regards to describing the structural properties related to tree size inequality in for- ested areas.

Avaliações e testes dos métodos MASW e ReMi por meio do tratamento de dados empíricos e sintéticos em um programa de processamento e inversão desenvolvido em MATLAB e sua implicação em um problema geológico na Bacia de Taubaté

Os métodos de ondas superficiais com ênfase nas ondas Rayleigh foram utilizados como o núcleo desse trabalho de Doutorado. Inicialmente, as ondas Rayleigh foram modeladas permitindo o estudo de sensibilidade de suas curvas de dispersão sob diferentes configurações de parâmetros físicos representando diversos modelos de camadas, em que pôde ser observado parâmetros com maior e menor sensibilidade e também alguns efeitos provocados por baixas razões de Poisson. Além disso, na fase de inversão dos dados a modelagem das ondas Rayleigh foi utilizada para a construção da função objeto, que agregada ao método de mínimos quadrados, a partir do método de Levenberg-Marquardt, permitiu a implementação de um algoritmo de busca local responsável pela inversão de dados das ondas superficiais. Por se tratar de um procedimento de busca local, o algoritmo de inversão foi complementado por uma etapa de pré-inversão com a geração de um modelo inicial para que o procedimento de inversão fosse mais rápido e eficiente. Visando uma eficiência ainda maior do procedimento de inversão, principalmente em modelos de camadas com inversão de velocidades, foi implementado um algoritmo de pós-inversão baseado em um procedimento de tentativa e erro minimizando os valores relativos da raiz quadrada do erro quadrático médio (REQMr) da inversão dos dados. Mais de 50 modelos de camadas foram utilizados para testar a modelagem, a pré-inversão, inversão e pós-inversão dos dados permitindo o ajuste preciso de parâmetros matemáticos e físicos presentes nos diversos scripts implementados em Matlab. Antes de inverter os dados adquiridos em campo, os mesmos precisaram ser tratados na etapa de processamento de dados, cujo objetivo principal é a extração da curva de dispersão originada devido às ondas superficiais. Para isso, foram implementadas, também em Matlab, três metodologias de processamento com abordagens matemáticas distintas. Essas metodologias foram testadas e avaliadas com dados sintéticos e reais em que foi possível constatar as virtudes e deficiências de cada metodologia estudada, bem como as limitações provocadas pela discretização dos dados de campo. Por último, as etapas de processamento, pré-inversão, inversão e pós-inversão dos dados foram unificadas para formar um programa de tratamento de dados de ondas superficiais (Rayleigh). Ele foi utilizado em dados reais originados pelo estudo de um problema geológico na Bacia de Taubaté em que foi possível mapear os contatos geológicos ao longo dos pontos de aquisição sísmica e compará-los a um modelo inicial existente baseado em observações geomorfológicas da área de estudos, mapa geológico da região e informações geológicas globais e locais dos movimentos tectônicos na região. As informações geofísicas associadas às geológicas permitiram a geração de um perfil analítico da região de estudos com duas interpretações geológicas confirmando a suspeita de neotectônica na região em que os contatos geológicos entre os depósitos Terciários e Quaternários foram identificados e se encaixaram no modelo inicial de hemi-graben com mergulho para Sudeste.

Western Hemisphere, 1740 (Image 1 of 2) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Carte nouvelle de la mer du Sud : dressée par ordre des principaux directeurs & tirée des memoires les plus recents et des relations des navigateurs les plus modernes, tant de France, que d'Espagne l'on ÿa joint, diverses remarques curieuses par raport aux decouvertes des graduations des manierres du pais que de la navigation. It was published by Donné au public, par And. & Henry de Leth ... sur le Pont de la Bourse au Pescheur ca. 1740. Scale [ca. 1:30,000,000]. Covers the Pacific and Atlantic oceans, and the Americas, with parts of Asia, Australia, Europe, and Africa. This layer is image 1 of 2 total images of the two sheet source map representing the western portion of the map. Text in French, Dutch, and Latin. The image inside the map neatline is georeferenced to the surface of the earth and fit to the 'Mercator' projection. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. Note: The central meridian of this map is not the same as the Prime Meridian and may wrap the International Date Line or overlap itself when displayed in GIS software. This map shows features such as drainage, cities and other human settlements, territorial boundaries, shoreline features, and more. Relief is shown pictorially. Includes historical and cultural notes, view of "Fort au Cap de Bonne Esperance," and other ill. Insets: Vera-cruz -- Baye de Rio Janeiro -- La Havane ... -- Le Detroit de Gibaltar -- La ville de Mexico -- Istme de Panama ou de Darien -- Baye de Porto Bello. This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection and the Harvard University Library as part of the Open Collections Program at Harvard University project: Organizing Our World: Sponsored Exploration and Scientific Discovery in the Modern Age. Maps selected for the project correspond to various expeditions and represent a range of regions, originators, ground condition dates, scales, and purposes.

Western Hemisphere, 1740 (Image 2 of 2) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Carte nouvelle de la mer du Sud : dressée par ordre des principaux directeurs & tirée des memoires les plus recents et des relations des navigateurs les plus modernes, tant de France, que d'Espagne l'on ÿa joint, diverses remarques curieuses par raport aux decouvertes des graduations des manierres du pais que de la navigation. It was published by Donné au public, par And. & Henry de Leth ... sur le Pont de la Bourse au Pescheur ca. 1740. Scale [ca. 1:30,000,000]. Covers the Pacific and Atlantic oceans, and the Americas, with parts of Asia, Australia, Europe, and Africa. This layer is image 2 of 2 total images of the two sheet source map representing the eastern portion of the map. Text in French, Dutch, and Latin. The image inside the map neatline is georeferenced to the surface of the earth and fit to a non-standard 'Mercator' projection with the central meridian at 172.66600 degrees west. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. Note: The central meridian of this map is not the same as the Prime Meridian and may wrap the International Date Line or overlap itself when displayed in GIS software. This map shows features such as drainage, cities and other human settlements, territorial boundaries, shoreline features, and more. Relief is shown pictorially. Includes historical and cultural notes, view of "Fort au Cap de Bonne Esperance," and other ill. Insets: Vera-cruz -- Baye de Rio Janeiro -- La Havane ... -- Le Detroit de Gibaltar -- La ville de Mexico -- Istme de Panama ou de Darien -- Baye de Porto Bello. This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection and the Harvard University Library as part of the Open Collections Program at Harvard University project: Organizing Our World: Sponsored Exploration and Scientific Discovery in the Modern Age. Maps selected for the project correspond to various expeditions and represent a range of regions, originators, ground condition dates, scales, and purposes.

Madison, Wisconsin, 1857 (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Madison : the capital of Wisconsin. It was published in 1857. Scale [ca. 1:6,000]. The image inside the map neatline is georeferenced to the surface of the earth and fit to the Wisconsin South State Plane NAD 1983 coordinate system (in Feet) (Fipszone 4803). All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This is a partial cadastral map showing features such as roads, railroads, property lots with names of selected property owners, drainage, selected buildings shown pictorially, and more. This layer is part of a selection of digitally scanned and georeferenced historic maps from The Harvard Map Collection as part of the Imaging the Urban Environment project. Maps selected for this project represent major urban areas and cities of the world, at various time periods. These maps typically portray both natural and manmade features at a large scale. The selection represents a range of regions, originators, ground condition dates, scales, and purposes.

Madison, Wisconsin, 1893 (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Map of Madison, Wisconsin : A.A.A.S. XLII meeting, August 17-24, 1893, compliments of the Local Committee. It was published by Tracy, Gibbs & Co., printer in 1893. Scale [ca. 1:20,000]. Covers a portion of Madison, Wisconsin. The image inside the map neatline is georeferenced to the surface of the earth and fit to the Wisconsin South State Plane NAD 1983 coordinate system (in Feet) (Fipszone 4803). All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as roads, railroads, street railroads, and stations, drainage, selected buildings, city ward boundaries, and more. Includes list of additions and corrections and inset: [Madison Region]. This layer is part of a selection of digitally scanned and georeferenced historic maps from The Harvard Map Collection as part of the Imaging the Urban Environment project. Maps selected for this project represent major urban areas and cities of the world, at various time periods. These maps typically portray both natural and manmade features at a large scale. The selection represents a range of regions, originators, ground condition dates, scales, and purposes.

Chile and Argentina, 1779 (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Carte du Chili méridional, du Rio de la Plata des Patagons, et du Détroit de Magellan : ce qui fait l'extremité australe de l'Amérique Meridle., par le sr. d'Anville. It was published by P. Santini in 1779. Scale [ca. 1:6,500,000]. Covers southern South America including portions of Chile, Argentina, Brazil, Uruguay, and the Falkland Islands. Map in French. The image inside the map neatline is georeferenced to the surface of the earth and fit to a non-standard 'World Sinusoidal' projection with the central meridian at 58.000000 degrees west. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as drainage, cities and other human settlements, territorial boundaries, shoreline features, and more. Relief is shown pictorially. Includes note. This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection and the Harvard University Library as part of the Open Collections Program at Harvard University project: Organizing Our World: Sponsored Exploration and Scientific Discovery in the Modern Age. Maps selected for the project correspond to various expeditions and represent a range of regions, originators, ground condition dates, scales, and purposes.

Central South America, 1779 (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Carte qui représente la parte méridionale du Brésil et du Pérou, le Chili septentrional et le Paraguay : ce qui fait la partie de milieu de L'Amérique Méridionale, par le sr. d'Anville. It was published by P. Santini, Chez M. Remondini in 1779. Scale [ca. 1:6,500,000]. Covers the central part of South America including parts of Brazil, Bolivia, Peru, Chile, Argentina, Paraguay, and Uruguay. Map in French. The image inside the map neatline is georeferenced to the surface of the earth and fit to a non-standard 'World Sinusoidal' projection with the central meridian at 58.000000 degrees west. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as drainage, cities and other human settlements, territorial boundaries, shoreline features, and more. Relief is shown pictorially. This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection and the Harvard University Library as part of the Open Collections Program at Harvard University project: Organizing Our World: Sponsored Exploration and Scientific Discovery in the Modern Age. Maps selected for the project correspond to various expeditions and represent a range of regions, originators, ground condition dates, scales, and purposes.

Liverpool, England, 1889 (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Plan of the Mersey docks and harbour estate with part of the city of Liverpool. It was published in 1889. Scale [ca. 1:10,750]. Covers portions of Liverpool and Birkenhead, England. The image inside the map neatline is georeferenced to the surface of the earth and fit to the 'British National Grid' coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as roads, railroads, drainage, built-up areas and selected buildings and industries, canals, docks, wharves, city districts, ground cover, parks and more. Includes list of references to excursions, places of interest and to wards in Birkenhead. This layer is part of a selection of digitally scanned and georeferenced historic maps from The Harvard Map Collection as part of the Imaging the Urban Environment project. Maps selected for this project represent major urban areas and cities of the world, at various time periods. These maps typically portray both natural and manmade features at a large scale. The selection represents a range of regions, originators, ground condition dates, scales, and purposes.

Liverpool, England, 1900 (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Bacon's plan of Liverpool : divided into 1/4 mile squares. It was published by G.W. Bacon & Co. in 1900. Scale [ca. 1:10,560]. Covers Liverpool, England. The image inside the map neatline is georeferenced to the surface of the earth and fit to the 'British National Grid' coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as roads, railroads and stations, drainage, built-up areas and selected buildings and industries, canals, docks, wharves, parks and more. Includes insets: Key map showing wards -- Continuation north on same scale. This layer is part of a selection of digitally scanned and georeferenced historic maps from The Harvard Map Collection as part of the Imaging the Urban Environment project. Maps selected for this project represent major urban areas and cities of the world, at various time periods. These maps typically portray both natural and manmade features at a large scale. The selection represents a range of regions, originators, ground condition dates, scales, and purposes.

Liverpool, England, 1900 (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: City of Liverpool : area 14,909 acres (exclusive of half of River Mersey). It was published by George Philip & Son L[td], The London Geographical Institute in 1900. Scale [ca. 1:15,400]. Covers portions of Liverpool and Birkenhead, England. The image inside the map neatline is georeferenced to the surface of the earth and fit to the 'British National Grid' coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as roads, railroads and stations, drainage, built-up areas and selected buildings and industries, canals, docks, wharves, parks, administrative boundaries, and more. Includes index to public parks, gardens, and recreation grounds, and inset: Extension of the Garston on same scale. This layer is part of a selection of digitally scanned and georeferenced historic maps from The Harvard Map Collection as part of the Imaging the Urban Environment project. Maps selected for this project represent major urban areas and cities of the world, at various time periods. These maps typically portray both natural and manmade features at a large scale. The selection represents a range of regions, originators, ground condition dates, scales, and purposes.

Liverpool, England, 1854 (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: Map of the borough of Liverpool : with Parliamentary boundaries, ecclesiastical divisions and a part of the Cheshire coast. It was published by engraved and published by H. Hilliar in 1854. Scale [ca. 1:17,000]. Covers portions of Liverpool and Birkenhead, England. The image inside the map neatline is georeferenced to the surface of the earth and fit to the 'British National Grid' coordinate system. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows features such as roads, railroads, drainage, built-up areas and selected buildings and industries, canals, docks, wharves, city districts, ground cover, parks and more. This layer is part of a selection of digitally scanned and georeferenced historic maps from The Harvard Map Collection as part of the Imaging the Urban Environment project. Maps selected for this project represent major urban areas and cities of the world, at various time periods. These maps typically portray both natural and manmade features at a large scale. The selection represents a range of regions, originators, ground condition dates, scales, and purposes.

Bahía Orange, Tierra del Fuego, Chile, 1891 (Raster Image)

This layer is a georeferenced raster image of the historic nautical chart entitled: Orange Harbour : Tierra del Fuego, surveyed by the U.S.Ex.Ex. 1839 ; R.H. Wyman U.S.N. Hydrographer to the Bureau of Navigation. It was published by Hydrographic Office in 1891. Scale [ca. 1:18,700]. Covers Bahía Orange, Tierra del Fuego, Chile. The image inside the map neatline is georeferenced to the surface of the earth and fit to the 'Mercator' projection. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. This map shows coastal features such as rocks, channels, points, coves, islands, bottom types, and more. Includes also selected land features such as drainage, relief, and more. Relief shown by hachures and spot heights; depths by soundings. Includes inset view: Pack Saddle off Orange Bay N.N.W. dist. 6 miles This layer is part of a selection of digitally scanned and georeferenced historic maps from the Harvard Map Collection and the Harvard University Library as part of the Open Collections Program at Harvard University project: Organizing Our World: Sponsored Exploration and Scientific Discovery in the Modern Age. Maps selected for the project correspond to various expeditions and represent a range of regions, originators, ground condition dates, scales, and purposes.