Métodos robustos em geoestatística

O objectivo principal da presente tese consiste no desenvolvimento de estimadores robustos do variograma com boas propriedades de eficiência. O variograma é um instrumento fundamental em Geoestatística, pois modela a estrutura de dependência do processo em estudo e influencia decisivamente a predição de novas observações. Os métodos tradicionais de estimação do variograma não são robustos, ou seja, são sensíveis a pequenos desvios das hipóteses do modelo. Essa questão é importante, pois as propriedades que motivam a aplicação de tais métodos, podem não ser válidas nas vizinhanças do modelo assumido. O presente trabalho começa por conter uma revisão dos principais conceitos em Geoestatística e da estimação tradicional do variograma. De seguida, resumem-se algumas noções fundamentais sobre robustez estatística. No seguimento, apresenta-se um novo método de estimação do variograma que se designou por estimador de múltiplos variogramas. O método consiste em quatro etapas, nas quais prevalecem, alternadamente, os critérios de robustez ou de eficiência. A partir da amostra inicial, são calculadas, de forma robusta, algumas estimativas pontuais do variograma; com base nessas estimativas pontuais, são estimados os parâmetros do modelo pelo método dos mínimos quadrados; as duas fases anteriores são repetidas, criando um conjunto de múltiplas estimativas da função variograma; por fim, a estimativa final do variograma é definida pela mediana das estimativas obtidas anteriormente. Assim, é possível obter um estimador que tem boas propriedades de robustez e boa eficiência em processos Gaussianos. A investigação desenvolvida revelou que, quando se usam estimativas discretas na primeira fase da estimação do variograma, existem situações onde a identificabilidade dos parâmetros não está assegurada. Para os modelos de variograma mais comuns, foi possível estabelecer condições, pouco restritivas, que garantem a unicidade de solução na estimação do variograma. A estimação do variograma supõe sempre a estacionaridade da média do processo. Como é importante que existam procedimentos objectivos para avaliar tal condição, neste trabalho sugere-se um teste para validar essa hipótese. A estatística do teste é um estimador-MM, cuja distribuição é desconhecida nas condições de dependência assumidas. Tendo em vista a sua aproximação, apresenta-se uma versão do método bootstrap adequada ao estudo de observações dependentes de processos espaciais. Finalmente, o estimador de múltiplos variogramas é avaliado em termos da sua aplicação prática. O trabalho contém um estudo de simulação que confirma as propriedades estabelecidas. Em todos os casos analisados, o estimador de múltiplos variogramas produziu melhores resultados do que as alternativas usuais, tanto para a distribuição assumida, como para distribuições contaminadas.

Assessing soil erosion due to land use change at the Alqueva reservoir surrounding area

Tese de doutoramento, Ciências do Mar, da Terra e do Ambiente, Faculdade de Ciências e Tecnologia, Universidade do Algarve, 2015

Geostatistical Prediction of Ocean Outfall Plume Characteristics Based on an Autonomous Underwater Vehicle

Geostatistics has been successfully used to analyze and characterize the spatial variability of environmental properties. Besides giving estimated values at unsampled locations, it provides a measure of the accuracy of the estimate, which is a significant advantage over traditional methods used to assess pollution. In this work universal block kriging is novelty used to model and map the spatial distribution of salinity measurements gathered by an Autonomous Underwater Vehicle in a sea outfall monitoring campaign, with the aim of distinguishing the effluent plume from the receiving waters, characterizing its spatial variability in the vicinity of the discharge and estimating dilution. The results demonstrate that geostatistical methodology can provide good estimates of the dispersion of effluents that are very valuable in assessing the environmental impact and managing sea outfalls. Moreover, since accurate measurements of the plume’s dilution are rare, these studies might be very helpful in the future to validate dispersion models.

Metodologias de Sistemas de Informação Geográfica em sistemas de produção florestal : uma aplicação geoestatística

As florestas são uma fonte importante de recursos naturais, desempenhando um papel fulcral na sustentabilidade ambiental. A sua gestão quer territorial quer económica, conduz a uma maximização da produção, sem alteração da qualidade da matéria-prima. Portugal apresenta mais de um terço do seu território coberto por floresta, apresentando uma possibilidade de aplicação de sistemas de gestão, territorial e económica que maximizem a sua produção. Os Sistemas de Informação Geográfica (SIG) são modelos da realidade em que é possível integrar toda a informação disponível sobre um assunto tendo por base um campo comum a todos as variáveis, a localização geográfica. Os SIG podem contribuir de diversas formas para um maior desenvolvimento das rotinas e ferramentas de planeamento e gestão florestal. A sua integração com modelos quantitativos para planeamento e gestão de florestas é uma mais-valia nesta área. Nesta dissertação apresentam-se modelos geoestatísticos, com recurso a Sistemas de Informação Geográfica, de apoio e suporte à produção de pinha em Pinheiro-manso (Pinus pinea L.). Procurando estimar as áreas com melhor propensão à produção, a partir de dados amostrais. Estes foram previamente estudados tendo sido selecionadas quatro variáveis: largura da copa, área basal, altura da árvore e produção de pinha. A geoestatística aplicada, inclui modelos de correlação espacial: kriging, onde são atribuídos pesos às amostras a partir de uma análise espacial baseada no variograma experimental. Foi utilizada a extensão Geostatistical Analyst do ArcGis da ESRI, para realizar 96 krigings para as quatro variáveis em estudo, com diferentes parametrizações, destes foram selecionados 8 krigings. Com base nos critérios de adequação dos modelos e da análise de resultados da predição dos erros - cross validation. O resultado deste estudo é apresentado através de mapas de previsão para a produção de pinha em Pinheiro manso, em que foram analisadas áreas com maior e menor probabilidade de produção tendo-se realizado análises de comparação de variáveis. Através da interseção de todas as variáveis com a produção, podemos concluir que os concelhos com maiores áreas de probabilidade de produção de pinha em Pinheiro manso, da área de estudo, são Alcácer do Sal, Montemor-o-Novo, Vendas Novas, Coruche e Chamusca. Com a realização de um cruzamento de dados entre os resultados obtidos dos krigings, e a Carta de Uso e Ocupação do Solo de Portugal Continental para 2007 (COS2007), realizaram-se mapas de previsão para a expansão do Pinheiro manso. Nas áreas de expansão conseguimos atingir aumentos mínimos na ordem dos 11% e máximo na ordem dos 61%. No total consegue-se atingir aproximadamente 128 mil ha para área de expansão do Pinheiro manso. Superando, os valores esperados pelos Planos Regionais de Ordenamento Florestal, abrangidos pela área da amostra em estudo, em que é esperado um incremento de cerca de 130 mil hectares de área de Pinheiro manso para 2030.

Using active learning for monitoring networks design: The example of wind power plants sites evaluation

Locating new wind farms is of crucial importance for energy policies of the next decade. To select the new location, an accurate picture of the wind fields is necessary. However, characterizing wind fields is a difficult task, since the phenomenon is highly nonlinear and related to complex topographical features. In this paper, we propose both a nonparametric model to estimate wind speed at different time instants and a procedure to discover underrepresented topographic conditions, where new measuring stations could be added. Compared to space filling techniques, this last approach privileges optimization of the output space, thus locating new potential measuring sites through the uncertainty of the model itself.

Modélisation de l'utilisation de l'habitat du béluga du Saint-Laurent en fonction de ses proies à l'embouchure de la rivière Saguenay et à la baie Sainte-Marguerite

Le béluga du Saint-Laurent est une espèce menacée au Canada et protégée par la Loi sur les espèces en péril du Canada. La détermination des fonctions biologiques de ses habitats essentiels est nécessaire afin d’assurer le rétablissement de la population. Parcs Canada a entamé en 2009 un suivi des proies du béluga dans deux de ses aires de fréquentation intensive situées dans le Parc marin du Saguenay–Saint-Laurent : l’embouchure de la rivière Saguenay et la baie Sainte-Marguerite. L’étude de l’abondance et de la distribution des proies est réalisée par sondage hydroacoustique le long de transects à l’aide d’un échosondeur multifréquences. Un protocole d’observations systématiques du béluga est mené simultanément aux sondages hydroacoustiques à partir de sites terrestres. Le premier objectif de cette étude est de développer la méthodologie concernant le traitement, la classification et la cartographie des données hydroacoustiques échantillonnées. L’objectif principal consiste à déterminer si l’abondance et la distribution des proies pélagiques ont une influence sur l’utilisation de ces deux habitats par le béluga. La cartographie de la biomasse relative de poissons a été réalisée pour la couche de surface, la couche en profondeur et pour l’ensemble de la colonne d’eau par krigeage ordinaire pour les deux habitats pour les 29 transects. À la baie Sainte-Marguerite, le nombre de bélugas observés augmente avec la biomasse relative des proies en surface et en profondeur. À l’embouchure de la rivière Saguenay, les résultats n’ont pas été concluants. Les résultats suggèrent que l’alimentation pourrait être l’une des fonctions biologiques de la baie Sainte-Marguerite.

Distribució espacial i ús de l'hàbitat de la comunitat de peixos a l'estany de Banyoles

En el marc d'un projecte més ampli sobre la comunitat de peixos de la conca lacustre de Banyoles, s'ha estudiat la distribució espacial de les diferents espècies així com l'ús que aquestes fan de l'hàbitat. El poblament piscícola de l'estany de Banyoles és el resultat d'un llarg historial d'introducció d'espècies exòtiques i extinció de les poblacions autòctones locals. S'ha revisat la seva composició actual detectant un total de 18 espècies (4 autòctones i 14 introduïdes) de les quals només 13 presenten una població estable. L'estudi de l'hàbitat s'ha centrat a l'Estany, l'element principal del sistema lacustre, analitzant per separat la zona litoral i la zona limnètica. En el primer cas s'han realitzat les captures d'individus mitjançant pesca elèctrica des d'una embarcació adaptada per aquesta pràctica. La totalitat del litoral ha estat dividida en trams de característiques homogènies on s'han obtingut les captures per unitat d'esforç per cada espècie. El mostreig s'ha desenvolupat entre l'estiu de 1997 i la primavera del 2000 realitzant un total de 10 campanyes de pesca. Les espècies més abundants al litoral són la perca americana (Micropterus salmoides) i el peix sol (Lepomis gibbosus), essent també presents la perca (Perca fluviatilis), carpa (Cyprinus carpio) i el gardí (Scardinius erythrophthalmus). S'han capturat altres espècies com ara anguila (Anguilla anguilla), bagra (Squalius cephalus), sandra (Sander lucioperca), carpí (Carassius auratus) i madrilleta vera (Rutilus rutilus), però són molt menys abundants en nombre. S'ha examinat, per cadascuna de les espècies, si existeix selecció de l'hàbitat i en cas afirmatiu, quin és el preferent en base a la classificació del litoral en sis tipus de vegetació predominant. Les espècies més abundants, perca americana i peix sol, ocupen tots els hàbitats disponibles però amb una densitat diferent. La perca mostra també una clara selecció de l'hàbitat a favor de les zones molt estructurades amb abundant presència de jonca litoral. Carpa i gardí seleccionen els ambients més fondos amb major presència de matèria orgànica d'origen vegetal procedent del bogar. En general els individus ocupen les zones amb una densitat de vegetació intermèdia, majoritàriament zones de jonca a l'estiu i zones amb mansega a l'hivern, on troben refugi i els recursos tròfics necessaris. La perca americana, a més, presenta una elevada fidelitat a un mateix punt del litoral al llarg de la seva vida. La zona limnètica ha estat prospectada mensualment mitjançant ecosondació, realitzant transectes perpendiculars a l'eix principal de l'Estany, cobrint la seva totalitat. La composició d'espècies s'ha obtingut a partir de les captures fetes amb xarxes (tresmalls) amb periodicitat estacional. L'anàlisi geoestadística de la densitat de peixos ha permès descriure l'estructura espacial d'aquesta a partir dels variogrames, així com la seva variabilitat tant espacial com temporal, i obtenir els mapes de densitat. A l'hivern, la densitat de peixos a la zona limnètica assoleix els seus valors mínims i els individus es troben formant agregats dispersos, pels diferents estrats de fondària. A partir de la primavera la densitat augmenta, pel reclutament i la major freqüència d'individus que abandonen el litoral; la densitat esdevé més homogènia a les primer capes de fondària. A l'estiu la densitat és màxima i l'estrat més homogeni coincideix amb la posició de la termoclina. Aquest estructura varia en disminuir la temperatura i barrejar-se la columna d'aigua, tornant a la situació hivernal. La perca i la madrilleta vera són les espècies predominants en aquest ambient, juntament amb la carpa. La seva distribució no és homogènia i respon a les característiques limnològiques de les diferents cubetes de l'Estany. Una particularitat d'aquest, relacionada amb el seu origen càrstic, es la formació d'una ploma hidrotermal que afecta la distribució dels peixos, probablement en augmentar la terbolesa. S'ha integrat l'ús de l'hàbitat de les espècies que ocupen tant la zona limnètica com la litoral a partir del seguiment d'individus, concretament de perca i bagra. S'ha utilitzat un sistema automàtic de posicionament que estima la localització dels individus marcats amb transmissor de telemetria acústica. L'anàlisi dels desplaçaments mostra un rang superior per la bagra en comparació amb la perca. Ambdues espècies mostren una orientació en els seus desplaçaments. La perca ocupa el litoral a la nit i es desplaça a la zona limnètica de dia, amb un ritme d'activitat marcat per dos màxims coincidint amb la sortida i posta de sol; en canvi la bagra mostra una major activitat nocturna amb zones de repòs properes al litoral. S'ha estimat igualment els dominis vital de cada individu marcat.

The Representative Soil Sampling Scheme of England and Wales: the spatial variation of topsoil nutrient status and pH between 1971 and 2001

The Representative Soil Sampling Scheme (RSSS) has monitored the soil of agricultural land in England and Wales since 1969. Here we describe the first spatial analysis of the data from these surveys using geostatistics. Four years of data (1971, 1981, 1991 and 2001) were chosen to examine the nutrient (available K, Mg and P) and pH status of the soil. At each farm, four fields were sampled; however, for the earlier years, coordinates were available for the farm only and not for each field. The averaged data for each farm were used for spatial analysis and the variograms showed spatial structure even with the smaller sample size. These variograms provide a reasonable summary of the larger scale of variation identified from the data of the more intensively sampled National Soil Inventory. Maps of kriged predictions of K generally show larger values in the central and southeastern areas (above 200 mg L-1) and an increase in values in the west over time, whereas Mg is fairly stable over time. The kriged predictions of P show a decline over time, particularly in the east, and those of pH show an increase in the east over time. Disjunctive kriging was used to examine temporal changes in available P using probabilities less than given thresholds of this element. The RSSS was not designed for spatial analysis, but the results show that the data from these surveys are suitable for this purpose. The results of the spatial analysis, together with those of the statistical analyses, provide a comprehensive view of the RSSS database as a basis for monitoring the soil. These data should be taken into account when future national soil monitoring schemes are designed.

Sampling the soil in long-term forest plots: The implications of spatial variation

Long-term monitoring of forest soils as part of a pan-European network to detect environmental change depends on an accurate determination of the mean of the soil properties at each monitoring event. Forest soil is known to be very variable spatially, however. A study was undertaken to explore and quantify this variability at three forest monitoring plots in Britain. Detailed soil sampling was carried out, and the data from the chemical analyses were analysed by classical statistics and geostatistics. An analysis of variance showed that there were no consistent effects from the sample sites in relation to the position of the trees. The variogram analysis showed that there was spatial dependence at each site for several variables and some varied in an apparently periodic way. An optimal sampling analysis based on the multivariate variogram for each site suggested that a bulked sample from 36 cores would reduce error to an acceptable level. Future sampling should be designed so that it neither targets nor avoids trees and disturbed ground. This can be achieved best by using a stratified random sampling design.

Using the variogram to explore imagery of two different spatial resolutions

The resolution of remotely sensed data is becoming increasingly fine, and there are now many sources of data with a pixel size of 1 m x 1 m. This produces huge amounts of data that have to be stored, processed and transmitted. For environmental applications this resolution possibly provides far more data than are needed: data overload. This poses the question: how much is too much? We have explored two resolutions of data-20 in pixel SPOT data and I in pixel Computerized Airborne Multispectral Imaging System (CAMIS) data from Fort A. P. Hill (Virginia, USA), using the variogram of geostatistics. For both we used the normalized difference vegetation index (NDVI). Three scales of spatial variation were identified in both the SPOT and 1 in data: there was some overlap at the intermediate spatial scales of about 150 in and of 500 m-600 in. We subsampled the I in data and scales of variation of about 30 in and of 300 in were identified consistently until the separation between pixel centroids was 15 in (or 1 in 225pixels). At this stage, spatial scales of about 100m and 600m were described, which suggested that only now was there a real difference in the amount of spatial information available from an environmental perspective. These latter were similar spatial scales to those identified from the SPOT image. We have also analysed I in CAMIS data from Fort Story (Virginia, USA) for comparison and the outcome is similar.:From these analyses it seems that a pixel size of 20m is adequate for many environmental applications, and that if more detail is required the higher resolution data could be sub-sampled to a 10m separation between pixel centroids without any serious loss of information. This reduces significantly the amount of data that needs to be stored, transmitted and analysed and has important implications for data compression.

Predictive vegetation mapping in the Mediterranean context: Considerations and methodological issues

The need to map vegetation communities over large areas for nature conservation and to predict the impact of environmental change on vegetation distributions, has stimulated the development of techniques for predictive vegetation mapping. Predictive vegetation studies start with the development of a model relating vegetation units and mapped physical data, followed by the application of that model to a geographic database and over a wide range of spatial scales. This field is particularly important for identifying sites for rare and endangered species and locations of high biodiversity such as many areas of the Mediterranean Basin. The potential of the approach is illustrated with a mapping exercise in the alti-meditterranean zone of Lefka Ori in Crete. The study established the nature of the relationship between vegetation communities and physical data including altitude, slope and geomorphology. In this way the knowledge of community distribution was improved enabling a GIS-based model capable of predicting community distribution to be constructed. The paper describes the development of the spatial model and the methodological problems of predictive mapping for monitoring Mediterranean ecosystems. The paper concludes with a discussion of the role of predictive vegetation mapping and other spatial techniques, such as fuzzy mapping and geostatistics, for improving our understanding of the dynamics of Mediterranean ecosystems and for practical management in a region that is under increasing pressure from human impact.

Mediterranean ecosystems: problems and tools for conservation

Mediterranean ecosystems rival tropical ecosystems in terms of plant biodiversity. The Mediterranean Basin (MB) itself hosts 25 000 plant species, half of which are endemic. This rich biodiversity and the complex biogeographical and political issues make conservation a difficult task in the region. Species, habitat, ecosystem and landscape approaches have been used to identify conservation targets at various scales: ie, European, national, regional and local. Conservation decisions require adequate information at the species, community and habitat level. Nevertheless and despite recent improvements/efforts, this information is still incomplete, fragmented and varies from one country to another. This paper reviews the biogeographic data, the problems arising from current conservation efforts and methods for the conservation assessment and prioritization using GIS. GIS has an important role to play for managing spatial and attribute information on the ecosystems of the MB and to facilitate interactions with existing databases. Where limited information is available it can be used for prediction when directly or indirectly linked to externally built models. As well as being a predictive tool today GIS incorporate spatial techniques which can improve the level of information such as fuzzy logic, geostatistics, or provide insight about landscape changes such as 3D visualization. Where there are limited resources it can assist with identifying sites of conservation priority or the resolution of environmental conflicts (scenario building). Although not a panacea, GIS is an invaluable tool for improving the understanding of Mediterranean ecosystems and their dynamics and for practical management in a region that is under increasing pressure from human impact.

Mediterranean ecosystems: problems and tools for conservation

Mediterranean ecosystems rival tropical ecosystems in terms of plant biodiversity. The Mediterranean Basin (MB) itself hosts 25 000 plant species, half of which are endemic. This rich biodiversity and the complex biogeographical and political issues make conservation a difficult task in the region. Species, habitat, ecosystem and landscape approaches have been used to identify conservation targets at various scales: ie, European, national, regional and local. Conservation decisions require adequate information at the species, community and habitat level. Nevertheless and despite recent improvements/efforts, this information is still incomplete, fragmented and varies from one country to another. This paper reviews the biogeographic data, the problems arising from current conservation efforts and methods for the conservation assessment and prioritization using GIS. GIS has an important role to play for managing spatial and attribute information on the ecosystems of the MB and to facilitate interactions with existing databases. Where limited information is available it can be used for prediction when directly or indirectly linked to externally built models. As well as being a predictive tool today GIS incorporate spatial techniques which can improve the level of information such as fuzzy logic, geostatistics, or provide insight about landscape changes such as 3D visualization. Where there are limited resources it can assist with identifying sites of conservation priority or the resolution of environmental conflicts (scenario building). Although not a panacea, GIS is an invaluable tool for improving the understanding of Mediterranean ecosystems and their dynamics and for practical management in a region that is under increasing pressure from human impact.

Monthly average temperature modelling

This research is associated with the goal of the horticultural sector of the Colombian southwest, which is to obtain climatic information, specifically, to predict the monthly average temperature in sites where it has not been measured. The data correspond to monthly average temperature, and were recorded in meteorological stations at Valle del Cauca, Colombia, South America. Two components are identified in the data of this research: (1) a component due to the temporal aspects, determined by characteristics of the time series, distribution of the monthly average temperature through the months and the temporal phenomena, which increased (El Nino) and decreased (La Nina) the temperature values, and (2) a component due to the sites, which is determined for the clear differentiation of two populations, the valley and the mountains, which are associated with the pattern of monthly average temperature and with the altitude. Finally, due to the closeness between meteorological stations it is possible to find spatial correlation between data from nearby sites. In the first instance a random coefficient model without spatial covariance structure in the errors is obtained by month and geographical location (mountains and valley, respectively). Models for wet periods in mountains show a normal distribution in the errors; models for the valley and dry periods in mountains do not exhibit a normal pattern in the errors. In models of mountains and wet periods, omni-directional weighted variograms for residuals show spatial continuity. The random coefficient model without spatial covariance structure in the errors and the random coefficient model with spatial covariance structure in the errors are capturing the influence of the El Nino and La Nina phenomena, which indicates that the inclusion of the random part in the model is appropriate. The altitude variable contributes significantly in the models for mountains. In general, the cross-validation process indicates that the random coefficient model with spatial spherical and the random coefficient model with spatial Gaussian are the best models for the wet periods in mountains, and the worst model is the model used by the Colombian Institute for Meteorology, Hydrology and Environmental Studies (IDEAM) to predict temperature.

SRTM resample with short distance-low nugget kriging

The shuttle radar topography mission (SRTM), was flow on the space shuttle Endeavour in February 2000, with the objective of acquiring a digital elevation model of all land between 60 degrees north latitude and 56 degrees south latitude, using interferometric synthetic aperture radar (InSAR) techniques. The SRTM data are distributed at horizontal resolution of 1 arc-second (similar to 30m) for areas within the USA and at 3 arc-second (similar to 90m) resolution for the rest of the world. A resolution of 90m can be considered suitable for the small or medium-scale analysis, but it is too coarse for more detailed purposes. One alternative is to interpolate the SRTM data at a finer resolution; it will not increase the level of detail of the original digital elevation model (DEM), but it will lead to a surface where there is the coherence of angular properties (i.e. slope, aspect) between neighbouring pixels, which is an important characteristic when dealing with terrain analysis. This work intents to show how the proper adjustment of variogram and kriging parameters, namely the nugget effect and the maximum distance within which values are used in interpolation, can be set to achieve quality results on resampling SRTM data from 3"" to 1"". We present for a test area in western USA, which includes different adjustment schemes (changes in nugget effect value and in the interpolation radius) and comparisons with the original 1"" model of the area, with the national elevation dataset (NED) DEMs, and with other interpolation methods (splines and inverse distance weighted (IDW)). The basic concepts for using kriging to resample terrain data are: (i) working only with the immediate neighbourhood of the predicted point, due to the high spatial correlation of the topographic surface and omnidirectional behaviour of variogram in short distances; (ii) adding a very small random variation to the coordinates of the points prior to interpolation, to avoid punctual artifacts generated by predicted points with the same location than original data points and; (iii) using a small value of nugget effect, to avoid smoothing that can obliterate terrain features. Drainages derived from the surfaces interpolated by kriging and by splines have a good agreement with streams derived from the 1"" NED, with correct identification of watersheds, even though a few differences occur in the positions of some rivers in flat areas. Although the 1"" surfaces resampled by kriging and splines are very similar, we consider the results produced by kriging as superior, since the spline-interpolated surface still presented some noise and linear artifacts, which were removed by kriging.