SAKWeb – Spatial autocorrelation and kriging web, a W3 geocomputation perspective

A thesis submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Information Systems

The Discontinuous Nature of Kriging Interpolation for Digital Terrain Modeling

Kriging is a widely employed method for interpolating and estimating elevations from digital elevation data. Its place of prominence is due to its elegant theoretical foundation and its convenient practical implementation. From an interpolation point of view, kriging is equivalent to a thin-plate spline and is one species among the many in the genus of weighted inverse distance methods, albeit with attractive properties. However, from a statistical point of view, kriging is a best linear unbiased estimator and, consequently, has a place of distinction among all spatial estimators because any other linear estimator that performs as well as kriging (in the least squares sense) must be equivalent to kriging, assuming that the parameters of the semivariogram are known. Therefore, kriging is often held to be the gold standard of digital terrain model elevation estimation. However, I prove that, when used with local support, kriging creates discontinuous digital terrain models, which is to say, surfaces with “rips” and “tears” throughout them. This result is general; it is true for ordinary kriging, kriging with a trend, and other forms. A U.S. Geological Survey (USGS) digital elevation model was analyzed to characterize the distribution of the discontinuities. I show that the magnitude of the discontinuity does not depend on surface gradient but is strongly dependent on the size of the kriging neighborhood.

Soil CO(2) emission estimated by different interpolation techniques

Soil CO(2) emissions are highly variable, both spatially and across time, with significant changes even during a one-day period. The objective of this study was to compare predictions of the diurnal soil CO(2) emissions in an agricultural field when estimated by ordinary kriging and sequential Gaussian simulation. The dataset consisted of 64 measurements taken in the morning and in the afternoon on bare soil in southern Brazil. The mean soil CO(2) emissions were significantly different between the morning (4.54 mu mol m(-2) s(-1)) and afternoon (6.24 mu mol m(-2) s(-1)) measurements. However, the spatial variability structures were similar, as the models were spherical and had close range values of 40.1 and 40.0 m for the morning and afternoon semivariograms. In both periods, the sequential Gaussian simulation maps were more efficient for the estimations of emission than ordinary kriging. We believe that sequential Gaussian simulation can improve estimations of soil CO(2) emissions in the field, as this property is usually highly non-Gaussian distributed.

Geostatistical Mapping of Outfall Plume Dispersion Data gathered with an autonomous underwater vehicle

The main purpose of this study was to examine the applicability of geostatistical modeling to obtain valuable information for assessing the environmental impact of sewage outfall discharges. The data set used was obtained in a monitoring campaign to S. Jacinto outfall, located off the Portuguese west coast near Aveiro region, using an AUV. The Matheron’s classical estimator was used the compute the experimental semivariogram which was fitted to three theoretical models: spherical, exponential and gaussian. The cross-validation procedure suggested the best semivariogram model and ordinary kriging was used to obtain the predictions of salinity at unknown locations. The generated map shows clearly the plume dispersion in the studied area, indicating that the effluent does not reach the near by beaches. Our study suggests that an optimal design for the AUV sampling trajectory from a geostatistical prediction point of view, can help to compute more precise predictions and hence to quantify more accurately dilution. Moreover, since accurate measurements of plume’s dilution are rare, these studies might be very helpful in the future for validation of dispersion models.

Rede de monitorização ambiental em tempo- real com sistemas móveis

A compreensão das interacções entre os oceanos, a linha de costa, a qualidade do ar e as florestas só será possível através do registo e análise de informação geo-temporalmente referenciada. Mas a monitorização de grandes áreas apresenta o problema da cobertura espacial e temporal, e os custos nela envolvidos pela impossibilidade de disseminar a quantidade de estações de monitorização necessários à compreensão do fenómeno. É necessário então definir metodologias de colocação de sensores e recolha de informação de forma robusta, económica e temporalmente útil. Nesta dissertação apresentamos uma estratégia de monitorização ambiental, para meios hídricos, (ou de grande dimensão) que baseada em sistemas móveis e alguns princípios da geoestatística, fornece uma ferramenta de monitorização mais económica, sem prejuízo da qualidade de informação. Os modelos usados na geoestatística assentam na ideia de que medidas mais próximas tendem a serem mais parecidas do que valores observados em locais distantes e fornece métodos para quantificar esta correlação espacial e incorporá-la na estimação. Os resultados obtidos sustentam a convicção do uso de veículos móveis em redes de sensores e que contribuímos para responder à seguinte questão “Qual a técnica que nos permite com poucos sensores monitorizar grandes áreas?”. A solução passará por modelos de estimação de grandezas utilizados na geoestatística associados a sistemas móveis.

Modelação da distribuição espacial da qualidade do ar em Lisboa usando sistemas de informação geográficas

Dissertação apresentada como requisito parcial para obtenção do grau de Mestre em Ciência e Sistemas de Informação Geográfica

Modelação da vegetação potencial da Serra da Lousã e a sua aplicação no contexto da restauração de ecossistemas florestais

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do grau de Mestre em Engenharia do Ambiente, perfil Engenharia Ecológica

Mapping the quality of life experience in Alfama: a case study in Lisbon, Portugal.

Dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science in Geospatial Technologies.

Parallelization of web processing services on cloud computing: A case study of Geostatistical Methods

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.

Evaluation of Spatial interpolation techniques for mapping climate variables with low sample density: a case study using a new gridded dataset of Bangladesh

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.

Extreme Precipitation Modelling Using Geostatistics and Machine Learning Algorithms

The paper presents an approach for mapping of precipitation data. The main goal is to perform spatial predictions and simulations of precipitation fields using geostatistical methods (ordinary kriging, kriging with external drift) as well as machine learning algorithms (neural networks). More practically, the objective is to reproduce simultaneously both the spatial patterns and the extreme values. This objective is best reached by models integrating geostatistics and machine learning algorithms. To demonstrate how such models work, two case studies have been considered: first, a 2-day accumulation of heavy precipitation and second, a 6-day accumulation of extreme orographic precipitation. The first example is used to compare the performance of two optimization algorithms (conjugate gradients and Levenberg-Marquardt) of a neural network for the reproduction of extreme values. Hybrid models, which combine geostatistical and machine learning algorithms, are also treated in this context. The second dataset is used to analyze the contribution of radar Doppler imagery when used as external drift or as input in the models (kriging with external drift and neural networks). Model assessment is carried out by comparing independent validation errors as well as analyzing data patterns.

Uncertainties in the prediction of spatial variability of soil CO2 emissions and related properties

The soil CO2 emission has high spatial variability because it depends strongly on soil properties. The purpose of this study was to (i) characterize the spatial variability of soil respiration and related properties, (ii) evaluate the accuracy of results of the ordinary kriging method and sequential Gaussian simulation, and (iii) evaluate the uncertainty in predicting the spatial variability of soil CO2 emission and other properties using sequential Gaussian simulations. The study was conducted in a sugarcane area, using a regular sampling grid with 141 points, where soil CO2 emission, soil temperature, air-filled pore space, soil organic matter and soil bulk density were evaluated. All variables showed spatial dependence structure. The soil CO2 emission was positively correlated with organic matter (r = 0.25, p < 0.05) and air-filled pore space (r = 0.27, p < 0.01) and negatively with soil bulk density (r = -0.41, p < 0.01). However, when the estimated spatial values were considered, the air-filled pore space was the variable mainly responsible for the spatial characteristics of soil respiration, with a correlation of 0.26 (p < 0.01). For all variables, individual simulations represented the cumulative distribution functions and variograms better than ordinary kriging and E-type estimates. The greatest uncertainties in predicting soil CO2 emission were associated with areas with the highest estimated values, which produced estimates from 0.18 to 1.85 t CO2 ha-1, according to the different scenarios considered. The knowledge of the uncertainties generated by the different scenarios can be used in inventories of greenhouse gases, to provide conservative estimates of the potential emission of these gases.

Evaluation of statistical and geostatistical models of digital soil properties mapping in tropical mountain regions

Soil properties have an enormous impact on economic and environmental aspects of agricultural production. Quantitative relationships between soil properties and the factors that influence their variability are the basis of digital soil mapping. The predictive models of soil properties evaluated in this work are statistical (multiple linear regression-MLR) and geostatistical (ordinary kriging and co-kriging). The study was conducted in the municipality of Bom Jardim, RJ, using a soil database with 208 sampling points. Predictive models were evaluated for sand, silt and clay fractions, pH in water and organic carbon at six depths according to the specifications of the consortium of digital soil mapping at the global level (GlobalSoilMap). Continuous covariates and categorical predictors were used and their contributions to the model assessed. Only the environmental covariates elevation, aspect, stream power index (SPI), soil wetness index (SWI), normalized difference vegetation index (NDVI), and b3/b2 band ratio were significantly correlated with soil properties. The predictive models had a mean coefficient of determination of 0.21. Best results were obtained with the geostatistical predictive models, where the highest coefficient of determination 0.43 was associated with sand properties between 60 to 100 cm deep. The use of a sparse data set of soil properties for digital mapping can explain only part of the spatial variation of these properties. The results may be related to the sampling density and the quantity and quality of the environmental covariates and predictive models used.

Semivariogram models for estimating fig fly population density throughout the year

The objective of this work was to select semivariogram models to estimate the population density of fig fly (Zaprionus indianus; Diptera: Drosophilidae) throughout the year, using ordinary kriging. Nineteen monitoring sites were demarcated in an area of 8,200 m2, cropped with six fruit tree species: persimmon, citrus, fig, guava, apple, and peach. During a 24 month period, 106 weekly evaluations were done in these sites. The average number of adult fig flies captured weekly per trap, during each month, was subjected to the circular, spherical, pentaspherical, exponential, Gaussian, rational quadratic, hole effect, K-Bessel, J-Bessel, and stable semivariogram models, using ordinary kriging interpolation. The models with the best fit were selected by cross-validation. Each data set (months) has a particular spatial dependence structure, which makes it necessary to define specific models of semivariograms in order to enhance the adjustment to the experimental semivariogram. Therefore, it was not possible to determine a standard semivariogram model; instead, six theoretical models were selected: circular, Gaussian, hole effect, K-Bessel, J-Bessel, and stable.

Spatial variability of the rainfall erosive potential in the State of Mato Grosso do Sul, Brazil

Information about rainfall erosivity is important during soil and water conservation planning. Thus, the spatial variability of rainfall erosivity of the state Mato Grosso do Sul was analyzed using ordinary kriging interpolation. For this, three pluviograph stations were used to obtain the regression equations between the erosivity index and the rainfall coefficient EI30. The equations obtained were applied to 109 pluviometric stations, resulting in EI30 values. These values were analyzed from geostatistical technique, which can be divided into: descriptive statistics, adjust to semivariogram, cross-validation process and implementation of ordinary kriging to generate the erosivity map.Highest erosivity values were found in central and northeast regions of the State, while the lowest values were observed in the southern region. In addition, high annual precipitation values not necessarily produce higher erosivity values.