IN BATHYMETRIC SURFACES: IDW OR KRIGING?

The representation of the submerged relief is very importance in diverse areas of knowledge such as Projects to build or reassess port dimensions, installation of moles, ducts, marinas, bridges, tunnels, mineral prospecting, waterways, dredging, silting control of river and lakes, and others. The depths of the aquatic bodies, indispensable for the representation of those, are obtained through the bathymetric surveys. However, the result of a bathymetric sampling is a grid of points that, for itself, it is not capable of generating directly the Digital Model of Depth (DMD), being necessary the use of interpolators. Currently, there are more than 40 available scientific methods of interpolation, each one with its particularities and characteristics. This study has the objective to analise, comparing, the efficiency of Universal Kriging (UK) and of the Inverse Distance Weighted (IDW) in the computational representation of bathymetric surfaces, varying in a decreasing way the quantity of sample points. Through the results, we can be stated the superiority of the interpolator Universal Kriging in efficiency in creating DMD with basis in the bathymetric surveys data

Probability of false alarm in the EWMA control graph for monitoring an autocorrelated process.

O presente trabalho teve por objetivo estimar a probabilidade do alarme falso provocada pelo gráfico de controle da média móvel ponderada exponencialmente (EWMA) em um processo autocorrelacionado ao longo dos subgrupos racionais, em função de diferentes combinações entre os valores dos termos: número de desvios-padrão (2 ≤ k ≤ 6), peso do subgrupo racional (0,01 ≤ λ ≤ 1) e autocorrelação de 1a ordem (ρ). Para estudá-los, foram simulados dados de uma variável aleatória Y, sob distribuição normal com média μ0 = 0 e desvio-padrão σ0 = 1 para um processo sob controle estatístico para até 50 subgrupos racionais com observações individuais (n = 1). Para a obtenção dos valores de Y ao longo dos 50 subgrupos racionais, foram realizadas dez situações diferentes de acordo com as seguintes autocorrelações de 1a ordem (ρ = 0; 0,1; 0,2; 0,3; 0,4; 0,5; 0,6; 0,7; 0,8; 0,9). Foram realizadas 1.000 simulações para cada situação. A probabilidade do alarme falso (α) diminuiu com os respectivos aumentos de k e λ. Por outro lado, essa probabilidade aumentou de acordo com o aumento de ρ. Portanto, caso a variável resposta Y seja monitorada pelo gráfico de controle EWMA em um processo autocorrelacionado, torna-se necessário aumentar os valores de k e de λ, à medida que a autocorrelação aumentar de grau. Isso implica em alargar os limites de controle, em função da adoção de valores de k acima de três, para que as probabilidades dos alarmes falsos possam se situar em níveis baixos, como, por exemplo, para valores menores do que 0,01. Para conferir α igual ou inferior a 0,1, 0,05 ou 0,01, de acordo com a autocorrelação de 1a ordem, recomendaram-se diferentes combinações de k e λ. Para ρ ≤ 0,6, recomendou-se λ = 0,01 combinado com valores de k aproximadamente iguais a 2,5 (ρ = 0), 2,7 (ρ = 0,1), 3,0 (ρ = 0,2), 3,3 (ρ = 0,3), 3,7 (ρ = 0,4), 4,4 (ρ = 0,5) e 5,3 (ρ = 0,6). Nessas situações, o efeito do λ sobre a diminuição do α foi pequena. Portanto, poderia se trabalhar com quaisquer valores até a unidade, sem haver a necessidade de mudar muito a magnitude do k. Porém, apesar da diminuição do λ implicar no aumento do k para manter a mesma probabilidade do alarme falso, tal decisão de indicar λ = 0,01 ocorreu pelo fato de buscar um maior distanciamento do gráfico de controle de Shewhart, que é igual ao EWMA para λ = 1. No entanto, para 0,7 ≤ ρ ≤ 0,9, foi necessário aumentar também o valor de λ, juntamente com o de k, para que a probabilidade do alarme falso fosse baixa. Nestes casos, foram estabelecidas as seguintes recomendações aproximadas de λ, para k = 6: 0,5 (ρ = 0,7), 0,6 (ρ = 0,8) e 0,95 (ρ = 0,9). Tais conclusões vão de encontro às de Costa et al. (2004) que propuseram o alargamento dos limites de controle, dado que a autocorrelação propicia uma estimativa da variabilidade aleatória provocada pelo processo. Neste trabalho, o alargamento do limite de controle ocorreu devido à imposição de valores de k maiores do que três durante a construção do gráfico de controle EWMA.This work aimed to estimate the probability of false alarm caused by the control graph of the exponentially weighted moving average (EWMA) in an autocorrelated process along rational subgroups, using different combinations of the values of the following terms: number of standard deviations (2 ≤ k ≤ 6), weight of the rational subgroup (0.01 ≤ λ ≤ 1) and first order correlation (ρ). To study these values, data of a random variable Y were simulated, under normal distribution with average μ0 = 0 and standard deviation σ0 = 1 for a statistically-controlled process of up to 50 rational subgroups , with individual observations (n = 1). To obtain the values of Y along the 50 rational subgroups, 10 different situations were performed, according to the following first order autocorrelations (ρ = 0; 0.1; 0.2; 0.3; 0.4; 0.5; 0.6; 0.7; 0.8; 0.9). A total of 1.000 simulations were carried out for each situation. A probability of false alarm (α) decreased with the respective increase of k and λ. On the other hand, this probability increassed with the increase of ρ. Thus, in case the response variable Y is monitored by the EWMA control graph under an autocorrelated process, it is necessary to increase the values of k and λ, as the autocorrelation increases in degree. This requires widening the control limits by adopting values of k above three, so that the false alarm probabilities may be found at low levels, such as values lower than 0.01. To confirm α equal or lower than 0.1, 0.05, or 0.01, according to the first order autocorrealation, different combinations of k and λ are recommended. For ρ ≤ 0.6, λ = 0.01 was recommended , combined with values of k aproximately equal to 2.5 (ρ = 0), 2.7 (ρ = 0.1), 3.0 (ρ = 0.2), 3.3 (ρ = 0.3), 3.7 (ρ = 0.4), 4.4 (ρ = 0.5) and 5.3 (ρ = 0.6).Under these situations, the effect of λ on the decrese of α was small. Thus, one could use any value up to the unit, without the need to change the magnitude of k too much. However, despite the fact that the decrease of λ leads to the increase of k in order to maintain the same false alarm probability, such decision to indicate λ = 0.01 was taken to search for a greater distancing from the Shewhart control graph, which is equal to EWMA for λ = 1. On the other hand, for 0.7 ≤ ρ ≤ 0.9, it was also necessary to increase the values of λ, together with that of k, to obtain a low false alarm probability. In such cases,the following recommendations approximate of λ, were established for k = 6: 0.5 (ρ = 0.7), 0.6 (ρ = 0.8) and 0.95 (ρ = 0.9). Such conclusions agree with those by Costa et al. (2004), who proposed widening the control limits, since autocorrealation provides an estimate of the random variability caused by the process. In this work, widening the control limits occurred due to the imposition of k values higher than three during the design of the EWMA control graph

Studies on the influence of popular affirmations on Classical Geostatistics

O presente trabalho teve por objetivo estudar assuntos abordados na Geoestatística de modo a preencher lacunas metodológicas que surgem naturalmente em áreas recentes da ciência e/ou que surgem de afirmações populares. Para isso, foi necessário realizar estudos teórico-práticos afim de se obter mais evidências e comprovações. Foram utilizados em todos os estudos conjuntos de dados reais. No primeiro capítulo foi feito um estudo quanto à precisão entre malhas amostrais regulares (malha hexagonal, malha quadrangular e malha triangular). No segundo capítulo foi realizado um estudo sobre a questão do uso do teste de Normalidade em uma análise geoestatística. Nesse estudo foi mostrada toda fundamentação teórica do principal teste de normalidade, teste de Shapiro-Wilk, e estudos práticos para essa comprovação. No terceiro capítulo realizou- se um estudo sobre a assimetria e o comprometimento de uma análise geoestatística para dados com essa característica. Finalmente, no quarto capítulo foram comparados três interpoladores geoestatísticos (krigagem simples, krigagem universal e krigagem regressão) quanto à eficácia na representação de modelos digitais de profundidade (MDP).The present work had the objective of studying subjects covered in Geostatistics in order to fill methodological gaps that arise naturally in recent areas of science and / or that emerge from popular affirmations. For this, it was necessary to carry out theoretical-practical studies in order to obtain more evidences and proofs. Actual data sets were used in all studies. In the first chapter a study was made on the precision between regular sample meshes, among them, hexagonal mesh, quadrangular mesh and triangular mesh. In the second chapter a study was carried out on the question of using the Normality test in a geostatistical analysis. In this study, the theoretical basis of the main normality test, Shapiro-Wilk test, and practical studies for this verification were shown. Already in the third chapter was carried out a study the asymmetry and the commitment of a geostatistical analysis for data with this characteristic. Finally, in the fourth chapter three geostatistical interpolators (simple kriging, universal kriging and regression kriging) were compared for the effectiveness of the representation of digital depth models (MDP).Coordenação de Aperfeiçoamento de Pessoal de Nível Superio

IN BATHYMETRIC SURFACES: IDW OR KRIGING?

Abstract: The representation of the submerged relief is very importance in diverse areas of knowledge such as Projects to build or reassess port dimensions, installation of moles, ducts, marinas, bridges, tunnels, mineral prospecting, waterways, dredging, silting control of river and lakes, and others. The depths of the aquatic bodies, indispensable for the representation of those, are obtained through the bathymetric surveys. However, the result of a bathymetric sampling is a grid of points that, for itself, it is not capable of generating directly the Digital Model of Depth (DMD), being necessary the use of interpolators. Currently, there are more than 40 available scientific methods of interpolation, each one with its particularities and characteristics. This study has the objective to analise, comparing, the efficiency of Universal Kriging (UK) and of the Inverse Distance Weighted (IDW) in the computational representation of bathymetric surfaces, varying in a decreasing way the quantity of sample points. Through the results, we can be stated the superiority of the interpolator Universal Kriging in efficiency in creating DMD with basis in the bathymetric surveys data

Neotropical freshwater fisheries : A dataset of occurrence and abundance of freshwater fishes in the Neotropics

The Neotropical region hosts 4225 freshwater fish species, ranking first among the world's most diverse regions for freshwater fishes. Our NEOTROPICAL FRESHWATER FISHES data set is the first to produce a large-scale Neotropical freshwater fish inventory, covering the entire Neotropical region from Mexico and the Caribbean in the north to the southern limits in Argentina, Paraguay, Chile, and Uruguay. We compiled 185,787 distribution records, with unique georeferenced coordinates, for the 4225 species, represented by occurrence and abundance data. The number of species for the most numerous orders are as follows: Characiformes (1289), Siluriformes (1384), Cichliformes (354), Cyprinodontiformes (245), and Gymnotiformes (135). The most recorded species was the characid Astyanax fasciatus (4696 records). We registered 116,802 distribution records for native species, compared to 1802 distribution records for nonnative species. The main aim of the NEOTROPICAL FRESHWATER FISHES data set was to make these occurrence and abundance data accessible for international researchers to develop ecological and macroecological studies, from local to regional scales, with focal fish species, families, or orders. We anticipate that the NEOTROPICAL FRESHWATER FISHES data set will be valuable for studies on a wide range of ecological processes, such as trophic cascades, fishery pressure, the effects of habitat loss and fragmentation, and the impacts of species invasion and climate change. There are no copyright restrictions on the data, and please cite this data paper when using the data in publications