Abstract: The present research determines and monitors critical points through a multi-criteria analysis in the urban center of the city of Riobamba for its subsequent representation in thematic noise maps. For the selection of critical points, a pondering matrix was made considering the following factors: citizen perception surveys, urban bus routes, proximity to public and private institutions, parks and initial measurements. The monitoring was carried out at 25 prioritized points from 7:00 am to 7:00 pm; the values obtained correspond to the minimum Leq(A), the Leq(A), and the maximum Leq(A). The main results indicates that the main source of noise are the popular markets, on Mondays, Tuesdays and Wednesdays, with Leq(A) ranges above 70 dB(A). It is observed that at all points the Leq(A) values exceed the national permissible limit at some time during the day. The noise maps were made using the Kriging method, through the Gaussian semivariogram model, for all days, with the exception of Wednesday when the rational quadratic semivariogram model was used. For these models the RMSE and ASE values indicate high model quality.

Resumen: La presente investigación determina y monitorea puntos críticos, a través de un análisis multricriterio, en el centro urbano de la Ciudad de Riobamba, para la posterior representación dentro de mapas temáticos de ruido. Para la selección de puntos críticos se realizó una matriz de ponderación considerando los siguientes factores: encuestas de percepción ciudadana, rutas de los buses urbanos, cercanías a instituciones públicas y privadas, parques y mediciones iniciales. Los monitoreos fueron realizados en 25 puntos priorizados desde las 7H00 hasta las 19H00, los valores obtenidos corresponden al Leq(A) mínimo, al Leq(A), y al Leq(A) máximo. Los resultados principales indican que la fuente primordial de ruido son los mercados populares, los días lunes, martes, y miércoles, con de rangos de Leq(A) superiores a 70 dB(A). Se observa que en todos los puntos los valores de Leq(A) sobrepasan en algún momento del día el límite permisible nacional. Los mapas de ruido se realizaron mediante el método Kriging, a través el modelo del semivariograma gaussiano, para todos los días, a excepción del miércoles que se usó el modelo de semivariograma cuadrático racional. Para estos modelos los valores de RMSE e ASE indican una alta calidad de los modelos.

Summary: The use of digital soil mapping allows obtaining quantitative information on soil distribution and functioning to provide alternatives for their management. The objective of this research is to perform the spatial prediction of soil properties through regression-kriging and serve as a basis for taking the necessary measures for a sustainable use of the resource. The study area is located in the wetland Cienaga de Chapala portion of Michoacán, Mexico. Soil sampling was systematic. In the laboratory, electrical conductivity, organic carbon, soluble cations calcium, potassium, magnesium, sodium (Ca, K, Mg, Na), total nitrogen and pH were determined for each soil sample. The dependent variables were total nitrogen, electrical conductivity, organic carbon and pH. The independent variables are the Landsat 8 satellite bands. Regression-kriging was applied for spatial prediction. The experimental semivariogram fit with theoretical models was consistent for the four soil properties, because it was a systematic sampling design and the sample size was 297 points. The root mean square error of the electrical conductivity spatial prediction was 4 because it showed a coefficient of variation of 355. Soils are considered having from low to very low total nitrogen content (<0.15%). At least 30% of the soils have salinity problems because their electrical conductivity is greater than 1.1 dS m-1. Organic carbon contents are considered medium to high (>0.6%). The pH of the soils is moderately alkaline.

Resumen: El empleo de cartografía digital de suelos permite obtener información cuantitativa sobre la distribución y funcionamiento de los suelos, para proponer alternativas de manejo sobre dicho recurso. El objetivo de este trabajo fue realizar la predicción espacial de propiedades de suelo a través de regresión-kriging y que sirva de base para tomar las medidas necesarias de un uso sostenible del recurso. El área de estudio se encuentra en la ciénaga de Chapala porción Michoacán, México. El muestreo de suelo fue sistemático. En laboratorio se determinó, a cada muestra de suelo, la conductividad eléctrica, carbono orgánico, los cationes solubles (Ca, K, Mg, Na), nitrógeno total y pH. Las variables dependientes fueron nitrógeno total, conductividad eléctrica, carbono orgánico y pH. Las variables independientes las bandas del satélite Landsat 8. Se aplicó regressión-kriging para la predicción espacial. El ajuste de semivariograma experimental con modelos teóricos fue consistente para las cuatro propiedades de suelos, porque fue un diseño de muestreo sistemático y el tamaño de muestra de 297 puntos. El error cuadrático medio de la predicción espacial de conductividad eléctrica fue de 4, por presentar un coeficiente de variación de 355. Los suelos se consideraron con contenido de nitrógeno total de bajo a muy bajo (< 0.15%). Al menos 30% de los suelos presenta problemas de salinidad debido a que su conductividad eléctrica es mayor de 1.1 dS m-1. Los contenidos de carbono orgánico se consideran de medios a altos (> 0.6%). El pH de los suelos es medianamente alcalino.

Resumen: La antracnosis es una enfermedad fúngica presente en el cultivo de aguacate que ocasiona pérdidas económicas considerables para el sector productivo del Estado de México. Para focalizar las medidas de control, es necesario conocer el comportamiento espacial y la dinámica de la enfermedad en condiciones de campo. El objetivo del estudio fue determinar el comportamiento espacial de la antracnosis en aguacate Hass en Coatepec Harinas y Tenancingo, Estado de México utilizando estadística clásica y geoestadística. La estadística clásica no mostró el comportamiento real de la antracnosis debido a que se presentaron ajustes a la Binomial Negativa y distribución de Poisson. Con la geoestadística, se obtuvo la representación del comportamiento espacial de la enfermedad a través de mapas que muestran la presencia de centros de agregación; los semivariogramas para cada fecha de muestreo presentaron distribuciones ajustadas en su mayoría a modelos de tipo gaussiano y exponencial con rangos que fluctuaron entre los 12 y los 56 m, indicando asociación entre los datos; el mayor porcentaje de superficie infectada fue de 99% para el primer muestreo de abril, mientras para el primer muestreo de noviembre, el mayor porcentaje fue de 98% en ambos municipios. La geoestadística permite conocer con precisión cuales son los patrones de distribución que siguen las enfermedades como la antracnosis en las zonas aguacateras en el Estado de México y facilita la implementación de programas de manejo integrado con mayor efectividad, contribuyendo así a disminuir el uso excesivo de productos químicos, favoreciendo la obtención de frutos más inocuos.

Abstract: Anthracnose is a fungal disease present in the avocado crop that causes considerable economic losses for the productive sector of the State of Mexico. To target control measures, it is important to know the spatial behavior and the dynamics that the disease follows under field conditions. The application of geostatistical methods facilitates this work. For this reason, the objective of this study was to determine the spatial behavior of anthracnose in the Hass avocado crop in Coatepec Harinas and Tenancingo, two producing municipalities in the State of Mexico using classical and geostatistical statistics. The results obtained through classical statistics did not show the real behavior of anthracnose because, in both municipalities, there were adjustments to a Negative Binomial representation as well as to a Poisson distribution. With the use of geostatistics, it was possible to obtain the representation of the spatial behavior of the disease through maps, which show the presence of aggregation centers; the semivariograms for each sampling date presented distributions adjusted mostly to Gaussian and exponential models with ranges that fluctuated between 12 and 56 m, indicating association between the data; likewise, the highest percentage of infected area was 99% for the first sampling in April, while for the first sampling in November, the highest percentage was 98% in both municipalities. Geostatistics makes it possible to know precisely what are the distribution patterns followed by diseases such as anthracnose in avocado-growing areas in the State of Mexico and facilitates the implementation of integrated management programs more effectively, thus contributing to reducing the excessive use of products chemicals, favoring the obtaining of more innocuous fruits.

Resumen: La fertilidad del suelo es la capacidad más importante en la nutrición de las plantas y su variabilidad espacial puede determinarse mediante técnicas geoestadísticas que permiten mapear y delimitar áreas de manejo. Una de las ventajas importantes de los sistemas de información geográf ica (SIG) es el análisis espacial, en particular el uso de las interpolaciones de diferentes variables físicas químicas del suelo. El objetivo del trabajo fue analizar la fertilidad del suelo en la comunidad de Santo Domingo, Huasca de Ocampo, Hidalgo; utilizando mapas temáticos creados por el método de interpolación Kriging ordinario y validados con las técnicas de validación en campo y cruzada para las variables de fertilidad del suelo: contenido de nutrientes N, P, K, Ca, Mg y Na, y las propiedades pH, CE, MO y CIC. La información estadística para las variables demostró ser uniforme y fácilmente predecible; a excepción del pH y MO donde se observa poca representatividad de la media asociadas a una variabilidad intrazonal. El modelo seleccionado para el ajuste del semivariograma experimental, que mejor ajustó al de las variables estudiadas, fue el modelo Gaussiano; a excepción de la variable CE la cual se ajustó al modelo esférico. Los resultados muestran suelos con pH<6.0, que indica suelos ácidos, por lo tanto, los nutrientes Ca, P y Mg están menos disponibles para la planta. Asimismo, los nutrientes primarios como el N, P y K se encuentran en cantidades def icientes. Se concluye que los mapas obtenidos en este estudio, a partir, del modelo Kriging ordinario y los dos tipos de validación utilizados, es una herramienta útil como aproximación y referencia para determinar en buena medida la distribución espacial y variabilidad de las propiedades de fertilidad de los suelos. Los valores de MO, N, K, P y pH def inieron principalmente el estado actual de la fertilidad de los suelos y evidencian su degradación.

Summary: Soil fertility is one of the most important elements in crop nutrition and its spatial variation can be determined through geostatistical techniques that allow mapping and delimiting management areas. One of the important advantages of geographic information systems (GIS) is spatial analysis, particularly the use of interpolations of dif ferent soil physicochemical variables. Thus, the objective of this research is to analyze soil fertility in the community of Santo Domingo, Huasca de Ocampo, Hidalgo, using thematic maps created by the ordinary Kriging interpolation method and validated with f ield and cross validation techniques for the soil fertility variables: nutrient content N, P, K, Ca, Mg and Na, and the properties pH, EC, MO and CIC. The statistical information for the variables proved to be uniform and easily predictable with the exception of pH and OM where little representativeness of the mean was observed associated with intrazonal variability. The model selected for the adjustment of the experimental semi-variogram, which best adjusted the variables studied, was the Gaussian model, except for the EC variable that was adjusted to the spherical model. The results show soils with low pH, which indicates acid soils, therefore, Ca, P and Mg nutrients are less available to the plant. Likewise, primary nutrients, such as N, P and K are found in def icient amounts. In conclusion, the maps obtained in this study from the ordinary Kriging model and the two types of validation used can be a useful tool as an approximation and reference to determine to a good extent the spatial distribution and variability of soil fertility properties. The values of MO, N, K, P and pH mainly def ined the current state of soil fertility and evidence its degradation.

Resumen La caña de azúcar (Saccharum spp. híbridos) es el cultivo agroindustrial más importante de regiones tropicales. Recientemente, en sus hojas se han observado estrías cloróticas asociadas con la bacteria Herbaspirillum rubrisubalbicans que afecta la capacidad fotosin tética de la planta y su rendimiento. El comportamiento espacio temporal es un elemento importante para el manejo integral de las enfermedades. Con el objetivo de determinar la distribución espacial del moteado clorótico en caña de azúcar en el sureste de México, se georreferenciaron 80 puntos en forma aleatoria en 2016 y 2017, para determinar la inci dencia de la enfermedad. Se generó un semivariograma experimental ajustado a un modelo teórico preestablecido y se estimó el Kriging. La incidencia de la enfermedad fue de 2,93% (2016) y 5,36% (2017) en las variedades ICP-MEX-92-1420, CP-72-2086, ITV-92-373, MEX-79434 y MEX-69-290. El comportamiento espacial se ajustó al modelo Penta-esférico en 2016 y Esférico en 2017. La interpolación espacial se validó con valores cercanos a cero de la Media del Error (ME), Raíz del Error Cuadrático Medio (RMSE) y Media Estandarizada del Error de predicción (MSPE), visualizándose en el mapa obtenido. Los resultados permitirán direccionar el manejo integral del moteado clorótico en caña de azúcar en la zona afectada.

Abstract Sugar cane (Saccharum spp. hybrids) is the most important agroindustrial crop of the tropics. Recently, sugar cane plants with chlorotic leaf streaking associated with the bacterium Herbaspirillum rubrisubalbicans have been observed. This disease impacts photosynthetic capacity and yield. Characterizing the spatio-temporal behavior of chlorotic mottling using prediction maps is an important element of integrated disease management. Here, we determine the spatial distribution of mottled stripe disease in sugar cane in southeastern Mexico. To do this, we randomly chose and georeferenced 80 points in commercial plots in 2016 and 2017 to determine the disease incidence. We generated an experimental semivariogram based on a predetermined theoretical model and estimated Kriging. The incidence was 2.93% in 2016 and 5.36% in 2017 in varieties ICP-MEX-92-1420, CP-72-2086, ITV-92-373, MEX-79434 and MEX-69-290. The spatial behavior of the bacteria fit the pentaspherical model in 2016 and the spherical model in 2017. Spatial interpolation was validated by Mean Error (ME), Root Mean Square Error (RMSE) and Mean Standardized Prediction Error (MSPE) values near zero, visualized using the generated map. The results will be used to guide management of mottled stripe disease in sugar cane in the affected area.

RESUMO Na agricultura de precisão a determinação de zonas de manejo dos atributos de solo e planta, é um processo complexo que demanda o conhecimento de muitas variáveis, o que dificulta o processo de gestão e tomada de decisão. Este estudo avaliou a variabilidade espacial da produtividade da cultura da soja e de atributos químicos do solo por meio de análise multivariada e geoestatística para a determinação de zonas de manejo específico em um Latossolo. A produtividade de soja e os atributos químicos do solo nas camadas 0-0.2 e 0.2-0.4 m de profundidade foram amostrados em 70 pontos de amostragem. Análises geoestatísticas e multivariadas foram então realizadas. As propriedades químicas do solo apresentaram maior variabilidade na profundidade de 0,2 a 0,4 m. Os parâmetros do semivariograma dos dados da análise de componentes principais (PCA) (PCA 1, PCA 2 e PCA 3) para ambas as profundidades foram mais homogêneos do que os dados originais. Os mapas de propriedades químicas do solo apresentaram alta similaridade com o mapa de produtividade da soja. A ACP explicou 65,34% (0 a 0,2 m) e 70,50% (0,2 a 0,4 m) da variabilidade dos dados, agrupando a produtividade da soja, matéria orgânica, pH, fósforo, potássio, cálcio, magnésio e sódio. A espacialização do PCA permitiu a definição das zonas de manejo indicadas pelo PCA 1, PCA 2 e PCA 3 para ambas as profundidades. O resultado indica que a área deve ser manejada utilizando diferentes estratégias de manejo da fertilidade do solo para aumentar a produtividade da soja.

ABSTRACT In precision agriculture, determining management zones for soil and plant attributes is a complex process that requires knowledge of several variables, which complicates management and decisionmaking processes. This study evaluated the spatial variability of soybean yield and soil chemical properties using geostatistical and multivariate analyses to define management zones in an Oxisol. The soybean yield and soil chemical properties between 0 to 0.2 and 0.2 to 0.4 m soil depths were sampled at 70 points. Geostatistical and multivariate analyses were then performed on these data. The soil chemical properties showed higher variability at 0.2 to 0.4 m soil depth. The semivariogram parameters of the principal component analysis (PCA) data (PCA 1, PCA 2, and PCA 3) for both depths were more homogeneous than the original data. The maps of soil chemical properties showed high similarity to the soybean yield map. The PCA explained 65.34% (0 to 0.2 m) and 70.50% (0.2 to 0.4 m) of data variability, grouping the soybean yield, organic matter, pH, phosphorous, potassium, calcium, magnesium, and sodium. PCA spatialization allowed for the definition of management zones indicated by PCA 1, PCA 2, and PCA 3 for both depths. The result indicates that the area must be managed using different strategies of soil fertility management to increase soybean yield.

RESUMEN El desarrollo agrícola exige una mayor adopción de maquinaria por parte de los productores para evitar el daño a la salud de los trabajadores por el exceso de ruido. En este escenario, este estudio presenta análisis utilizando geoestadística y Control Estadístico de Procesos (SPC) en el mapeo de la variabilidad espacial de la magnitud del ruido emitido por un microtractor para identificar zonas saludables para los trabajadores. El estudio se llevó a cabo en la Universidad Federal de Lavras (UFLA), donde los niveles de ruido se recolectaron en puntos distribuidos en una cuadrícula de muestra regular de 2,0×2,0 m alrededor de la máquina. La dependencia espacial del ruido se analizó ajustando el semivariograma de tipo onda e interpolando por kriging ordinario y el SPC a través de cartas de control individuales. Fue posible observar valores de ruido superiores a 85 dB(A) en un radio de hasta 6 m alrededor del tractor en funcionamiento. El valor máximo de 91 dB(A) se obtuvo desde el asiento del operador, permitiendo así una exposición diaria máxima de 3,5 h. Además, se observó que las personas ubicadas a distancias mayores a 4 m del microtractor no necesitan usar equipo de protección personal para una exposición de 8 h de trabajo.

ABSTRACT Agricultural development requires greater adoption of machinery by producers to avoid damage to the worker's health due to excessive noise. In this scenario, this study aimed to analyze the noise magnitude emitted by a micro-tractor using geostatistics and Statistical Process Control (SPC) in mapping spatial variability to identify healthy zones for workers. The study was carried out at the Federal University of Lavras (UFLA), where noise levels were collected at points distributed in a regular 2.0×2.0 m sample grid around the machine. The spatial dependence of noise was analyzed by adjusting the wave-type semivariogram and interpolating by ordinary kriging and the SPC through individual control charts. It was possible to observe alarming noise values above 85 dB(A) in a radius of up to 6 m around the tractor in operation. The maximum value of 91 dB(A) was obtained from the operator's seat, thus allowing maximum daily exposure of 3.5 h. In addition, it was observed that people located at distances greater than 4 m from the micro-tractor do not need to wear personal protective equipment for an exposure of 8 h of work.

Resumo Compreender as variações espaciais de variáveis dendrométricas em inventário florestal contínuo é imprescindível para subsidiar ações de manejo, além de permitir intensidades amostrais que reflitam em acurácia com menor custo do inventário. Nesse contexto, o objetivo deste trabalho foi avaliar a estrutura de dependência espacial de variáveis dendrométricas ao longo do tempo e em diferentes intensidades amostrais em povoamento de eucalipto. As hipóteses testadas foram que a estrutura de dependência espacial de variáveis dendrométricas se altera com o crescimento em povoamentos de eucalipto e que a intensidade amostral influencia nesta estrutura. As variáveis diâmetro a 1,30 m do solo, área basal, altura total, altura média das árvores dominantes e volume de madeira foram obtidas em inventário florestal contínuo, aos 3,5, 4,5 e 5,5 anos, em 80 unidades amostrais permanentes (400 m²), distribuídas aleatoriamente em um povoamento de eucalipto (394 ha), localizado em Abaeté, Minas Gerais. Foram avaliadas as intensidades de uma unidade amostral a cada 4,9 (n = 80), 7,3 (n = 54) e 16,4 (n = 24) hectares. Considerou-se a maior intensidade amostral como referência para as demais. Os modelos de semivariância esférico, exponencial e gaussiano foram ajustados ao semivariograma experimental, em que o modelo de melhor ajuste foi utilizado pela krigagem ordinária na espacialização das variáveis analisadas. Os resultados demonstraram predominância de forte dependência espacial das variáveis dendrométricas, independentemente da idade e intensidade amostral, sobretudo para altura média das árvores dominantes e volume de madeira. A menor intensidade amostral influenciou negativamente na dependência espacial da área basal, em todas as idades. A estrutura de dependência espacial não é influenciada pelo aumento da idade do povoamento, sendo recomendada a análise geoestatística destas variáveis em inventário florestal contínuo, considerando a intensidade amostral de uma unidade amostral a cada 16,4 hectares.

Abstract Understanding the spatial variations of dendrometric variables in a continuous forest inventory is essential to support management actions, in addition to allowing sample intensities that reflect accuracy with lower inventory cost. The objective of this study was to evaluate the spatial dependence structure of dendrometric variables over time and in different sample intensities in eucalyptus stands. The hypotheses considered were that the spatial dependence structure of dendrometric variables changes along the growth in eucalyptus stands and the sample intensity influences this structure. The variables diameter at 1.30 m of soil, basal area, total height, mean height of dominant trees and volume of wood were obtained in continuous forest inventory, at 3.5, 4.5 and 5.5 years, from 80 plots (400 m²) distributed randomly in the stand (394 ha) located in Abaeté, Minas Gerais state. Were evaluated the sample intensities of one plot every 4.9 (n = 80), 7.3 (n = 54), and 16.4 (n = 24) hectares. The highest sample intensity was reference for the others. The spherical, exponential and gaussian semivariance models were adjusted to the experimental semivariogram, where the best fit model was used by ordinary kriging in the spatialization of the analyzed variables. The results showed a predominance of strong spatial dependence of dendrometric variables, regardless of age and sample intensity, especially for mean height of dominant trees and volume of wood. The lower sample intensity influenced negatively the spatial dependence of the basal area at all ages. The structure of spatial dependence is not influenced by the increase in the age of the stand, and the geostatistical analysis of these variables is recommended in a continuous forest inventory, considering the sample intensity of one plot of each 16.4 hectares.

Abstract In this work it was analyzed the spatial variability of soil available phosphorus, as premise of sustainable management in a sugarcane agrosystem. The study it was carried out in the year 2015, among the coordinates 22º 25' 42" N to 22º 29' 39" N and 80º 57' 22" W to 80º 52' 43" W, on a Ferralsol soil, in Matanzas, Cuba. The soil sampling it was adjusted for smaller o equal to five hectares, for 671 soil samples collected in 4086, 23 hectares. The exponential model fitted to the experimental semivariogram, found a range of 235 meters for this element. Specific sites associated with categories of the studied element were defined, which did not match with structures for fertilizer management in sugarcane agrosystem, which demonstrated the need of variable doses of phosphoric fertilizer within sugarcane fields, to contribute to the sustainability of this agrosystem.

RESUMEN En este trabajo se analizó la variabilidad espacial del fósforo asimilable del suelo, como premisa del manejo sostenible en un agrosistema azucarero. El estudio se realizó en el año 2015, entre las coordenadas 22º 25' 42" N a 22º 29' 39" N y 80º 57' 22" O a 80º 52' 43" O de suelo Ferralsol, en Matanzas, Cuba. El muestreo de suelo se ajustó a áreas menores o iguales a cinco hectáreas, para un total de 671 muestras colectadas en 4086,23 hectáreas. El modelo exponencial ajustado al semivariograma experimental, arrojó un rango de 235 metros para este elemento. Se definieron sitios específicos asociados a categorías del elemento estudiado, que no coinciden con las estructuras para el manejo de fertilizantes en el agrosistema azucarero, lo que demostró la necesidad de dosis variables del fertilizante fosfórico dentro de los campos de caña de azúcar, para contribuir a la sostenibilidad de este agrosistema.

En la actualidad la necesidad de obtener un predio urbano para construir una unidad habitacional es imperante. El propósito fue determinar el modelo geoestadístico óptimo para la tasación del precio de lotes urbanos en la ciudad de Puno. La metodología aplicada analizó 145 predios en venta los que se dividieron en cuatro zonas urbanas ubicadas por su rumbo, además se usó análisis estructural de datos para las variables área y precio. Los resultados mostraron el área fue de 90,66 ± 10,63 m², con respecto a los precios prediales la media fue de 107367,03 ± 18772,30 nuevos soles, la coherencia gráfica del semivariograma para la variable precio es el hole effect con un nivel de confianza de 97,52%.

At present, the need to obtain an urban property to build a housing unit is prevalent. The purpose was to determine the optimal geostatistical model for the valuation of the price of urban lots in the city of Puno. The methodology applied analyzed 145 properties for sale which were divided into four urban zones located by their direction, also used structural data analysis for the variables area and price. The results showed that the area was 90.66 ± 10.63 m², with respect to property prices the average was 107367.03 ± 18772.30 nuevos soles, the graphic coherence of the semi variogram for the price variable is the hole effect with a confidence level of 97.52%.

Resumen Los modelos digitales de elevación mejoran la precisión en el análisis del terreno. Este trabajo tuvo como objetivo comparar diferentes métodos de interpolación utilizando criterios estadísticos en un levantamiento topográfico de 339 puntos levantados con estación total en la zona de San Juan de Lagunillas (Venezuela). Se documentó la existencia de un proceso de tendencia significativa con autocorrelación espacial modelada mediante un semivariograma gaussiano isotrópico. Los kriging consiguieron residuales menores a un error mínimo tolerable igual 0.1 m. El kriging residual fue el mejor evaluado en la validación cruzada con exclusión (error medio absoluto de 0.71 m). El kriging disyuntivo tuvo menor media del error pero un amplio rango del error y el mayor error medio absoluto (12.8 m). Los otros kriging tienen medias de la varianza del error superiores a 1.3 m y errores mínimos absolutos superiores a 0.85 m. Debido a la alta dependencia en la forma de especificación de los modelos se recomiendan las ayudas gráficas para un mejor ajuste.

Abstract Digital Elevation Models improve accuracy in terrain analysis. This work compared different interpolation methods using statistical criteria in a topographic survey of 339 points raised with a total station in the “San Juan de Lagunillas” area (Venezuela). The existence of a signiftablaicant trend process with spatial autocorrelation modeled by an isotropic Gaussian semivariogram was documented. The kriging allowed to obtain residuals less than a minimum tolerable error equal to 0.1 m. The residual kriging was the best evaluated in cross validation with exclusion (absolute mean error of 0.71 m). The disjunctive kriging showed a lower error average but a wider error range and the highest mean absolute error (12.8 m). The other kriging showed mean error variance greater than 1.3 m and absolute minimum errors greater than 0.85 m. Due to the high dependence on the model specification form, graphics are recommended for a better fit.

Resumo O desempenho espacial das variáveis ambientais envolvidas na produção de rosas é um dos fatores de maior interesse atual no setor ornamental colombiano. O objetivo deste trabalho foi a avaliação de uma estufa passiva através de uma abordagem experimental que incluiu a captura e registro de dados através de uma rede de 40 sensores uniformemente distribuídos dentro da estufa. O processamento de dados foi feito através da aplicação de técnicas geoestatísticas que permitiram a obtenção de gráficos de contorno para 5 níveis de intensidade de radiação. Os resultados da análise exploratória mostraram que o desempenho da temperatura, umidade relativa e déficit de pressão de vapor não são os mais adequados para a produção de rosas, principalmente para as condições do período noturno em que a temperatura apresentou valores abaixo de 12,5 °C, a umidade relativa estava acima de 90% e o déficit de pressão de vapor estava abaixo de 0,1 kPa. Por outro lado, na análise estrutural, o modelo circular do semivariograma teórico foi o que apresentou o melhor grau de ajuste em relação aos dados experimentais, encontrando que existe uma forte dependência espacial para as variáveis estudadas. A previsão dos pontos não amostrados foi feita através do método de kriging ordinário, encontrando que existem gradientes horizontais de temperatura e umidade relativa dentro da estufa que aumentam de magnitude de acordo com o nível de radiação, atingindo valores de 6.1 °C e 30.4%.

Abstract The spatial behavior of the environmental variables involved in rose production is one of the factors of greatest current interest in the Colombian ornamental sector. The aim of this work consisted in the evaluation of a passive greenhouse through an experimental approach that included the capture and recording of data through a grid of 40 sensors homogeneously distributed inside the greenhouse. The data processing was carried out through the application of geostatistical techniques that allowed to obtain contour plots for 5 levels of radiation intensity. The results of the exploratory analysis showed that the behavior of temperature, relative humidity and vapour pressure deficit are not the most suitable for rose production, mainly for the conditions of the night period where the temperature exhibited values below 12.5 °C, the relative humidity was above 90% and the vapour pressure deficit was below 0.1 kPa. On the other hand in the structural analysis the circular model of theoretical semivariogram was the one that better degree of adjustment presented in comparison with the experimental data finding that a strong spatial dependency exists for the studied variables, the prediction of the not sampled points was made by means of the method of ordinary kriging finding that horizontal gradients of temperature and relative humidity exist inside the greenhouse that increases in magnitude according to the level of radiation arriving to reach values of 6.1 °C and 30.4%.

Resumo Este trabalho teve como objetivo selecionar modelos de semivariograma para estimar tendências de precipitação mensal no Estado da Paraíba-Brasil usando krigagem comum. A metodologia envolve a aplicação de interpolação geoestatística de registros de precipitação de 51 anos de 69 estações de chuva em todo o estado. A análise de semivariogramas mostrou que meses específicos apresentaram forte dependência espacial (Índice de Dependência Espacial - IDE <25%). As tendências foram submetidas aos seguintes modelos: circular, esférico, pentassesférico, exponencial, gaussiano, quadrático racional, K - Bessel e tetrasspherical. Os melhores modelos de ajuste foram selecionados por validação cruzada e Índice de Comparação de Erros (ICE). Cada conjunto de dados (mês) possuía uma estrutura de dependência espacial específica, o que tornava necessário definir modelos específicos de semivariograma, a fim de aprimorar o ajuste do semivariograma experimental. Além disso, o mapa mensal de tendências foi plotado para justificar os modelos escolhidos.

Abstract This work aimed to select semivariogram models to estimate trends in monthly precipitation in Paraiba State-Brazil using ordinary kriging. The methodology involves the application of geostatistical interpolation of precipitation records of 51 years from 69 rainfall stations across the state. Analysis of semivariograms showed that specific months had a strong spatial dependence (Index of Spatial Dependence - IDE < 25%). The trends were subjected to the following models: circular, spherical, pentaspherical, exponential, Gaussian, rational quadratic, K-Bessel and tetraspherical. The best fit models were selected by cross-validation and Error Comparison Index (ECI). Each data set (month) had a particular spatial dependence structure, which made it necessary to define specific models of semivariogram in order to enhance the adjustment of the experimental semivariogram. Besides, the monthly trend map was plotted to justify the chosen models.

Resumen Este documento propone una carta de control CUSUM multivariada espacial para monitorear la media de una sola característica de un producto o proceso, cuando las mediciones se toman en diferentes ubicaciones en cada elemento muestreado. Para estimar la matriz de varianza y covarianza, se utilizan algunas herramientas de la geoestadística, teniendo en cuenta la correlación espacial entre las mediciones. El desempeño de esta carta de control se explora por simulación y su uso se ilustra con un ejemplo.

Abstract This paper proposes a spatial multivariate CUSUM control chart in order to monitor the mean of a single characteristic of a product or process, when the measurements are taken in different locations on each sampled item. To estimate the variance and covariance matrix some tools from the geostatistics are used, taking into account the spatial correlation between the measurements. The performance of this control chart is explored by simulation and its use is illustrated with an example.

Resumo Este estudo teve como objetivo mapear chuvas intensas com durações de 10, 30, 720 e 1440 minutos, associadas aos tempos de retorno de 10, 50 e 100 anos, para o Estado do Tocantins. Foram aplicadas séries históricas de 95 postos pluviométricos localizados no Estado do Tocantins e proximidades, com período padronizado de 1983 a 2013. Foi conduzido um estudo geoestatístico, avaliando-se os modelos de semivariograma esférico, exponencial e gaussiano, ajustados pelo método dos mínimos quadrados ponderados. A partir deste estudo, o modelo que apresentou o menor erro médio com base na validação cruzada foi aplicado ao processo de mapeamento por krigagem ordinária. Houve bom desempenho das técnicas geoestatísticas, podendo-se destacar o modelo esférico para o mapeamento da precipitação máxima diária anual, e o modelo gaussiano para as chuvas calculadas pela metodologia de desagregação. Verificou-se ainda que as áreas de ocorrência das chuvas intensas de maior severidade no estado estão no Bico do Papagaio (norte), Ilha do Bananal (sudoeste) e noroeste do estado.

Abstract This study aimed to map heavy rainfall with durations of 10, 30, 720 and 1440 minutes, associated with return times of 10, 50 and 100 years for the Tocantins State. Historical series of 95 pluviometric stations located in the Tocantins State and nearby were applied, with standard period from 1983 to 2013. A geostatistical study was conducted, evaluating the spherical, exponential and gaussian semivariogram models, adjusted by the weighted least squares method. From this study, the model that presented the smallest average error based on cross-validation was applied to the mapping process by ordinary kriging. There was good performance of the geostatistical techniques, being possible to highlight the spherical model for the mapping of the annual maximum daily precipitation and the Gaussian model for the rains calculated by the methodology of disaggregation. It was also verified that the areas of intense rainfall of greater severity in the state are in the Bico do Papagaio (north), Bananal Island (southwest) and northwest of the state.