ABSTRACT This study aimed to identify whether there is an association between types of storage and categories of commercialization and use of grains, group the types of storage with the categories of commercialization, and group static and dynamic capacities of the units in the state of Paraná, Brazil. The data were obtained from the Brazilian Registry System of Storage Units for the 2014/2015 season. The association between variables under study was carried out with the chi-square test of independence and correspondence analysis. The cluster analysis consisted of the unweighted pair group method with arithmetic mean and considered a measure of mixed dissimilarity obtained for sets composed of qualitative and quantitative variables. A significant association was observed between the type of silo battery with the grain usage characteristic and cooperatives that commercialize the grain for use in the domestic market (CICOOPT); between the bulk warehouse and cooperatives that commercialize the grain in the foreign market (CIECOOPT); and between the silo and grain sellers who commercialize the grain in the domestic market (CI). Most types of storage units were grouped in Group 1, with a predominance of the CI characteristic and small to medium size static and dynamic capacity.

ABSTRACT Spatial variability description of soil chemical properties by thematic maps depends substantially on suitable geostatistical models. One of the parameters composing a geostatistical model is nugget effect. This study aimed to evaluate the simultaneous influence of nugget effect and sampling design on geostatistical model estimation and estimation of soil chemical properties at unsampled sites, considering simulated data. Our results will be used as scientific basis for spatial variability analyses of soil chemical properties in agricultural areas. Given the simulation results and agricultural data, we concluded that the high nugget effect values obtained here reduced spatial estimation efficiency. Moreover, a systematic sampling design promoted the least accurate estimates of geostatistical model and at non-sampled sites. Despite that, these nugget effect estimates should be kept in the analysis. However, further studies will be needed to investigate which factors are responsible for such high nugget effect values.

ABSTRACT In the study of spatial variability of soil attributes, it is essential to define a sampling plan with adequate sample size. This study aimed to evaluate, through simulated data, the influence of parameters of the geostatistical model and sampling configuration on the optimization process, and resize and reduce the sample size of a sampling configuration of a commercial area composed of 102 points. For this, an optimization process called genetic algorithm (GA) was used to optimize the efficiency of the geostatistical model estimation based on the Fisher information matrix. The simulated data evidenced that the variation of the nugget effect or practical range did not significantly alter the sample size. GA was efficient in reducing the sample size, determining for soil chemical attributes a sample size between 30 and 40 points (29.41 to 39.22% of the initial sampling grid). The presence of spatial dependence was observed for all soil chemical attributes in the two sampling configurations (initial and optimized). The optimized sampling configuration evidenced an increase in trend intensity in the north direction and a more efficient estimation of parameters of the linear spatial regression model.

ABSTRACT The goal of this study was to use the spatial bootstrap method to model the spatial dependence structure of soybean yield and soil chemical attributes in an agricultural area. The study involved developing confidence intervals in probability plots to determine the probability distributions assumed by the data; determine the empirical distributions of the semivariances and model parameters, allowing to obtain statistics and confidence intervals; and to construct maps for the variables. The quantile-quantile plots indicated that the data follows a normal distribution. The confidence intervals for the semivariances helped to model the spatial dependence structure, and the descriptive statistics of the bootstrap replicates of the model parameters allowed to test the consistency of the estimates. The soil chemical attributes (calcium, potassium, and organic matter) were at levels suitable for soybean cultivation. However, the pH was below the ideal range in most of the study area, and water stress during cultivation decreased the mean yield. Therefore, according to the results, a recommendation to the farmer is to correct the soil pH to increase the yield.

ABSTRACT This work aimed to study the spatial autocorrelation of the total static capacity storage, the total number of warehouses in 2013/2014 (CONAB) and the average of the total grain production (soybean, corn 1st and 2nd crops and wheat) in the harvest years 2008/2009 to 2013/2014 (SEAB) in Paraná State, Brazil. The study was based on Moran's global autocorrelation index, Moran's local and Moran's bivariate correlation. It was possible to identify regions with low and high total grain production. There was positive spatial autocorrelation for the Total Static Storage Capacity (TSSC) and Total Quantity of Warehouses (TQW). For the total grain production, significant spatial autocorrelation were found. The total static storage capacity showed similarity between the studied regions. When evaluating the bivariate spatial correlation between Total Production of Harvested Grains (TPHG) in relation to the total static storage capacity and total quantity of warehouses, the presence of positive spatial correlation was observed. The results indicated that Moran's global autocorrelation and local indexes showed significant patterns of spatial autocorrelation, as well as the bivariate spatial correlation indexes in the studied variables.

ABSTRACT Spatial variability depends on the sampling configuration and characteristics associated with the georeferenced phenomenon, such as geometric anisotropy. This study aimed to determine the influence of the sampling design on parameter estimation in an anisotropic geostatistical model and the spatial estimation of a georeferenced variable at unsampled locations. Datasets were simulated with geometric anisotropy, considering five values for the anisotropic ratio (1, 2, 3, 4, 5), and three sampling designs: lattice, random and lattice plus close pairs. The simulation results were used as a reference to select anisotropic models to describe the spatial dependence structure in chemical soil properties. For each dataset (with either simulated or chemical soil properties), the values of the georeferenced variables at unsampled locations were estimated by kriging, considering estimated isotropic and anisotropic geostatistical models. The choice of the sampling design influenced the spatial estimation of the georeferenced variable and the quality of the estimation of the geostatistical anisotropic model. The incorporation of geometric anisotropy in the spatial estimation of simulated data sets and soil chemical properties produced differences in the spatial estimation and improved the level of detail of subregions in thematic maps.

Abstract The uniformity of water application is an important factor in the evaluation of sprinkler irrigation systems. This uniformity depends on the type of sprinkler and its operating conditions, such as the arrangement and spacing between the sprinklers in the area; velocity and wind direction during the period of water application and the pressure variation of the irrigation system. The objective of this study was to model, analyze and compare the structure of spatial dependence, as well as the spatial variability of the water depths applied by a sprinkler irrigation system with compensating and non-compensating sprinklers, using geostatistical methods and measurements of accuracy or similarity between the applied water depth maps. The experiment was carried out in an agricultural area, in the city of Cascavel-Paraná-Brazil. A total area of 10 × 10 m was used, with 04 compensating and 04 non-compensating sprinklers installed at a height of 1.5 m. For each type of sprinkler, water levels were measured in 100 collectors spaced 1 × 1 m in the study area in 32 trials. On each test sprinkling was carried out for one hour. The conditions of wind, temperature and air humidity were evaluated at the beginning of each test and at 10-minute intervals with a climatological station. As the geostatistical analysis showed the existence of directional trends, the coordinates were incorporated as covariates to the linear spatial model in the study of the spatial dependence of the average depth of the irrigation water for the two types of sprinklers. The spatial dependence structure that best fits the data when using the compensating sprinklers was the Gaussian model and when the non-compensating sprinklers were used, it was the exponential model. The spatial variability maps of average irrigation water depth (mm) of the trials, obtained by universal kriging, revealed that for both sprinklers there was an increase in the mean level average values in the northwest-southeast direction (135° in the azimuth system) in the area under study, influenced by wind direction and velocity during the execution of the experiment.

ABSTRACT This study aims to quantify the uncertainties associated to the parameters of a Gaussian spatial linear model (GSLM) and the assumption of normality residuals in the modeling of the spatial dependence of the soybean yield as a function of soil chemical attributes. The spatial bootstrap methods were used to determine the point and interval estimators associated with the model parameters. Hypothesis tests were carried out on the significance of the model parameters and the quantile-quantile probability plot was elaborated to verify the data normality. The uncertainties associated to the parameters of the spatial dependence structure were quantified and the potassium content, phosphorus content and soil pH covariates were significant to explain the soybean yield mean. These covariates were used in the elaboration of a new model, which provided the elaboration of a contour map of soybean yield. Analysis of the quantile-quantile plot indicated that soybean yield data follow a normal probability distribution.

ABSTRACT: The t-Student distribution has been used to the spatial dependence modelling of soybean yield as an alternative to the normal distribution, being used for data with heavier tails or discrepant values. However, a usual Student t-distribution does not allow direct comparisons of geostatistical methods with a normal distribution. The aim of this study was to assess the soybean yield spatial variability through a reparameterized t-Student linear model, comparing the results with those of a Gaussian linear model. For parameter estimation, a complete maximum likelihood (CML) method was used through an expectation-maximization (EM) algorithm. The maps constructed with both reparameterized t-Student and normal distributions are dissimilar and present a kappa index (K) equivalent to 0.64. The reparameterized t-Student distribution is an alternative in studying data with discrepant values, showing the ability to decrease the influence of these points.

ABSTRACT The survey information from growing regions, the interaction with the vegetation index and climatic variables is of great importance in the search for soybean productivity increase. Paraná is the second largest soybean producer in Brazil and presents great spatial variability, both in periods of the crop cycle as in soil and climate. The objective of this study was to analyze the spatial correlation of soybean productivity, the enhanced vegetation index (EVI) and agrometeorological variables (water balance, global radiation and average temperature) in the state of Paraná, on a decendial scale, using the Moran global autocorrelation index between the 2010/2011 and 2012/2013 crop years. Similarity was found in the average productivities in 2010/2011 and 2012/2013. In 2011/2012 the state average was 2.38 t ha−1 lower in 10.19% compared to the national average, caused by the water deficit in flowering and grain filling phases. As a consequence, spatial autocorrelation indicated a higher similarity in productivity among municipalities with a Moran index of 0.735. The use of vegetation indices and agrometeorological variables allowed the identification of different sowing periods between regions and great climatic variability, influencing the soybean productivity.

RESUMO Na análise de dados espaciais em agricultura, a presença de pontos influentes pode alterar consideravelmente os resultados das análises de dependência espacial e, consequentemente, a construção dos mapas. Quando se referem a atributos físico-químicos do solo e da produtividade, os mapas devem representar uma estimativa eficiente das condições reais do campo, já que são importantes informações utilizadas para a manutenção de um sistema agrícola de manejo localizado, com a otimização da aplicação de insumos agrícolas, visando à maior produtividade. Este trabalho teve por objetivo apresentar as técnicas gráficas hair-plot, de influência local (Ci e |Lmax|) de identificação de observações influentes em dados contínuos espaciais georreferenciados, coletados em uma área experimental de cultivo comercial, com 167,35 hectares, onde o sistema agrícola de manejo localizado é adotado. Como resultados apresentam-se os pontos potencialmente influentes e os mapas construídos com e sem eles. Na comparação entre os mapas com e sem estes pontos, as métricas de comparação dos mapas mostraram a importância da identificação dos pontos influentes em uma base de dados espaciais. Sendo assim, a existência de pontos influentes deve ser investigada para entender o motivo de seu comportamento atípico, já que eles modificam, consideravelmente, os mapas gerados.

ABSTRACT Influencing points in agricultural spatial analysis may change considerably results on spatial dependence and hence map building. With regards to physico-chemical soil properties and crop yield, such maps should efficiently estimate current field conditions, being important for an agricultural site-specific management, optimizing thus input applications in order to increase yields. This study aimed to analyze hair-plot graphic techniques, with local influence (Ci and |Lmax|) to identify influencing points within a set of georeferenced spatial continuous data. These information were gathered from an experimental area with 167.35 hectares, wherein an agricultural site-specific management has been adopted. As a result, we obtained potentially influencing points and then outlined maps with and without the use of them. By comparing both maps, we could note by metric comparison that it is of major importance to identify those points on a spatial database. Thus, such investigations must be carried out to understand cases of unusual performance, since they considerably modify the generated maps.

RESUMO A agricultura de precisão proporciona aos agricultores identificar e tratar de forma adequada as variações encontradas na área agrícola. As zonas de manejo (ZMs) permitem a implantação da agricultura de precisão de forma viável e relativamente mais econômica. A forma mais importante para definir ZMs é usando o algoritmo fuzzy C-means. Um problema consiste em como selecionar a variável a ser usada como layer de entrada no processo fuzzy. Assim, o objetivo deste trabalho, foi testar a hipótese de que variáveis redundates podem prejudicar o processo de delineamento de ZMs. Este trabalho foi desenvolvido em uma área de 19,6 ha e 15 agrupamentos de ZMs foram gerados por meio do o algoritmo fuzzy C-means, dividindo-se em duas a cinco classes. Cada agrupamento usou uma composição diferente de variáveis, que são os atributos cobre, silte, argila, e altitude. Foi encontrado que algumas combinações dessas variáveis produziu melhores ZMs. Nenhuma combinação de variáveis produziu desempenho estatisticamente melhor que a ZM gerada apenas com as variáveis não redundantes. Assim, as variáveis redundantes podem ser descartadas. O agrupamento com todas as variáveis não forneceu maior separação e organização dos dados entre as classes de ZM, não sendo recomendado.

ABSTRACT Precision agriculture (PA) allows farmers to identify and address variations in an agriculture field. Management zones (MZs) make PA more feasible and economical. The most important method for defining MZs is a fuzzy C-means algorithm, but selecting the variable for use as the input layer in the fuzzy process is problematic. BAZZI et al. (2013) used Moran’s bivariate spatial autocorrelation statistic to identify variables that are spatially correlated with yield while employing spatial autocorrelation. BAZZI et al. (2013) proposed that all redundant variables be eliminated and that the remaining variables would be considered appropriate on the MZ generation process. Thus, the objective of this work, a study case, was to test the hypothesis that redundant variables can harm the MZ delineation process. BAZZI This work was conducted in a 19.6-ha commercial field, and 15 MZ designs were generated by a fuzzy C-means algorithm and divided into two to five classes. Each design used a different composition of variables, including copper, silt, clay, and altitude. Some combinations of these variables produced superior MZs. None of the variable combinations produced statistically better performance that the MZ generated with no redundant variables. Thus, the other redundant variables can be discredited. The design with all variables did not provide a greater separation and organization of data among MZ classes and was not recommended.

RESUMO O Estado do Paraná caracteriza-se por uma grande variabilidade de épocas de semeadura (DS) e, consequentemente, pelo desenvolvimento máximo vegetativo (DMDV), colheita (DC) e ciclo (CI) para a cultura da soja. O objetivo deste trabalho foi estimar essas datas para o período de primavera-verão do ano-safra de 2011/2012, por meio de séries temporais de imagens do Índice de Vegetação Realçado (do inglês Enhanced Vegetation Index - EVI) do sensor Modis (Moderate Resolution Imaging Spectroradiometer). Gerou-se um perfil espectrotemporal médio de EVI, considerando todos os pixels mapeados como soja dentro de cada município. Estes dados serviram de entrada no software Timesat para estimar os decêndios do ciclo da cultura (DS, DMDV, DC e CI) por municípios. Os resultados mostraram que existe grande variabilidade de datas de plantio em diferentes mesorregiões do Estado. Verificaram-se também divergências entre os resultados encontrados e os dados oficiais de DS e DC. A maior parte da semeadura (65,16%) esteve entre o terceiro decêndio de outubro e o primeiro decêndio de novembro. A maior parte da área de soja do Estado do Paraná (65,46%) teve seu DMDV em janeiro e colheita em março (53,92%).

ABSTRACT Soybean sowing can be performed at a various dates (DS) in Paraná state, with subsequent maximum vegetative development (DMDV), harvest (DC) and cycle (CI). The purpose of this study was to estimate these dates within spring-summer season from the 2011/ 2012 crop harvest, by means of temporal series of the Enhanced Vegetation Index (EVI) from Moderate Resolution Imaging Spectroradiometer (Modis) sensor. We generated an average EVI spectro-temporal profile considering all pixels mapped as soybean within each municipality. These data were used as input to the Timesat software for estimates of 10-day crop cycle periods (DS, DMDV, DC and CI). The results demonstrated great variability of dates at different areas of the Paraná state. We could also observe differences between our results and official estimates for DS and DC. Sowing was majorly (65.16%) performed in the third 10-day period of October and in the first 10-day period of November. Most of the Southern Paraná soybean area (65.46%) had their maximum vegetative development (MDV) in January and harvest in March (53.92%).

RESUMO Neste trabalho, teve-se o objetivo de estudar e comparar mapas temáticos da produtividade da soja para diferentes grades amostrais, utilizando métodos geoestatísticos (função semivariância e krigagem). A análise foi realizada com dados da produtividade de soja em t ha-1 numa área comercial com grades regulares e distâncias entre pontos de 25x25 m, 50x50 m, 75x75 m e 100x100 m, com 549; 188; 66 e 44 pontos amostrais, respectivamente, e dados obtidos pelo monitor de colheita. Também foram gerados esquemas amostrais otimizados, com o algoritmo chamado Têmpera Simulada, usando a maximização da medida de acurácia exatidão global, como critério de otimização. Foi verificado que fatores como o tamanho da amostra e a densidade amostral influenciaram na descrição da distribuição espacial da produtividade da soja feita por meio dos mapas temáticos. Quando se aumentou o tamanho amostral, houve aumento da eficiência dos mapas temáticos quanto à descrição da variabilidade espacial da produtividade da soja (maiores valores dos índices de acurácia e os menores valores para a soma quadrada do erro de estimação). Além disso, os mapas mais acurados foram obtidos considerando as configurações amostrais otimizadas com 188 e 549 pontos amostrais.

ABSTRACT This study aimed to compare thematic maps of soybean yield for different sampling grids, using geostatistical methods (semivariance function and kriging). The analysis was performed with soybean yield data in t ha-1 in a commercial area with regular grids with distances between points of 25x25 m, 50x50 m, 75x75 m, 100x100 m, with 549, 188, 66 and 44 sampling points respectively; and data obtained by yield monitors. Optimized sampling schemes were also generated with the algorithm called Simulated Annealing, using maximization of the overall accuracy measure as a criterion for optimization. The results showed that sample size and sample density influenced the description of the spatial distribution of soybean yield. When the sample size was increased, there was an increased efficiency of thematic maps used to describe the spatial variability of soybean yield (higher values of accuracy indices and lower values for the sum of squared estimation error). In addition, more accurate maps were obtained, especially considering the optimized sample configurations with 188 and 549 sample points.

RESUMO Este trabalho teve como objetivo comparar mapas temáticos construídos a partir de conjuntos de dados referentes à produtividade da soja, com diferentes grades amostrais regulares de 25x25 m; 50x50 m; 75x75 m e 100x100 m, utilizando técnicas de krigagem. No ajuste dos modelos teóricos a semivariâncias experimentais, utilizou-se para a estimação dos parâmetros o método de máxima verossimilhança. A comparação dos mapas temáticos foi realizada por meio dos índices de acurácia, obtidos a partir da matriz de erros. Foi verificado que fatores tais, como o tamanho amostral e a densidade amostral entre pontos, interferem na escolha do modelo teórico espacial, nas estimativas dos parâmetros e na construção dos mapas temáticos.

ABSTRACT The purpose of this paper was to compare thematic maps constructed from data sets related to soybean productivity with different regular sampling grids of 25x25 m, 50 x50 m, 75 x 75 m and 100x100 m, using kriging techniques. In the theoretical models fitted to the experimental semivariances, it was used the maximum likelihood method for parameter estimation. The comparison of thematic maps were made by accuracy indices, obtained from the error matrix. The results showed that factors such as sample size and sample density between points interfere in the choice of the theoretical spatial model, the parameter estimates and the construction of thematic maps.