Jack knifing for semivariogram validation

The semivariogram function fitting is the most important aspect of geostatistics and because of this the model chosen must be validated. Jack knifing may be one the most efficient ways for this validation purpose. The objective of this study was to show the use of the jack knifing technique to validate geostatistical hypothesis and semivariogram models. For that purpose, topographical heights data obtained from six distinct field scales and sampling densities were analyzed. Because the topographical data showed very strong trend for all fields as it was verified by the absence of a sill in the experimental semivariograms, the trend was removed with a trend surface fitted by minimum square deviation. Semivariogram models were fitted with different techniques and the results of the jack knifing with them were compared. The jack knifing parameters analyzed were the intercept, slope and correlation coefficient between measured and estimated values, and the mean and variance of the errors calculated by the difference between measured and estimated values, divided by the square root of the estimation variances. The ideal numbers of neighbors used in each estimation was also studied using the jack knifing procedure. The jack knifing results were useful in the judgment of the adequate models fitted independent of the scale and sampling densities. It was concluded that the manual fitted semivariogram models produced better jack knifing parameters because the user has the freedom to choose a better fit in distinct regions of the semivariogram

Small relief shape variations influence spatial variability of soil chemical attributes Pequenas variações das formas de relevo influenciam a variabilidade espacial de atributos químicos do solo

Soils with small variations in relief and under the same management system present differentiated spatial variabilities of their attributes. This variability is a function of soil position in the landscape, even if the relief has little expression. The aim of this work was to investigate the effects of relief shape and depth on spatial variability of soil chemical attributes in a Typic Hapludox cultivated with sugar cane at two landscape compartments. Soil samples were collected in the intercrossing points of a grid, in the traffic line, at 0-0.2 m and 0.6-0.8 m depths, comprising a set of 100 georeferenced points. The spatial variabilities of pH, P, K, Ca, Mg, cation exchange capacity and base saturation were quantified. Small relief shape variations lead to differentiated variability in soil chemical attributes as indicated by the dependence on pedoform found for chemical attributes at both 0-0.2 m and 0.6-0.8 m depths. Because of the higher variability, it is advisable to collect large number of samples in areas with concave and convex shapes. Combining relief shapes and geostatistics allows the determination of areas with different spatial variability for soil chemical attributes.<br>Solos submetidos ao mesmo sistema de manejo em locais com pequena variação de relevo, manifestam variabilidade espacial diferenciada de seus atributos. Esta variabilidade é condicionada pela posição dos solos na paisagem ou no declive, mesmo que o relevo seja de pequena expressão. O estudo teve como objetivo avaliar a influência da forma do relevo na variabilidade espacial de atributos químicos em um latossolo cultivado com cana-de-açúcar em dois compartimentos da paisagem. Os solos foram amostrados nos pontos de cruzamento de uma malha, com intervalos regulares de 10 m, perfazendo um total de 100 pontos, nas profundidades de 0-0,2 m e 0,6-0,8 m. Foi avaliado a variabilidade espacial do pH, fósforo (P), potássio (K), cálcio (Ca), magnésio (Mg), acidez potencial (H+Al), capacidade de troca catiônica (CTC) e saturação por bases (V%). Pequenas variações nas formas do relevo condicionaram variabilidade diferenciada para os atributos químicos do solo. Os atributos químicos estudados apresentaram-se dependentes da pedoforma em ambas profundidades estudadas. Um maior número de amostras devem ser coletados em áreas com forma de relevo côncavo e convexo devido à maior variabilidade. O uso conjunto das formas do relevo e geoestatística possibilita definir áreas com diferentes variabilidades espaciais para atributos químicos do solo

Spatial variability of soil acidity attributes and the spatialization of liming requirement for corn Variabilidade espacial de atributos de acidez do solo e espacialização da necessidade de calagem para o milho

In Brazil, technicians, in most cases, ignore the aspects related to the spatial variability of the soil acidity attributes when liming requirement is calculated. The objective of this study was to validate the liming practice, evaluating the presence of spatial variability of the soil acidity attributes and the existence of areas with differentiated liming requirement, which were calculated by different methods. The experiment was carried out in an area cultivated with corn under conventional management and irrigation. The soil (0-0.2 m) was sampled in a conventional way (composite soil sample) and in a systematic scheme, by use of a grid sampling. In sequence to the soil fertility attributes analysis, it was calculated the liming requirement, according to the methods of SMP pH, aluminum neutralization and elevation of soil Ca and Mg levels, and increase of the soil base saturation. After the descriptive analysis of the data set was accomplished, the semivariograms were calculated and the maps were obtained through the kriging technique. Absence of spatial dependence, as well as the non necessity of limestone application, was observed for the Al neutralization calculation method. Spatial dependence was only verified for the soil acidity attributes and to the liming requirement calculated by the base saturation and SMP pH methods; for these two methods, the semivariogram ranges obtained varied from 35.7 to 200.5 m. The results have highlighted the existence of differentiated liming requirement zones when the variability of the soil acidity attributes was considered in the calculation of the dose and type of limestone to be used for corn soil acidity correction.<br>No Brasil, a prática de calagem desconsidera, na maioria das vezes, os aspectos relacionados à variabilidade espacial dos atributos de acidez do solo. Objetivou-se, neste estudo, validar a prática da calagem, avaliando a presença de variabilidade espacial de atributos de acidez do solo e a existência de áreas com necessidades diferenciadas de corretivo, por meio de diferentes métodos de cálculo da necessidade de calagem. O experimento foi realizado em lavoura de milho sob manejo convencional. O solo foi amostrado de forma convencional (amostra composta) e sistemática (mediante uso de grade amostral), na profundidade de 0-0,2 m. Posteriormente à análise de fertilidade de rotina, determinaram-se as necessidades de calagem segundo os métodos do tampão SMP, da neutralização de alumínio e elevação do Ca e Mg, e da saturação por bases. Após análise descritiva, foram obtidos os semivariogramas e os mapas por krigagem. Ausência de dependência espacial, assim como da necessidade de aplicação do corretivo calcário foram observadas para o método da neutralização de Al. A dependência espacial foi encontrada para os atributos de acidez do solo e para as necessidades de calagem calculadas pelos métodos de saturação por bases e pH SMP, com alcances variando entre 35,7 e 200,5 m. Esses últimos mostraram também, uma coincidência regionalizada entre as maiores demandas de calcário. Os resultados permitiram evidenciar a existência de zonas de aplicação de calcário diferenciadas, quando consideradas a variabilidade dos atributos de acidez do solo no cálculo espacializado da dose e o tipo de corretivo calcário a ser utilizado