José Ruy Porto de Carvalho

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.

Detrending non stationary data for geostatistical applications

The use of geostatistics requires at least that the intrinsic hypothesis be satisfied. The presence of a trend in the data invalidates this hypothesis. One of the ways of solving this problem is by subtracting a function fitted to the original data and working with the residuals. This technique also represents a change to a smaller scale of the variability and surface roughness. This paper describes the detrending technique of subtracting a trend surface fitted by the least squares method and discusses the results using topographical data as examples. The objective is to show how the detrending technique works for different scales and degrees of trend and how to interpret the results. It is shown that the simplest the surfaces fitted that does the work of removing the trend the best are the results obtained. The use of jack knifing is proved useful to validate the resulting semivariograms. For most of the applications and depending upon the scale, a linear or a parabolic surface works reasonably well. The back transformation of the data afterwards is very easily done by adding back the subtracted trend surface.

Interpoladores geoestatísticos na análise da distribuição espacial da precipitação anual e de sua relação com altitude

O objetivo deste trabalho foi quantificar a contribuicao da variavel auxiliar altitude, na estimativa da distribuicao espacial da precipitacao anual media no Estado de Sao Paulo. A estatistica quadrado medio do erro (QME) foi usada em dois conjuntos de observacoes de precipitacao anual media (1957 a 1997): o completo, com 1.027 observacoes, e o reduzido, com 445. Bolsoes de precipitacao foram perfeitamente definidos nos mapas de variabilidade espacial que utilizaram o conjunto completo de dados, e indicaram a existencia de possiveis microclimas. O interpolador geoestatistico de krigagem ordinaria apresentou desempenho 82 vezes mais preciso que o interpolador do inverso do quadrado da distância, quando o QME foi usado como criterio de comparacao para o conjunto de dados completo. Para o conjunto reduzido, essa magnitude foi de duas vezes. Os erros de estimacao obtidos por krigagem ordinaria foram menores no conjunto completo, enquanto os obtidos por cokrigagem ordinaria foram menores no reduzido. Isso indica que esses interpoladores devem ser usados para determinacao da distribuicao espacial da precipitacao anual media. O uso da altitude como variavel auxiliar beneficia o interpolador de cokrigagem ordinaria e define microrregioes mais uniformes quanto a distribuicao espacial da precipitacao anual media.

Assessment of heavy metals in soils of a vineyard region with the use of principal component analysis

O manejo agricola com agroquimicos pode levar a contaminacao dos solos por metais pesados. O objetivo deste trabalho foi aplicar a Analise dos Componentes Principais e tecnicas de geoprocessamento para identificar a origem dos metais pesados Cu, Fe, Mn, Zn, Ni, Pb, Cr e Cd como contaminantes potenciais em solos agricolas. O estudo foi desenvolvido em uma area cultivada com vinhedos no Estado de Sao Paulo, Brazil. Amostras de solos foram coletadas e georeferenciadas por GPS sob diferentes usos e coberturas. As concentracoes dos metais nos solos foram obtidas pelo metodo de extracao com DTPA. As concentracoes de Cu e Zn foram consideradas altas na maioria das amostras pesquisadas, sendo maiores nas areas cultivadas com vinhedos sob aplicacoes de fungicidas por decadas. As concentracoes de Cu e Zn apresentaram correlacao. As tecnicas de geoprocessamento e a Analise dos Componentes Principais indicaram enriquecimento do solo com Cu e Zn devido ao uso e manejo dos vinhedos com agroquimicos nas decadas anteriores.

Spatio-Temporal Modeling of Data Imputation for Daily Rainfall Series in Homogeneous Zones

Spatio-temporal modelling is an area of increasing importance in which models and methods have often been developed to deal with specific applications. In this study, a spatio-temporal model was used to estimate daily rainfall data. Rainfall records from several weather stations, obtained from the Agritempo system for two climatic homogeneous zones, were used. Rainfall values obtained for two fixed dates (January 1 and May 1, 2012) using the spatio-temporal model were compared with the geostatisticals techniques of ordinary kriging and ordinary cokriging with altitude as auxiliary variable. The spatio-temporal model was more than 17% better at producing estimates of daily precipitation compared to kriging and cokriging in the first zone and more than 18% in the second zone. The spatio-temporal model proved to be a versatile technique, adapting to different seasons and dates.

Computational system for geostatistical analysis

O uso da geoestatistica como tecnica para identificacao da estrutura espacial de varios fenomenos vem crescendo em aplicacoes agricolas. Este trabalho apresenta um sistema computacional implementado em ambiente Windows (Borland Delphi), voltado a analise espacial de dados por meio de ferramentas, como estatisticas descritivas, modelagem de semivariogramas medios, direcionais e cruzados, auto-validacao (Jack-Knifing) e krigagem. A fim de avaliar a acuracia dos resultados, o sistema foi testado por meio de um conjunto de dados de carbono e nitrogenio publicados em literatura. O sistema foi eficiente no processo de analise geoestatistica para manipulacao da rotina computacional num ambiente MS-DOS. A tentativa de desenvolvimento no Windows permitiu ao usuario modelar graficamente o semivariograma com maior grau de interacao, sendo esta funcionalidade raramente disponivel em programas similares. Devido a sua rapida prototipacao e simplicidade apos a incorporacao de rotinas correlatas, o ambiente Delphi apresenta a principal vantagem de permitir a evolucao do sistema.

Model for Multiple Imputation to Estimate Daily Rainfall Data and Filling of Faults

Modeling by multiple enchained imputation is an area of growing importance. However, its models and methods are frequently developed for specific applications. In this study the model for multiple imputation was used to estimate daily rainfall data. Daily precipitation records from several meteorological stations were used, obtained from system AGRITEMPO for two homogenous climatic zones. The precipitation values obtained for two dates (Jan. 20th 2005 and May 2nd 2005) using the multiple imputation model were compared with geo-statistics techniques ordinary Kriging and Co-kriging with the altitude as an auxiliary variable. The multiple imputation model was 16% better for the first zone and over 23% for the second one, compared to the rainfall estimation obtained by geo-statistical techniques. The model proved to be a versatile technique, presenting coherent results with the conditions of different zones and times.