ABSTRACT Soil is a medium that stores and transfers air, water, nutrients and heat to microorganisms and plants. Its water storage capacity is studied by analysing water retention curves (WRCs), which establish the relationship between soil water content and the force with which water is retained. The objective of this work was to evaluate the capacity of functional geostatistics in predicting the spatial distribution of water retention curves in two types of soils. Experimental areas with two types of soil, Andisol and Oxisol, were selected, and a regular grid of 75 sites was established, from which water retention curves were obtained at two depths. The curves were subjected to geostatistical functional analysis (GF), and the applicability of this method was evaluated by obtaining the usable water table (LAA) and comparing the results with experimental data obtained using traditional methods. Based on cross-validation, it was verified that GF produced a better fit for the Andisol since the coefficient of determination between the LAA values for the measured data and predictions was high, with an R2 of 99%; however, the proposed methodology was also reliable for the Oxisol, since an R2 of 94% was obtained at the two depths studied.

RESUMO O solo é um sistema que armazena e transfere ar, água, nutrientes e calor para microrganismos e plantas. Sua capacidade de armazenamento de água é estudada analisando a curva de retenção de água (WRC), que estabelece a relação entre a umidade do solo e a força com que ela é retida. O objetivo deste trabalho foi avaliar a capacidade preditiva da geoestatística funcional na distribuição espacial das curvas de retenção de água em dois tipos de solos. Foram selecionadas duas áreas experimentais, um Andisol e um Oxisol, nas quais foi estabelecida uma grade regular com 75 pontos, das quais foram obtidas curvas de retenção de água em duas profundidades. As curvas foram submetidas à análise geoestatística funcional (GF), sua aplicabilidade foi avaliada obtendo a tabela de água utilizável (LAA) e sua posterior análise espacial por métodos tradicionais nos quais os resultados foram comparados com os dados experimentais. Com base na validação cruzada, verificou-se que o uso de GF tem um melhor ajuste para o Andossolo, uma vez que o coeficiente de determinação entre os valores de LAA obtidos com os dados observados e aqueles obtidos com as previsões foi alto, com R2 de 99%; no entanto, para o Latossolo, a metodologia proposta também é confiável, uma vez que foi obtido um R2 de 94% nas duas profundidades estudadas.

Resumen. La geoestadística puede usarse como método de predicción de datos faltantes en series temporales. El procedimiento se basa en el estudio de la estructura de autocorrelación temporal de la serie de tiempo por medio de la función de variograma, que es estimada por mínimos cuadrados (geoestadística clásica) o por máxima verosimilitud (geoestadística basada en modelo), y en usar posteriormente Kriging para hacer predicción de los valores faltantes. En este trabajo se comparan a través de simulación las dos aproximaciones (geoestadística clásica y basada en modelo) en el contexto de series temporales autorregresivas.

Abstract. Geostatistics can be used as a method for predicting missing data in time series. The procedure is based on estimating the temporal autocorrelation structure by means of the semivariance function, by least squares (classical geostatistics) or maximum likelihood (model-based geostatistics), and posteriorly using Kriging for doing prediction of missing data in the time series. In this work we compare classical and model-based geoestatistics in the context of time series using simulated autorregresive time series.

ABSTRACT Knowledge of agricultural soils is a relevant factor for the sustainable development of farming activities. Studies on agricultural soils usually begin with the analysis of data obtained from sampling a finite number of sites in a particular region of interest. The variables measured at each site can be scalar (chemical properties) or functional (infiltration water or penetration resistance). The use of functional geostatistics (FG) allows to perform spatial curve interpolation to generate prediction curves (instead of single variables) at sites that lack information. This study analyzed soil penetration resistance (PR) data measured between 0 and 35 cm depth at 75 sites within a 37 ha plot dedicated to livestock. The data from each site were converted to curves using non-parametric smoothing techniques. In this study, a B-splines basis of 18 functions was used to estimate PR curves for each of the 75 sites. The applicability of FG as a spatial prediction tool for PR curves was then evaluated using cross-validation, and the results were compared with classical spatial prediction methods (univariate geostatistics) that are generally used for studying this type of information. We concluded that FG is a reliable tool for analyzing PR because a high correlation was obtained between the observed and predicted curves (R2 = 94 %). In addition, the results from descriptive analyses calculated from field data and FG models were similar for the observed and predicted values.

Curvas espacialmente correlacionadas están presentes en un amplio rango de disciplinas aplicadas. En este trabajo se describe el paquete R geofd que implementa predicción por kriging ordinario para este tipo de datos. Inicialmente las curvas son suavizadas usando bases de funciones de Fourier o B-splines. Posteriormente la dependencia espacial entre las curvas es estimada por la función traza-variograma. Finalmente los parámetros del predictor kriging ordinario son estimados resolviendo un sistema de ecuaciones basado en la estimación de la función traza-variograma. Se ilustra el paquete analizando datos reales y simulados.

Spatially correlated curves are present in a wide range of applied disciplines. In this paper we describe the R package geofd which implements ordinary kriging prediction for this type of data. Initially the curves are pre-processed by fitting a Fourier or B-splines basis functions. After that the spatial dependence among curves is estimated by means of the trace-variogram function. Finally the parameters for performing prediction by ordinary kriging at unsampled locations are by estimated solving a linear system based estimated trace-variogram. We illustrate the software analyzing real and simulated data.

Se muestra cómo las estadísticas descriptivas funcionales y el análisis en componentes principales funcional (ACPF) pueden emplearse en la evaluación empírica del supuesto de estacionariedad considerado en la modelación de variables regionalizadas. Se toma como ejemplo información georreferenciada correspondiente a mediciones de profundidad recogidas en 114 sitios de la Ciénaga Grande de Santa Marta, Colombia.

It is shown how summary statistics of functional data and functional principal components analysis (FPCA) can be used to evaluate the stationarity assumption considered in modeling of regionalized variables. As an example is taken georeferenced information of depth measured at 114 locations at Ciénaga Grande de Santa Marta, Colombia.

Se efectuó una investigación con el fin de modelar la variabilidad espacial de algunas propiedades del suelo y su relación con la variación de la producción en un cultivo de papa (Solanum tuberosum L.), como base para identificar algunos indicadores de calidad de suelos en el departamento de Cundinamarca, región andina de Colombia. Mediante la realización de diversos análisis espaciales se encontró una alta variabilidad espacial de las propiedades del suelo y de la producción dentro del lote. Por otra parte, se encontró que el pH, la suma de bases y saturación de Al son las características de mayor influencia sobre el rendimiento, por lo tanto, pueden ser utilizadas como indicadores de calidad del suelo, bajo las condiciones del estudio. Con relación al muestreo, las redes, con 14 y 26 puntos, distancias entre puntos de 30 x 30 y 15 x 30, tuvieron varianzas de predicción aceptables y costos razonables, por lo tanto, se consideran apropiadas para las condiciones del estudio.

The spatial variability of some soil properties and their relationship with varying production in potato crop (Solanum tuberosum L.) was modelled as the basis for identifying some soil quality indicators in Cundinamarca department, Colombia, Andean region. Spatial analysis revealed high spatial variability in soil properties and production among lots. It was also found that pH, the sum of exchangeable bases, and aluminum saturation were the characteristics that most influenced yield. They could, thus, be used as indicators of soil quality in the conditions employed for this study. Sampling networks having 14 and 26 points (30 m x 30 m and 15 m x 30 m distances between points) presented acceptable prediction variation and returned reasonable costs, thereby being considered suitable for the conditions used in this study.