In various scientific fields properties are represented by functions varying over space. In this paper, we present a methodology to make spatial predictions at non-data locations when the data values are functions. In particular, we propose both\ud an estimator of the spatial correlation and a functional kriging predictor. We adapt an\ud optimization criterion used in multivariable spatial prediction in order to estimate the\ud kriging parameters. The curves are pre-processed by a non-parametric fitting, where\ud the smoothing parameters are chosen by cross-validation. The approach is illustrated\ud by analyzing real data based on soil penetration resistances.Postprint (published version

Registro de acceso restringido Este recurso no está disponible en acceso abierto por política de la editorial. No obstante, se puede acceder al texto completo desde la Universitat Jaume I o si el usuario cuenta con suscripción. Registre d'accés restringit Aquest recurs no està disponible en accés obert per política de l'editorial. No obstant això, es pot accedir al text complet des de la Universitat Jaume I o si l'usuari compta amb subscripció. Restricted access item This item isn't open access because of publisher's policy. The full--text version is only available from Jaume I University or if the user has a running suscription to the publisher's contents.

Classification problems of functional data arise naturally in many applications. Several approaches have been considered for solving the problem of finding groups based on functional data. In this paper we are interested in detecting groups when the functional data are spatially correlated. Our methodology allows to find spatially homogeneous groups of sites when the observations at each sampling location consist of samples of random functions. In univariable and multivariable geostatistics various methods of incorporating spatial information into the clustering analysis have been considered. Here we extend these methods to the functional context in order to fulfill the task of clustering spatially correlated curves. In our approach we initially use basis functions to smooth the observed data and then we weight the dissimilarity matrix among curves by either the trace-variogram or the multivariable variogram calculated with the coefficients of the basis functions. As an illustration the methodology is applied to a real data set corresponding to average daily temperatures measured at 35 Canadian weather stations.

Spatially correlated functional data is present in a wide range of environmental disciplines and, in this context, efficient prediction of curves is a key issue. We present an approach for spatial prediction based on the functional linear point-wise model adapted to the case of spatially correlated curves. First, a smoothing process is applied to the curves by expanding the curves and the functional parameters in terms of a set of Fourier basis functions. The number of basis functions is chosen by cross-validation. Then, the spatial prediction of a curve is obtained as a pointwise linear combination of the smoothed data. The prediction problem is solved by estimating a linear model of coregionalization to set the spatial dependence among the fitted coefficients. We extend an optimization criterion used in multivariable geostatistics to the functional context. The method is illustrated by smoothing and predicting temperature curves measured at 35 Canadian weather stations.

Functional data featured by a spatial dependence structure occur in many environmental sciences when curves are observed, for example, along time or along depth. Recently, some methods allowing for the prediction of a curve at an unmonitored site have been developed. However, the existing methods do not allow to include in a model exogenous variables that, for example, bring meteorology information in modeling air pollutant concentrations. In order to introduce exogenous variables, potentially observed as curves as well, we propose to extend the so-called kriging with external drift-or regression kriging-to the case of functional data by means of a three-step procedure involving functional modeling for the trend and spatial interpolation of functional residuals. A cross-validation analysis allows to choose smoothing parameters and a preferable kriging predictor for the functional residuals. Our case study considers daily PM 10 concentrations measured from October 2005 to March 2006 by the monitoring network of Piemonte region (Italy), with the trend defined by meteorological time-varying covariates and orographical constant-in-time variables. The performance of the proposed methodology is evaluated by predicting PM 10 concentration curves on 10 validation sites, even with simulated realistic datasets on a larger number of spatial sites. In this application the proposed methodology represents an alternative to spatio-temporal modeling but it can be applied more generally to spatially dependent functional data whose domain is not a time interval.

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The identification of area‐wise homogeneous precipitation regions helps to unveil similar precipitation patterns and amounts, where similar atmospheric processes at diverse temporal scales are likely to occur. However, although scientifically and socially relevant, the regionalization of precipitation is challenging, specially in areas of complex orography and with sparse monitoring. This limits our understanding of complex spatio‐temporal dependencies and hinders any information‐based resource management decision‐making. Gridded satellite precipitation products are useful in this context, even though they contain bias errors. Spatial functional data analysis (sFDA) is a novel technique that considers time as well as space dependencies by means of spatial autocorrelation and complete time functions, one for each spatial point. Therefore, the aim of this study is to evaluate sFDA as a tool to regionalize seasonality and intensity precipitation patterns, having Ecuador as a case study. The Tropical Rainfall Measuring Mission (TRMM 3B43) satellite precipitation is used to create an exhaustive spatial delineation. To the best of our knowledge, this is the first time that a sFDA regionalization approach is performed on gridded satellite precipitation. The complex orography and heat‐driven atmospheric processes in Ecuador's latitude make it a highly non‐trivial case to test the aforementioned technique. As a result, five relevant regions of precipitation seasonality were spatially delineated and temporally characterized. Three of them were zonally oriented, and two meridional‐wise in the coast. In addition, 20 relevant intensity regions across Ecuador were identified specially in regions with sparse monitoring. The regions were related to regional climate processes. However, limitations were found in regions with important orographic precipitation and locally variability patterns, probably due to the shortcomings of TRMM precipitation quantification. After the successful application of hierarchical regionalization using sFDA in a tropical region with sparse monitoring, it is reasonable to conclude that sFDA is a robust method to detect compact and meaningful homogeneous areas.

Registro de acceso restringido Este recurso no está disponible en acceso abierto por política de la editorial. No obstante, se puede acceder al texto completo desde la Universitat Jaume I o si el usuario cuenta con suscripción. Registre d'accés restringit Aquest recurs no està disponible en accés obert per política de l'editorial. No obstant això, es pot accedir al text complet des de la Universitat Jaume I o si l'usuari compta amb subscripció. Restricted access item This item isn't open access because of publisher's policy. The full--text version is only available from Jaume I University or if the user has a running suscription to the publisher's contents.