This paper is focus on spatial functional variables whose observa- tions are realizations of a spatio-temporal functional process. In this context, a new smoothing method for functional data presenting spa- tial dependence is proposed. This approach is based on a P-spline estimation of a functional spatial regression model. As alternative to other geostatistical smoothing methods (kriging and kernel smooth- ing, among others), the proposed P-spline approach can be used to estimate the functional form of a set of sample paths observed only at a finite set of time points, and also to predict the corresponding func- tional variable at a new location within the plane of study. In order to test the good performance of the proposed method, two simulation studies and an application with real data will be developed and the results will be compared with functional kriging.Financial support from the project P11-FQM-8068 from Consejería de Innovación, Ciencia y Empresa. Junta de Andalucía, Spain and the projects MTM2013-47929-P and MTM 2011-28285-C02-C2 from Secretaría de Estado Investigación, Desarrollo e
Innovación, Ministerio de Economía y Competitividad, Spain
