We consider the problem on additive model building for spatial functional regression, where a scalar response is related to the components of a square-integrable spatial functional process. We propose a methodology that leads to the minimisation of a spatially weighted \(\ell _2\) -error norm with a group LASSO type penalty, which constitutes our selection criterion. The originality of this proposed method is that we consider spatially dependent functional data as covariates. A simulation study highlights the importance of the choice of the spatial weight matrix as well as the appreciable asymptotic behaviour of the estimators. Precisely, our method selects better in the case of strong spatial dependency than in the independent data case and increasing the sample size clearly improves the number of selected components using the proposed criterion for this study with probability converging to 1.