This paper investigates the problem of adjusting for spatial effects in genomic prediction. Despite being seldomly considered in genome-wide association studies (GWAS), spatial effects often affect phenotypic measurements of plants. We consider a Gaussian random field (GRF) model with an additive covariance structure that incorporates genotype effects, spatial effects and subpopulation effects. An empirical study shows the existence of spatial effects and heterogeneity across different subpopulation families while simulations illustrate the improvement in selecting genotypically superior plants by adjusting for spatial effects in genomic prediction.