Often in spatial regression problems, the covariates could be high-dimensional and have a non-linear relationship with the response. Furthermore, the functional relationship between the response and the covariates are often smoother than the spatial correlation. We propose a Gaussian spatial additive model on regular lattice where the large scale effects of the spatial covariates are modeled by smooth functions and the small scale spatial variability is modeled using a random field on the lattice. In order to facilitate variable selection, we impose sparse group lasso penalty on the smooth functions and derive a penalized h-likelihood method for simultaneous model selection and spatial adjustments. We derive novel estimating equations for estimating the precision parameters based on the profiled h-likelihood. We demonstrate our method using Arsenic contamination data from Bangladesh.