In agricultural studies it is often important to predict the performance of genetically different plants. To make sure predictions are done well, it is necessary to make sure they are not influenced by effects of the field on which they are planted. These field effects or spatial effects are in practice often quite complicated and can be due to a wide variety of reasons. To get a better view of these field effects a good mathematical model is desired. In this paper a model is presented which helps to find these field effects. This model tries to estimate the field effect by comparing data of the same plant on different positions of the field. Data is obtained in a finite amount of positions, which means that the model finds the field effect in a finite amount of positions as well. This field effect is found using a cross-validation technique obtained from Tikhonov regularization. The field effect in a finite amount of positions is extended to a field effect in every position of the field. To do this in a good way a kernel method is used, the advantage of which is that it does not depend on a mesh. This kernel method is here applied with a kernel function that is based on Gaussian distribution. This model is applied to several fields of crops to get a view of the performance of the model on real data.