The production of Integrated Circuit (IC) is subject to high quality standard, and many control steps are incorporated in complex manufacturing processes. Conventionally, Statistical Process Control (SPC) tools such as control charts are intensively used for the sake of quality monitoring improvement in semiconductor production plants. The ICs are produced on thin slices of semiconductor materials, called wafers. In our study, a wafer is a 300-mm diameter circular domain. To monitor its quality, several types of physical metrology measurements (such as thickness, depth, width, angles and overlay) are collected on a fixed number of preselected locations. However, standard SPC techniques hardly detect defects such as curvature change, which is critical in semiconductors manufacturing, as different wafer “profiles”, related to different process issues, may have the same mean and variance over the measurement points. Furthermore, spatial correlation is not taken into account. To overcome these problems, the two-phase profile monitoring procedure [3] is often preferred: 1. For each time step, fit a response surface based on the measurement points ; 2. Monitor the response surface parameters over time. In this work, we focus on step 1. Our contributions are twofold. Firstly, we compare different approximation techniques in circular domains: Zernike regression [1, 4] , and Gaussian process regression [1, 2] with standard and customized covariance kernels. Secondly, we exhibit the link between the model and key process parameters.