In this study, we propose a correlation based variational change detection (CVCD) method for elevation models. In essence, CVCD aims to produce smooth change maps while preserving the details of the terrain by minimizing a variational cost function. Proposed cost function is constructed with a novel data fidelity term using normalized correlation coefficient and l(1)-norm total variation regularization term. An effective algorithm is suggested to minimize the cost function using simple approximations in an iterative method. Quantitative experiments on synthetic noisy data show that CVCD can provide a detection rate of 95% while staying in the low false alarm regime, i.e. less than 10(-2). Also, qualitative experiments on real-world data show the success of the CVCD for the changes with different characteristics.