This paper proposes an algorithm for fusing digital surface models (DSM) obtained by heterogenous sensors. Based upon prior confidence knowledge, each DSM can be weighted locally adaptively and therefore strengthen or lessen its influence on the fused result. The proposed algorithm is based on variational methods of first and second order, minimizing a global energy functional comprising of a data term forcing the resulting DSM being similar to all of the input height information and incorporating additional local smoothness constraints. By applying these additional constraints in the form of favoring low gradients in the spatial direction, the surface model is forced to be locally smooth and in contrast to simple mean or median based fusion of the height information, this global formulation of context-awareness reduced the noise level of the result significantly. Minimization of the global energy functional is done with respect to the <i>L</i>₁ norm and therefore is robust to large height differences in the data, which preserves sharp edges and fine details in the fused surface model, which again simple mean- and median-based methods are not able to do in comparable quality. Due to the convexity of the framed energy functional, the solution furthermore is guaranteed to converge towards the global energy minimum. The accuracy of the algorithms and the quality of the resulting fused surface models is evaluated using synthetic datasets and real world spaceborne datasets from different optical satellite sensors.