Source depth estimation with a vertical linear array generally involves mode filtering, followed by matched-mode processing. However, this method has two main limitations: the problem of mode filtering is ill-posed in the case of partially spanning arrays; matched-mode processing is sensitive to environmental mismatch. Therefore, concerns for robustness motivate a simpler approach. The problem of depth estimation is reduced to a binary classification problem: source depth discrimination. Its aim is to evaluate whether the source is near the surface or submerged. These two hypotheses are formulated in terms of normal modes, using the concept of trapped and free modes. Several classification rules, based on modal filtering or on subspace projections, are studied. Monte-Carlo methods are used to evaluate their performance and compute receiver operating characteristics. This allows the choice of a discrimination threshold according to some expected performance. The benefits of considering a source depth discrimination problem rather than a source localization one are highlighted. The influence of noise and environmental mismatch are investigated, as well as the choice of the discrimination depth and the choice of the limit between trapped and free modes.