Several studies have shown that Large Eddy Simulation results are highly sensitive to the sub-grid scale (SGS) model used in the simulation. Diffusion type models with ad-hoc imposed coefficients (Smagorisnky) and dynamic scale invariant models are still widely used despite their theoretical and practical deficiencies. A Lagrangian dynamic sub-grid scale parameterization is implemented in this study. Both a scale independent and a scale dependent parameterizations are tested and compared with a Smagorinsky SGS model. The Lagrangian model computes the SGS coefficients dynamically at each point in the domain and averages over pathlines. The LES code with the Lagrangian parameterizations is then used to simulate a neutral atmospheric boundary layer flowing over a heterogeneous surface. The effects of changes in surface roughness on turbulence structures are investigated. The blending layer height and its variation with patch length and surface parameters are studied.