Flux-gradient and flux-turbulent statistical relationships for momentum and heat fluxes based on Monin-Obukhov (MO) similarity theory have been widely used for estimating fluxes in the surface layer. Moreover, these flux-gradient relationships are used exclusively in soil-vegetation-atmosphere (SVAT) transfer schemes. However, a number of studies show significant discrepancies between turbulent fluxes derived from MO similarity and measured directly by eddy covariance or energy budget techniques for rough and heterogeneous surfaces. In this paper, we discuss the application of MO similarity using mean profiles of temperature and wind speed and variance in temperature and vertical velocity. These data were collected in the USDA-ARS Experimental Range near Las Cruces, New Mexico over a mesquite dune site. This site contains complex topography and heterogeneous cover where 0.5 m tall mesquite vegetation grow on dunes that are 1-2 m in height and 10's of meters in width. Very little, if any, vegetation exists in the interspace region, which has length scales on the order of 20 m. Comparison of fluxes evaluated with MO similarity and the appropriateness of flux-turbulent statistic relationships for momentum and heat fluxes will be evaluated and discussed.