Common closure schemes for large eddy simulation (LES) typically rely upon the assumption that subgrid-scale fluxes are aligned against spatial gradients of transported quantities. Direct testing of this assumption is needed to evaluate the structure and geometric form of these closure schemes. Field experimental data of velocity and temperature measurements from sonic anemometer arrays in the atmospheric surface layer are analyzed using tools from statistical geometry. We show: (1) The most likely orientation of the subgrid-scale (SGS) heat flux lies within a plane that is spanned by the temperature gradient vector and its product with the velocity gradient tensor. (2) The preferred filtered fluid deformation is axisymmetric extension and the preferred subgrid stress state is axisymmetric contraction. (3) The filtered fluctuating vorticity is preferentially aligned with the mean vorticity, the streamwise direction, and the intermediate strain-rate eigenvector. (4) The alignment between eigenvectors of the SGS stress and filtered strain rate are in qualitative agreement with prior laboratory measurements at much lower Reynolds numbers. A bimodal distribution is observed, which can be reduced to co-alignment using the mixed model. (5) A geometric interpretation of energy dissipation reveals the dependence of SGS dissipation on alignment angles between the eigendirections of the SGS stress and the filtered strain rate tensors. (6) Two dimensional filtering can be a good surrogate for three dimensional filtering if the filter scale is reinterpreted, otherwise the we delineate a new approach. And, (7) The vector alignment of the SGS force with the divergence of the Smagorinsky and nonlinear models is investigated under near neutral, unstable, and stable atmospheric stabilities. It is shown that the nonlinear formulation has a high probability of alignment with the SGS force across all stabilities, while the alignment of the Smagorinsky model depends on atmospheric stability.