  In large-eddy simulations, subgrid-scale (SGS) processes are parameterized as
a function of filtered grid-scale variables. First-order, algebraic SGS models
are based on the eddy-viscosity assumption, which does not always hold for
turbulence. Here we apply supervised deep neural networks (DNNs) to learn SGS
stresses from a set of neighboring coarse-grained velocity from direct
numerical simulations (DNSs) of the atmospheric boundary layer at friction
Reynolds numbers Re_{\tau} up to 1243 without invoking the eddy-viscosity
assumption. The DNN model was found to produce higher correlation of SGS
stresses compared to the Smagorinsky model and the Smagorinsky-Bardina mixed
model in the surface and mixed layers and can be applied to different grid
resolutions and various stability conditions ranging from near neutral to very
unstable. The additional information on potential temperature and pressure were
found not to be useful for SGS modeling. Deep learning thus demonstrates great
potential for LESs of geophysical turbulence.
