  We develop a novel data-driven approach to modeling the atmospheric boundary
layer. This approach leads to a nonlocal, anisotropic synthetic turbulence
model which we refer to as the deep rapid distortion (DRD) model. Our approach
relies on an operator regression problem which characterizes the best fitting
candidate in a general family of nonlocal covariance kernels parameterized in
part by a neural network. This family of covariance kernels is expressed in
Fourier space and is obtained from approximate solutions to the Navier--Stokes
equations at very high Reynolds numbers. Each member of the family incorporates
important physical properties such as mass conservation and a realistic energy
cascade. The DRD model can be calibrated with noisy data from field
experiments. After calibration, the model can be used to generate synthetic
turbulent velocity fields. To this end, we provide a new numerical method based
on domain decomposition which delivers scalable, memory-efficient turbulence
generation with the DRD model as well as others. We demonstrate the robustness
of our approach with both filtered and noisy data coming from the 1968 Air
Force Cambridge Research Laboratory Kansas experiments. Using this data, we
witness exceptional accuracy with the DRD model, especially when compared to
the International Electrotechnical Commission standard.
