Review of "Investigation of non-equilibrium turbulence decay in the atmospheric boundary layer using Doppler lidar measurements"

This is a well-written manuscript containing thought-provoking results. However, there are several fundamental issues which need to be addressed before the paper can be accepted.

1. The authors borrowed newly developed non-equilibrium theories from turbulence literature and applied them to boundary layer turbulence. In the original theoretical development, the buoyancy effects are not included. So, the authors neglected the effects of stratification altogether (see their comment on page 11). In a transitional boundary layer, the impacts of atmospheric stability cannot be neglected. In the revised manuscript, some efforts must be made to include the effects of stability in the derivations [e.g., Eq. (8)].
2. The authors briefly mentioned 3rd-order structure functions in the manuscript. I would like to see evidence that the Lidar data conform to the 4/5th law (Karman-Howarth equation) prior to evening transition.
3. Give at least a few examples of EDR estimated via second-order and third-order structure functions and compare them against Equations (1) and (2). Please clearly show the structure functions and fitted slopes in the revised manuscript. [Add these materials in Section 5.3].
4. Elaborate on the (relative) accuracy of longitudinal and vertical velocity estimation from Lidar observations. Give references.
5. Do the results hold for the longitudinal velocity component? Why not?
6. The empirical Equation (1) is conventionally used in conjunction with TKE. What is the justification for using it only for the vertical velocity scale? One cannot invoke isotropy here.   
7. Figure 4 (left panel): in the entire convective boundary layer, the inertial-range slope is close to -2. Why? Can we trust the observational data?