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A new method is introduced to identify coherent structures in the convective boundary layer, based on optimizing the vertical scalar flux in a two-fluid representation of turbulent motions as simulated by a large-eddy simulation. The new approach partitions the joint frequency distribution (JFD) of the vertical velocity and a transported scalar into coherent structures (fluid 2) and their environment (fluid 1) by maximizing that part of the scalar flux resolved by the mean properties in fluid 2 and fluid 1. The proposed method does not rely on any a priori criteria for the partitioning of the flow nor any pre-assumptions about the shape of the JFD. Different flavours of the optimization approach are examined based on maximizing either the total (fluid 1    $$+$$   +     fluid 2) or the fluid-2 resolved scalar flux, and on whether all possible partitions or only a subset are considered. These options can result in different derived area fractions for the coherent structures. The properties of coherent structures diagnosed by the optimization method are compared to the conditional sampling of a surface-emitted decaying tracer, in which coherent structures are defined as having tracer perturbation greater than some height-dependent threshold. Results show that the optimization method is able to smoothly define coherent thermal structures in both the horizontal and the vertical. Moreover, optimizing the turbulent transfer by the fluid-2 resolved flux produces very similar coherent structures to the tracer threshold method, especially in terms of their area fraction and updraft velocities. Nonetheless, further analysis of the partitioning of the JFD reveals that, even though the area fraction of coherent structures might be similar, their definition can occupy different quadrants of the JFD, implying the contribution of different physical mechanisms to the turbulent transfer in the boundary layer. Finally, the kinematic and thermodynamic characteristics of the coherent structures are examined based on their definition criteria.

Diagnosing Coherent Structures in the Convective Boundary Layer by Optimizing Their Vertical Turbulent Scalar Transfer