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We survey temperature patterns and heat transport in convective boundarylayers (CBLs) from the perspective that these are emergent properties offar-from-equilibrium, complex dynamical systems. We introduce a two-temperature(2T) toy model to define the cross-sectional areas of plumes, and connect thescaling properties of temperature gradients, temperature variance and heattransport to this area. We examine temperature ($T$) probability densityfunctions and $w$-$T$ joint probability density functions, $T$ spectra and $wT$cospectra observed both within and above the surface friction layer. Here $w$is vertical velocity. In our discussion of $T$ spectra and $wT$ cospectra wefocus on the self-similarity property of the plumes and flux events above theSFL. We interpret the $z^{1/2}$ dependence of the mixed length scale forwavenumbers in the $T$ spectra as reflecting the cross-sectional areas of theplumes, and so with the $z^{-1/2}$ form of the temperature profile, where $z$is observation height. We introduce new scaling results for $T$ spectra and$wT$ cospectra from within the surface friction layer (SFL), based on a datafrom the SLTEST experiment. We confirm earlier results showing that the scalingbehaviours of $T$ spectra and $wT$ cospectra change for heights below$z/z_s<0.1$, where $z_s$ the height of the SFL, and come to display propertiesassociated with random diffusion. We conclude by contrasting our interpretationof the role of buoyancy as a system-wide action in CBL flows with that ofRichardson, whose ideas inform the current interpretation of the statisticalfluid mechanics model of boundary-layer flows.

Temperature profiles, plumes and spectra in the surface layer of convective boundary layers