Univariate Flux Partition Functions for Planetary Boundary Layer Schemes at Gray Zone Resolutions

Abstract

Abstract When the horizontal grid spacing of a numerical weather prediction model approaches kilometer scale, the so-called gray zone range, turbulent fluxes in the convective boundary layer (CBL) are partially resolved and partially subgrid scale (SGS). Knowledge of the partition between resolved and SGS turbulent fluxes is key to building scale-adaptive planetary boundary layer (PBL) schemes that are capable of regulating the SGS fluxes with varying grid spacing. However, flux partition depends not only on horizontal grid spacing, but also on local height, bulk stability of the boundary layer, and the particular turbulent flux. Such multivariate functions are difficult to construct analytically, so their implementations in scale-adaptive PBL schemes always involve certain levels of approximation that can lead to inaccuracies. This study introduces a physically based perspective for the flux partition functions that greatly simplifies their implementation with high accuracy. By introducing an appropriate scaling length λ that accounts for both height and bulk stability dependencies, the dimensionality of the partition functions is reduced to a single dimensionless group. Based on the analysis of a comprehensive large-eddy simulation dataset of the CBL, it is further shown that λ’s height and bulk stability dependencies can be separately represented by a similarity length scale and a stability coefficient. The resulting univariate partition functions are incorporated into a traditional first-order PBL scheme as a proof of concept. Our results show that the augmented scheme well-reproduces the SGS fluxes at gray zone resolutions. Significance Statement Flux partition functions are a key component in most scale-adaptive planetary boundary layer (PBL) schemes developed for kilometer- and subkilometer-resolution numerical weather prediction models. They regulate the parameterized turbulent fluxes as a function of horizontal grid spacing, while they also depend on height and atmospheric stability. Such multivariate dependencies forbid simple analytical expressions, and as a result, partition functions implemented in scale-adaptive PBL schemes are generally simplified at the cost of accuracy in previous works. This study investigates the possibility of constructing partition functions that are both accurate and easy to parameterize. Utilizing a physically based length scale, univariate partition functions are built, evaluated, and put into a conventional PBL scheme to improve the gray zone turbulence parameterization.