The resistance law for stably stratified atmospheric planetary boundary layers

Evgeny Kadantsev,Evgeny Mortikov,Sergej Zilitinkevich

doi:10.1002/qj.4019

Abstract

AbstractThe resistance law for stably and neutrally stratified atmospheric planetary boundary layers (PBL) entered textbooks on boundary‐layer meteorology but, until now, remains practically unused in modelling applications. This is not surprising. The law has been formulated and validated only for idealised cases, such as truly neutral PBL – implying neutral stratification across the entire atmosphere, nocturnal stable PBL – stably stratified near the surface but developed against the neutrally stratified free flow, and (more recently) conventionally neutral PBLs – neutrally stratified near the surface but developed against stable stratification in the free flow. We derive and validate the general formulation of the resistance law accounting for the integral effect on PBL of stable stratifications at the surface and in the free atmosphere. Such long‐lived stable PBLs, typical of wintertime at high latitudes, were until recently overlooked in boundary‐layer meteorology, not to mention weather and climate models. The proposed general formulation of the resistance law covers long‐lived stable PBLs and opens up prospects for their improved modelling.

Highlights

The classical resistance law for the steady-state atmospheric planetary boundary layer (PBL) links the geostrophic drag coefficient Cg and the cross-isobaric angle α with the PBL governing parameters: k Cg cos α = ln(CgRo) −A, k sin α = ±B
This is proper only for Truly Neutral (TN) PBL characterised by zero buoyancy flux at the surface, Fbs = 0, and neutral stratification in the free atmosphere aloft
Zilitinkevich and Esau (2002; 2005) have revealed theoretically and verified against both observational data and large-eddy simulation (LES) that PBLs with zero buoyancy flux at the surface, traditionally identified as merely neutral, are strongly affected by the static stability in the free atmosphere, whereas Equation (1) holds true, but A and B become functions of another dimensionless parameter: μN

Summary

INTRODUCTION

The above derivations do not take into account stratification of density, which is why coefficients A and B in Equation (1) appear as dimensionless universal constants This is proper only for Truly Neutral (TN) PBL characterised by zero buoyancy flux at the surface, Fbs = 0, and neutral stratification in the free atmosphere aloft. Zilitinkevich and Esau (2002; 2005) have revealed theoretically and verified against both observational data and large-eddy simulation (LES) that PBLs with zero buoyancy flux at the surface, traditionally identified as merely neutral, are strongly affected by the static stability in the free atmosphere, whereas Equation (1) holds true, but A and B become functions of another dimensionless parameter: μN. Until recently this method was based on the resistance law for neutrally stratified PBLs which strongly limited its accuracy

THEORETICAL MODEL

VERIFICATION AND CALIBRATION OF THE MODEL

CONCLUSIONS