A Nonlocal First-Order Closure PBL Parameterization for Sensible Heat Flux using Flux Imbalance Models

In numerical weather prediction models, the local first-order closure of turbulence, also known as K-theory, is widely used to parameterize the turbulent flux in the surface roughness layer. The non-local effects of large eddies in turbulent flows are not resolved by K-theory, leading to the flux imbalance that the simulated and measured fluxes are typically smaller than the true heat flux. Higher order closure schemes mitigate the flux imbalance problem but lead to increased complexity in parameterization and higher demands on computational resources. At the same time, flux imbalance models based on large eddy simulation results have been able to capture non-local effects of the energy-containing large eddies that span the entire boundary layer and improve the flux imbalances on both simulation results and eddy covariance measurements. These models inspired us to propose a new modified K-theory based on a correction factor that includes the non-local effects mentioned above, without using an extra term (e.g. counter-gradient flux). The formulation of the modified K-theory is straightforward and requires atmospheric stability parameters (u*/w*) and the ratio of measurement to boundary layer height (z/Zi), which are readily available in simulations and observations. To test the performance of the modified K-theory, an idealized large eddy simulation was performed over a dry convective boundary layer with a prescribed sensible heat flux at the land surface. The result shows that the K-theory underestimates the sensible heat flux by 18% due to the mesoscale circulations, while the proposed modified K-theory reduces the underestimation to less than 6%, offering the potential to improve the parameterization in numerical weather prediction.