A Local Similarity Function for Katabatic Flows Derived From Field Observations Over Steep‐ and Shallow‐Angled Slopes. Issue 23 (28th November 2021) - Hang, Chaoxun; Oldroyd, Holly J.; Giometto, Marco G.; Pardyjak, Eric R.; Parlange, Marc B.
Abstract: Katabatic flows are notoriously difficult to model for a variety of reasons. Notably, the assumptions underpinning Monin‐Obukhov similarity theory (MOST) are inherently violated by the sloping terrain, causing the traditional flux‐gradient relations used in numerical weather prediction models to break down. Focusing on turbulent momentum transport, we show significant flux divergence, further violating MOST assumptions, and that the traditional parameterizations fail even with local scaling for katabatic flow. In response, we propose a modified local‐MOST stability‐correction function, informed by near‐surface turbulence observations collected over two mountainous slopes with inclination angles ( α ) of α ≈ 7.8 ° and α ≈ 35.5 ° . The proposed relation includes α directly, making data from both slopes collapse with unprecedented agreement. RMSE between measured fluxes and estimates from the proposed and Businger et al. (1971, https://doi.org/10.1175/1520-0469(1971)028<0181:FPRITA>2.0.CO;2 ) relations show significant improvement. Results can be used to inform future development of wall‐model and turbulence closures in the katabatic flow layer. Plain Language Summary: Katabatic flows form by colder (higher density) air, caused by surface cooling, descending along a slope under the force of gravity. They are notoriously difficult to represent in numerical weather prediction models for a variety of reasons. Most notably, these numerical models use an equation for turbulent momentum transport, which translates how surface conditions impact the atmosphere (and vice versa), which fails for katabatic flows because it was developed using measurements from sites over horizontal, homogeneous land surfaces. In this work, we focus on turbulent momentum transport and show stark differences between observations from katabatic flows and the traditional predictions. To address these critical problems, we propose a modified equation, informed by near‐surface turbulence observations collected over two mountainous slopes with different inclination angles ( α ), α ≈ 7.8 ° and α ≈ 35.5 ° . The proposed equation includes α directly and shows unprecedented agreement with katabatic flow data. Results can be used to inform future development of numerical simulations of katabatic flows to better relate the sloping terrain and their influences on the near‐surface atmosphere. Key Points: Momentum flux‐gradient relations over slopes are significantly different from the classic ones over horizontal surfaces Including tangent of the slope angle makes the momentum flux‐gradient relation below the jet peak suitable for steep and shallow slopes Turbulent mixing for katabatic flows is more vigorous than over horizontal terrain for the same stability