A Nonlinear Impedance Relation for the Surface Winds in Pressure Disturbances

Abstract

The ''impedance relation'' between the wind perturbation within an ageostrophic atmospheric disturbance and its pressure perturbation and intrinsic propagation speed has been in use for decades. The correlation between wind and pressure perturbation was established through this relation. However, a simple Lagrangian model of an air parcel traversing an idealized sinusoidal wave in the pressure field indicates that the impedance relation produces significant errors. Examination of the nonlinearized horizontal momentum equation with a sinusoidal disturbance in pressure reveals an additional nonlinear term in the impedance relation, not previously included.In this paper, the impedance relation is rederived, with the solution being the original equation with the addition of the nonlinear term. The new equation is then evaluated against the Lagrangian model of an air parcel traversing an idealized gravity wave, as well as three observed cases. It is shown that the new impedance relation is indeed more accurate in predicting wind perturbations in disturbances based on pressure perturbations and intrinsic speed than the accepted equation. Implications for determination of the intrinsic phase speed of a disturbance when pressure and wind perturbations are known (another widely used application of the impedance relation) are also discussed.

Winds at the Mars 2020 Landing Site: 1. Near‐Surface Wind Patterns at Jezero Crater

“…The relatively long period of these waves suggests that the origin is not local. Neglecting Coriolis forces and assuming a linear relationship between wind and pressure perturbations at the first order (Banfield et al., 2020; Coleman & Knupp, 2010), the phase speed, c , can be computed by c = u + Pʹ /( ρ · uʹ ), where u is the wind speed, ρ is the atmospheric density, and Pʹ and uʹ are the pressure and wind perturbations, respectively. It leads to phase speeds of 26–28 ms −1 and horizontal wavelengths of 70–90 km.…”

Central and Eastern U.S. Surface Pressure Variations Derived from the USArray Network

“…While many of the phenomena mentioned above tend to occur largely unnoticed, large-amplitude gravity waves, wake lows, and other mesoscale convective systems (MCSs) leading to severe weather have received much attention during recent decades (Ramamurthy et al 1993;Coleman and Knupp 2009;Coleman and Knupp 2010;Adams-Selin and Johnson 2013). A mix of microbarograph traces and pressure observations at hourly or longer intervals have been the most common tools available to study such events (Bosart et al 1998).…”

A Review of Three Significant Wake Lows over Alabama and Georgia

“…The wake low was propagating toward the southeast (from 3108) at 16 m s 21 . Since the perturbation winds in a wake low are in the opposite direction of the wake low propagation, ambient easterly low-level winds (also opposite of the propagation direction) enhanced the net winds in the wake low (e.g., Coleman and Knupp 2009).…”

“…3a, the lower levels of the atmosphere were rather stable, with average N between 0.015 and 0.020 s 21 , but slightly less stable air was located above 1500 m MSL. Coleman (2008) showed that, for any vertical displacements above a point in the atmosphere, where p9 is the pressure perturbation at height z, N is the Brunt-Vä isä lä frequency fN5[(g/u)(du/dz)] 1/2 g, r 0 is the unperturbed density at each z, and dz is the vertical displacement at each height. Therefore, for a given vertical displacement, the pressure perturbation below it will have larger magnitude when the static stability is higher, consistent with the discussion in section 1.…”

“…The wind event discussed herein was a wake low, but it is possible that the entire MCS could have been associated with a long-wavelength internal gravity wave, in a waveconditional instability of the second kind (CISK; e.g., Lindzen 1974) process. The fairly rapid movement of this wake low, and the ambient low-level winds being nearly parallel to the wake low's movement, likely reduced the winds somewhat (e.g., Coleman and Knupp 2009). However, the very large magnitude of the pressure falls still indicates that wind perturbations should be around 20 m s 21 , according to the nonlinear impedance relation (Coleman and Knupp 2010), and this is consistent with surface observations.…”