Characteristics for the sources and sinks of gravity waves in an orographic heavy snowfall event

doi:10.1007/s11707-021-0961-2

Front. Earth Sci.

2023, Vol. 17

Issue (2) : 604-619 https://doi.org/10.1007/s11707-021-0961-2

RESEARCH ARTICLE

Characteristics for the sources and sinks of gravity waves in an orographic heavy snowfall event

Shuping MA^1,², Lingkun RAN^1,²(

), Jie CAO^1,^3,⁴, Baofeng JIAO¹, Kuo ZHOU¹

¹. Key Laboratory of Cloud–Precipitation Physics and Severe Storms, Institute of Atmospheric Physics (LACS), Chinese Academy of Sciences, Beijing 100029, China
². University of Chinese Academy of Sciences, Beijing 100049, China
³. Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, Norman OK 73072, USA
⁴. Key Laboratory of Meteorological Disaster (KLME), Ministry of Education & Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters (CIC-FEMD), Nanjing University of Information Science & Technology, Nanjing 210044, China

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Abstract

The characteristics of the mesoscale gravity waves during a snowfall event on November 30, 2018 over the Ili Valley and the northern slope of the Tianshan Mountains are analyzed based on the Weather Research and Forecasting model simulation. The vertical distribution of $R o$ is similar to that of the residual of the nonlinear balance equation ( $Δ N B E$ ), with their high-value areas located over the leeward slope and the fluctuations extending upwardly with time, indicating the characteristics of strong ageostrophy and non-equilibrium of atmospheric motions. In addition, the $R o$ and $Δ N B E$ are first developed in the lower layers over the leeward slope, revealing that the generation of the gravity waves is closely related to the topography. Thus, the topographic uplifting greatly affects this snowfall, and the ageostrophic motion in the whole troposphere and the lower stratosphere, as well as the unbalanced motions between convergence and divergence over the peak and the leeward slope are conductive to the development of the inertia-gravity waves. In terms of the horizontal scale of the gravity waves, the Barnes’ band-pass filter is applied to separate the mesoscale waves and the synoptic-scale basic flow. The vertical distributions of the vorticity and divergence perturbations have a phase difference of π/2, indicating the polarization state of gravity waves. The analyses on the sources and sinks of gravity waves by the non-hydrostatic wave equation show that the main forcing term for orographic gravity waves is the second-order nonlinear term, whose magnitude mainly depends on the nonlinear thermal forcing. This term is mainly related to the vertical transport of potential temperature perturbations. During the snowfall, the potential temperature perturbations are mainly caused by the topographic relief and the release of condensation latent heat. Therefore, the gravity waves in this snowfall are caused by the topographic forcing and condensation latent heating.

Keywords gravity wave Fourier transform nonlinear balance equation non-hydrostatic wave equation

Corresponding Author(s): Lingkun RAN

Online First Date: 30 June 2022 Issue Date: 04 August 2023

Cite this article:

Shuping MA,Lingkun RAN,Jie CAO, et al. Characteristics for the sources and sinks of gravity waves in an orographic heavy snowfall event[J]. Front. Earth Sci., 2023, 17(2): 604-619.

URL:

https://academic.hep.com.cn/fesci/EN/10.1007/s11707-021-0961-2
https://academic.hep.com.cn/fesci/EN/Y2023/V17/I2/604

Tab.1 Mode scheme settings

Fig.1 (a) 12-h accumulated snowfall from observations (color dot, units: mm) at 0000 UTC on December 1, the grid area indicates where the terrain height is greater than 3 km; (b) 12-h accumulated snowfall from simulations (shading, units: mm), where the gray shading denotes the terrain height (units: km), the north-west-south-east gray shading near point A indicate the northern slope of the Tianshan Mountains, point B indicate the Ili Valley, and the south-west-north-east gray shading near point C indicate the southern slope of the Tianshan Mountains; 700hPa (c) observed and (d) simulated water vapor fluxes (units: g?cm^?1?hPa^?1?s^?1) at 1800 UTC on Nov 30; 850hPa (e) observed and (f) simulated horizontal flow fields (arrows) and wind speed (shading, units: m?s^?1) at 1800 UTC on November 30.

Fig.2 Cross-sections of the vertical velocity field (shading, units: m?s^?1), wind vector (vectors, units: m?s^?1), tropopause height (gray solid line, units: km), hydrometeor (contours, units: 10^?4 kg?kg^?1) and 30-min precipitation (green solid line, units: mm) along 44.5°N at (a) 1330 UTC, (b) 1600 UTC and (c) 2000 UTC on November 30, 2018.

Fig.3 Cross-sections of

R o

(shading), tropopause height (gray solid line, units: km), hydrometeor (black solid lines, units: 10^?4 kg?kg^?1) and 30-min precipitation (green solid line, units: mm) along 44.5°N at (a) 1330 UTC, (b) 1600 UTC and (c) 2000 UTC on November 30, 2018.

Fig.4 Cross-sections of (a)

Δ N B E

, (b)

2 J (u, v)

, (c)

f ζ ? β u

, (d)

α ? 2 P

(shading, units: 10^?6 s^?2), tropopause height (gray solid line, units: km), hydrometeor (black solid lines, units: 10^?4 kg?kg^?1) and 30-min precipitation (green solid line, units: mm) along 44.5°N at 1600 UTC on November 30, 2018.

Fig.5 The power spectral density of the vertical velocity at the height of 12 km along 44.5°N (units: m²?s^?2). The solid lines represent the wave phase velocity of ?4 m?s ^?1 and ?10 m?s ^?1.

Fig.6 The (a) phase spectrum and (b) coherence spectrum of the vertical vorticity and the horizontal divergence at the height of 12 km along 44.5°N at 2000 UTC on November 30, 2018.

Fig.7 The band-pass filter response function

B R

Fig.8 Cross-sections of the perturbations on the divergence field (shading, units: 10^?4 s^?1) and vorticity field (contours, units: 10^?4 s^?1), the tropopause height (gray solid line, units: km), and 30-min precipitation (green solid line, units: mm) along 44.5°N at (a) 1330 UTC, (b) 1600 UTC and (c) 2000 UTC on November 30, 2018.

Terms and components of the non-hydrostatic wave equation	Physical meanings
$F G 0$	Basic state term
$F G 1$	First-order linear forcing term
$F G 2$	Second-order nonlinear forcing term
$F G S$	Thermodynamic term
$F T 0$	Forcing term for the basic state of potential temperature
$F T 1$	Linear forcing term for potential temperature
$F T 2$	Quadratic forcing term for potential temperature
$F T S$	Adiabatic forcing term
$F W 1$	Linear forcing term for vertical velocity
$F W 2$	Quadratic forcing term for vertical velocity
$F D 0$	Forcing term for the basic state of the divergence
$F D 1$	Linear forcing term for divergence
$F D 2$	Quadratic forcing term for divergence
$F V 0$	Forcing term for the basic state of the vertical vorticity
$F V 1$	Linear forcing term for vertical vorticity
$F V 2$	Quadratic forcing term for vertical vorticity

Tab.2 Physical meanings for the terms in Eqs. (13)–(28)

Fig.9 Cross-sections of the (a) basic state term (shading, units: 10^?13 m^?1?s^?3), (b) first-order linear term (units: 10^?12 m^?1?s^?3), (c) second-order nonlinear term (units: 10^?12 m^?1?s^?3), (d) thermodynamic term (units: 10^?12 m^?1?s^?3), tropopause height (gray solid line, units: km), hydrometeor (contours, units: 10^?4 kg?kg^?1) and precipitation (green solid line, units: mm) along 44.5°N at 1600 UTC on November 30, 2018.

Fig.10 Cross-sections of the (a)

? g ? h 2 F T 2

(shading, units: 10^?12 m^?1?s^?3), (b)

? v ′ ? ? θ ′ θ ˉ

(shading, units: 10^?5 s^?1), (c)

? u e ? θ ′ θ ˉ ? x

(shading, units: 10^?6 s^?1), (d)

? v e ? θ ′ θ ˉ ? y

(shading, units: 10^?6 s^?1), (e)

? w e ? θ ′ θ ˉ ? y

(shading, units: 10^?6 s^?1), tropopause height (gray solid line, units: km), hydrometeor (contours, units: 10^?4 kg?kg^?1), and precipitation (green solid line, units: mm) along 44.5°N at 1600 UTC on November 30, 2018.

Fig.11 Cross-sections of the (a) potential temperature

θ

(contours, units: K), (b) potential temperature perturbation

θ ′

(contours, units: K), (c)

θ ′ θ ˉ

(contours), (d) latent heat during the microphysical processes (shading, units: 10^?4 K s^?1), tropopause height (gray solid line, units: km), hydrometeor (contours, units: 10^?4 kg?kg^?1) and precipitation (green solid line, units: mm) along 44.5°N at 1600 UTC on November 30, 2018.

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