The Use of Semigeostrophic Theory to Diagnose the Behaviour of an Atmospheric GCM

Cullen, M. J. P.

doi:10.3390/fluids3040072

Cited by 7 publications

(15 citation statements)

References 31 publications

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“…B. Quantification of the diabatic influence on the balanced flow through the ageostrophic advection of PV mechanism A new semi‐geotriptic (SGT) balance tool (Cullen, 2018) was used to estimate the balanced ageostrophic flow at tropopause level and to attribute it as a response to geostrophic or diabatic forcing. The model is appropriate in the situation of the large horizontal static stability contrast where horizontal surfaces intersect the tropopause (outside the regime of validity for the QG model). In SGT dynamics, the Ertel PV is approximately conserved, and the advecting velocity is well approximated by the geostrophic and ageostrophic winds deduced as functions of pressure.…”

Section: Discussionmentioning

confidence: 99%

“…Cullen (2018) shows how eliminating the wind velocity from () using the continuity equation yields an elliptic equation for the pressure tendency

\partial π / \partial t

which can be stepped forwards in time (equation (33) in Cullen, 2018). The updated pressure field can be used as a prognostic variable to derive the next time‐step values for the geotriptic wind,

θ_{v}

and also the ageotriptic wind from ().…”

Section: Methodsmentioning

confidence: 99%

“…A brief description of the mathematical formalism of the SGT tool is outlined here; for the derivation and further details tha reader is referred to Sections 2.1 and 2.2 of Cullen (2018). Geotriptic and hydrostatic balance are defined by:

\begin{align} c_{p normald} θ_{normalv} \nabla_{normalh} π prefix- false(f v_{normale}, prefix- f u_{normale} false) & = \frac{\partial}{\partial r} true(K_{m} \frac{\partial {boldu}_{normale}}{\partial r} true), \end{align}

\begin{align} c_{p normald} θ_{normalv} \frac{\partial π}{\partial r} & = prefix- g, \end{align}

where c p d is the specific heat of dry air at constant pressure,

θ_{v}

the virtual potential temperature,

π

Exner pressure, K m a stability‐dependent diffusion coefficient in the boundary layer and g the gravitational acceleration.…”

Section: Methodsmentioning

confidence: 99%

“…Re‐arrangement of the three components of the momentum equation and making the geotriptic momentum approximation leads to ():

B Q^{'} [\begin{matrix} u prefix- u_{normale} \\ v prefix- v_{normale} \\ w \end{matrix}] + c_{p d} θ_{v} \frac{\partial}{\partial t} (\nabla π) = B H^{'},

where the first term on the left‐hand side is a vector with the ageotriptic wind and vertical motion as components, weighted by the matrices B and Q ′ described in (17) and (21) of Cullen (2018). The second term on the left‐hand side is the Eulerian time derivative of the pressure gradient.…”

Section: Methodsmentioning

confidence: 99%

“…In step B, the Semi‐Geotriptic (SGT) balance tool created by (Cullen, 2018) is used to partition the 3D ageostrophic flow in the H‐Res forecasts into a "balanced‐flow component" calculated from the geostrophic forcing of a generalisation to the omega equation, a "diabatic component" attributed to ageostrophic flow response to diabatic heating and a remainder described as the "unbalanced component". These components are used in turn to calculate the influence of advection of PV at tropopause level in generating Rossby wave disturbances.…”

Section: Introductionmentioning

confidence: 99%

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Linking rapid forecast error growth to diabatic processes

Sánchez

Methven

Gray

et al. 2020

Quart J Royal Meteoro Soc

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The predictability of high‐impact weather events over the North Atlantic is controlled by synoptic‐scale systems and the mesoscale structures embedded within them. Despite forecast uncertainty being greatest at small scales at the initial time, forecast error projects strongly onto synoptic and larger scales within days. Different stages of error growth have previously been identified including: convective instability, baroclinic instability and the influence of divergent outflow on the tropopause position, and interactions between disturbances at tropopause level. Evidence is presented for "predictability barriers" (PBs) identified with events on certain validation dates during the North Atlantic Waveguide and Downstream impact Experiment (NAWDEX) where ensemble spread grows more quickly than usual, but ensemble‐mean forecast error grows even faster. An advective mechanism for diabatic influence on the development of tropopause ridges is hypothesised to be linked to the PB events. A semi‐geostrophic balance tool is used to attribute the response of the 3D ageostrophic flow to geostrophic and diabatic forcing, enabling a novel diagnostic for Diabatically Induced Ageostrophic Advection (DIAA) of potential vorticity. It is shown that predictability barriers are linked to events with strong diabatic influence on tropopause advection during the NAWDEX period. Error growth exceeds ensemble spread rate by approximately 4/3 during strong DIAA events, showing that predictive skill is considerably lower in these situations.

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Section: Discussionmentioning

confidence: 99%

“…Cullen (2018) shows how eliminating the wind velocity from () using the continuity equation yields an elliptic equation for the pressure tendency

\partial π / \partial t

which can be stepped forwards in time (equation (33) in Cullen, 2018). The updated pressure field can be used as a prognostic variable to derive the next time‐step values for the geotriptic wind,

θ_{v}

and also the ageotriptic wind from ().…”

Section: Methodsmentioning

confidence: 99%

\begin{align} c_{p normald} θ_{normalv} \nabla_{normalh} π prefix- false(f v_{normale}, prefix- f u_{normale} false) & = \frac{\partial}{\partial r} true(K_{m} \frac{\partial {boldu}_{normale}}{\partial r} true), \end{align}

\begin{align} c_{p normald} θ_{normalv} \frac{\partial π}{\partial r} & = prefix- g, \end{align}

where c p d is the specific heat of dry air at constant pressure,

θ_{v}

the virtual potential temperature,

π

Exner pressure, K m a stability‐dependent diffusion coefficient in the boundary layer and g the gravitational acceleration.…”

Section: Methodsmentioning

confidence: 99%

“…Re‐arrangement of the three components of the momentum equation and making the geotriptic momentum approximation leads to ():

B Q^{'} [\begin{matrix} u prefix- u_{normale} \\ v prefix- v_{normale} \\ w \end{matrix}] + c_{p d} θ_{v} \frac{\partial}{\partial t} (\nabla π) = B H^{'},

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Linking rapid forecast error growth to diabatic processes

Sánchez

Methven

Gray

et al. 2020

Quart J Royal Meteoro Soc

Self Cite

View full text Add to dashboard Cite

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A balanced model of a hurricane vortex coupled to a boundary layer

Beare,

Cullen

2023

Quart J Royal Meteoro Soc

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The boundary layer plays a key role in several aspects of hurricane dynamics. Here we focus on its contribution to the balanced circulation. Previous studies, whilst including centrifugal terms, have not included an explicit balance in the boundary layer. Here, we improve the balanced theory to include an Ekman balance, the so‐called Frictional Axisymmetric Vortex (FAV). This approach is analogous to semi‐geostrophic theory that includes a realistic boundary‐layer diffusion: semi‐geotriptic (SGT) theory. We formulate the FAV for an axisymmetric system in cylindrical polar coordinates. We then derive a Sawyer‐Eliassen equation for the vertical circulation. Example solutions for both an idealised hurricane‐scale and synoptic‐scale vortex are compared.This article is protected by copyright. All rights reserved.

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Examining the dynamics of a Borneo vortex using a balance approximation tool

Hardy

Methven

Schwendike

et al. 2023

Preprint

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Abstract. Cyclonic vortices that are weaker than tropical storm category can bring heavy precipitation as they propagate across the South China Sea and across surrounding countries. Here we investigate the structure and dynamics responsible for the intensification of a Borneo vortex that moved from the north of Borneo across the South China Sea and impacted Vietnam and Thailand in late October 2018. This case study is examined using Met Office Unified Model (MetUM) simulations and an idealised semi-geotriptic (SGT) balance approximation tool. Satellite observations and a MetUM simulation with 4.4 km grid initialised at 12 UTC on 21 October 2018, show that the westward-moving vortex is characterised by a coherent maximum in total column water, and by a comma-shaped precipitation structure with the heaviest rainfall to the northwest of the circulation centre. The Borneo vortex is comprised of a low-level cyclonic circulation and a mid-level wave embedded in the background easterly shear flow, which strengthens with height up to around 7 km. Despite being in the Tropics at 6º N, the low-level vortex and mid-level wave are well represented by SGT balance dynamics. The mid-level wave propagates along a vertical gradient in moist stability, i.e., the product between the specific humidity and the static stability, at 4.5 to 5 km and is characterised by a coherent signature in the potential vorticity, meridional wind, and balanced vertical velocity fields. The vertical motion is dominated by coupling with diabatic heating and in quadrature with the potential vorticity so that the diabatic wave propagates westwards, relative to the flow, at a rate consistent with prediction from moist semi-geostrophic theory. Initial vortex development at low levels is consistent with baroclinic growth initiated by the mid-level diabatic Rossby wave, which propagates on baroclinic shear flow on the southern flank of a large-scale cold surge.

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The Use of Semigeostrophic Theory to Diagnose the Behaviour of an Atmospheric GCM

Cited by 7 publications

References 31 publications

Linking rapid forecast error growth to diabatic processes

Linking rapid forecast error growth to diabatic processes

A balanced model of a hurricane vortex coupled to a boundary layer

Examining the dynamics of a Borneo vortex using a balance approximation tool

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