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

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. The SG Approximation to the UM Equations

#### 2.2. The Diagnostic Equations

#### 2.3. Application

#### 2.4. Computational Aspects

## 3. Results

#### 3.1. Experimental Setup

#### 3.2. Comparison of Diagnostic and Model-Derived Ageotriptic Winds

#### 3.3. Use of a Modified Static Stability to Represent Latent Heat Release

#### 3.4. Effect of Tropical Heating on the Subtropical Jet

#### 3.5. Effect of Boundary Layer Heating

## 4. Discussion

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

GCM | General Circulation Model |

SEE | Sawyer–Eliassen equation |

SG | semi-geostrophic |

SGT | semi-geotriptic |

UM | Unified Model |

WTG | Weak Temperature Gradient |

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**Figure 2.**Vertical velocity at 4000m, units ms${}^{-1}$: (

**a**) directly output from UM; (

**b**) calculated from Equation (20) with heating rates at 4000 m, units ${}^{\circ}$K day${}^{-1}$; (

**c**) combined heating from precipitation schemes in UM; and (

**d**) latent heating deduced as in Section 2.3 (see text).

**Figure 3.**(

**a**) Heating rate at 4000 m, units ${}^{\circ}$K day${}^{-1}$; (

**b**) zonal geostrophic wind units ms${}^{-1}$ at 11,500 m; (

**c**) diagnosed zonal geostrophic wind tendency at 11,500 m, units ms${}^{-2}$; and (

**d**) (22) coefficient of

**BQ**’ matrix, Equation (21), at 11,500 m, units ${10}^{8}\times $s${}^{-2}$.

**Figure 4.**Diagnostics calculated over a region ${10}^{\circ}$ S to 10${}^{\circ}$ N and ${100}^{\circ}$ E to 130${}^{\circ}$ E at 80 m height above the surface: (

**a**) Boundary layer heating, units ${}^{\circ}$K day${}^{-1}$; (

**b**) total zonal wind calculated from Equation (20); and (

**c**) total meridional wind calculated from Equation (20).

© 2018 Crown Copyright, Met Office. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Cullen, M. The Use of Semigeostrophic Theory to Diagnose the Behaviour of an Atmospheric GCM. *Fluids* **2018**, *3*, 72.
https://doi.org/10.3390/fluids3040072

**AMA Style**

Cullen M. The Use of Semigeostrophic Theory to Diagnose the Behaviour of an Atmospheric GCM. *Fluids*. 2018; 3(4):72.
https://doi.org/10.3390/fluids3040072

**Chicago/Turabian Style**

Cullen, Mike. 2018. "The Use of Semigeostrophic Theory to Diagnose the Behaviour of an Atmospheric GCM" *Fluids* 3, no. 4: 72.
https://doi.org/10.3390/fluids3040072