An overview of the theory behind the dionysos equations
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Université du Québec à Montréal. An overview of the theory behind the Dionysos equations. Peter Zwack Jean-François Caron Christian Pagé. Department of Earth and Atmospheric Sciences www.dionysos.uqam.ca. Standard 50 hPa Gridded GEM Model (100km) Simulation Fields at 3 Hour Intervals.

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An overview of the theory behind the dionysos equations

Université du Québec à Montréal

An overview of the theory behind the Dionysos equations

Peter Zwack

Jean-François Caron

Christian Pagé

Department of Earth and Atmospheric Sciences

www.dionysos.uqam.ca


Standard 50 hPa Gridded GEM Model (100km) Simulation Fields at 3 Hour Intervals

  • Vorticity Advection

  • Friction*

  • Orography*

  • Laplacian Temperature Advection

  • Laplacian Latent Heating*

  • Laplacian Sensible Heating*

Calculate

Forcings

Output

* Parameterized Forcing

Input

Contribution of Individual Forcings Piecewise from Any Particular Part of the Atmosphere To

Balance Diagnostics - DIONYSOS

  • Surface Pressure

  • Geopotential

  • Temperature

  • Horizontal Wind

  • Latent Heating Profile*

  • Surface Sensible Heat Flux

  • Orography

  • *Currently deduced using model vertical motion and precipitation

  • Vertical Motion

  • Vorticity Tendencies

  • Geostrophic Vorticity Tendencies

  • Divergence and divergent wind

  • Temperature Tendencies

  • Height and Pressure Tendencies

  • Vorticity and Temperature Advections Tendencies


Omega equation

F at 3 Hour Intervals

F

F

F

F

Forcing

Ageostrophic vorticity tendency term

Included using an iterative process using non-linear balance equation

Only Assumption : Hydrostatic

Omega Equation

Generalized Omega Equation (Räisänen, MWR 1995)

Forcing


Model Input - 3 hours intervals at 3 Hour Intervals

Diagnostics Output Times

Diagnostic Sequence


Diagnostic sequence

Continuity Equation at 3 Hour Intervals

Thermodynamic Equation

  • Vorticity Advection

  • Friction*

  • Orography*

  • Lap. Temperature Advection

  • Lap. Latent Heating*

  • Lap. Sensible Heat Flux*

Vorticity Equation

Dynamic Forcings

Iteration to include the AG tendency as a correction term

Thermodynamic Forcings

* Parameterized Forcing

Diagnostic Sequence

Sequence for each individual forcing

Model Input

After all computations, all fields are filtered (<6Dx) to remove numerically generated noise

Omega

Equation

Forcing

Non Linear Balance Equation

Geostrophic Definition


Diagnostic vorticity tendencies
Diagnostic - Vorticity Tendencies at 3 Hour Intervals

Diagnostics of Vorticity Tendencies

Full Vorticity Equation - No Assumptions


Methodology vorticity tendencies

Laplacian of sensible heating at 3 Hour Intervals

Methodology - Vorticity Tendencies

Vorticity Tendency - Thermodynamic forcing

Laplacian of Sensible Heating

Diagnostics of vorticity tendencies


Methodology vorticity tendencies1

Vorticity advection at 3 Hour Intervals

Methodology - Vorticity Tendencies

Vorticity Tendency - Dynamic forcing

Vorticity Advection

Diagnostics of vorticity tendencies


Methodology temperature tendencies
Methodology - Temperature Tendencies at 3 Hour Intervals

Thermodyamic Equation

Diagnostics of temperature tendencies


Methodology temperature tendencies1

Laplacian of latent heat release at 3 Hour Intervals

Methodology - Temperature Tendencies

Contribution of Latent Heat Released

(Example of thermodynamic forcing)

Diagnostics of temperature tendencies


Methodology temperature tendencies2

Friction at 3 Hour Intervals

Methodology - Temperature Tendencies

Contribution of Friction

(Example of Dynamic Forcing)

Diagnostics of temperature tendencies


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