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An overview of the theory behind the Dionysos equationsPowerPoint Presentation

An overview of the theory behind the Dionysos equations

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### An overview of the theory behind the Dionysos equations

Université du Québec à Montréal

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

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 EquationGeneralized Omega Equation (Räisänen, MWR 1995)

Forcing

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 SequenceSequence 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 at 3 Hour Intervals

Diagnostics of Vorticity Tendencies

Full Vorticity Equation - No Assumptions

Laplacian of sensible heating at 3 Hour Intervals

Methodology - Vorticity TendenciesVorticity Tendency - Thermodynamic forcing

Laplacian of Sensible Heating

Diagnostics of vorticity tendencies

Vorticity advection at 3 Hour Intervals

Methodology - Vorticity TendenciesVorticity Tendency - Dynamic forcing

Vorticity Advection

Diagnostics of vorticity tendencies

Methodology - Temperature Tendencies at 3 Hour Intervals

Thermodyamic Equation

Diagnostics of temperature tendencies

Laplacian of latent heat release at 3 Hour Intervals

Methodology - Temperature TendenciesContribution of Latent Heat Released

(Example of thermodynamic forcing)

Diagnostics of temperature tendencies

Friction at 3 Hour Intervals

Methodology - Temperature TendenciesContribution of Friction

(Example of Dynamic Forcing)

Diagnostics of temperature tendencies

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