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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

slide2

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

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

slide4

Model Input - 3 hours intervals

Diagnostics Output Times

Diagnostic Sequence

diagnostic sequence

Continuity Equation

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

Diagnostics of Vorticity Tendencies

Full Vorticity Equation - No Assumptions

methodology vorticity tendencies

Laplacian of sensible heating

Methodology - Vorticity Tendencies

Vorticity Tendency - Thermodynamic forcing

Laplacian of Sensible Heating

Diagnostics of vorticity tendencies

methodology vorticity tendencies1

Vorticity advection

Methodology - Vorticity Tendencies

Vorticity Tendency - Dynamic forcing

Vorticity Advection

Diagnostics of vorticity tendencies

methodology temperature tendencies
Methodology - Temperature Tendencies

Thermodyamic Equation

Diagnostics of temperature tendencies

methodology temperature tendencies1

Laplacian of latent heat release

Methodology - Temperature Tendencies

Contribution of Latent Heat Released

(Example of thermodynamic forcing)

Diagnostics of temperature tendencies

methodology temperature tendencies2

Friction

Methodology - Temperature Tendencies

Contribution of Friction

(Example of Dynamic Forcing)

Diagnostics of temperature tendencies

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