New dynamics in the Met Office UM

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New dynamics in the Met Office UM

• Terry Davies
• Met Office
• Bracknell, UK

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New Dynamics - Main features

• Non-hydrostatic deep atmosphere equations
• Hybrid-height terrain-following vertical
  coordinate
• Charney-Phillips vertical staggering
• C-grid horizontal staggering
• 2 time-level semi-implicit predictor-corrector
  scheme
• Semi-Lagrangian advection
• 3d variable-coefficient iterative elliptic solver
  
• No reference profile nor vertical separation

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New Dynamical Core
Old Formulation
New Formulation

• Semi-Lagrangian advection
• Semi-implicit time integration
• Horizontal staggering - C grid
• Vertical staggering - Charney- Phillips
• Hybrid-height co-ordinate
• Non-hydrostatic formulation

• Eulerian 4th order advection
• Split-explicit time integration
• Horizontal staggering - B grid
• Vertical staggering - Lorenz
• Sigma-pressure co-ordinate
• Quasi-hydrostatic formulation

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2 time-level semi-implicit, semi-Lagrangian

• Efficiency - long timestep
• Advection accuracy and shape preservation
• Reduced filtering
• Better stability and reduced noise
• Better coupling with physics and data
  assimilation

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Vertical and Horizontal Grid Staggering

• Horizontal staggering - Awakawa c-grid
• No grid decoupling
• Better geostrophic adjustment for wavelengths of
  gridsize less than Rossby radius of deformation
• Vertical staggering - Charney-Phillips
• No computational modes
• More consistent with thermal wind balance
• Can have complications in coupling with boundary
  layer parametrisation

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Predictor-Corrector with no basic state profile

• Remove compromises involved with choice of basic
  state profile
• Better vertical coupling of physics and data
  assimilation
• Improved stability and reduced noise

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Non-hydrostatic deep atmosphere equations Height
as vertical coordinate

• Full equations used with (virtually) no
  approximations
• Suitable for running at very high resolution

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Predictor - Corrector Solution Method
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Idealised configurations

• 1-d vertical
• 2-d horizontal - global shallow water
• 2-d slice - limited area 1-d horizontal and 1-d
  vertical
• 3-d limited area - with/without Earths rotation,
  with/without physics, dry/wet - approaching LES,
  CRM
• 3-d global dynamical core - simplified physics
• 3-d global idealised - with/without Earths
  rotation
• Aquaplanet - 3-d global, full physics, no land

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Issues addressed using idealised tests

• Numerical convergence
• Coding errors
• Formulation, algorithm changes
• Accuracy - parameter sensitivity, conservation
  and positivity
• Efficiency
• Stability
• Grids and domains
• Boundary conditions - upper, lower and lateral
• Simplified physics - wave propagation, energy
  transfers, balance, orographic effects, etc.

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Idealised configurations in UM5.3

• 3-d global dynamical core - simplified physics
• 3-d global idealised - with/without Earths
  rotation, with/without physics, dry/wet, inviscid
• 3-d limited area - with/without Earths rotation,
  with/without physics, dry/wet, inviscid, updated
  or fixed lateral boundary conditions, cyclic or
  bicyclic lateral boundary conditions .
  approaching LES, CRM
• Aquaplanet - 3-d global, full physics, no land
• User options to specify initial data profiles,
  idealised orography (cosine hills, ridges etc)
  and vertical grids

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Conservation of moisture 3
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Conservation of moisture 5

• To impose conservation constraint need to know
  density at time-level n1
• Density updated after solver
• For passive tracers perform semi-Lagrangian step
  after solver
• For moisture we need to perform a prediction step
  to allow for moist processes in dynamics.
  Conservative step requires a repeat of the
  semi-Lagrangian step after solver

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Moisture variables
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Density
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Continuity and moisture

• Many hydrostatic primitive equation models do not
  properly allow for moist effects in the
  continuity equation.
• The derivation of the continuity equation in a
  generalised vertical coordinate system involves
  an elimination of density using the hydrostatic
  equation without recognising that different
  densities are involved.

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Continuity equation
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Moisture variables
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Configurations run

• Global (432x325x38) plus 3DVAR running in
  parallel since August 2001 - operational in
  mid-June.
• Mesoscale (UK, 11km) running in parallel since
  October 2001 - operational as above.
• Climate, HadGEM (192x145x38 or 96x73x38). AMIP
  runs.
• Coupled model run for 30 years.
• Stratospheric (96x73, 50 or 60 levels, lid mainly
  around 60km - spectral GWD - QBO)

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Global forecast model
Benefits
Problems

• Reduced NH RMSE in summer and at early FC ranges
  in winter
• Deeper extratropical cyclones
• Improved tropical cyclone predictions
• Reduced temperature biases
• Improved stratospheric circulation statistics
  (eddy temperature fluxes)
• Reduced noise in ND forecasts.
• Improved radiative balance - OLR

• Tropical upper level wind RMSE too large (6-10)
• SH errors larger - analysis differences
• Grid point storms at N216 - controlled by RH
  based CAPE.
• Tuning of orographic and BL drag and diffusion
  still required.

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Climate model
Benefits
Problems

• Improved marine stratocumulus
• Reduced stratospheric cold bias
• Improved radiative balance - OLR

• Tropical precipitation - large isolated
  large-scale precipitation rates
• Hadley circulation too strong - increased errors
  in divergent circulations
• Summers too dry over Europe