Why do moisture convergence deep convection schemes work for more scales than those they were in principle designed for?

1
Why do moisture convergence deep convection
schemes work for more scales than those they were
in principle designed for?

• Jean-François Geleyn
• ONPP/CHMÚ CNRM/Météo-France
• (on an incentive from Philippe Bougeault and
  using ideas
• of Brian Mapes() and Jean-Marcel Piriou)
• CCWS, Tartu, Estonia, 24-1-2005
• () in The physics and parameterisation of moist
  atmospheric convection, pp.321-358, NATO ASI
  Series, 1997, Kluwer Academic Publishers,
  Dordrecht

2
P. Bougeault (pers. com. - 12/1/04)

• I was well conscious about this limitation (of
  the moisture convergence closure) in 85, but the
  problem is that I mostly wanted to fit GATE data,
  where there is no correlation between CAPE and
  rainfall, while there is a strong correlation
  between MOCON and rainfall. But, as Mapes
  rightly says, the latter does not guarantee a
  causal link because one might mix cause and
  consequence.
• But, since it works on this basis at Meteo-France
  as well as at ECMWF for 20 years, this cannot be
  that wrong either!

3
Why is deep-convection so special in the
parameterisation trade?

• Because such a parameterisation automatically
  requires some knowledge of the models resolved
  tendencies (closure problem).
• Because it is a non-hydrostatic phenomenon that
  we try to parameterise in a hydrostatic-type
  framework (for the scales -above 10km- where we
  need such a parameterisation).
• Because the basic atmospheric state always looks
  at the edge of a yes/no behaviour.
• Because visible convection appears like a local
  auto-organised process while its invisible
  influence and conditions of existence are very
  much of a large-scale type.

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Why do we need a parameterisation of
deep-convection?

• Because for models that do not resolve the 10km
  scale, associated clouds are clearly sub-grid and
  look like the result of an auto-organisation
  process.
• Because without it, resolved microphysics of
  clouds and precipitation takes over the vertical
  stabilising role, but at the wrong scale with
  sometimes catastrophic consequences on the
  modelled atmosphere.
• Not because it helps maintaining the correct
  local vertical gradients of temperature and
  humidity but because it controls the intensity of
  larger-scale dynamical adjustment motions (Hadley
  cell, ).

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Convective instability is a local property
Conditional instability of the first kind
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The mass-flux approach

• Hypotheses
• steady cloud
• negligible updraft area

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The mass-flux approach (Bougeaults 1985 variant)
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The CISK vs. WISHE controversy
Static view (there is also a wave-propagation
equivalent)
Conditional Instability of the Second Kind
Wind Induced Surface Heat Exchange
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The CISK vs. WISHE main difference
But the truth seems to be situation- and scale
dependent !
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The Quasi-Equilibrium (QE) concept history

• Whatever causality is at work, QE is verified at
  very large scale, but not necessarily below.
• Study of the phenomenology of convection pushed
  to the concept of mass-flux formulation for
  convective parameterisation schemes.
• This shifted the old problem of convective
  closure from budgets to complex questions about
  the dynamics of convective circulations.
• But the (misleading?) answer was to replace the
  search of an additional convective impact under
  given local circumstances by that of a full
  convective answer to a non-convective forcing.

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The Quasi-Equilibrium (QE) concept controversy

• CISK idea of QE convective circulations are
  determining the larger scale vertical
  velocities that in turn force convection.
• WISHE idea of QE being in a lift, you are not
  going up because the counter-weight goes down.
• Anti-QE thinking (20 years lost, they say)
• Scales are not separable (the invisible part
  of convection is at the scale of the Rossby
  radius of deformation)
• Forcing and answer are not really separable
  either (at least scale-dependent in a model where
  the return flow must be accounted for in the same
  grid-box)!
• There is no under-law of convective regions
  dynamics that aggregates local behaviours to a
  simple balance.

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QE and causality. Le Châteliers principle as an
answer? (1/2)

• Chemical reactions QE if the modification of
  some parameters does displace the equilibrium,
  other forces counteract the primary evolution,
  but only partly.
• Mapes (1997)
• If convective heating follows cooling by
  adiabatic ascent (WISHE in full QE meaning) the
  resulting effect will be cooling
• If convective heating precedes cooling by
  adiabatic ascent (CISK in full QE meaning) the
  resulting effect will be heating.
• Test to be done by statistical differences
  between observations of active and non-active
  periods.

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QE and causality. Le Châteliers principle as an
answer? (2/2)
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QE gt scale separation. Which concept to replace
that? (Mapes, 97)
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Vertical velocity. Which representativeness?
Which use?
For any conservative quantity ? one may
symbolically write
In other words, the computed large-scale vertical
velocity is just the average of the (rare) cloud
ascents and of a slightly sinking environment
everywhere. Hence the large scale vertical
advection term is dynamically meaningless (but
model-wise unavoidable) and has to be compensated
by a good estimate of the mass flux, slightly
bigger thanks to surface evaporation.
Thus, if QE is doubtful, the mass-flux
parameterisation should never use the diagnosed
large-scale vertical velocity as input.
16
What else do we have as input for the closure
assumption?

• CAPE (Convective Available Potential Energy)
• CIN (Convective INhibition energy)
• Moisture convergence a good old concept first
  introduced by Kuo (1965, 1974) in order to get
  rid of convective adjustment
• Moisture availability an extension of the
  previous concept that tries to get rid of the QE
  constraint through adding local auto-organised
  moisture sources for a bulk convective
  condensation (a synthesis of the 3 above ones?)

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Standard ingredients of a convective
parameterisation (and new ideas?)
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Summary

• The MOCON ? Rainfall link is sufficiently
  stronger than any equivalent (at large scale and
  in a steady environment) for schemes
  intelligently based on such a closure to be very
  robust and applicable even if the balance is less
  accurate.
• Going further implies to stop thinking
  large-scale forcing vs. cloud balancing
• Introducing a local organisation source of
  moisture leads to the overall concept of (CAPE-
  CIN-dependent) moisture availability
• The cloud-stationarity hypothesis might be
  relaxed
• What then really counts is the Bulk Convective
  Condensation rate (BCC).
• Bougeaults 85 scheme anticipates such steps, but
  not enough for meso-scale-organised and/or dry
  environmental cases.