Radiativeconvective models

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Radiative-convective models

• Adam Sobel
• Columbia University
• GCC Summer School, Banff

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What is a radiative-convective (or,
single-column) model?
Basically, a model which has no horizontal
degrees of freedom and so represents vertical
energy transfers only. It is a purely
thermodynamic model cannot model momentum in any
reasonable way without a horizontal coordinate.
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Fundamentals(e.g., Yanai et al. 1973, JAS 30,
611-627)
Start from primitive equations for dry static
energy scpT gz and specific humidity q.
Average over a grid cell and make some standard
assumptions, and obtain equations for the
grid-averaged variables
Where the convective heating Qc Lv(c-e) ?/?p
(?s) (L_v latent heat of condensation,
ccondensation, eevaporation)
And moisture sink Qq (e-c) ?/?p (?q) sQc
dp Lv P ?sps LvP H sQq dp -P
?qps E-P integrals taken from surface up to
nominal tropopause where ? 0
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Assumptions

• Horizontal transfers of energy at the subgrid
  scale are negligible compared to those in the
  vertical - plane-parallel assumption for
  convective and turbulent fluxes as well as
  radiative (QR?FR/?p)
• We will need to parameterize the terms on RHS
  Qc, QR, Qq, in terms of mean quantities T, q
  (same as in GCMs). Not at all obvious that this
  can be done.

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What is a radiative-convective (or,
single-column) model?
An RCM solves the equations for s (equivalently,
T or ?) and q
At a single horizontal location, representing an
area from a GCM grid box to an entire planet.
The physics terms, Qs, are parameterized.
The advection terms, containing u and ?, cannot
be computed internally, as the velocities depend
on momentum, incl. pressure gradients etc.
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What do we do about the advection terms? 3
choices

• Assume they are zero appropriate for an entire
  planet. Then the steady state is
  radiative-convective equilibrium Qc QR, and
  EP
• Prescribe them from observations, or some other
  way
• Parameterize them too, somehow

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Application 1a global mean climate theory

• A la Manabe and colleagues, 1960s
• Advection terms set to zero, as appropriate for
  global average
• counterpart to energy balance models which
  include meridional transport, but whose vertical
  energy transfers are highly simplified in RCM,
  vertical is taken more seriously, horizontal is
  not dealt with
• questions what determines the global mean
  temperature of the planet, at surface and in free
  troposphere? How do tropospheric temperature
  structure and absorber amounts influence middle
  atmosphere (assumed in radiative equilibrium)?

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Radiative vs. radiative-convective equilibria
Simple convective scheme adjustment of T(z) to
prevent lapse rate from exceeding critical
value. No explicit consideration of humidity
(except radiatively). Energy conserved. Warms
the troposphere and cools the surface.
Manabe and Strickler 1964, J. Atmos. Sci. 21,
361-385.
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A brief word about convective parameterizations
Most modern convective schemes are, one way
or another, adjustment schemes. This means that
they tend to force the temperature profile
towards a particular vertical structure, usually
something close to a moist adiabat. The scheme
fires if the near-surface air is relatively warm
and moist (high moist static energy or equivalent
potential temperature) compared to the dry
static energy or potential temperature of the
free troposphere. The scheme will then warm the
troposphere and/or cool and dry the boundary
layer to stabilize the sounding. Modern schemes
do not require grid-scale saturation in order to
fire though Manabes MCA did.
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Water vapor feedback
Based on obs of seasonal cycle, assume fixed
relative rather than specific humidity in simple
RCM. Result climate sensitivity to changes in
CO2, etc., significantly increased. Quantitatively
, this result is in the range obtained by
full coupled GCMs today.
Manabe and Wetherald, 1967 Thermal Equilibrium
of the Atmosphere with a Given Distribution of
Relative Humidity JAS, 24, 241259
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Example 1b spatially varying RCE as an input to
dry models for the circulation

• Some features of the atmospheric circulation may
  be
• understood in terms of dry dynamics. Models in
  which the
• thermodynamic equation is
• d?/dt (?e(y,z) - ?)/?
• have been useful for this purpose (e.g.,
  Schneider and
• Lindzen 1977 Held and Hou 1980) Since for a
  steady solution
• with no flow ? ?e, ?e is the RCE solution. The
  idea is that
• the moist physics can be entirely parameterized
  as relaxing
• towards ?e on a fixed time scale ?. To complete
  the theory,
• we have to compute ?e with an explicit moist
  model.

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RCE Calculations with Emanuel single-column model
(Renno et al. 1994, JGR, 99, 14429-14441)

• Convective and (clear-sky) radiation
  parameterizations
• Slab ocean mixed layer
• Annual average insolation (function of latitude)
• CO2, Ozone at reasonable values
• Surface wind speed7 m/s
• Surface albedo tuned to give reasonable climate
  near equator

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Rad-conv. equilibrium temperature as a function
of latitude, annual average radiation
Albedo tuned to give realistic sounding at
equator. Note x axis only goes to 45 degrees,
already well below freezing at surface.
Circulation needed to warm up Canada!
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Application 2 testing physical parameterizations

• test bed for GCMs see how the
  parameterizations function without added
  complexity of interactions with dynamics
• Large-scale advection terms specified, e.g. from
  obs though this is not trivial to do, as
  requires accurate divergence vertical velocity.
  In most places routine obs are not enough, field
  expts required
• Compare T and q to obs. Comparing precipitation
  or convective heating is not generally meaningful.

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Example simulations of ASTEX Lagrangian field
experiment (1992) - Boundary layer dynamics
Bretherton et al., Bound. Layer Meteor., 93,
341-380. ½ the models were actually LES rather
than SCM Questions what controls low
cloudiness? Entrainment physics, cloud
microphysics, surface flux feedbacks but just
simulations of ABL, free troposphere
essentially completely given. Single column
follows low-level flow.
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inversion height
liquid water path
Rate of change of inversion height is a measure
of entrainment rate
Related to cloud albedo
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Example testing deep convection schemes
Temperature error with (above) without
(below) downdrafts
time
Sud and Walker 1993, Mon. Wea. Rev. 121,
3019-3039 Adding downdrafts to a scheme, see the
difference. Forced by time series of advection
terms from GATE field experiment. Compare
temperature humidity to obs.
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Precipitation is not a meaningful variable to
compare to obs!
Dominant balance in s equation is ??s/?p ¼ Qc
QR, variations QcÀ QR, and ?s/?p ¼ const, so
Qc?, and PsQc dp. Thus if ? given, P is too,
almost independently of model physics (which is
what were trying to test)
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• Errors in T, q in such tests are more meaningful.
  But
• even then, success doesnt mean the scheme is
  correct,
• because in the full GCM, the dynamics are
  different
• the scheme will be interacting with the advection
  terms.
• In the deep tropics, it may be just as valid to
  consider the
• rather different limit in which ? is completely
• determined by the heating the s equation
  reduces to
• ??s/?p Qc QR
• which is diagnostic for \omega, instead of
  prognostic for
• s (or T). We must give up on prediction of
  temperature
• but thats ok, because it doesnt vary much
  anyway in the
• deep tropics. This is the so-called weak
  temperature
• gradient (WTG) approximation.

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Justification for WTG
Precip is a more interesting field than
tropospheric temperature, in the
tropics. Tropospheric temperature has very small
gradients. Precip looks something like SST, but
sharper.
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Some WTG simulations (Sobel Bretherton 2000,
J. Climate 13, 4378-4392)
Comparing obs SST-P relation to that
computed using Emanuel RCM with T(p) held fixed,
no urq
Comparing precip in QTCM of Neelin and Zeng
(2000, JAS 57, 1741-1766) to WTG RCMs with same
physics, at each grid point
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Summary

• An RCM is a 1D model representing vertical energy
  transfers advective, radiative, convective
• Advective terms must be imposed, ignored, or (in
  some recent approaches) parameterized
• Advective terms 0 is radiative-convective
  equilibrium, which is adequate to understand
  some gross aspects of the global mean climate
• Advective terms imposed when representing a
  single column, e.g. for testing parameterizations
• In the latter case, precipitation/heating is not
  a meaningful output (at least over tropical
  oceans)
• There are some new approaches to parameterizing
  large-scale dynamics for tropical applications

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Temperature
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Specific humidity
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Relative humidity
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Moist static energy