Climate model parameterizations
Phil Austin
Tuesday, July 27
source: Bony et al., 2006
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Summary from Monday:
Monday summary
2/30
Summary from Monday:
I
Climate models use F = ma, conservation of energy (and
entropy) and conservation of mass to calculate the evolution
of temperature, humidity, wind speed, cloud cover, etc. on a
grid.
Monday summary
2/30
Summary from Monday:
I
Climate models use F = ma, conservation of energy (and
entropy) and conservation of mass to calculate the evolution
of temperature, humidity, wind speed, cloud cover, etc. on a
grid.
I
The energy conservation and water conservation equations are:
dhm
=d
dt
dqT
= −rate of precip removal + rate of precip evaporation
dt
where hm is the moist static energy, which depends on the
temperature, vapor, and potential energy of the air, qT is the
total specific humidity ((mass vapor)/(mass air)), and d is the
diabatic heating is due to radiation.
Monday summary
2/30
Today’s lecture: parameterizations
Coverage:
Tuesday intro
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Today’s lecture: parameterizations
Coverage:
I
Tuesday intro
Calculating the radiative heating/cooling of the atmosphere
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Today’s lecture: parameterizations
Coverage:
I
Calculating the radiative heating/cooling of the atmosphere
I
Diagnosing cloud fraction and cloud overlap
Tuesday intro
3/30
Today’s lecture: parameterizations
Coverage:
I
Calculating the radiative heating/cooling of the atmosphere
I
Diagnosing cloud fraction and cloud overlap
I
Using satellites to validate climate/forecast models
Tuesday intro
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What is a parameterization?
Parameterizations
4/30
What is a parameterization?
I
How do we calculate the effect of fluctuations in wind,
temperature, specific humidity and radiation that occur at
scales smaller than the 200 km grid size? These sub-grid scale
fluctuations can transfer energy and water to and from the
resolved scale flow
Parameterizations
4/30
What is a parameterization?
I
I
How do we calculate the effect of fluctuations in wind,
temperature, specific humidity and radiation that occur at
scales smaller than the 200 km grid size? These sub-grid scale
fluctuations can transfer energy and water to and from the
resolved scale flow
For example:
Parameterizations
4/30
What is a parameterization?
I
I
How do we calculate the effect of fluctuations in wind,
temperature, specific humidity and radiation that occur at
scales smaller than the 200 km grid size? These sub-grid scale
fluctuations can transfer energy and water to and from the
resolved scale flow
For example:
I
Parameterizations
The reflectivity of a grid cell depends on the spatial
distribution of the cloud liquid water
4/30
What is a parameterization?
I
I
How do we calculate the effect of fluctuations in wind,
temperature, specific humidity and radiation that occur at
scales smaller than the 200 km grid size? These sub-grid scale
fluctuations can transfer energy and water to and from the
resolved scale flow
For example:
I
I
Parameterizations
The reflectivity of a grid cell depends on the spatial
distribution of the cloud liquid water
The kinetic energy of air in the grid scale depends on
convective plumes, or the waves developed by air flowing over
mountains
4/30
What is a parameterization?
I
I
How do we calculate the effect of fluctuations in wind,
temperature, specific humidity and radiation that occur at
scales smaller than the 200 km grid size? These sub-grid scale
fluctuations can transfer energy and water to and from the
resolved scale flow
For example:
I
I
I
Parameterizations
The reflectivity of a grid cell depends on the spatial
distribution of the cloud liquid water
The kinetic energy of air in the grid scale depends on
convective plumes, or the waves developed by air flowing over
mountains
The mass of liquid water in a grid scale depends on removal by
falling precipitation
4/30
Coupling between processes
Parameterizations
5/30
Main atmospheric processes and variables
Parameterizations
6/30
heating rate d: observed energy fluxes
Current estimated net imbalance of ≈ 1 W m−2 . How are these
fluxes changing over time?
(Kiehl et al., 2009)
Radiation
7/30
Start with longwave emitters/absorbers: H2 O, CO2
Radiation
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H2 O transmission: US standard atmosphere
Water vapor rotates as well as bends. This makes its transmission
spectrum especially complicated. It absorbs at a broad range of
wavelengths, and remits radiation depending on the wavelength
and temperature.
Radiation
9/30
H2 O transmission: US standard atmosphere
Water vapor rotates as well as bends. This makes its transmission
spectrum especially complicated. It absorbs at a broad range of
wavelengths, and remits radiation depending on the wavelength
and temperature.
I absorptivity= a = 1 - transmissivity
Radiation
9/30
H2 O transmission: US standard atmosphere
Water vapor rotates as well as bends. This makes its transmission
spectrum especially complicated. It absorbs at a broad range of
wavelengths, and remits radiation depending on the wavelength
and temperature.
I absorptivity= a = 1 - transmissivity
I emissivity = = absorptivity (“Good absorbers are good
Radiation
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Modeled emission: Looking down at the surface (T=300
K) from 12 km, no atmosphere. Longwave flux = σT 4
Radiation
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Now add 270 ppm CO2 and a temperature profile.
105 W m−2 is trapped by the atmosphere
Radiation
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Now add tropical water vapor and trap another 61 W m−2
Radiation
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Finally, double the CO2 to 540 ppm and trap another 4
W m−2
Radiation
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Greenhouse warming: 1 layer energy balance
emissivity=absorptivity is determined by the concentrations of the
greenhouse gasses. Total emission is determined by the emissivity
and the vertical temperature profile: Longwave Flux = σT 4 .
Equilibrium greenhouse
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Now double CO2 and raise absorptivity to 81%
Equilibrium greenhouse
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Now double CO2 and raise absorptivity to 81%
I
Tsurface changes about 1.2 K for 4 W m−2 net forcing. This is
the zero feedback response of the planet.
Equilibrium greenhouse
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Now double CO2 and raise absorptivity to 81%
I
Tsurface changes about 1.2 K for 4 W m−2 net forcing. This is
the zero feedback response of the planet.
I
Repeat this with an atmosphere that is warmer than the
surface and find that the extra emission produces net cooling,
because emission from the warmer air is larger than
absorption from surface.
Equilibrium greenhouse
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Could CO2 absorption saturate at large concentrations?
No. Harvey (2001)
Equilibrium greenhouse
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Next step: cloud layering and cloud fraction
(Kiehl et al., 2009)
Cloud fraction
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Cloud fraction
We need to know the cloud fraction as a function of height for
situations like this:
Cloud fraction
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or this:
Cloud fraction
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or this:
Cloud fraction
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Parameterizing cloud fraction: statistical cloud schemes
Cloud fraction
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Parameterizing cloud fraction: statistical cloud schemes
I
Cloud fraction
Basic idea: use cloud simulations at very high resolution
(25-100 m), and small domains (6 km - 300 km), to establish
a relationship between the gridcell specific humidity and
energy and the cloud fraction (Charboreau and Bechtold,
2003)
21/30
Parameterizing cloud fraction: statistical cloud schemes
I
Basic idea: use cloud simulations at very high resolution
(25-100 m), and small domains (6 km - 300 km), to establish
a relationship between the gridcell specific humidity and
energy and the cloud fraction (Charboreau and Bechtold,
2003)
I
Define the saturation deficit, Q ≈ (q vapor − q critical )/σq ,
where σq is the standard deviation of qvapor , q is the gridcell
average, and qcritical is a critical value.
Cloud fraction
21/30
Parameterizing cloud fraction: statistical cloud schemes
I
Basic idea: use cloud simulations at very high resolution
(25-100 m), and small domains (6 km - 300 km), to establish
a relationship between the gridcell specific humidity and
energy and the cloud fraction (Charboreau and Bechtold,
2003)
I
Define the saturation deficit, Q ≈ (q vapor − q critical )/σq ,
where σq is the standard deviation of qvapor , q is the gridcell
average, and qcritical is a critical value.
I
Get qcritical , σq from simulations like this animation
(cloud fields.avi)
Cloud fraction
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Two simulated storms over land and water
TOGA simulates large scale convection over the tropical ocean,
while ARM is summertime thunderstorm convection over
Oklahoma. Simulate the cloud systems for 60 hours, saving cloud
fraction, qT , σq .
Cloud fraction
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Cloud fraction (N) vs. Q1
The result: the dependence of cloud fraction on excess saturation
Q1 is similar for TOGA-tropical (circles) and ARM-Oklahoma (+).
CGCM4 uses this to get the fractional cloudiness in each grid cell
in the model.
Cloud fraction
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Validating cloud statistics: the A-train
An orbiting constellation of satellites measure emission, absorption,
scattering using radiometers (Aqua), radars (Cloudsat) and lidars
(CALIPSO).
Cloud fraction validation
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An example scene: Mixed phase ice/water clouds from
satellite
Cloud fraction validation
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Same scene: A-B transect using radar and lidar
Ice crystals on the left side block the lidar, are but barely visible to
Cloud fraction validation
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Three climate models vs radar/lidar observations: cloud
fraction
Chepfer, 2009
Cloud fraction validation
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ECMWF forecast model (top), satellite lidar (bottom)
Cloud fraction validation
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CGCM4: Monte Carlo independent column approximation
Barker et al., 2004
Cloud layering
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Summary
Summary
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Summary
I
Summary
The radiative heating rate depends on the vertical and
horizontal distribution of greenhouse gasses (including water
vapor) and clouds
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Summary
Summary
I
The radiative heating rate depends on the vertical and
horizontal distribution of greenhouse gasses (including water
vapor) and clouds
I
Cloud distributions are specified by a sub-gridscale
parameterization that links the grid-averaged specific humidity
to cloud fraction
I
The parameters are determined by modeling the same kind of
meteorologcial situation with high resolution cloud models,
and global cloud statistics with satellites.
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Summary
Summary
I
The radiative heating rate depends on the vertical and
horizontal distribution of greenhouse gasses (including water
vapor) and clouds
I
Cloud distributions are specified by a sub-gridscale
parameterization that links the grid-averaged specific humidity
to cloud fraction
I
The parameters are determined by modeling the same kind of
meteorologcial situation with high resolution cloud models,
and global cloud statistics with satellites.
I
Cloud layers are overlapped by randomly constructing vertical
profiles with the correct vertical correlation and averaging the
radiative fluxes from many realizations of the profiles in each
grid cell.
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