cloud microphysics modeling: the state of the art wojciech w. grabowski mesoscale and microscale...
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Cloud microphysics modeling: the state of the art
Wojciech W. Grabowski
Mesoscale and Microscale Meteorology Laboratory
NCAR, Boulder, Colorado, USA
An introduction to cloud microphysics modeling
Wojciech W. Grabowski
Mesoscale and Microscale Meteorology Laboratory
NCAR, Boulder, Colorado, USA
parameterization2 problem:parameterized microphysics in
parameterized clouds
parameterization problem:parameterized microphysics in
(under)resolved clouds
microphysics at its native scale
Cloud microphysics across scales
cloud base(activation of
cloud droplets)
airflow
interfacial instabilities
calm (low-turbulence)
environment
turbulent cloud
Bjorn Stevens, RICO
Eulerian versus Lagrangian methodology (continuous medium versus particle-
based)
Explicit treatment of aerosol effectsversus mimicking impacts of aerosols
Warm (no-ice) versus ice-bearing clouds
Precise and complex versus approximate and easy to apply
Understanding the physics versus numerical implementation
Explicit treatment of aerosol effects (particle-based)
versus mimicking impacts of aerosols (continuous medium)
Water vapor is a minor constituent:
mass loading is typically smaller than 1%; thermodynamic properties (e.g., specific heats etc.) only slightly modified;
Suspended small particles (cloud droplets, cloud ice):
mass loading is typically smaller than a few tenths of 1%, particles are much smaller than the smallest scale of the flow; multiphase approach is not required, but sometimes used with simplifications (e.g., DNS with suspended droplets, Lagrangian Cloud Model);
Precipitation (raindrops, snowflakes, graupel, hail):
mass loading can reach a few %, particles are larger than the smallest scale the flow; simplified multiphase approach needed only for very-small-scale modeling.
Droplet size exaggerated compared to the mean distance!
water vapor
temperature
gradients of the temperature and water vapor near the droplet (established on a time scale of ~millisecond) go to
~10 droplet radii…
T, qv
Vaillancourt et al. JAS 2001
M for macroscopic…
Vaillancourt et al. JAS 2001
Vaillancourt et al. JAS 2001Δr~1μm, Δt~10-8s
Vaillancourt et al. JAS 2001
Vaillancourt et al. JAS 2001
…perhaps expected considering that the volume affected by the gradients is small compared to the entire volume,
about 0.1%...
Lagrangian:
Eulerian:
compressible
anelastic
Ψ(x,y,z,t)
Ψ(x, y, z, t)
Ψ(x+uΔt, y+vΔt, z+wΔt, t+Δt)
Ψ(x, y, z, t+Δt)
Lagrangian versus Eulerian governing equations
EULERIAN MODELING OF THE CONDENSED PHASE
Continuous medium approach: apply density as the main field variable (density of water vapor,
density of cloud water, density of rainwater, etc…)
In practice, mixing ratios are typically used. Mixing ratio is the ratio between the density (of water vapor, cloud water…) and the dry air density.
Mixing ratio versus specific
humidity…
And we also need equation for the temperature. If only phase changes are included, then potential temperature
equation is:
Modeling of cloud microphysics:
solving a system of PDEs
(advection/diffusion type) coupled
through source terms…
A very simple (but useful) model: rising adiabatic parcel…
Take a parcel from the surface and
move it up…
… by solving these equations.
qv
qc
Look not only on the patterns (i.e., processes), but also on specific numbers (e.g., temperature change, mixing ratios, etc).
Invariant variables:
total water,
liquid water potential temperature,
equivalent potential temperature.
Note: equivalent potential temperature is closely related to moist static energy, cpT + gz + Lqv…
Adding rain or drizzle:
What determines the concentration of cloud droplets?
To answer this, one needs to understand formation of cloud droplets, that is, the activation of cloud
condensation nuclei (CCN).
This typically happens near the cloud base, when the rising air parcel approaches saturation.
Computational example:
Nucleation and growth of cloud droplets in a parcel of air rising with vertical velocity of 1 m/s;
60 bins used;
1D flux-form advection applied in the radius space;
Difference between continental/polluted and maritime/pristine aerosols
f=f(r,z) or f=f(r,t)
maritime
a=100 cm-3
continental
a=1000 cm-3 N = a Sb
b=0.50.
0.
0.
1. 1.
0.
0.
0.
600. 600.
20. 20.
0. 500. 500.0.
maritime continental
0. 0.
150. 150.
0. 0.
2. 2.
500. 500.0.0.
maritime continental
0. 0.
150. 150.
0. 0.
2. 2.
!
Grazing trajectory
Growth of water droplets by gravitational collision-coalescence:
Droplet inertia is the key; without it, there will be no collisions. This is why collision efficiency for droplets smaller than 10 μm is very small.
Collision efficiency:
-
cloud water: qc , Nc
drizzle/rain water: qr , Nr
Nucleation of cloud droplets: link to CCN characteristics
Drizzle/rain development: link to mean droplet size
e.g., Morrison and Grabowski JAS 2007, 2008
Double-moment warm-rain microphysics:
a compromise between bulk and bin microphysics
LAGRANGIAN MODELING OF THE CONDENSED PHASE
Lagrangian treatment of the condensed phase:
Eulerian dynamics, energy and water vapor transport:
Lagrangian physics of “super-particles”
a single “super-particle” represents a number of the same airborne
particles (aerosol, droplet, ice crystal, etc.) with given attributes
Coupling
mid – mass of the super-particle
Mid – concentration of super-particles
ΔV – volume of the gridbox
Andrejczuk et al. 2008, 2010
Andrejczuk et al. 2010
CCN of 190 cm-3
CCN of 1295 cm-3
9 hr
3 hr
Andrejczuk et al. 2010
CCN of 190 cm-3
CCN of 1295 cm-3
9 hr
3 hr
Summary:
A wide range of modeling approaches exists that one can use in modeling various aspects of cloud microphysics. Most of them are within the framework of Eulerian modeling, but use of Lagrangian microphysics is rapidly expanding.
The approach selected needs to be tailored to the specific problem at hand. If multiscale dynamics (e.g., convectively coupled waves in the tropics) is the focus, application of as simple microphysics as possible makes sense to use computer time to widen the range of spatial scales. If small-scale dynamics-microphysics interaction is the focus (e.g., entrainment), more emphasis on microphysics is needed.
The multiscale nature of clouds (the range of spatial scales), difficulties of cloud observations (in-situ and remote sensing), and increasing appreciation of the role of clouds in weather and climate make the cloud physics an appealing area of research.