Vertical Diffusion
Yusuke Ishiguro & Justin Luk
ATM S 380
So what is vertical diffusion?
Three Components:
1.
2.
3.
Shallow convection which redistributes moisture and dry static energy
between two layers in cases of conditional instability
Slow diffusion of moisture in stable conditions
Fast redistribution of dry static energy occurring when the lapse rate is
close to dry-adiabatic
So what does that mean?
Let’s break it down . . . .
Shallow Convection
❖
Thermally driven turbulent mixing, where vertical lifting is capped below
500 mbar
➢
In SPEEDY, it is considered convection that occurs between levels N and N-1
Conditions for Shallow Convection
❖
For convection to occur between levels N and N-1, the following condition
must be met:
❖
Where MSE is moist static energy and MSS is saturation moist static
energy
➢
MSE is used instead of MSS at level N to prevent the process from occurring in dry regions
Static Energy
❖
❖
Moist Static Energy (MSE) describes the state of an air parcel
➢
A combination of the internal energy, potential energy, and latent energy of a parcel
➢
Calculated by adiabatically lifting a parcel to the top of the atmosphere and allowing all
water vapor to condense and release latent heat
Saturation Moist Static Energy (MSS)
➢
MSE when the parcel is at saturation (RH = 100%)
Shallow Convection Code
If there is deep convection, set the
static energy flux and temperature
tendencies at levels N and N-1.
Shallow Convection Code
If there is a difference in relative
humidity, set the relative humidity
flux and relative humidity
tendency at levels N and N-1
If the condition for shallow
convection is met, set the relative
humidity flux and relative
humidity tendency at levels N and
N-1
Dry Static Energy
A thermodynamic variable similar to potential temperature except that kinetic
energy is dissipated into heat.
●
a.
b.
Cp is specific heat at constant pressure
φ is geopotential, equals gz
Vertical Diffusion in Stable Environments
In stable conditions, or at higher levels, vertical diffusion is activated wherever the
vertical gradient of a (scalar) variable is outside some reference bounds. Let ΓA be the
reference gradient of variable A with respect to a generic vertical coordinate Z. The
difference between the values of A at adjacent levels is checked against ΓA, and if:
Ak+1 − Ak > ΓA ( Zk+1 − Zk )
then a net upward flux of A is defined at the interface between the two layers:
uFAk+h = F∗ vdf ( A∗ k − Ak ).
Vertical Diffusion Code
If the sigma value at the half level of k is
greater than 0.5, then vertical diffusion will
occur.
If the relative humidity difference is less
than the relative humidity (DRH0), the
amount of flux will be changed.
Redistribution of Dry Static Energy
Occurs when the lapse rate is close to the dry-adiabatic limit.
Dry Static Energy Code
Diffusion occurs when SEk < SE*k