3. Model Setup and Initialisation
3.1 Domain Parameters and Boundary Conditions
For the 3d models we give the following grid and boundary specifications:
- Domain Size:
- Domain Width : 6400 m
- Domain Length : 6400 m
- Domain Height : 3000 m
- No. of Grid Points:
- x grid points: 64
- y grid points: 64
- z grid points: 75
- Implying a Resolution:
- dx = 100 m
- dy = 100 m
- dz = 40 m
- Boundary conditions:
- Lateral: Periodic
- Top : In order to minimize spurious reflection of upward propagating
gravity waves, you may want to use a sponge layer for damping
perturbations. The sponge layer should not start any lower than
200 m above the mean inversion height.
- Bottom : Prescribed Fluxes. See section 3.3 for more details.
For the 2d models the same boundary specifications apply. Use for the
grid specifications:
- Domain Size:
- Domain Width : 409600 m
- Domain Height : 3000 m
- No. of Grid Points:
- x grid points: 64*64 = 4096
- z grid points: 75
- Implying a Resolution:
For the 1d models the only relevant specification is the vertical resolution.
We prescribe the same vertical resolution dz=40m as used for the 2d/3d-models
in order to keep resolution effects out of the intercomparison as much
as possible.
REMARK: It appears that some 1d-models have difficulties with
the (high) 40m resolution because of "hard-coded" resolution
dependancies. Therefore, only those 1d-modellers who really have
insurmountable problems with the 40m resolution can use a more coarse
resolution. In that case we request to use the ECMWF-standard
resolution. In the Appendix one
can find the level heights and the corresponding initial fields and
forcings for this more coarse resolution.
3.2 Wind and Thermodynamic Profiles
Based on the observed profiles the following initial setup for the
horizontal wind components (u,v), liquid potential temperature
(theta_l) and the specific total water content (q_t) is proposed. Other profiles
such as pressure, absolute temperature, etc, can be deduced assuming
hydrostatic equilibrium. Initially, it can be assumed that there is zero
liquid water (q_l=0.0), so that:
theta = theta_l
q_v = q_t
(Tables with the profiles for the prescribed vertical 40m resolution can be
found in the Appendix )
u [m/s]
0 < z < 700 -8.75
z > 700 -8.75 + 1.8E-3 * (z - 700)
v [m/s]
z > 0 0.0
q_t [g/kg]
0 < z < 520 17.0 + (16.3 - 17.0)/(520) * z
520 < z < 1480 16.3 + (10.7 - 16.3)/(1480 - 520) * (z - 520)
1480< z < 2000 10.7 + (4.2 - 10.7) /(2000 - 1480) * (z - 1480)
z > 2000 4.2 - 1.2E-3*(z - 2000)
theta_l [K]
0 < z < 520 298.7
520 < z < 1480 298.7 + (302.4 - 298.7)/(1480 - 520) * (z - 520)
1480< z < 2000 302.4 + (308.2 - 302.4)/(2000 - 1480) * (z - 1480)
z > 2000 308.2 + 3.65E-3 * (z - 2000)
The sensible and latent heat fluxes are prescribed for the 1d, 2d and 3d
models as:
wtheta = wtheta_l = 8 x 10^-3 K m/s
wqt = wqv = 5.2 x 10^-5 m/s
The momentum fluxes are prescribed by
uw = -u(u*^2) / (u^2+v^2)^(1/2)
vw = -v(u*^2) / (u^2+v^2)^(1/2)
where u* = 0.28 m/s and the velocities (u and v) are the values at the
lowest grid point level in the model. This way, only the total momentum flux
is fixed to u*^2.
REMARK: It appears that for some 1d-models it is not trivial to
prescribe surface fluxes because of the use of implicit schemes. If
this gives serious problems one can use an interactive surface layer scheme,
provided that the fluxes remain within 10% of the
prescribed surface fluxes!
Additional surface characteristics:
surface pressure: ps = 1015 mb sea
sea surface potential temperature: ths = 299.1 K
implying a sea surface temperature: ts = 300.375 K
sea surface specific humidity: qvs = 22.45 g/kg
For all 3d, 2d and 1d models the large scale advection, subsidence and
radiation are prescribed according to:
Large Scale Subsidence w [m/s]
Apply the subsidence on the prognostic fields q_t, theta_l, u and v.
0 < z < 1500 - (0.0065/1500) * z
1500 < z < 2100 - 0.0065 + 0.0065/(2100 - 1500) * (z - 1500)
z > 2100 0.0
Radiative Cooling, dtheta/dt (K/sec)
0 < z < 1500 -2.315 * 10^-5
1500 < z < 2500 -2.315 * 10^-5 + 2.315 * 10^-5 /(2500 - 1500) * (z - 1500)
z > 2500 0.0
Remark: It appears that it is important for some 1d-models that
above the inversion the heating due to subsidence is exactly
compensated by radiative cooling (due to the relative long
time-integration of 36 hours). We therefore prescribe that above the
inversion, i.e. for z>2000 the prescribed radiative cooling is simply
choosen to be minus the heating due to subsidential heating. In
formula:
( d theta_l / dt )_rad = w_subs ( d theta_l / dz )
For the 3d/2d-runs where the simulation time is much shorter this
modification can be ignored.
Large Scale Horizontal Advection
The only significant diagnosed large scale advection term is a low
level drying of about 1 g/kg day^-1 (Holland and Rasmusson
1973). We therefore prescribe a moisture tendency dq_t/dt in
the subcloud layer due to horizontal advection of:
0 < z < 300 - 1.2 * 10^-8 s^-1
300 < z < 500 - ( 1.2 * 10^-8 - 1.2 * 10^-8 * (z-300)/(500-300) ) s^-1
z > 500 0
All other large scale advection terms should be put to zero.
3.5 The Geostrophic Wind
The zonal u-component of the geostrophic is decreasing with 1.8 * 10^-3 s^-1
corresponding with the observed wind above the mixed layer. The
geostrophic v-component is assumed to be zero.
z > 0: : u_g = - 10 + 1.8 * 10^-3 * z [m/s]
z > 0: : v_g = 0.0 [m/s]
3.6 Initial pertubations
The 3d and 2d models are initialised with random fluctutions of theta_l
and q_t at the lowest 40 levels given by:
theta : [-0.1 , +0.1 ] (K)
q_t : [-2.5*10^-2, +2.5*10^-2] (g/kg)
Initial subgrid profile of subgrid TKE:
TKE 0 < z < 3000 : 1 - z/3000 m^2/s^2
3.7 Other Parameters and Remarks
Latitude: 15 Degr. implying a
Coriolis parameter: 0.376 * 10^-4 s^-1
c_p 1005. J kg^-1 K^-1
g 9.81 m s^-2
Rd 287. J kg^-1 K^-1
L 2.5 * 10^6 J kg^-1
surface pressure 1015 mb
The microphysics parameterizations in the 2d and 3d modelss should be
switched off.
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