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REGIONAL SPECTRAL MODELS
Saji Mohandas
National Centre for
Medium Range
Weather
Forecasting
NCMRWF, Dept. Of Sc & Tech., Govt. of India
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-------------------------------------------------------------Research
Computer&Network Application
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GSM RSM Eta MM5 WAVE
Regional Spectral Modeling: Issues
• Usual orthogonal basis functions do not
satisfy a given time-dependent lateral
boundary conditions
Solutions for lateral boundary:
Assume cyclic (HIRLAM)
Assume zero (Tatsumi, 1986)
Non-zero boundary causes serious difficulties
when semi-implicit scheme is used
Types of basis functions used
• Double Fourier series
• Chebyshev series
• Fourier series with cyclic boundary
conditions
• Harmonic- sine series
Double Fourier series
•  F cos kx cos ly
•  F cos kx sin ly
•  F sin kx cos ly
•  F sin kx sin ly
where x = x/Lx, y = y/Ly
k,l - wave numbers
Lx, Ly – domain lengths
• For alias free truncations
I > (3K + 5)/2 + 1
J > (3L + 5)/2 + 1
Truncation: Elliptical
k2 + (Lx/Ly)2 l2  K2 or
k2 +(I-1)2/(J-1)2 l2 K2
Perturbation method
• To predict the small scale details while retaining
the large scale (Hoyer, 1987; Juang and
Kanamitsu, 1994)
• Perturbation = Regional field – Base field
• Ap = A – Ag
• Base field is the coarse grid model forecasts which
is run prior to RSM
• Perturbation is converted to wave space for time
integration
Perturbation method uses information from the
coarse grid model over the entire model domain
while the conventional method includes the
external information only through the lateral
boundaries
Perturbation method...
• Perturbation field satisfies the wall
boundary conditions
• Nesting with the coarse grid model is done
such that the perturbation smoothly
approaches zero at the lateral boundary
(Blending)
• Lateral boundary relaxation following
Tatsumi (1986)
Perturbation method …
• Spectral transformation only for the
perturbations
• Nonlinear physics computations are done in
physical space on the full regional field
• Same structure and physics for both the
models
• Semi-implicit time integration in wave
space on perturbations
Perturbation method …
• Amplitude of perturbations tend to be small suitable for climatic simulations
• Lateral boundary relaxation cleaner and natural for
perturbations
• Easy to apply semi-implicit scheme
• Diffusion can be applied to perturbations
• Disadvantage: difficulty in converting physics
u*1( i ,j) =∑∑U1(m,n) . Cn cos(n∏j/J) . Sm sin(m∏i/I)
v*1( i ,j) =∑∑ V1(m,n) . Cn sin(n∏j/J) . Sm cos(m∏i/I)
T1( i ,j) =∑∑T1 (m,n) . Cn cos(n∏j/J) . Sm cos(m∏i/I)
Q1( i ,j) =∑∑ Q1(m,n) . Cn cos(n∏j/J) . Sm cos(m∏i/I)
q1( i ,j) =∑∑q1 (m,n) . Cn cos(n∏j/J) . Sm cos(m∏i/I)
u*=u/m,v*=v/m
(Cm,Sm)=(Cn,Sn)=(1,0) if m,n=0
Cm=-Sm=Cn=-Sn=2
if m,n  0
Step by step computational procedure
1. Run global model. Ag(n,m) at all times
2. Analysis over regional domain At(x,y)
3. Ag(n,m) ==> Spher. trans. ==> Ag(x,y)
4. Ar(x,y)=At(x,y) - Ag (x,y)
5. Ar(x,y) ==>Fourier trans. ==> Ar(k,l)
Now Ar(k,l) satisfies zero b.c.
6. Ar(k,l) ==>Fourier trans. ==> Ar(x,y)
7. Ag(m,n) ==> Spher. trans.==>Ag(x,y)
Ag(m,n) ==>Spectral trans. ==>Ag(x,y)/ x
Ag(m,n) ==>Spectral trans. ==>Ag(x,y)/ y
8. At(x,y) = Ag(x,y) + Ar(x,y)
At(x,y)/ x = Ag(x,y)/ x + Ar(x,y)/ x
At(x,y)/ y = Ag(x,y)/ y + Ar(x,y)/ y
9. Compute full model tendencies
At(x,y)/ t
Note that this is non zero at the boundaries
10. Get perturbation tendency
Ar(x,y)/t = At(x,y)/ t - Ag(x,y)/t
11. Convert to spectral space
Ar(x,y)/t =>Fourier trans.=>Ar(k,l)/t
(Now At(k,l)/ t satisfies boundary cond.)
12. Advance Ar(k,l) in time
Ar(k,l)t+t = Ar(k,l)t-t + Ar/ t 2t
Go back to step 6.
Lateral Boundary relaxation
A
t
t 1
= F – μ (A
μ =
–
t 1
A
)
g
( in seconds)
1

= 1 -  max I , J 
I,J – half grid points
i0,j0- central grid point
n=15
| i  i0 |
| j  j0 |
n
Blending for perturbation tendencies
is given by
A
A
=
α
(F
d t ) + α Fm
t
Fd – dynamics tendency
Fm – phyisics tendency
1
g
• Implicit diffusion
• A local diffusion to diffuse areas of strong
wind
• Asselin time filter
• Provision for Digital Filter Initialisation
• High resolution orography (interpolated
from US Navy data)
• Semi-implicit adjustment for physics
RSM at NCMRWF
•
•
•
•
Basis functions: Double sine-cosine series
Res: 50Km (Hor) 18  (Vert)
Wave num: 54 (Zon) 47 (Mer)
Domain:3N-39N, 56-103E (97X84 grid
points)
• Time step: 300 sec
• Nesting period: 6 hour
• Forecast period: 5 days
• Initial condition: Global model analysis
interpolated to regional domain
• Boundary condition: Global model forecasts
• Lateral boundary relaxation: Tatsumi (1986)
• Physics: Same as the improved version of
NCEP GSM (Kanamitsu, 1989; Kanamitsu
et.al., 1991)
• Only difference is the deep convective
scheme (Kuo replaced by SAS)
• Called Version 0
Physics package
• Diagnostic clouds that interact with
radiation.
• Deep convective parameterization.
• Large scale condensation based on
saturation.
• Vertical diffusion based on static stability
and wind shear.
• Long and Short wave radiation (called
every one hour).
Physics package….
• Shallow convection based on K-profile
• Evaporation of precipitation based on
Kessler’s method
• Gravity wave drag
• Horizontal diffusion
• Surface processes (flux computation using
similarity theory)
• Two-layer soil hydrology with a simple
vegetation effect
RSM Forecasts – SW Monsoon
• Better distribution of rainfall especially over
west coast of peninsula
• Easterly wind bias over North Indian planes
• Southward bias in the track of Monsoon low
pressure systems
• Cyclonic bias over the south peninsula off
the east coast
Sensitivity of land surface
parameterisation on RSM forecasts
Saji Mohandas
E. N. Rajagopal
National Centre for Medium Range Weather Forecasting,
New Delhi
Land surface processes
• One of the most sensitive component of
NWP models
• Influence the lower boundary conditions for
dynamics and thermodynamics of the
atmosphere
• Should be able to provide the adequate feed
back mechanism for PBL and other physical
processes
LSP experiments with RSM
• Two types of land surface parameterisation
schemes used
• Experiment was conducted for August 2001
• Used T80 global model forecasts as the
initial and boundary conditions
• Global surface analysis is used as surface
boundary conditions
LSP schemes used for the study
• LSP1 (with one layer soil moisture) where
evapotranspiration is a function of potential
evaporation
• LSP2 (with two layer soil moisture) where
the evaporation consists of 3 components
namely evapotranspiration, evaporation
from bare soil and canopy re-evaporation
Day-3 Sys. Error, Wind (M/S), (a)LSP1 & (b)LSP2
Day-3 Prec. (CM) AUG 2001
(a)NCMRWF Anal(1.5X1.5), (b)LSP1 & ©LSP2
Soil Moisture M;
M/t = R – E + Sn
R- prec.
E- Evap.
Sn – Snow melt
Skin Temperature Ts;
Cs Ts/t = Rs + Rl + L + H + G
Cs – Spec. heat
Rs –net SW
Rl – Net LW
L- Latent heat
H –Sens. Heat
G- Ground Heat Flux
D3 LSP1
D3 LSP2
Soilm(%)
Stemp(K)
LSP1
LSP2-LSP1
NETSWF(W/m**2)
NETLWF(W/M**2)
LSP1
LSP2-LSP1
Sens-HF(W/m**2)
Late-HF(W/m**2)
Ground-HF(W/m**2)
Conclusions
• Both versions of LSP schemes produced
comparative results showing easterly wind bias
over Central India and weakening of Somali
current
• Rainfall amount was slightly higher for LSP2
• RMSE s were slightly higher for LSP2 at lower
troposphere
• The difference is mainly over A.P. region where
the maximum impact on surface energy balance is
due to larger evaporation in LSP2 compared to
LSP1
Future plans
• Implementation of new version of NCEP
RSM
• Implementation of the regional assimilation
and Analysis scheme
• Use of RegCM/RSM at NCMRWF as a
platform for carrying out seasonal/climate
simulations and impact studies