REGIONAL SPECTRAL MODELS

Saji Mohandas

National Centre for Medium Range

Weather Forecasting

NCMRWF, Dept. Of Sc & Tech., Govt. of India |--------------------------------------------------------------Research Computer&Network Application |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 + 1Truncation: Ellipticalk2 + (Lx/Ly)2 l2 K2 ork2 +(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=0Cm=-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)/ xAg(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)/ xAt(x,y)/ y = Ag(x,y)/ y + Ar(x,y)/ y

9. Compute full model tendencies At(x,y)/ tNote that this is non zero at the boundaries

10. Get perturbation tendencyAr(x,y)/t = At(x,y)/ t - Ag(x,y)/t

11. Convert to spectral spaceAr(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 2t

Go back to step 6.

Lateral Boundary relaxation

t

A

= F – μ (A

t1 – At

g

1)

μ =

1 ( in seconds)

= 1 - max I

ii |0| , J

jj |0| n I,J – half grid points i0,j0- central grid point n=15 Blending for perturbation tendencies is given by t

A

1

= α (Fd - t

Ag

) + α Fm

Fd – dynamics tendency Fm – phyisics tendency

• 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 + SnR- prec.E- Evap.

Sn – Snow melt

Skin Temperature Ts;

Cs Ts/t = Rs + Rl + L + H + GCs – Spec. heat

Rs –net SWRl – Net LWL- Latent heatH –Sens. Heat

G- Ground Heat Flux

Soilm(%)

Stemp(K)

D3 LSP1 D3 LSP2

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)

LSP1 LSP2-LSP1

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