Computation and analysis of the Kinetic Energy Spectra of
a SI-SL Model GRAPES
Dehui Chen and Y.J. Zheng and Z.Y. Jin
State key Laboratory of Severe Weather (LaSW) Chinese Academy of Meteorological Science (CAM
S)
( for MCS-Typhoon conference on 31 Oct.- 3 Nov. 2006 in Boulder, US-NCAR)
Outline
Introduction Methodology Exper. design
Conclusion Results
•Why ?•Atmo. KES•Models KES
•2D-DCT•Model•Data•Exp. design
• Impacts of diff. t, x△ △• KES – spin up• SL vs Eulerian
• △t vs x△• H. eff. Resol.• Spin up time• GRAPES vs WRF
Further work
•△t vs p. schm • Interpolation•Preci. spectra
1. Introduction
KES analysis
• The accuracy, stability and conservation (mass,
energy) have to be well considered in a numerical
model design
• KES is one of the most fundamental spectra to
examine in order to understand the dynamical
behavior of the atmosphere
• KES analysis is used to evaluate the performance
of the numerical model GRAPES
GRAPESV. coordinate
H. terr. Flw v. co
PhysicalsFull phy. package
ModelUnified model
DAS3/4DVAR
Coding Modul. Parall
Dynamic corefull compressible
HY/NH
DicretizationSI-SL
Grid systemLat.-Long.
About GRAPES (Global/Regional Assimilation PrEdiction System. Since 2000)
KES analysis?
• The Semi-Lagragian model promises an advantage of using a larger time step over an Eulerian model
• A question could be asked: Can a SL model preserve the physical features when a larger t is used△ ?
• Further more, when the spatial resolution is increased, can a SL model capture the structure of meso or smaller scales? Will the resolved large scale system be contaminated?
The atmospheric KES observed
Large scale (approxim. spectral slope of -3)
Meso scale (approxim. Spectral slope of -5/3)
From Dr. B. Skamarock
Charney(1947) 、 Smagorinsky(1953) 、 Saltzman and Teweles(1964): KES~K-3
Nastrom and Gage (1985) 、Lindborg （ 1999 ） : KES~K-3, K-5/3
KES by MM5, COAMPS and WRF-ARW
From Dr. B. Skamarock
KES by WRF-ARW with different x△
From Dr. B. Skamarock
2. Methodology
2. Methodology
• The method of 2D-DCT (2 Dimensional, Discrete Cosine Transform) is used for the calculation of GRAPES’s KES (Denis et al., 2002) without de-trending and periodicity
2. Methodology (cont.)
• In practice, the KE spectrum derived from the model’s horizontal wind field is: vertically averaged from the 12th to 26th layer of the model;
• and temporally averaged from 12 to 36 h forecasts.
• The KE spectrum is computed without the lateral boundary (5 grid point zone) of the limited area model.
3. Experiment design
Model configuration
SI - SL scheme
Arakawa-C staggered grid
Charney-Philips staggered layer
No-hydrostatic
Microphysical: NCEP 3-class simple ice scheme
Long/short wave radiation: RRTM/Dudhia
Full compressible primitive equations
PBL: MRF scheme
Kain-Fritsch scheme
Vertical L31, top-35km
3. Experiment design
• I.C. and L.B.C.: NCEP analysis 1o×1o; L26; Interval: 6 hours
• △t= 60s – 1800s
• △x= 5km – 50km
• 3DVAR: Non
4. Results
The impact of △t and △x on KES of GRAPES
Smaller △t , closer to ideal line
The impact of △t and △x on KES of GRAPES
Smaller △t , closer to ideal line
The impact of △t and △x on KES of GRAPES
Smaller △t , closer to ideal line
The impact of △t and △x on KES of GRAPES
Better, △t = 180s
The impact of △t and △x on KES of GRAPES
Better, △t = 60s
The impact of △t and △x on KES of GRAPES
feasible, △t = 30s
Remarks:
• (1) KES dramatically deviates from Lindborg reference at about 5 x△ , in which KES begins to decay rapidly. So, 5 x△ is defined as the highest effective resolution.
• (2) Smaller t,△ KES closer to Lindborg reference for x=50△ o – 10o.
• (3) It exists an “optimal” t△ when x△ is smaller than a threshold ( x≤0.05△ o)
Relationship between the effective t and x△ △
Spin up time of KES
Longer FT, more KES(about 5 hrs)
GRAPES vers WRF
In term of KES, GRAPES is comparable to WRF
Conclusion
1
23
4
5
Longer FT is, more KES are developed(about 5 hrs vs 5hrs)
There is a fit choice for both
t and x△ △
Highest effective resolution of
GRAPES is 5dx
In term of KES, GRAPES is comparable to WRF
Future works
Further works
Precipi. spectra
• How long is the t△ to be needed
to guarantee the validation of the ph. schemes
InterpolationSome Issues
• Investigate the preci. spectra to understand the intera. between sub-grid and grid scale preci.
• Impacts of diff. interpolation algorithms on decaying of KE
