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Computation and analysis of the Kinetic Energy Spectra of a SI-SL Model GRAPES

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 (CAMS). ( for MCS-Typhoon conference on 31 Oct.- 3 Nov. 2006 in Boulder, US-NCAR).

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Computation and analysis of the Kinetic Energy Spectra of a SI-SL Model GRAPES

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  1. 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 (CAMS) ( for MCS-Typhoon conference on 31 Oct.- 3 Nov. 2006 in Boulder, US-NCAR)

  2. Outline Introduction Methodology Exper. design • Why ? • Atmo. KES • Models KES • Model • Data • Exp. design • 2D-DCT Conclusion Results Further work • △t vs △x • H. eff. Resol. • Spin up time • GRAPES vs WRF • Impacts • of diff. △t, △x • KES – spin up • SL vs Eulerian • △t vs p. schm • Interpolation • Preci. spectra

  3. 1. Introduction

  4. 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

  5. Grid system Lat.-Long. Dicretization SI-SL Model Unified model Dynamic core full compressible HY/NH GRAPES V. coordinate H. terr. Flw v. co DAS 3/4DVAR Physicals Full phy. package Coding Modul. Parall About GRAPES (Global/Regional Assimilation PrEdiction System. Since 2000)

  6. 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?

  7. The atmospheric KES observed Charney(1947)、Smagorinsky(1953)、Saltzman and Teweles(1964): KES~K-3 Large scale (approxim. spectral slope of -3) Nastrom and Gage (1985)、Lindborg（1999）: KES~K-3, K-5/3 Meso scale (approxim. Spectral slope of -5/3) From Dr. B. Skamarock

  8. KES by MM5, COAMPS and WRF-ARW From Dr. B. Skamarock

  9. KES by WRF-ARW with different △x From Dr. B. Skamarock

  10. 2. Methodology

  11. 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

  12. 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.

  13. 3. Experiment design

  14. Full compressible primitive equations Model configuration Microphysical: NCEP 3-class simple ice scheme Long/short wave radiation: RRTM/Dudhia SI - SL scheme Arakawa-C staggered grid PBL: MRF scheme Charney-Philips staggered layer Kain-Fritsch scheme Vertical L31, top-35km No-hydrostatic

  15. 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

  16. 4. Results

  17. The impact of △t and △x on KES of GRAPES Smaller △t , closer to ideal line

  18. The impact of △t and △x on KES of GRAPES Smaller △t , closer to ideal line

  19. The impact of △t and △x on KES of GRAPES Smaller △t , closer to ideal line

  20. The impact of △t and △x on KES of GRAPES Better, △t = 180s

  21. The impact of △t and △x on KES of GRAPES Better, △t = 60s

  22. The impact of △t and △x on KES of GRAPES feasible, △t = 30s

  23. 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=50o – 10o. • (3) It exists an “optimal” △t when △x is smaller than a threshold (△x≤0.05o)

  24. Relationship between the effective △t and △x

  25. Spin up time of KES Longer FT, more KES (about 5 hrs)

  26. GRAPES vers WRF In term of KES, GRAPES is comparable to WRF

  27. 2 3 1 4 5 Conclusion Highest effective resolution of GRAPES is 5dx Longer FT is, more KES are developed (about 5 hrs vs 5hrs) There is a fit choice for both △t and △x In term of KES, GRAPES is comparable to WRF Future works

  28. Further works • Investigate the preci. spectra to understand the intera. between sub-grid and grid scale preci. • Impacts of diff. interpolation algorithms on decaying of KE • How long is the △t to be needed to guarantee the validation of the ph. schemes Some Issues Interpolation Precipi. spectra

  29. Thank You !

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