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 in Boulder, US-NCAR)

Outline IntroductionMethodologyExper. design ConclusionResults 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

GRAPES V. coordinate H. terr. Flw v. co Physicals Full phy. package Model Unified model DAS 3/4DVAR Coding Modul. Parall Dynamic core full compressible HY/NH Dicretization SI-SL Grid system Lat.-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

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 1 o ×1 o ; 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 – 10 o. (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 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