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;in~rricnn .\Ietvor~~logici{l SocicLy 1'rintt.d in U. S. ;I. An Alternate Scale Representation of Atmospheric Energy Spectra L)cp/. JJ :11111o~pl1t~ric Science, C)ldrudo .>'toie L:r~ir c r~i i y , ].'or/ C;~liilr, c \l+nuscript received i Septcinber 1971) :ilthoagh it is known that 311 rpati:rl scitles arc nonlinearly interrelated in any prediction model of the atn~c~sl)lic~-c, truncation demands a limit to scale resolution. One is therefore compelled to 1)aranieterii:e sub-resolution scales, ho1)efully in such a nlanner that they Jescril.)e observed statistics. Such statistics II:LVC Ixen S~I I~V I I frecluently as energy spectra. of synoptic scales in terms of the planetary wavenumbcr.-111 alternate representation is the presentation of the energy in terms (of the degree of i~ 1,egendre polynomiul csp;u~sion; this rel~resentation may he more advantaxeous insofar as it presents a tn-o-din~ensional s1)cctr:ll incics .irguments itre presented which indeed suggest the appropriateness of the irlcles. Two months 1) i ;~tmospheric \vind dats itt five pressure levels and on a hemispheric grid were analyzed to establish energy 5pcctra. 7'he spectra are ~iescribetl both as a function of time and :ts a function of wavenumber lor time averages. Csing a five-1t:vel lineitr I.)aroclinic mode,l, stability characteristics for 1:ach wave component for the obscrved aon;ll nntl vertical profiles were established. Based on these results, the energy data, were tit logurit1~1iiic:rlly 11) : least squitres to the \vavcnumber (,both planetary tvavenumber and Legendre polynon~ial ~legrccj. Energy slopes show v i t l~e~ close to-3 n71len utilizing the two-dimensional indcs in the non-bar()-(:linically iorcctl scale range. These results suggest the use of this indes in studying scale parameterization..

As an effort toward improving climate model–component performance and accuracy, an atmospheric-component climate model has been developed, entitled the Spectral Element Atmospheric Climate Model and denoted as CAM_SEM. CAM_SEM includes a unique dynamical core coupled at this time to the physics component of the Community Atmosphere Model (CAM) as well as the Community Land Model. This model allows the inclusion of local mesh refinement to seamlessly study imbedded higher-resolution regional climate concurrently with the global climate. Additionally, the numerical structure of the model based on spectral elements allows for application of state-of-the-art computing hardware most effectively and economically to produce the best prediction/simulation results with minimal expenditure of computing resources. The model has been tested under various conditions beginning with the shallow water equations and ending with an Atmospheric Model Intercomparison Project (AMIP)-style run that uses initial conditions and physics comparable to the CAM2 (version 2 of the NCAR CAM climate model) experiments. For uniform resolution, the output of the model compares favorably with the published output from the CAM2 experiments. Further integrations with local mesh refinement included indicate that while greater detail in the prediction of mesh-refined regions—that is, regional climate—is observed, the remaining coarse-grid results are similar to results obtained from a uniform-grid integration of the model with identical conditions. It should be noted that in addition to spectral elements, other efficient schemes have lately been considered, in particular the finite-volume scheme. This scheme has not yet been incorporated into CAM_SEM. The two schemes—finite volume and spectral element—are quasi-independent and generally compatible, dealing with different aspects of the integration process. Their impact can be assessed separately and the omission of the finite-volume process herein will not detract from the evaluation of the results using the spectral-element method alone.

The authors describe a recent development and some applications of a spectral element dynamical core. The improvements and development include the following: (i) the code was converted from FORTRAN 77 to FORTRAN 90; (ii) the dynamical core was extended to the generalized terrain-following, or hybrid η, vertical coordinates; (iii) a fourth-order Runge–Kutta (RK4) method for time integration was implemented; (iv) moisture effects were added in the dynamical system and a semi-Lagrangian method for moisture transport was implemented; and (v) the improved dynamical core was coupled with the Community Atmosphere Model version 2 (CAM2) physical parameterizations and Community Land Model version 2 (CLM2) in such a way that it can be used as an alternative dynamical core in CAM2. This spectral element version of CAM2 is denoted as CAM-SEM. A mass fixer as used in the Eulerian version of CAM2 (CAM-EUL) is also implemented in CAM-SEM. Results from multiyear simulations with CAM-SEM (coupled with CLM2) with climatology SST are also presented and compared with simulations from CAM-EUL. Close resemblances are shown in simulations from CAM-SEM and CAM-EUL. The authors found that contrary to what is suggested by some other studies, the high-order Lagrangian interpolation (with a limiter) using the spectral element basis functions may not be suitable for moisture and other strongly varying fields such as cloud and precipitation.

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