The Lin-Rood Finite Volume FV Dynamical Core: Tutorial .

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The Lin-Rood Limited Volume (FV) Dynamical Center: Instructional exercise. Christiane Jablonowski National Place for Climatic Examination Stone, Colorado. NCAR Instructional exercise, May/31/2005. Subjects that we talk about today. The Lin-Rood Limited Volume (FV) dynamical center History: where, when, who,
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The Lin-Rood Finite Volume (FV) Dynamical Core: Tutorial Christiane Jablonowski National Center for Atmospheric Research Boulder, Colorado NCAR Tutorial, May/31/2005

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Topics that we talk about today The Lin-Rood Finite Volume (FV) dynamical center History: where, when, who, … Equations & a few experiences into the numerics Algorithm and code plan The lattice Horizontal determination Grid stunning: the C-D matrix idea Vertical framework and remapping procedure Practical guidance when running the FV dycore Namelist and netcdf factors (input & yield) Dynamics - material science coupling Hybrid parallelization idea Distributed-shared memory parallelization approach: MPI and OpenMP Everything you might want to know

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Who, when, where, … FV transport calculation created by S.- J. Lin and Ricky Rood (NASA GSFC) in 1996 2D Shallow water show in 1997 3D FV dynamical center around 1998/1999 Until 2000: FV dycore mostly utilized as a part of information absorption framework at NASA GSFC Also: transport conspire in \'Effect\', disconnected tracer transport In 2000: FV dycore was added to NCAR\'s CCM3.10 (now CAM3) Today (2005): The FV dycore may turn into the default in CAM3 Is utilized as a part of WACCAM Is utilized as a part of the atmosphere display at GFDL

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Dynamical centers of General Circulation Models Dynamics Physics FV: No unequivocal dissemination (other than dissimilarity damping)

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The NASA/NCAR limited volume dynamical center 3D hydrostatic dynamical center for atmosphere and climate forecast: 2D even conditions are fundamentally the same as the shallow water conditions 3 rd measurement in the vertical bearing is a gliding Lagrangian facilitate: unadulterated 2D transport with vertical remapping steps Numerics: Finite volume approach moderate and monotonic 2D transport plot upwind-one-sided orthogonal 1D fluxes, administrator part in 2D van Leer second request plot for time-found the middle value of numerical fluxes PPM third request plot (piecewise explanatory technique) for prognostic factors Staggered matrix (Arakawa D-lattice for prognostic factors)

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The 3D Lin-Rood Finite-Volume Dynamical Core Momentum condition in vector-invariant shape Continuity condition Pressure angle term in limited volume frame Thermodynamic condition, likewise for tracers (supplant ): The prognostics factors are: p: weight thickness, =Tp -  : scaled potential temperature

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Finite volume guideline Continuity condition in flux frame: Integrate more than one time step  t and the 2D limited volume  with range A : Integrate and adjust: Time-arrived at the midpoint of numerical flux Spatially-found the middle value of weight thickness

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Finite volume rule Apply the Gauss disparity hypothesis: unit ordinary vector Discretize:

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Orthogonal fluxes crosswise over cell interfaces Flux frame guarantees mass preservation G i,j+1/2 F i-1/2,j F i+1/2,j (i,j) G i,j-1/2 Upwind-one-sided: Wind course F: fluxes in x heading G: fluxes in y course

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Quasi semi-Lagrange approach in x bearing CFL y = v * t/y < 1 required G i,j+1/2 F i-5/2,j F i+1/2,j (i,j) G i,j-1/2 CFL x = u * t/y > 1 conceivable: executed as a whole number move and fragmentary flux computation

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Numerical fluxes & subgrid conveyances first request upwind steady subgrid appropriation second request van Leer direct subgrid dispersion third request PPM (piecewise illustrative strategy) allegorical subgrid dissemination "Monotonocity" versus \'positive unmistakable\' imperatives Numerical dissemination Explicit time venturing plan: Requires brief time steps that are steady for the speediest waves (e.g. gravity waves) CGD website page for CAM3:

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Subgrid appropriations: steady (first request) x 1 x 2 x 3 x 4 u

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Subgrid dispersions: piecewise direct (second request) van Leer x 1 x 2 x 3 x 4 u See points of interest in van Leer 1977

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Subgrid disseminations: piecewise explanatory (third request) PPM x 1 x 2 x 3 x 4 u See subtle elements in Carpenter et al. 1990 and Colella and Woodward 1984

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Monotonicity requirement Prevents over-and undershoots Adds dispersion not permitted van Leer Monotonicity limitation brings about discontinuities x 1 x 2 x 3 x 4 u See subtle elements of the monotinity imperative in van Leer 1977

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Simplified stream graph subcycled 1/2 t just: figure C-lattice time-mean winds stepon dynpkg cd_core c_sw d_p_coupling trac2d physpkg te_map full t: refresh all D-matrix factors d_sw p_d_coupling Vertical remapping

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Grid staggerings (after Arakawa) B framework u v u v A network u v u v u v C network v u D framework u v u Scalars: v u

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Regular scope - longitude network Converging network lines at the shafts diminish the physical separating  x Digital and Fourier channels evacuate temperamental waves at high scopes Pole focuses are mass-focuses

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Typical flat resolutions Time step is the "material science" time step: Dynamics are subcyled utilizing the time step t/"nsplit" is ordinarily 8 or 10 CAM3: check (dtime=1800s because of physical science ?) WACCAM: check (nsplit = 4, dtime=1800s for 2 o x2.5 o ?) Defaults:

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Idealized baroclinic wave experiment The coarse determination does not catch the development of the baroclinic wave Jablonowski and Williamson 2005

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Idealized baroclinic wave experiment Finer determination: Clear strengthening of the baroclinic wave

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Idealized baroclinic wave experiment Finer determination: Clear escalation of the baroclinic wave, it begins to join

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Idealized baroclinic wave experiment Baroclinic wave design focalizes

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Idealized baroclinic wave experiment: Convergence of the FV flow Global L 2 mistake standards of p s Solution begins uniting at 1deg Shaded locale demonstrates the instability of the reference arrangement

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Floating Lagrangian vertical organize 2D transport computations with moving limited volumes (Lin 2004) Layers are material surfaces, no vertical shift in weather conditions Periodic re-mapping of the Lagrangian layers onto reference lattice WACCAM: 66 vertical levels with model top around 130km CAM3: 26 levels with model top around 3hPa (40 km)

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Physics - Dynamics coupling Prognostic information are vertically remapped (in cd_core) before dp_coupling is called (in dynpkg) Vertical remapping routine registers the vertical speed  and the surface weight p s d_p_coupling and p_d_coupling (module dp_coupling) are the interfaces to the CAM3/WACCAM physical science bundle Copy/add the information from the "progression" information structure to the "physical science" information structure (lumps), A-network Time - split material science coupling: prompt updates of the A-matrix factors the request of the material science parameterizations matters material science propensities for u & v reports on the D network are gathered

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Practical tips Namelist factors: What do IORD, JORD, KORD mean? IORD and JORD at the model top are distinctive (see cd_core.F90) Relationship between dtime nsplit (what happens on the off chance that you don\'t choose nsplit or nsplit =0, default is registered in the routine d_split in dynamics_var.F90) time interim for the material science & vertical remapping step Input/Output: Initial conditions: stunned wind segments US and VS required (D-lattice) Wind at the shafts not anticipated but rather inferred User\'s Guide:

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Practical tips Namelist factors: IORD, JORD, KORD decide the numerical plan IORD: plot for flux figurings in x course JORD: conspire for flux computations in y bearing KORD: plot for the vertical remapping step Available choices: - 2 : straight subgrid, van-Leer, unconstrained 1 : constant subgrid, first request 2 : linear subgrid, van Leer, monotonicity imperative (van Leer 1977) 3 : parabolic subgrid, PPM, monotonic (Colella and Woodward 1984) 4 : illustrative subgrid, PPM, monotonic (Lin and Rood 1996, see FFSL3) 5 : allegorical subgrid, PPM, positive unmistakable limitation 6 : explanatory subgrid, PPM, semi monotone imperative Defaults: 4 (PPM) on the D framework (d_sw), - 2 on the C network (c_sw)

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"Half and half" Computer Architecture SMP: symmetric multi-processor Hybrid parallelization system conceivable: Shared memory (OpenMP) inside a hub Distributed memory approach (MPI) crosswise over hubs Example: NCAR\'s Bluesky (IBM) with 8-way and 32-way hubs

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Schematic parallelization strategy 1D Distributed memory parallelization (MPI) over the scopes: Proc. NP 1 2 Eq. 3 4 SP 0 Longitudes 340

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Schematic parallelization system Each MPI space contains \'apparition cells\' (corona areas): duplicates of the neighboring information that have a place with various processors NP Proc. 2 Eq. 3 apparition cells for PPM SP 0 Longitudes 340

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Schematic parallelization system Shared memory parallelization (in CAM3 regularly) in the vertical bearing through OpenMP compiler orders: Typical circle: do k = 1, plev … enddo Can frequently be parallelized with OpenMP (check conditions): !$OMP PARALLEL DO … do k = 1, plev … enddo

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Schematic parallelization method Shared memory parallelization (in CAM3 frequently) in the vertical heading by means of OpenMP compiler mandates: k CPU e.g.: accept 4 parallel "strings" and a 4-way SMP hub (4 CPUs) !$OMP PARALLEL DO … do k = 1, plev … enddo 1 4 5 2 8 3 4 plev

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Thank you ! Any inquiries ??? Tracer transport ? Fortran code …

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References Carpenter, R., L., K. K. Droegemeier, P. W. Woodward and C. E. Hanem 1990: Application of the Piecewise Parabolic Method (PPM) to Meteorological Modeling. Mon. Wea. Rev., 118, 586-612 Colella, P., and P. R. Woodward, 1984: The piecewise allegorical strategy (PPM) for gas-dynamical reproductions. J. Comput. Phys., 54,174-201 Jablonowski, C. furthermore, D. L. Will

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