Advanced Research WRF (ARW) Technical Note - MMM - University ...

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WRF-Var System • Incremental formulation of the model-space cost function. • Quasi-Newton or conjugate gradient minimization algorithms. • Analysis increments on un-staggered Arakawa-A grid. • Representation of the horizontal component of background error B via recursive filters (regional) or power spectra (global). The vertical component is applied through projection onto climatologically-averaged eigenvectors of vertical error. Horizontal/vertical errors are non-separable (horizontal scales vary with vertical eigenvector). • Background cost function (Jb) preconditioning via a control variable transform U defined as B = UU T . • Flexible choice of background error model and control variables. • Climatological background error covariances estimated via either the NMC-method of averaged forecast differences or suitably averaged ensemble perturbations. • Unified 3D-Var (4D-Var under development), global and regional, multi-model capability. WRF Software Framework • Highly modular, single-source code for maintainability. • Portable across a range of available computing platforms. • Support for multiple dynamics solvers and physics modules. • Separation of scientific codes from parallelization and other architecture-specific codes. • Input/Output Application Program Interface (API) enabling various external packages to be installed with WRF, hence allowing WRF to easily support various data formats. • Efficient execution on a range of computing platforms (distributed and shared memory, vector and scalar types). • Use of Earth System Modeling Framework (ESMF) timing package. • Model coupling API enabling WRF to be coupled with other models such as ocean, and land models. 4
Chapter 2 Governing Equations The ARW dynamics solver integrates the compressible, nonhydrostatic Euler equations. The equations are cast in flux form using variables that have conservation properties, following the philosophy of Ooyama (1990). The equations are formulated using a terrain-following mass vertical coordinate (Laprise, 1992). In this chapter we define the vertical coordinate and present the flux form equations in Cartesian space, we extend the equations to include the effects of moisture in the atmosphere, and we further augment the equations to include projections to the sphere. 2.1 Vertical Coordinate and Variables The ARW equations are formulated using a terrain-following hydrostatic-pressure vertical coordinate denoted by η and defined as η = (ph − pht)/µ where µ = phs − pht. (2.1) ph is the hydrostatic component of the pressure, and phs and pht refer to values along the surface and top boundaries, respectively. The coordinate definition (2.1), proposed by Laprise (1992), is the traditional σ coordinate used in many hydrostatic atmospheric models. η varies from a value of 1 at the surface to 0 at the upper boundary of the model domain (Fig. 2.1). This vertical coordinate is also called a mass vertical coordinate. Since µ(x, y) represents the mass per unit area within the column in the model domain at (x, y), the appropriate flux form variables are V = µv = (U, V, W ), Ω = µ ˙η, Θ = µθ. (2.2) v = (u, v, w) are the covariant velocities in the two horizontal and vertical directions, respectively, while ω = ˙η is the contravariant ‘vertical’ 5 η 0 0.2 0.4 0.6 0.8 1.0 P ht = constant P hs Figure 2.1: ARW η coordinate.
Page 1 and 2: NCAR/TN-468+STR NCAR TECHNICAL NOTE
Page 3 and 4: Contents Acknowledgments ix 1 Intro
Page 5: 8.4.3 Rapid Update Cycle (RUC) Mode
Page 8 and 9: 9.2 Sketch of the role of Stage 0 c
Page 10 and 11: viii
Page 13 and 14: Chapter 1 Introduction The developm
Page 15: 1.2 Major Features of the ARW Syste
Page 19 and 20: 2.3 Inclusion of Moisture In formul
Page 21 and 22: the earth. In this formulation we h
Page 23 and 24: Chapter 3 Model Discretization 3.1
Page 25 and 26: and lead to the acoustic time-step
Page 27 and 28: forward step, i.e., step (1) in Fig
Page 29 and 30: { Δy y u i-1/2,j+1 u i-1/2,j v i,j
Page 31 and 32: In the current version of the ARW,
Page 33 and 34: for Cr > 0, and (U t q) i+ 1 2 = U
Page 35 and 36: Chapter 4 Turbulent Mixing and Mode
Page 37 and 38: Symmetry sets the remaining tensor
Page 39 and 40: If ∆x is less than the user-speci
Page 41 and 42: 4.2 Filters for the Time-split RK3
Page 43: where γr is a user specified dampi
Page 46 and 47: exception of the baroclinic wave te
Page 48 and 49: STATIC DATA GRIB DATA SI SYSTEM GRI
Page 50 and 51: 5.2.3 Generating Lateral Boundary D
Page 52 and 53: a boundary on which the condition i
Page 54 and 55: On the coarse grid, the specified b
Page 56 and 57: 1-Way ARW WRF Simulation Two Consec
Page 58 and 59: V V V V U U U U U V V V V V V V
Page 60 and 61: V V V V U U U U U V V V V V V U
Page 62 and 63: coarse grid and fine grid is consis
Page 64 and 65: Table 8.1: Microphysics Options Sch
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and it is the water vapor and total
Page 68 and 69:
8.2.2 Betts-Miller-Janjic The Betts
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Table 8.3: Land Surface Options Sch
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Table 8.5: Radiation Options Scheme
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Table 8.6: Physics Interactions. Co
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Chapter 9 Variational Data Assimila
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supply the following: i) a default
Page 81 and 82:
9.2.4 First Guess at Appropriate Ti
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of its useful life. The development
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The second stage of gen be (gen be
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Appendix A Physical Constants The f
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Symbols Definition l0 minimum lengt
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Subscripts/Superscripts Definition
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NWP Numerical Weather Prediction OS
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Davies, H. C., and R. E. Turner, 19
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Lin, Y.-L., R. D. Farley, and H. D.
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Walko, R. L., W. R. Cotton, M. P. M
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Advanced Research WRF (ARW) Technical Note - MMM - University ...

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