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

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(2.34), mixing terms (described in Chapter 4), and parameterized physics (described in Chapter 8). Also note that the equation of state (2.21) cannot be written in perturbation form because of the exponent in the expression. For small perturbation simulations, accuracy for perturbation variables can be maintained by linearizing (2.21) for the perturbation variables. 10
Chapter 3 Model Discretization 3.1 Temporal Discretization The ARW solver uses a time-split integration scheme. Generally speaking, slow or low-frequency (meteorologically significant) modes are integrated using a third-order Runge-Kutta (RK3) time integration scheme, while the high-frequency acoustic modes are integrated over smaller time steps to maintain numerical stability. The horizontally propagating acoustic modes (including the external mode present in the mass-coordinate equations using a constant-pressure upper boundary condition) are integrated using a forward-backward time integration scheme, and vertically propagating acoustic modes and buoyancy oscillations are integrated using a vertically implicit scheme (using the acoustic time step). The time-split integration is similar to that first developed by Klemp and Wilhelmson (1978) and analyzed by Skamarock and Klemp (1992). The time-split RK3 scheme is described in general terms in Wicker and Skamarock (2002). The primary differences between the descriptions found in the references and the ARW implementation are associated with our use of the mass vertical coordinate and a flux-form set of equations, along with our use of perturbation variables for the acoustic component of the timesplit integration. The acoustic-mode integration is cast in the form of a correction to the RK3 integration. 3.1.1 Runge-Kutta Time Integration Scheme The RK3 scheme, described in Wicker and Skamarock (2002), integrates a set of ordinary differential equations using a predictor-corrector formulation. Defining the prognostic variables in the ARW solver as Φ = (U, V, W, Θ, φ ′ , µ ′ , Qm) and the model equations as Φt = R(Φ), the RK3 integration takes the form of 3 steps to advance a solution Φ(t) to Φ(t + ∆t): Φ ∗ = Φ t + ∆t 3 R(Φt ) (3.1) Φ ∗∗ = Φ t + ∆t 2 R(Φ∗ ) (3.2) Φ t+∆t = Φ t + ∆tR(Φ ∗∗ ) (3.3) where ∆t is the time step for the low-frequency modes (the model time step). In (3.1) – (3.3), superscripts denote time levels. This scheme is not a true Runge-Kutta scheme per se because, 11
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 and 16: 1.2 Major Features of the ARW Syste
Page 17 and 18: Chapter 2 Governing Equations The A
Page 19 and 20: 2.3 Inclusion of Moisture In formul
Page 21: the earth. In this formulation we h
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
Page 66 and 67: and it is the water vapor and total
Page 68 and 69: 8.2.2 Betts-Miller-Janjic The Betts
Page 70 and 71: Table 8.3: Land Surface Options Sch
Page 72 and 73:
Table 8.5: Radiation Options Scheme
Page 74 and 75:
Table 8.6: Physics Interactions. Co
Page 77 and 78:
Chapter 9 Variational Data Assimila
Page 79 and 80:
supply the following: i) a default
Page 81 and 82:
9.2.4 First Guess at Appropriate Ti
Page 83 and 84:
of its useful life. The development
Page 85 and 86:
The second stage of gen be (gen be
Page 87:
Appendix A Physical Constants The f
Page 90 and 91:
Symbols Definition l0 minimum lengt
Page 92 and 93:
Subscripts/Superscripts Definition
Page 94 and 95:
NWP Numerical Weather Prediction OS
Page 96 and 97:
Davies, H. C., and R. E. Turner, 19
Page 98 and 99:
Lin, Y.-L., R. D. Farley, and H. D.
Page 100:
Walko, R. L., W. R. Cotton, M. P. M
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