Advanced Research Weather and Forecast Model (WRF-ARW)

Mesoscale Meterological ModelingATMO 558

March 2016Jamie Moker

Overview

- Started in 1990s with NCAR, NCEP, OU, NRL, FAA- ARW version supported at NCAR Mesocale and

Microscale division- Used both operationally and with research- Fully compressible- Can use realistic cases or idealized cases- non-hydrostatic with a hydrostatic option- uses time splitting for acoustic considerations- Has a terrain-following vertical coordinate- Capable of incorporating data assimilation methods

Vertical mass coordinate, ƞ

p is the hydrostatic component of pressurephs is the pressure at the surfacepht is the pressure at model top (constant)

- Ƞ is traditional sigma coordinate (LaPrise, 1992)- Ƞ is terrain-following- Ƞ varies from 1 at terrain to 0 at model top

Mass flux form of variables

Horizontal and Vertical covariant velocities

Vertical contracovariant vertical velocity

θ is pot. temperature (conserved), φ = gz (geopotential), p is pressure, α = 1/ρ (inverse density)

Governing Equations (dry)

Conservation of momentum

X-componentY-componentZ-component

Inverse-density diagnostic relation

Equation of State

Conservation of heat

Conservation of mass

Material derivative of geopotential

Expansion identities with a being ageneric variable

PGF in eta coordinatesTendency advection Coriolis, etc.

Governing Equations (moist)

Mass flux form of variables become:

Vertical coordinate defined for dry air

New governing equations become:X momentumY momentumZ momentumEnergyMassGeopotential Material DerivativeMoisture

Inverse-density diagnostic relation for dry air

Equation of State (now including moisture)

Inverse density for dry and wet air combined

Mixing ratios for water vapor, cloud vapor, etc.

Metric Terms and Map Factors- Horizontal distance between grids in ARW is constant in isotropic

projections (i.e. Lambert Conformal) but changes with anisotropic projections (latitude-longitude)

- With isotropic projections,- When you project to a sphere, the distance between grids must change,

called map factors in ARW

Map Factors

Redefine momentum variables with the map factors in mind:

+

New U-momentum

New V-momentum

New W-momentum

* The right side of these equations will contain curvature and Coriolis terms

Isotropic where m = mx = my (e.g. Lambert Conformal)

Anisotropic where mx /= my (e.g. latitude-longitude)

Remaining non-momentum equations

EnergyMassGeopot. Material DerivativeMoisture

Inverse-density diagnostic relation

Equation of State

Perturbation Form of the EquationsReference states are in hydrostatic balance so they are only a function of z-bar

x-comp:

y-comp:

z-comp:

- Energy and moisture equations not affected by hydrostatic balance

Mass

Geopotential

State

p, φ, and α in the reference sounding are functions of x, y and η because ηvaries in the horizontal

When expanding these, any primes multiplied together become negligible

Treatment of sound waves / Time splittingTo account for soundwaves, we must define a new set of perturbed equations:

Ideal gas law (state) is linearized for each acoustic time step- This removes γ in the exponent

Vertical coordinate definition

and cs is the speed of sound

If A is a generic variableA’’ deviation from large time stepAt* value at acoustic time step

where

Treatment of sound waves / Time splitting

The RHS remains fixed for all acoustic time steps within the larger time step

Let’s use the x-component of the momentum flux equation as an example to calculate the correction to the main time step due to the filtering out of sound waves

The LHS changes within each acoustic time step, τ

Combine above linearized state and vertical coordinate equations and take �𝜕𝜕 𝜕𝜕𝜂𝜂 (the “vertical” derivative):

where

𝜕𝜕 𝜂𝜂𝑝𝑝′′ is the linearized vertical pressure gradient in an acoustic time step

𝐶𝐶 =𝛾𝛾𝑝𝑝𝑡𝑡∗

𝜇𝜇𝑡𝑡∗𝛼𝛼𝑑𝑑𝑡𝑡∗

Diabatic heatingadjustment term

vertical coordinate adjustment term

Treatment of sound waves / Time splitting

RHS of the dynamic equations that are FIXED for each acoustic time step

LHS of dynamic equations that change for each acoustic time step

Parameterized Processes

Microphysics- Kessler, Purdue Lin, WSM3, WSM5, WSM6, Eta GCP, Thompson, Goddard, Morrison 2-Moment (most for ice phase)

Cumulus - Kain-Fritsch, Betts-Miller-Janjic, Grell-Devenyiensemble, Grell-3

Surface Layer - MM5, Eta, or PX similarity theory

Land Surface Model - 5-layer thermal diffusion, Noah, RUC, Pleim-Xiu with other options

Planetary Boundary Layer - Medium Range Forecast (MRF), YonseiUniversity (YSU), Mellor-Yamada-Janjic (MYJ), AssemmetricalConvection Model version 2 (ACM2)

Parameterized Processes

Longwave radiation - Rapid Radiative Transfer Model (RRTM), Eta Geophysical Fluid Dynamics Laboratory (GFDL), NCAR Community Atmosphere Model (CAM 3.0),

Shortwave radiation - Eta Geophysical Fluid Dynamics Laboratory (GFDL), MM5 (Dudhia), Goddard, CAM

Wicker, L. J. and W. C. Skamarock, 2002: Time splitting methods for elastic models using forward time schemes, Mon. Wea. Rev., 130, 2088–2097.

Skamarock, W. C., and Coauthors, 2008: A description of the Advanced Research WRF version 3. NCAR Tech. Note TN-475+STR, 113 pp. [Available online at http://www.mmm.ucar.edu/wrf/users/docs/arw_v3_bw.pdf.]

References