1

RadiationParameterization

in WRF

John NobleMeteorology 245

17 Dec. 2007

Outline

• Radiation overview and equations• Necessity of parameterization• Historical overview• WRF radiation schemes

– Longwave– Shortwave

• Gallus and Bresch study• Future developments

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Radiation

• Radiation is propagation of energy byelectromagnetic (EM) waves.

• Solar radiation is the fundamental energysource for the Earth and atmosphere, theunequal distribution reaching the Earthleads to differential heating and horizontalgradients that in turn drive atmosphericcirculations.

Radiative flux

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Solar spectral energy curve

Spectral energy curve at sea level and extrapolated outside theatmosphere. Darkened areas represent gaseous absorption inthe atmosphere. (From Lacis and Hansen 1974)

Longwave spectral energy curve

Radiation emitted from the Earth and atmosphere is inthe “longwave” (LW) or infrared (IR) band, where λvaries from 4.0 – 25 µm.

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Blackbody Intensity

A blackbody is a theoretical substance thatabsorbs and emits the maximum possibleintensity of radiant energy at a certainwavelength. This intensity was determinedby Max Planck as

B! T( ) =2h! 3c2

e

hc!KBT "1#

$%&

Stefan-Boltzman law

Integrating over all wavenumbers yields theblackbody flux density given by the Stefan-Boltzman law

!B T( ) = ! B" T( )d"0

#

$ = %T 4

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Emissivity

Emissivity is given by the ratio of emittedmonochromatic intensity to correspondingblackbody radiation

!"=I"(emitted)

B"T( )

Absorptivity, reflectivity,& transmissivity

Monochromatic absorptivity, reflectivity,and transmissivity are respectively given by

!"=I"(absorbed)

I"(incident)

, R"=I"(reflected)

I"(incident)

, T"=I"(transmitted)

I"(incident)

and related by

!"+ R

"+ T

"= 1

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Radiative transfer

Radiative transfer (RT) describes the effectsof radiation passing through a medium. Thechange of monochromatic intensity ofradiation passing through the atmosphere isgiven by

dI! = "I!#rk!ds

Flux density

The mean flux density of radiation reachingthe outer atmosphere is ~1368 W m-2 and isgiven by

FS= I

Scos! d"

#"$ and passing through a layer as

F!"# $!( ) = 2% I!

#" $! ,µ( )0

1

& µ dµ

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Flux transmissivity

The flux transmissivity passing though anatmospheric layer can be formulated as

T!f= 2 e

"#! µµ dµ

0

1

$

Necessity of parameterization

• Line-by-line integration of above equationsover wavenumber in the IR band iscomputationally intensive, requiringsummation over ~106 points

• Thus, the goal of radiation parameterizationis to estimate total radiative flux quicklyand accurately, where total is the sum ofsurface fluxes and vertical RFD.

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Flux densities

Upward and downward flux densities needto be determined in order to calculateheating/cooling rates for any layer by

!T

!t=1

"cp

!

!zFD# F

U( )

Historical overview

There are two general radiation parameterization methods:

• The first is an empirical approach that relatesbulk properties to the radiative flux, essentiallyestimating downwelling LW radiation at theground from surface observations.

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Empirical approach

This approach is the simplest, computationallycheapest, and least accurate. The inherentassumptions in this approach neglect RFDabove the ground and emission fromatmospheric gases except water vapor(Stensrud 2007).

Empirical method

• The earliest radiative transfer models wereempirical and were accurate only in the clearsky conditions they were designed for (Goody1952).

• They were unable to make accuratecalculations when scatterers were presentsince they lacked information regarding theabsorption coefficient. Rogers and Walshaw(1966) proposed a LW method known as“cooling to space”.

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Two-stream method

The second approach is the two-streammethod that solves the LW radiative transferequations that formulate upward anddownward fluxes as a function of height.

FU z( ) = !B" 0( )#"fz,0( )d" +

0

$

% !B" z '( )d#"

f

dzz, z '( )dz 'd"

0

z

%0

$

%

FD z( ) = !B" z '( )d#"

f

dz 'z, z '( )dz 'd"

0

$

%

Two-stream method

• The first term in accounts for attenuation ofLW radiation emitted from the surface,while the second term represents theemittance of LW radiation by theatmosphere. accounts for atmosphericcontributions (Stensrud 2007; Liou 2002).

• LW parameterization schemes differ as afunction of approach to calculate the aboveintegrals (Stensrud 2007).

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Two-stream method

• Sasamori (1972) introduced a two-streammethod that was later adopted andpopularized by Pielke (1984).

• There are several parameterizations thattake different approaches to solving theintegrals in the full equations (not shown).The first makes a simplifying assumptionthat eliminates the need to integrate over allviewing angles.

Two-stream method

• The second approach integrates theabsorption coefficient over the optical path.

• The third linearly interpolates betweenstored values for the absorption coefficientsthat have been calculated over the full rangeof atmospheric conditions and stored. Thisapproach has higher computational expensethan previous (Stresund 2007).

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correlated-k method

• The correlated-k method provides analternative to line-by-line integration of RTequations for flux density andtransmissivity .

• RT calculations for a given spectral bandare performed using a small number ofabsorption coefficients that arerepresentative of the coefficients for allfrequencies in the band.

correlated-k method

• The correlated-k method maps k(v) fromspectral space to a space defined by acumulative probability density function,g(k), where g(k) is the fraction of theindividual values of k(v) within the intervaldelta v with values smaller than k. Themapping transformation, v → k produces anew function, that is monotonic, smooth,and amenable to approximation bysummation.

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correlated-k method

Transformation of flux transmissivity yields

T! "1

#!e$k!u d! = e

$k g( ) udg

0

1

%#!%

correlated-k method

Binning the data allows the above equationto be discretized into an approximation

T! = e"k gj( ) u

#gjj=1

M

$

that reduces the number of calculations byseveral orders of magnitude

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Absorption coefficients

Absorption coefficients due to CO2 for a layer (P = 507mb) in the midlatitude summer atmosphere for thespectral range 630–700 cm-1 (a) as a function ofwavenumber and (b) after being rearranged inascending order.

g–space bands & weights

Boundaries and weights of subintervals ing–space used in RRTM. (From Mlawer etal. 1997)

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WRF radiation schemes

• WRF architecture allows use andcomparison of various physics algorithms.

• WRF includes two longwave radiationschemes: Rapid Radiative Transfer Modelscheme that accounts for multiple bands andtrace gases and GFDL scheme that includescloud microphysics effects.

• Both utilize look-up tables and provideatmospheric heating from radiative fluxdivergence.

WRF SW radiation schemes

• WRF includes three SW radiation schemes,i.e. Goddard shortwave, GFDL, and simpleshortwave schemes, all of which includeabsorption, reflection, and scattering(Skamarock et al. 2007).

• The primary source of SW radiation is solarinsolation that can be scattered, reflected, orabsorbed. Reflection causes upward fluxesdue to surface albedo.

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WRF LW radiation schemes

• LW radiation includes IR radiation absorbed andemitted by gases and the surface. Upward LWradiative flux from the surface is determined by itsemissivity, a function of surface temperature andland-use type (Skamarock et al. 2007).

• Positive RFD relates to the radiative warming rate,while negative relates to the radiative cooling rate.Radiative transfer parameterizations can be themost computationally expensive of all the physicalparameterizations.

SW radiation

• The factors effecting downward SW flux,include: the albedo and absorption ofclouds ; solar zenith angle increases pathlength and reduces ; scattering and watervapor absorption in clear air. Thecombination of these attenuating effects areformulated by:

Sd z( ) = µS0! dScs + dSca + dSs + dSa( )

z

top

"

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Simple SW radiation scheme

• The simple SW radiation scheme is based onDudhia (1989) and is taken from MM5. It hasdownward integration of solar flux that accountsfor clear-air scattering, H2O vapor absorption, andcloud absorption and reflection. It utilizes look-uptables for clouds (Skamarock et al. 2007);

• SW radiation reflected upward by clouds and thesurface are ignored. SW radiation calculationsare performed every 10 minutes.

RRTM LW Scheme

• The rapid and accurate radiative transfermodel (RRTM) aims to calculate fluxes andcooling rates comparable with the line-by-line radiative transfer model (LBLRTM),while performing a smaller number ofradiative transfer operations. This isaccomplished by use of the correlated-kmethod, with k-distributions obtained fromLBLRTM (Mlawer et al. 1997).

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RRTM LW Scheme

• LW radiation absorption occurs for H2O vapor,CO2, O3, CH4, N2O, CFC-11, CFC-12, CFC-22,and other species. It is necessary to subdivide theLW band into a number of spectral intervals thatcontain strong absorption due to certain species.Contributions from the major absorbing speciesare then determined with a high degree ofaccuracy, while those from the minor species aredetermined with a less detailed approach (Mlaweret al. 1997). RRTM bands and implementedspecies are shown in .

Absorption coefficients

Absorption coefficients due to CO2 for a layer (P = 507mb) in the midlatitude summer atmosphere for thespectral range 630–700 cm-1 (a) as a function ofwavenumber and (b) after being rearranged inascending order.

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RRTM LW Scheme

• Radiative transfer calculations are performed foreach subinterval in each band. The subintervalsare processed in the same way that a spectral pointis processed in the LBLRTM.

• The major difference is the number of requiredcalculations: 106 spectral points per band vs. 16intervals in g-space per band for LBLRTM andRRTM respectively. RRTM flux and cooling ratesare finally compared and validated against thosedetermined from LBLRTM.

RRTM bands

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RRTM Development Strategy

Gallus and Bresch 2006

• Gallus and Bresch examined rainfall forecastsensitivity as a function of model physics,dynamics, and initial conditions in simulations of15 rainfall events in the central U.S. duringAugust 2002 (Gallus and Bresch 2006).

• Two dynamical cores and two physics packageswere used in a total of four configurations thatwere all initialized with ETA output. Dynamicalcores used were the nonhydrostatic mesoscalemodel (NMM) and the Advanced Research WRF(ARW).

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Gallus and Bresch 2006

• The first physics package (NCEP) used the Betts-Miller-Janic convection scheme, GFDL radiationpackage, and Mellor-Yamada-Janic PBL scheme.

• The second physics package (NCAR) incorporated theKain-Fritsch convective scheme, Dudhia rapidradiative transfer model (RRTM), and YonseiUniversity PBL scheme. Additional physicalschemes (e.g. Ferrier et al. microphysics, Noah landsurface model) were identical in all runs. Simulationswere performed at 8-km grid spacing with 60 verticallayers, using 1200 UTC ETA 40-km Gridded Binary(GRIB) output for initial and lateral boundaryconditions (Gallus and Bresch 2006).

Gallus and Bresch 2006

• Results indicate that NCAR physics with bothdynamic cores generally overestimated peak rain rates(Gallus and Bresch 2006). and 3 show a 12–18-hforecast period for WRF runs and observationsrespectively, indicating greater intensity and finerstructure from the NCAR physics.

• Each of the simulations has significant differencesfrom the observations. Gallus and Bresch (2006)concluded that peak rain rate sensitivity is more afunction of physics package than dynamic core, whiletotal rain volume is more a function of dynamics thanphysics. The two radiation schemes did not causenotable differences.

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Gallus and Bresch 2006

• Results indicate that NCAR physics with bothdynamic cores generally overestimated peak rain rates(Gallus and Bresch 2006). and 3 show a 12–18-hforecast period for WRF runs and observationsrespectively, indicating greater intensity and finerstructure from the NCAR physics.

• Each of the simulations has significant differencesfrom the observations. Gallus and Bresch (2006)concluded that peak rain rate sensitivity is more afunction of physics package than dynamic core, whiletotal rain volume is more a function of dynamics thanphysics. The two radiation schemes did not causenotable differences.

Gallus and Bresch 2006

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Gallus and Bresch 2006

Evaluation of parameterizations

The ability to use different configurations ofparameterization schemes is a strong point for WRF.This allows researchers to justapose differentcombinations and thus better evauate individual andcombined schemes.

Parameterization schemes are constantly evolving, andalthough the ones identified in this essay representsignificant improvements over previous versions, theyhave the inherent limitations of the era in which theywere developed.

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Future development

• The new version of the Goddard scheme illustratesthis. The new Goddard scheme has a correct two-stream adding approximation in diffuse transmissivity,while the old scheme had an incorrect diffusetransmissitivity – a critical bug in the code.

• The new scheme delta-Eddington approximation forreflection and transmittance of direct and diffuseradiation, while the old uses delta-Eddingtonapproximation for direct radiation, but it usesequations in Sagan and Pollock (JGR, 1967) fordiffuse radiation.