Timor Wienrib 036139962 Itai Friedland 035893080 Influence of clouds and hydrometeors on radio propagation in atmospheric communication links Timor Wienrib 036139962 Itai Friedland 035893080

Introduction Clouds have a large effect on the radiative heating–cooling of the atmosphere and the earth’s surface. There are many difficulties in modeling clouds such as the parameterizations of cloud generation, development, and dissipation, as well as cloud microphysical properties (water content, phase, particle shape, and size distribution) and optical properties (extinction coefficient, single-scattering albedo, scattering phase function). We focus here on the parameterization of single-scattering properties and cloud overlapping.

Difficulties involved in the parameterization for cloud single-scattering properties are many. The single-scattering coalbedo of ice crystals is significantly larger than that of water droplets. The optical properties of ice clouds are functions of the size, shape, and orientation of ice crystals, which vary over a large range. The single-scattering coalbedo of ice and water particles vary rapidly with wavelength.

Parameterization for the mean effective single-scattering coalbedo for a wide spectral interval depends not only on the absorption by clouds but also on the water vapor within and above cloud layers. Clouds are not horizontally homogeneous and do not always cover the entire sky. All these problems make the parameterizations for cloud optical properties very difficult.

Parameterizations for cloud single-scattering properties Influence of clouds and hydrometeors on radio propagation in The cloud single-scattering properties that affect radiative transfer are : Extinction (attenuation) coefficient Cross Section of Single-scattering (albedo) Asymmetry factor lalalaaa

Extinction (attenuation) Coefficient Influence of clouds and hydrometeors on radio propagation in The extinction coefficient is given by: Where: σ(r) - Extinction cross-section of a particle with a size r λ - Wavelength n(r)dr - Number of particles within the size range dr per unit volume C - Cloud water mass concentration βλ = ∫ σλ(r) n(r) dr/C lalalaaa

The cross-section of single-scattering (single-scattering albedo) Influence of clouds and hydrometeors on radio propagation in The single scattering albedo is simply the probability that, given an interaction between the photon and particle, the particle will be scattered rather than absorbed It is given by the ratio the scattering coefficient to the total extinction coefficient : Where: s - Scattering a – Absorption The Single-scattering coalbedo is: 1 - ωλ ωλ= βsλ/ β λ = βsλ /(βsλ + βaλ) lalalaaa

Influence of clouds and hydrometeors on radio propagation in Asymmetry factor Influence of clouds and hydrometeors on radio propagation in Asymmetry factor—The mean cosine of the scattering angle, found by integration over the complete scattering phase function. It is given by : Where: Pλ - Scattering phase function of polydispersion cloud particles µ - Cosine of the scattering angle. gλ = ½ ∫ pλ(µ) µ dµ lalalaaa

A linear and logarithmic averaging over a band There is no unique method for deriving ω over a broad band. It can only be empirically determined based on the amounts of cloud particles and water vapor encountered in the earth’s atmosphere.

We define the linear and logarithmic averaging over a band as (1-ω’)=Σ(1- ωλ) βλsλΔλ/ ΣβλsλΔλ and Log(1-ω’’)=Σlog (1-ωλ) βλsλΔλ/ΣβλsλΔλ Where: sλ - solar insolation at the top of the atmosphere Δλ - a narrow spectral interval where optical properties can be treated as constants.

The effective mean single-scattering coalbedo The effective mean single-scattering coalbedo of a band is then computed from: (1-ω)=h(1-ω’)+(1-h)(1-ω’’) The weight h should be close to 1 for the spectral bands with weak absorption and should decrease as absorption increases. It is to be determined empirically.

g = ΣgλωλβλsλΔλ / ΣωλβλsλΔλ Compared to ωλ, the extinction coefficient (βλ) and the asymmetry factor (gλ) vary rather smoothly with λ. Their effective mean values over a wide spectral band can be accurately approximated by: β = ΣβλsλΔλ / ΣsλΔλ and g = ΣgλωλβλsλΔλ / ΣωλβλsλΔλ

The regression coefficients Theoretical considerations and radiative transfer calculations have shown that cloud single-scattering properties are not significantly affected by details of the particle size distribution and can be adequately parameterized as functions of the effective particle size. we parameterize the single-scattering properties for a broad spectral band by: β=a0 +a1/re 1-ω=b0 +b1re+b2re2 g=c0 +c1re+c2re2 Where a, b, and c are regression coefficients, and re is the effective particle size defined to be proportional to the ratio of the total volume of cloud particles to the total cross-sectional area, Ac, of cloud particles.

Water droplets/Ice crystals size For spherical water droplets, the effective size is given by : hexagonal ice crystals randomly oriented in space, the effective size is: The cloud optical thickness, τ, is then given by: rω = ∫r3n(r)dr / ∫r2n(r)dr = (3/4 ρw )*(C/Ac) ρw - density of water )*(C/Ac) ri=(2√3/3 ρi ρi - density of water τ=βCz z - geometric thickness of a cloud layer

Ice and Water clouds The size, shape, and refractive indices are different for ice crystals and water droplets The extinction coefficient of ice clouds is smaller than that of water clouds, because ice crystals are much larger than water droplets.

The four bands by spectral range we divide the solar spectrum into four wide bands and parameterize the single-scattering properties for these bands. The spectral ranges of these four bands are given in the following table h (water cloud) h (ice cloud) Spectral range (μm) Band 1 0.18-0.7 2/3 0.7-1.22 2 1/3 1.22-2.27 3 2.27-10 4

The extinction coefficient of ice and water clouds as a function of the effective particle size The extinction coefficient varies weakly with spectral band but strongly with particle size. In spite of a large difference in the particle size distribution, the ice particle extinction coefficients for all ice clouds nearly fall onto a single curve β=a0 +a1/re Water cloud Ice cloud Spectral band a1 a0 1.65 (-)6.59 * 10-3 2.52 3.33 * 10-n 1 1.72 (-)1.01 * 10-2 2 1.85 (-)1.66 * 10-2 3 2.16 (-)3.39 * 10-2 4

Extinction Coefficient (m2g-1) Ice Clouds Extinction Coefficient (m2g-1) ri (µm)

Extinction Coefficient (m2g-1) rw (µm)

The single-scattering coalbedo of ice and water clouds as a function of the effective particle size For a given particle size, the single-scattering coalbedo varies by three orders of magnitude among the three IR bands. 1-ω=b0 +b1re+b2re2 Water cloud Ice cloud Spectral band b2 b1 b0 1 (-)4.15 * 10-8 8.45 * 10-6 7.15 * 10-8 7.46 * 10-6 (-)2.6 * 10-6 2 (-)6.5 * 10-6 8.88 * 10-4 (-)1.99 * 10-4 (-)1.34 * 10-6 7.37 * 10-4 2.15 * 10-3 3 (-)3.69 * 10-4 1.79 * 10-2 1.21 * 10-2 (-)1.04 * 10-5 2.99 * 10-3 8.94 * 10-2 4

Single-Scattering co-albedo ri (µm)

Single-Scattering co-albedo rw (µm)

The asymmetry factor of ice and water clouds as a function of the effective particle size The asymmetry factor varies between 0.78 and 0.94 for different bands and particle sizes g=c0+c1re+c2re2 Water cloud Ice cloud Spectral band c2 c1 c0 (-)1.49 * 10-6 5.29 * 10-3 8.26 * 10-1 (-)2.64 * 10-6 1.05 * 10-3 7.46 * 10-1 1 (-)2.33 * 10-4 8.32 * 10-3 7.94 * 10-1 (-)3.67 * 10-6 1.2 * 10-3 7.49 * 10-1 2 (-)3.82 * 10-4 1.37 * 10-2 7.45 * 10-1 (-)3.96 * 10-6 1.42 * 10-3 7.61 * 10-1 3 5.52 * 10-5 2.57 * 10-3 8.35 * 10-1 (-)3.85 * 10-6 1.26 * 10-3 8.41 * 10-1 4

Asymmetry Factor ri (µm)

Asymmetry Factor rw (µm)

Cloud Overlapping Clouds could occur at various heights with fractional cover. Nearly all radiative transfer algorithms used in atmospheric models apply only to horizontally homogeneous atmosphere. Horizontal inhomogeneity is not allowed. A way to deal with a partial cloudiness situation is to divide the sky into sections.

Within each section, an atmospheric layer is either free of clouds or filled totally with a homogeneous cloud. Radiative fluxes are then computed for each section, and the total SW heating is the sum of all sections weighted by the fractional cover of individual sections. A cloud that partially fills a layer is usually smeared over the entire layer. The optical thickness τ is adjusted by a factor dependent on the fractional cloud cover.

The effect of τ on radiation is highly nonlinear. The effective optical thickness corresponding to a cloud smeared to cover the entire sky is a function of τ, f, and the solar zenith angle, as well as whether scaling is based on reflection or absorption. f is the fractional cloud cover. Scaling of τ is further complicated by a large range of the way clouds in various layers overlap.

Maximum-random Overlapping Clouds are identified as high, middle, and low separated roughly by the 400- and 700-mb levels. Cloud layers in each of the three height groups are assumed to be maximally overlapped. Cloud layers among different groups are assumed to be randomly overlapped. Scaling of τ is applied only to the maximally overlapped clouds within each of the three height groups.

Within each height group, clouds are smeared over the extent of the maximum cloud amount, fm. the atmosphere is then divided into <2n sections, where n < 3 is the number of height groups containing clouds. Within each section, a layer is either totally cloud filled or cloud free. Fluxes are first computed for each section and then summed over all sections weighted by the fractional cover of individual sections.

The Maximum-random cloud overlapping scheme

Scaling of optical thickness To simplify the scaling of τ, we assume that reflection is more important to climate than absorption. The radiation algorithm requires calculations of reflection/transmission of a cloud layer, separately for direct and diffuse radiation. the optical thickness of a cloud layer is scaled by factors xs and x’s τb=xsτ for direct radiation τf=x'sτ for diffuse radiation

Direct and Diffused Radiation

a layer with a fractional cloud cover, f , and an optical thickness, τ, is reduced to a layer with: fractional cloud cover, f m. equivalent optical thicknesses τb for direct radiation and τf for diffuse radiation. In addition to the solar zenith angle, cloud cover, and optical thickness, an optimal cloud scaling should, in principle, also depend on the fractional cover and optical thickness of other cloud layers.

Optical Thickness 1τ > 2τ > 3τ > 4τ 1τ 2τ 3τ 4τ LOS LOS LOS

Conclusions We have developed parameterizations for computing cloud single-scattering properties and for scaling the optical thickness in a partial cloudiness situation. Due primarily to large differences in particle size and shape, differences in the single-scattering properties of ice and water clouds are large. The extinction coefficient, single-scattering albedo, and asymmetry factor are parameterized separately for ice and water clouds as functions of the effective mean particle size.

The single scattering coalbedo varies greatly with wavelength, and the approach to averaging the single-scattering coalbedo over a broad spectral band is empirically determined so that errors in flux calculations are minimized. Depending upon the strength of absorption, the averaging ranges between linear and logarithmic. Multiple-scattering radiative transfer models used in atmospheric models are developed for horizontally homogeneous atmospheres. Therefore, scaling of cloud optical thickness in an atmosphere with multiple cloud layers is necessary to make computations affordable.

Clouds are identified as high, middle, and low, separated approximately by the 400- and 700- mb levels. Clouds are assumed to be maximally overlapped within each height group but randomly overlapped among the three height groups. The scaling functions are calculated using a radiative transfer model and then empirically adjusted so that errors in the fluxes at the TOA and at the surface introduced by the scaling are minimized. They are separately applied to direct and diffuse radiation.

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