Cloud Radar in Space: CloudSat While TRMM has been a successful precipitation radar, its dBZ minimum detectable signal does not allow views of light precipitation and/or clouds (except some anvils) due to wavelength and sensitivity Going to a higher frequency increases sensitivity to smaller particles (D 6 ) However, Mie effects (cutoff at ) are more likely to occur, so there is some tradeoff W-Band (mm-wave) is an attractive option, since it is sensitive to many large cloud particles It has been demonstrated as an excellent airborne (Wyoming King Air) and ground-based platform, in combination with lidar, to estimate IWC and LWC in clouds Attenuation and Mie effects in precipitation limit the maximum retrievable rain rate (depending on the DSD) to about dBZ (overlap with TRMM?)

Radar energy becomes more susceptible to Mie scattering as wavelength gets shorter or particles get larger (cutoff at x =  *D/ - from geometric optics) - above this cutoff, Rayleigh assumption breaks down and backscattered energy (in this case, Z) is reduced

Attenuation vs. Wavelength While CloudSat is more sensitive to smaller particles at W- Band vs. Ku-Band for TRMM, it is susceptible to attenuation and Mie scattering effects Stephens et al. (2002) Attenuation Rates for TRMM (left) Vs. Cloudsat (right)

Attenuation (or absorption) is related to reflectivity by a relationship k = a Z b Assuming a and b for various hydrometeor species has uncertainty, but safer than for Z-R relationship Rain at 10°C

Attenuation In deriving the radar equation, we assumed that the distance between the volume and the target was filled with a non-attenuating medium; that is, there was no power loss due to absorption (attenuation) by the medium. In practice this is obviously not the case as the propagation path is filled with gases (air molecules), cloud particles, and precipitation particles. Depending on wavelength and the concentration of molecules, cloud particles, and precipitation-sized particles, power loss due to attenuation can be very significant. This power loss of either the transmitted power moving out to the target, or the backscattered power returning from the target is a result of both: Scattering Power loss (by particles along the path) Absorption In general the attenuation can be represented by, dP r = -2 k L P r dr(1) where P r is returned power (taken to represent the average returned power), dP r is the reduction in returned power associated with absorption and scattering by the medium, r is range, and k L is the attenuation coefficient with units of m -1. Factor of 2 required for out and back paths. Integrating (1), P r = P r 0 e -2  k L dr (2) where P r 0 is the non-attenuated power.

Attenuation Equation (2) may also be written in the following form, 10 log (P r / P r 0 ) = -2   dr(3) where limits on the integral run from 0 to range r. Here  is the attenuation coefficient, expressed in units of dB/length. Also,  = 10 k L log(e). In general, attenuation can be caused by gases, cloud particles, and precipitation particles. Therefore, r 10 log (P r / P r 0 ) = -2  (  g +  c +  p ) dr(4) 0 where  g is the attenuation by gases (dB/km),  c is the attenuation by cloud particles (dB/km) and  p is the attenuation by precipitation particles (dB/km).

Attenuation by Gases Battan (1973) At radar wavelengths, attenuation by gases is associated with absorption only. Scattering is negligible at radar wavelengths. For various molecules like water vapor and oxygen, vibrational and rotational states are excited by microwave radiation. As the molecule relaxes to its ground state, this absorbed energy is radiated by the molecule or taken up as an increase in internal energy by the molecules. Attenuation by gaseous absorption can be very substantial at wavelengths near 1 cm over long path lengths near the Earth’s surface. Obviously, we will expect a pressure dependence on gaseous absorption since molecular concentrations fall off exponentially with height. The plot at the left shows gaseous attenuation in units of dB/km for oxygen and water vapor. Obviously this spectral dependence has influenced the choice of wavelengths used in radar meteorology.

Attenuation by Gases Doviak and Zrnic (1993) The adjacent figure shows the two way attenuation due to gases for a standard atmosphere. Attenuation depends not only on the length of the propagation path but also on the depth of the troposphere penetrated. An empirical formula that approximates the two way attenuation for elevation angles (  e ) and slant ranges < 200 km is given below. For S-Band: 2  g = [ exp (-  e /1.8)] x (1 - exp{-r/[ exp (-  e /2.2)]}) 10 cm,  g = 1.4 dB for a 100-km path (out & back) C-band can be found by multiplying by 1.2 X-band can be found by multiplying by 1.5

For cloud particles, k (c+p) L = [ (8  2 / ) (  a 3 ) Im (-K) ] Usually, it is easier to estimate liquid (or ice) water content in a cloud than it is to measure the DSD. Since M = (4  /3)a 3 , then k c = [ (6  /  ) Im (-K)] M = K 1 M (M in units of g/m 3 ) For clouds: Attenuation decreases with increasing wavelength At 5 & 10 cm, can neglect attenuation by clouds Attenuation increases with decreasing T Attenuation much lower in ice clouds compared to water clouds for same water content Attenuation by Cloud Particles

Attenuation by Cloud and Precipitation Particles Attenuation by cloud and precipitation particles can be due to both absorption and scattering. Attenuation will therefore be dependent upon particle size, shape, and composition. General considerations Mie scattering theory provided an expression for the back scattering cross section. We also looked at the Rayleigh approximation to Mie backscatter for particles small compared to the incident wavelength. Mie theory also provides additional cross sections; specifically, Q s = scattering cross section; the area which, when multiplied by the incident intensity gives the total power scattered by the particle. Q a = absorption cross section, the area which, when multiplied by the incident intensity gives the total power absorbed by the particle. Q t = attenuation cross section; the area which, when multiplied by the incident intensity gives the total power removed from the incident wave by scattering and absorption. Hence, Q t = Q s + Q a For Rayleigh conditions, Q s = (128/3)  5 -4 a 6  K  2 Q a = 8  2 -1 a 3 Im (-K) Q t = Q s + Q a

These equations relate to a single particle. Obviously a meteorological radar illuminates an ensemble of particles on any pulse. So, need to generalize these equations for a pulse volume, which is a function of range and antenna beamwidth. Define Σ Q t = Σ (Q s + Q a ) = k (c+p) L Here the summation of the cross sections is taken over a pulse volume. k is defined as the attenuation coefficient and has units of m -1. P r = P r 0 e -2  (ΣQ t ) dr When Q t in cm 2 and volume under consideration is 1 m 3, k (c+p) L =  Σ Q t = Σ Q t (dB/km) vol vol For  <<, Q s << Q a, and k (c+p) L = [ (8  2 / ) (  a 3 ) Im (-K) ] ( small particles ) k (c+p) L =  (Q s + Q a ) (large particles,   )

Attenuation by Rainfall For drops < 1 mm and S-band, can use cloud equation (D << ). For shorter wavelengths, Q t must be computed from full Mie equations. In general, Q t  radius k>3, eliminating a simple relationship between Q t and rain mixing ratio. In practice, attenuation by rain is given in terms of rainfall rate, R. Contribution to precipitation by single particle of mass M i R i = M i (w i - w u ) ; w i = terminal fallspeed of drop of mass M i w u = updraft speed R = (4  /3)  L  N r r 3 (w r - w u ) dr ; Divide by  L to get depth/time Ryde (1946) found  p (dB/km) = f(R),  p = K 2 R , where K 2 and  are functions of. Since Z = aR b, then  p can be written as  p = cZ d (Z in mm 6 /m 3 )

C-band resonance effects at D > 5 mm

Attenuation by Hail

X-Band

S-Band

Stephens et al. (2002)

Estimating precipitation from spaceborne radar (single wavelength - TRMM) Need to invert Z to R (use Z = a R b ) Z is attenuated (by gases, cloud, and precipitation), so need to correct Use surface reference technique (estimate path integrated attenuation or PIA and redistribute k in vertical) or k-Z relationship to correct Z for each assumed hydrometeor type Then use corrected Z to estimate R via Z-R relationship (with adjustment from attenuation correction if available) Reference: Iguchi et al. (2000, Journal of Applied Meteorology)