Estimating vertical profiles of ice water content and snowfall rate from radar measurements in the G-band

We present theory and simulations to show that at frequencies of order 200 GHz (G-band) the radar cross sec- tion (σr) of ice particles larger than ∼ a quarter wavelength (0.375 mm) is nearly directly proportional to their mass (m). Hence measurements of radar reflectivity (Z) at this fre- quency are directly proportional to the ice water content (IWC), with no other assumptions about the shape or breadth of the particle size distribution required. For the same rea- son, vertically pointing Doppler velocities at this frequency provide the mass-weighted mean vertical velocity of the par- ticles, and the product of Z with the mean Doppler velocity (MDV) is proportional to the snowfall rate (S). This presents the opportunity for straightforward and accurate retrievals of ice microphysics. We explore the sensitivity of such retrievals to the scat- tering model for ice particles. We find that all seven mod- els examined, four with random orientation and three with horizontal orientation, have σr ∝ m in this regime, but that the coefficient of proportionality varies between models. The dominant factor controlling this coefficient is the mass-size relationship for the ice particles, and specifically the mass of a wavelength-sized ice particle. If this information is known, or can be assumed, then the ice population param- eters above can be retrieved with high accuracy. For mass- weighted mean diameters Dm > 0.5 mm the variation in the IWC–Z relationship is within ≈ 30 %, and the variation in the S–(Z × MDV) relationship is within ≈ 15 %. The method is applied to retrieve IWC and S during two case studies, with measurements from the GRaCE 200 GHz Doppler radar at Chilbolton Observatory in the UK. In the first of these case studies, retrieved snowfall rates from par- ticles falling aloft in a precipitating ice cloud were com- pared to gauge data at the surface. In the second case study, retrieved ice water contents from a deep non-precipitating stratiform ice cloud were compared to measurements made using an evaporative water content probe on board the Facil- ity for Airborne Atmospheric Measurements (FAAM) BAe- 146 instrumented research aircraft. In both cases a statisti- cal comparison was necessary because of imperfect coloca- tion of the radar measurements and in-situ/gauge sampling. The measurements fall within the distributions of the re- trieved water content and snowfall fields, and follow consis- tent trends with time (Case 1) and height (Case 2), providing evidence that this method produces realistic retrievals. Application of the same technique at even higher radar fre- quencies would allow clouds with smaller particles (e.g. in high altitude cirrus clouds) to be characterised. Because of the increased gaseous attenuation at such frequencies, the latter may be more practical from airborne or spaceborne platforms.