Atmos. Meas. Tech., 10, 2557–2571, 2017 https://doi.org/10.5194/amt-10-2557-2017 © Author(s) 2017. This work is distributed under the Creative Commons Attribution 3.0 License. A variational technique to estimate snowfall rate from coincident radar, snowflake, and fall-speed observations Steven J. Cooper1, Norman B. Wood2, and Tristan S. L’Ecuyer3 1Department of Atmospheric Sciences, University of Utah, Salt Lake City, UT, USA 2Cooperative Institute for Meteorological Satellite Studies, University of Wisconsin–Madison, Madison, WI, USA 3Department of Atmospheric and Oceanic Sciences, University of Wisconsin–Madison, Madison, WI, USA Correspondence to: Steven J. Cooper ([email protected]) Received: 1 February 2017 – Discussion started: 15 February 2017 Revised: 12 June 2017 – Accepted: 13 June 2017 – Published: 20 July 2017 Abstract. Estimates of snowfall rate as derived from radar 1 Introduction reflectivities alone are non-unique. Different combinations of snowflake microphysical properties and particle fall speeds can conspire to produce nearly identical snowfall rates for The high-latitude regions play a critical role in shaping cli- given radar reflectivity signatures. Such ambiguities can re- mate response to anthropogenic forcing. Model predictions sult in retrieval uncertainties on the order of 100–200 % for suggest that it is these areas that are most susceptible to individual events. Here, we use observations of particle size change and will experience the most dramatic temperature distribution (PSD), fall speed, and snowflake habit from the increase in response to the release of greenhouse gases into Multi-Angle Snowflake Camera (MASC) to constrain esti- the atmosphere (Manabe and Stouffer, 1980; Holland and mates of snowfall derived from Ka-band ARM zenith radar Bitz, 2003; Serreze and Francis, 2006). Observed changes in (KAZR) measurements at the Atmospheric Radiation Mea- the Arctic over the late 20th century and early 21st century surement (ARM) North Slope Alaska (NSA) Climate Re- have been dramatic and have included increased surface tem- search Facility site at Barrow. MASC measurements of mi- perature and decreased sea ice, permafrost, glacial ice sheet, crophysical properties with uncertainties are introduced into and spring Arctic snow cover extents (Serreze et al., 2000; a modified form of the optimal-estimation CloudSat snow- Frauenfeld et al., 2004; Dyurgerov and Meier, 2005; Stroeve fall algorithm (2C-SNOW-PROFILE) via the a priori guess et al., 2008, 2014; Brown et al., 2010; Perlwitz et al., 2015, and variance terms. Use of the MASC fall speed, MASC among numerous others). PSD, and CloudSat snow particle model as base assumptions Snowfall can dramatically change surface conditions at resulted in retrieved total accumulations with a −18 % dif- high-latitude regions, acting to increase shortwave surface ference relative to nearby National Weather Service (NWS) albedo while impacting sensible and latent heat fluxes and observations over five snow events. The average error was longwave emission (Cohen and Rind, 1991). Changes in 36 % for the individual events. Use of different but reason- snow cover can feed back on snow cover, sea ice, and able combinations of retrieval assumptions resulted in esti- permafrost distributions (Brown, 2000; Ramonovsky et al., mated snowfall accumulations with differences ranging from 2002; Holland et al., 2006; Vavrus, 2007), where the effects −64 to C122 % for the same storm events. Retrieved snow- on permafrost in turn may affect high-latitude carbon storage. fall rates were particularly sensitive to assumed fall speed Snowfall changes at higher north latitudes may also impact and habit, suggesting that in situ measurements can help to freshening of the North Atlantic Ocean and the strength of constrain key snowfall retrieval uncertainties. More accurate the Atlantic Meridional Overturning Circulation. Peterson et knowledge of these properties dependent upon location and al. (2006) attributed more than half of the cumulative fresh- meteorological conditions should help refine and improve water input anomaly in the Arctic and high-latitude North ground- and space-based radar estimates of snowfall. Atlantic oceans over the previous 50 years to increases in net precipitation over land and oceans, exceeding the estimated Published by Copernicus Publications on behalf of the European Geosciences Union. 2558 S. J. Cooper et al.: A variational technique to estimate snowfall rate contributions from glacial melt and sea ice reduction. Snow- tinues the global monitoring of snowfall with dual-frequency fall is also important as it provides mass influx for vast glacial Ka-band and Ku-band radar and extensive ground measure- ice sheets such as those found in Antarctica and Greenland ment activities (Skofronick-Jackson et al., 2015). (Lenaerts et al., 2013; Palerme et al., 2014). The distribu- Despite such efforts, validation activities suggest that un- tion of snowfall helps define ice sheet dynamics, and the rel- certainties in retrieved snowfall rates can still be on the ative difference between snowfall and melt will impact the order of 200 % for individual snow events (Wood, 2011). long-term survival of these glaciers (Van Tricht et al., 2016). In our retrieval scheme, instead of using a priori guesses Significant loss of ice sheets may have deleterious effects on of snowflake microphysical properties from field campaigns human society through a corresponding rise of global ocean such as C3VP, we used coincident observations of snowflake levels (Gardner et al., 2013; Jacob et al., 2012). microphysical properties from the Multi-Angle Snowflake The quantitative estimation of snowfall at the global scale Camera (MASC; Garrett et al., 2012) to constrain the radar- from spaceborne measurements has occurred only recently. based retrieval approach. The MASC takes multiple images Initial retrieval approaches were based on passive microwave of snowflakes in free fall while simultaneously measuring fall measurements (Skofronick-Jackson et al., 2004; Noh et al., speed. From these pictures, estimates of snowflake maximum 2006) with a shift in emphasis to radar observations with particle dimension, habit, and other properties that could be the launch of the CloudSat Cloud Profiling Radar (CPR) in used to refine a radar retrieval scheme are estimated. It should 2006. Matrosov et al. (2007) and Liu (2008a) demonstrated be noted, however, that any instrument that measures snow the first-order capability of the CloudSat CPR to retrieve ver- particle properties or fall speed, e.g., the Precipitation Imag- tical profiles of dry snowfall. Kulie and Bennartz (2009), in ing Package (Newman et al., 2009), could replace the role of turn, used CloudSat CPR reflectivities to estimate global dry the MASC in the variational approach presented in this work. snowfall rate for a year of CloudSat data. They found that We describe here a retrieval technique for snowfall rate snowfall estimates depended critically upon assumed rela- and its application to five snow events as observed at the tionships between radar reflectivity and snowfall particle size Atmospheric Radiation Measurement (ARM) North Slope distributions (PSDs) and shapes. Alaska (NSA) Climate Research Facility site at Barrow. These studies suggest that estimates of snowfall as derived Our scheme uses ground-based Ka-band ARM zenith radar from radar reflectivities alone are non-unique. Numerous dif- (KAZR) measurements for reflectivity profiles and was di- ferent combinations of snowflake microphysical properties rectly modified from the W-band CloudSat 2C-SNOW- and snow particle fall speeds may yield nearly identical sur- PROFILE algorithm. The flexible optimal-estimation frame- face snowfall rates for a given reflectivity profile. As such, work was used to incorporate coincident MASC observations use of traditional Ze–S relationships to quantify snowfall into the radar-based scheme through the retrieval a priori cannot be expected to produce accurate results for all snow- terms. A primary objective was to identify those combina- fall events. tions of retrieval assumptions that allowed the best match From an operational retrieval perspective, clever selection with snowfall observations at the Barrow site for five snow of representative snowflake microphysical properties may events during April and May 2014. Another objective was produce estimates of snowfall amounts that agree well with to quantify the sensitivity of snowfall rate retrieval results reported values for climate or regional applications. For ex- to the key microphysical assumptions of particle size distri- ample, Wood et al. (2015; but see also Wood, 2011) devel- bution, habit, and fall speed from the MASC. These results oped snowflake models for the CloudSat snowfall retrieval were contrasted with snowfall rates found using alternate as- algorithm based upon field campaigns focused on cold- sumptions such as the Locatelli and Hobbs (1974, hereafter season clouds and precipitation, principally the Canadian LH74) particle dimension–fall speed parameterizations, ob- CloudSat–CALIPSO Validation Project (C3VP, Hudak et al., served KAZR Doppler velocities, and previous field cam- 2006). They used this a priori knowledge of snowfall micro- paign estimates of snow particle size distributions. In Sect. 2, physics to refine expected snowfall–radar reflectivity rela- we discuss the methodology including the CloudSat snowfall tionships for the optimal-estimation-based (Rodgers, 2000) retrieval scheme, the MASC observations,