Differentiating Freezing Drizzle and Freezing Rain in HRRR Model Forecasts

Sarah A. Tessendorf aNational Center for Atmospheric Research, Boulder, Colorado

Search for other papers by Sarah A. Tessendorf in
Current site
Google Scholar
PubMed
Close
,
Allyson Rugg aNational Center for Atmospheric Research, Boulder, Colorado

Search for other papers by Allyson Rugg in
Current site
Google Scholar
PubMed
Close
,
Alexei Korolev bEnvironment and Climate Change Canada, Toronto, Ontario, Canada

Search for other papers by Alexei Korolev in
Current site
Google Scholar
PubMed
Close
,
Ivan Heckman bEnvironment and Climate Change Canada, Toronto, Ontario, Canada

Search for other papers by Ivan Heckman in
Current site
Google Scholar
PubMed
Close
,
Courtney Weeks aNational Center for Atmospheric Research, Boulder, Colorado

Search for other papers by Courtney Weeks in
Current site
Google Scholar
PubMed
Close
,
Gregory Thompson aNational Center for Atmospheric Research, Boulder, Colorado

Search for other papers by Gregory Thompson in
Current site
Google Scholar
PubMed
Close
,
Darcy Jacobson aNational Center for Atmospheric Research, Boulder, Colorado

Search for other papers by Darcy Jacobson in
Current site
Google Scholar
PubMed
Close
,
Dan Adriaansen aNational Center for Atmospheric Research, Boulder, Colorado

Search for other papers by Dan Adriaansen in
Current site
Google Scholar
PubMed
Close
, and
Julie Haggerty aNational Center for Atmospheric Research, Boulder, Colorado

Search for other papers by Julie Haggerty in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Supercooled large drop (SLD) icing poses a unique hazard for aircraft and has resulted in new regulations regarding aircraft certification to fly in regions of known or forecast SLD icing conditions. The new regulations define two SLD icing categories based upon the maximum supercooled liquid water drop diameter (Dmax): freezing drizzle (100–500 μm) and freezing rain (>500 μm). Recent upgrades to U.S. operational numerical weather prediction models lay a foundation to provide more relevant aircraft icing guidance including the potential to predict explicit drop size. The primary focus of this paper is to evaluate a proposed method for estimating the maximum drop size from model forecast data to differentiate freezing drizzle from freezing rain conditions. Using in situ cloud microphysical measurements collected in icing conditions during two field campaigns between January and March 2017, this study shows that the High-Resolution Rapid Refresh model is capable of distinguishing SLD icing categories of freezing drizzle and freezing rain using a Dmax extracted from the rain category of the microphysics output. It is shown that the extracted Dmax from the model correctly predicted the observed SLD icing category as much as 99% of the time when the HRRR accurately forecast SLD conditions; however, performance varied by the method to define Dmax and by the field campaign dataset used for verification.

Significance Statement

Aircraft icing is a hazardous condition that can lead to aviation accidents. We are working to improve forecasts of when aircraft icing conditions occur, especially with respect to a special type of icing condition that occurs from larger supercooled liquid drops that can more detrimentally impact some aircraft than icing from small drops. We investigated a method to distinguish two types of large drop icing in operational forecast models: freezing drizzle and freezing rain. These findings suggest that forecast models are capable of distinguishing these two types of icing, which can provide valuable information to aviation weather forecasters. However, there are improvements that still need to be made to improve how often models accurately predict supercooled large drop icing.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Sarah A. Tessendorf, saraht@ucar.edu

Abstract

Supercooled large drop (SLD) icing poses a unique hazard for aircraft and has resulted in new regulations regarding aircraft certification to fly in regions of known or forecast SLD icing conditions. The new regulations define two SLD icing categories based upon the maximum supercooled liquid water drop diameter (Dmax): freezing drizzle (100–500 μm) and freezing rain (>500 μm). Recent upgrades to U.S. operational numerical weather prediction models lay a foundation to provide more relevant aircraft icing guidance including the potential to predict explicit drop size. The primary focus of this paper is to evaluate a proposed method for estimating the maximum drop size from model forecast data to differentiate freezing drizzle from freezing rain conditions. Using in situ cloud microphysical measurements collected in icing conditions during two field campaigns between January and March 2017, this study shows that the High-Resolution Rapid Refresh model is capable of distinguishing SLD icing categories of freezing drizzle and freezing rain using a Dmax extracted from the rain category of the microphysics output. It is shown that the extracted Dmax from the model correctly predicted the observed SLD icing category as much as 99% of the time when the HRRR accurately forecast SLD conditions; however, performance varied by the method to define Dmax and by the field campaign dataset used for verification.

Significance Statement

Aircraft icing is a hazardous condition that can lead to aviation accidents. We are working to improve forecasts of when aircraft icing conditions occur, especially with respect to a special type of icing condition that occurs from larger supercooled liquid drops that can more detrimentally impact some aircraft than icing from small drops. We investigated a method to distinguish two types of large drop icing in operational forecast models: freezing drizzle and freezing rain. These findings suggest that forecast models are capable of distinguishing these two types of icing, which can provide valuable information to aviation weather forecasters. However, there are improvements that still need to be made to improve how often models accurately predict supercooled large drop icing.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Sarah A. Tessendorf, saraht@ucar.edu
Save
  • Ashenden, R., and J. D. Marwitz, 1998: Characterizing the super-cooled large droplet environment with corresponding turbo-prop aircraft response. J. Aircr., 35, 912920, https://doi.org/10.2514/2.2386.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Baker, B., Q. Mo, R. P. Lawson, D. O’Connor, and A. Korolev, 2009: Drop size distributions and the lack of small drops in RICO rain shafts. J. Appl. Meteor. Climatol., 48, 616623, https://doi.org/10.1175/2008JAMC1934.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Benjamin, S. G., J. Brown, and T. Smirnova, 2016a: Explicit precipitation-type diagnosis from a model using a mixed-phase bulk cloud-precipitation microphysics parameterization. Wea. Forecasting, 31, 609619, https://doi.org/10.1175/WAF-D-15-0136.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Benjamin, S. G., and Coauthors, 2016b: A North American hourly assimilation and model forecast cycle: The Rapid Refresh. Mon. Wea. Rev., 144, 16691694, https://doi.org/10.1175/MWR-D-15-0242.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bernstein, B. C., 2000: Regional and local influences on freezing drizzle, freezing rain, and ice pellet events. Wea. Forecasting, 15, 485508, https://doi.org/10.1175/1520-0434(2000)015<0485:RALIOF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bernstein, B. C., F. McDonough, M. K. Politovich, B. G. Brown, T. P. Ratvasky, and D. R. Miller, 2005: Current icing potential (CIP): Algorithm description and comparison with aircraft observations. J. Appl. Meteor., 44, 969986, https://doi.org/10.1175/JAM2246.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bernstein, B. C., R. M. Rasmussen, F. McDonough, and C. Wolff, 2019: Keys to differentiating between small- and large-drop icing conditions in continental clouds. J. Appl. Meteor. Climatol., 58, 19311953, https://doi.org/10.1175/JAMC-D-18-0038.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Berry, E. X., and R. L. Reinhardt, 1974a: An analysis of cloud drop growth by collection. Part I: Double distributions. J. Atmos. Sci., 31, 18141824, https://doi.org/10.1175/1520-0469(1974)031<1814:AAOCDG>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Berry, E. X., and R. L. Reinhardt, 1974b: An analysis of cloud drop growth by collection. Part II: Single initial distributions. J. Atmos. Sci., 31, 18251831, https://doi.org/10.1175/1520-0469(1974)031<1825:AAOCDG>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bocchieri, J. R., 1980: The objective use of upper air soundings to specify precipitation type. Mon. Wea. Rev., 108, 596603, https://doi.org/10.1175/1520-0493(1980)108<0596:TOUOUA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brown, P. R. A., and P. N. Francis, 1995: Improved measurements of the ice water content in cirrus using a total-water probe. J. Atmos. Oceanic Technol., 12, 410414, https://doi.org/10.1175/1520-0426(1995)012<0410:IMOTIW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cober, S. G., and G. A. Isaac, 2012: Characterization of aircraft icing environments with supercooled large drops for application to commercial aircraft certification. J. Appl. Meteor. Climatol., 51, 265284, https://doi.org/10.1175/JAMC-D-11-022.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cober, S. G., and G. A. Isaac, 2013: Reply to “Comments on ‘Characterization of aircraft icing environments with supercooled large drops for application to commercial aircraft certification.’” J. Appl. Meteor. Climatol., 52, 16731675, https://doi.org/10.1175/JAMC-D-12-0213.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cober, S. G., J. W. Strapp, and G. A. Isaac, 1996: An example of supercooled drizzle drops formed through a collision–coalescence process. J. Appl. Meteor., 35, 22502260, https://doi.org/10.1175/1520-0450(1996)035<2250:AEOSDD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cober, S. G., G. A. Isaac, and J. W. Strapp, 2001a: Characterizations of aircraft icing environments that include supercooled large drops. J. Appl. Meteor., 40, 19842002, https://doi.org/10.1175/1520-0450(2001)040<1984:COAIET>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cober, S. G., G. A. Isaac, and J. W. Strapp, 2001b: Assessing cloud-phase conditions. J. Appl. Meteor., 40, 19671983, https://doi.org/10.1175/1520-0450(2001)040<1967:ACPC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cober, S. G., B. Bernstein, R. Jeck, E. Hill, G. Isaac, J. Riley, and A. Shah, 2009: Data and analysis for the development of an engineering standard for supercooled large drop conditions. FAA Tech. Rep. DOT/FAA/AR-09/10, https://www.faa.gov/about/office_org/headquarters_offices/ang/library/.

  • Cooper, W. A., W. R. Sand, M. K. Politovich, and D. L. Veal, 1984: Effects of icing on performance of a research aircraft. J. Aircr., 21, 708715, https://doi.org/10.2514/3.45018.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cortinas, J. V., B. C. Bernstein, C. C. Robbins, and J. W. Strapp, 2004: An analysis of freezing rain, freezing drizzle, and ice pellets across the United States and Canada: 1976–90. Wea. Forecasting, 19, 377390, https://doi.org/10.1175/1520-0434(2004)019<0377:AAOFRF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • DiVito, S., B. C. Bernstein, D. L. Sims, J. T. Riley, S. D. Landolt, J. A. Haggerty, M. Wolde, and A. Korolev, 2020: In-Cloud ICing and Large-drop Experiment (ICICLE) Part 1: Overview. 20th Conf. on Aviation, Range, and Aerospace Meteorology (ARAM), Boston, MA, Amer. Meteor. Soc., 14.1, https://ams.confex.com/ams/2020Annual/webprogram/Paper369402.html.

  • Field, P. R., A. J. Heymsfield, and A. Bansemer, 2006: Shattering and particle interarrival times measured by optical array probes in ice clouds. J. Atmos. Oceanic Technol., 23, 13571371, https://doi.org/10.1175/JTECH1922.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Finstad, K. J., E. P. Lozowski, and L. Makkonen, 1988: On the median volume diameter approximation for droplet collision efficiency. J. Atmos. Sci., 45, 40084012, https://doi.org/10.1175/1520-0469(1988)045<4008:OTMVDA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gilmore, M. S., and J. M. Straka, 2008: The Berry and Reinhardt autoconversion parameterization: A digest. J. Appl. Meteor. Climatol., 47, 375396, https://doi.org/10.1175/2007JAMC1573.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., and J. L. Parrish, 1979: Techniques employed in the processing of particle size spectra and state parameter data obtained with T-28 aircraft platform. NCAR Tech. Note NCAR/TN-137+1A0, 78 pp.

  • Huffman, G. J., and G. A. Norman Jr., 1988: The supercooled warm rain process and the specification of freezing precipitation. Mon. Wea. Rev., 116, 21722182, https://doi.org/10.1175/1520-0493(1988)116<2172:TSWRPA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Isaac, G. A., S. G. Cober, J. W. Strapp, A. V. Korolev, A. Tremblay, and D. L. Marcotte, 2001: Recent Canadian research on aircraft in-flight icing. Can. Aeronaut. Space J., 47, 213221.

    • Search Google Scholar
    • Export Citation
  • Kajikawa, M., K. Kikuchi, Y. Asuma, Y. Inoue, and N. Sato, 2000: Supercooled drizzle formed by condensation-coalescence in the mid-winter season of the Canadian Arctic. Atmos. Res., 52, 293301, https://doi.org/10.1016/S0169-8095(99)00035-6.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Korolev, A. V., 2007: Reconstruction of the sizes of spherical particles from their shadow images. Part I: Theoretical considerations. J. Atmos. Oceanic Technol., 24, 376389, https://doi.org/10.1175/JTECH1980.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Korolev, A. V., and B. Sussman, 2000: A technique for habit classification of cloud particles. J. Atmos. Oceanic Technol., 17, 10481057, https://doi.org/10.1175/1520-0426(2000)017<1048:ATFHCO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Korolev, A. V., and P. R. Field, 2015: Assessment of the performance of the inter-arrival time algorithm to identify ice shattering artifacts in cloud particle probe measurements. Atmos. Meas. Tech., 8, 761777, https://doi.org/10.5194/amt-8-761-2015.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Korolev, A. V., J. W. Strapp, and G. A. Isaac, 1998: Evaluation of accuracy of PMS optical array probes. J. Atmos. Oceanic Technol., 15, 708720, https://doi.org/10.1175/1520-0426(1998)015<0708:EOTAOP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Korolev, A. V., and Coauthors, 2020: A new look at the environmental conditions favorable to secondary ice production. Atmos. Chem. Phys., 20, 13911429, https://doi.org/10.5194/acp-20-1391-2020.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marshall, J. S., and W. M. Palmer, 1948: The distribution of raindrops with size. J. Meteor., 5, 165166, https://doi.org/10.1175/1520-0469(1948)005<0165:TDORWS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Martin, G. M., D. W. Johnson, and A. Spice, 1994: The measurement and parameterization of effective radius of droplets in warm stratocumulus clouds. J. Atmos. Sci., 51, 18231842, https://doi.org/10.1175/1520-0469(1994)051<1823:TMAPOE>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Martner, B. E., R. M. Rauber, R. M. Rasmussen, E. T. Prater, and M. K. Ramamurthy, 1992: Impacts of a destructive and well-observed cross-country winter storm. Bull. Amer. Meteor. Soc., 73, 169172, https://doi.org/10.1175/1520-0477(1992)073<0169:IOADAW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marwitz, J. D., M. K. Politovich, B. C. Bernstein, F. M. Ralph, P. J. Neiman, R. Ashenden, and J. Bresch, 1997: Meteorological conditions associated with the ATR-72 aircraft accident near Roselawn, Indiana on 31 October 1994. Bull. Amer. Meteor. Soc., 78, 4152, https://doi.org/10.1175/1520-0477(1997)078<0041:MCAWTA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ohtake, T., 1963: Hemispheric investigations of warm rain by radiosonde data. J. Appl. Meteor., 2, 594607, https://doi.org/10.1175/1520-0450(1963)002<0594:HIOWRB>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pobanz, B. M., J. D. Marwitz, and M. K. Politovich, 1994: Conditions associated with large-drop regions. J. Appl. Meteor., 33, 13661372, https://doi.org/10.1175/1520-0450(1994)033<1366:CAWLDR>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Politovich, M. K., 1989: Aircraft icing caused by large supercooled droplets. J. Appl. Meteor., 28, 856868, https://doi.org/10.1175/1520-0450(1989)028<0856:AICBLS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Politovich, M. K., and B. Bernstein, 1995: Production and depletion of supercooled liquid water in a Colorado winter storm. J. Appl. Meteor., 34, 26312648, https://doi.org/10.1175/1520-0450(1995)034<2631:PADOSL>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rasmussen, R. M., and Coauthors, 1992: Winter Icing and Storms Project (WISP). Bull. Amer. Meteor. Soc., 73, 951974, https://doi.org/10.1175/1520-0477(1992)073<0951:WIASP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rasmussen, R. M., B. C. Bernstein, M. Murakami, G. Stossmeister, J. Reisner, and B. Stankov, 1995: The 1990 Valentine’s Day arctic outbreak. Part I: Mesoscale and microscale structure and evolution of a Colorado Front Range shallow upslope cloud. J. Appl. Meteor., 34, 14811511, https://doi.org/10.1175/1520-0450-34.7.1481.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rasmussen, R. M., I. Geresdi, G. Thompson, K. Manning, and E. Karplus, 2002: Freezing drizzle formation in stably stratified layer clouds: The role of radiative cooling of cloud droplets, cloud condensation nuclei, and ice initiation. J. Atmos. Sci., 59, 837860, https://doi.org/10.1175/1520-0469(2002)059<0837:FDFISS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rauber, R. M., M. K. Ramamurthy, and A. Tokay, 1994: Synoptic and mesoscale structure of a severe freezing rain event: The St. Valentine’s Day ice storm. Wea. Forecasting, 9, 183208, https://doi.org/10.1175/1520-0434(1994)009<0183:SAMSOA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rauber, R. M., L. S. Olthoff, M. K. Ramamurthy, and K. E. Kunkel, 2000: The relative importance of warm rain and ice processes in freezing precipitation events. J. Appl. Meteor., 39, 11851195, https://doi.org/10.1175/1520-0450(2000)039<1185:TRIOWR>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sand, W. R., W. A. Cooper, M. K. Politovich, and D. L. Veal, 1984: Icing conditions encountered by a research aircraft. J. Climate Appl. Meteor., 23, 14271440, https://doi.org/10.1175/0733-3021-23.10.1427.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schultz, P., and M. K. Politovich, 1992: Towards the improvement of aircraft-icing forecasts for the continental United States. Wea. Forecasting, 7, 491500, https://doi.org/10.1175/1520-0434(1992)007<0491:TTIOAI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tessendorf, S. A., and Coauthors, 2017: Developing improved products to forecast and diagnose aircraft icing conditions based upon drop size. AIAA Aviation Forum Proc., Denver, CO, AIAA, AIAA 2017-4473, https://doi.org/10.2514/6.2017-4473.

    • Crossref
    • Export Citation
  • Tessendorf, S. A., and Coauthors, 2019: A transformational approach to winter orographic weather modification research: The SNOWIE Project. Bull. Amer. Meteor. Soc., 100, 7192, https://doi.org/10.1175/BAMS-D-17-0152.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thompson, G., and T. Eidhammer, 2014: A study of aerosol impacts on clouds and precipitation development in a large winter cyclone. J. Atmos. Sci., 71, 36363658, https://doi.org/10.1175/JAS-D-13-0305.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thompson, G., R. Bruintjes, B. G. Brown, and F. Hage, 1997: Intercomparison of in-flight icing algorithms. Part I: WISP94 real-time icing prediction and evaluation program. Wea. Forecasting, 12, 878889, https://doi.org/10.1175/1520-0434(1997)012<0878:IOIFIA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thompson, G., R. M. Rasmussen, and K. Manning, 2004: Explicit forecasts of winter precipitation using an improved bulk microphysics scheme. Part I: Description and sensitivity analysis. Mon. Wea. Rev., 132, 519542, https://doi.org/10.1175/1520-0493(2004)132<0519:EFOWPU>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thompson, G., P. R. Field, R. M. Rasmussen, and W. D. Hall, 2008: Explicit forecast of winter precipitation using an improved bulk microphysics scheme. Part II: Implementation of a new snow parameterization. Mon. Wea. Rev., 136, 50955115, https://doi.org/10.1175/2008MWR2387.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thompson, G., M. K. Politovich, and R. M. Rasmussen, 2017: A numerical weather model’s ability to predict characteristics of aircraft icing environments. Wea. Forecasting, 32, 207221, https://doi.org/10.1175/WAF-D-16-0125.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Williams, E. R., M. F. Donovan, D. J. Smalley, J. M. Kurdzo, and B. J. Bennett, 2020: The 2017 Buffalo Area Icing and Radar Study (BAIRS II). FAA Project Rep. ATC-447, 184 pp.

  • Xu, M., G. Thompson, D. Adriaansen, and S. Landolt, 2019: On the value of time-lag-ensemble averaging to improve numerical model predictions of aircraft icing conditions. Wea. Forecasting, 34, 507519, https://doi.org/10.1175/WAF-D-18-0087.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 580 0 0
Full Text Views 470 284 18
PDF Downloads 510 283 18