Potentials in Improving Predictability of Multiscale Tropical Weather Systems Evaluated through Ensemble Assimilation of Simulated Satellite-Based Observations

Yue Ying Department of Meteorology and Atmospheric Science, and Center for Advanced Data Assimilation and Predictability Techniques, The Pennsylvania State University, University Park, Pennsylvania

Search for other papers by Yue Ying in
Current site
Google Scholar
PubMed
Close
and
Fuqing Zhang Department of Meteorology and Atmospheric Science, and Center for Advanced Data Assimilation and Predictability Techniques, The Pennsylvania State University, University Park, Pennsylvania

Search for other papers by Fuqing Zhang in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

As a follow-up of our recent paper on the practical and intrinsic predictability of multiscale tropical weather and equatorial waves, this study explores the potentials in improving the analysis and prediction of these weather systems through assimilating simulated satellite-based observations with a regional ensemble Kalman filter (EnKF). The observing networks investigated include the retrieved temperature and humidity profiles from the Advanced TIROS Operational Vertical Sounder (ATOVS) and global positioning system radio occultation (GPSRO), the atmospheric motion vectors (AMVs), infrared brightness temperature from Meteosat-7 (Met7-Tb), and retrieved surface wind speed from the Cyclone Global Navigation Satellite System (CYGNSS). It is found that assimilating simulated ATOVS thermodynamic profiles and AMV winds improves the accuracy of wind, temperature, humidity, and hydrometeors for scales larger than 200 km. The skillful forecast lead times can be extended by as much as 4 days for scales larger than 1000 km. Assimilation of Met7-Tb further improves the analysis of cloud hydrometeors even at scales smaller than 200 km. Assimilating CYGNSS surface winds further improves the low-level wind and temperature. Meanwhile, the impact from assimilating the current-generation GPSRO data with better vertical resolution and accuracy is comparable to assimilating half of the current ATOVS profiles, while a hypothetical 25-times increase in the number of GPSRO profiles can potentially exceed the impact from assimilating the current network of retrieved ATOVS profiles. Our study not only shows great promises in further improving practical predictability of multiscale equatorial systems but also provides guidance in the evaluation and design of current and future spaceborne observations for tropical weather.

© 2018 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: Professor Fuqing Zhang, fzhang@psu.edu

This article has a companion article which can be found at http://journals.ametsoc.org/doi/abs/10.1175/JAS-D-17-0157.1

Abstract

As a follow-up of our recent paper on the practical and intrinsic predictability of multiscale tropical weather and equatorial waves, this study explores the potentials in improving the analysis and prediction of these weather systems through assimilating simulated satellite-based observations with a regional ensemble Kalman filter (EnKF). The observing networks investigated include the retrieved temperature and humidity profiles from the Advanced TIROS Operational Vertical Sounder (ATOVS) and global positioning system radio occultation (GPSRO), the atmospheric motion vectors (AMVs), infrared brightness temperature from Meteosat-7 (Met7-Tb), and retrieved surface wind speed from the Cyclone Global Navigation Satellite System (CYGNSS). It is found that assimilating simulated ATOVS thermodynamic profiles and AMV winds improves the accuracy of wind, temperature, humidity, and hydrometeors for scales larger than 200 km. The skillful forecast lead times can be extended by as much as 4 days for scales larger than 1000 km. Assimilation of Met7-Tb further improves the analysis of cloud hydrometeors even at scales smaller than 200 km. Assimilating CYGNSS surface winds further improves the low-level wind and temperature. Meanwhile, the impact from assimilating the current-generation GPSRO data with better vertical resolution and accuracy is comparable to assimilating half of the current ATOVS profiles, while a hypothetical 25-times increase in the number of GPSRO profiles can potentially exceed the impact from assimilating the current network of retrieved ATOVS profiles. Our study not only shows great promises in further improving practical predictability of multiscale equatorial systems but also provides guidance in the evaluation and design of current and future spaceborne observations for tropical weather.

© 2018 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: Professor Fuqing Zhang, fzhang@psu.edu

This article has a companion article which can be found at http://journals.ametsoc.org/doi/abs/10.1175/JAS-D-17-0157.1

Save
  • Bei, N., and F. Zhang, 2007: Impacts of initial condition errors on mesoscale predictability of heavy precipitation along the mei-yu front of China. Quart. J. Roy. Meteor. Soc., 133, 8399, https://doi.org/10.1002/qj.20.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bei, N., and F. Zhang, 2014: Mesoscale predictability of moist baroclinic waves: Variable and scale-dependent error growth. Adv. Atmos. Sci., 31, 9951008, https://doi.org/10.1007/s00376-014-3191-7.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, F., and J. Dudhia, 2001: Coupling an advanced land surface hydrology model with the Penn State–NCAR MM5 modeling system. Part I: Model implementation and sensitivity. Mon. Wea. Rev., 129, 569585, https://doi.org/10.1175/1520-0493(2001)129<0569:CAALSH>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chou, M. D., and M. J. Suarez, 1999: A solar radiation parameterization for atmospheric studies. NASA Tech. Rep. Series on Global Modeling and Data Assimilation 104606, Vol. 15, 40 pp.

    • Search Google Scholar
    • Export Citation
  • Cook, K. L. B., P. Wilczynski, C. J. Fong, N. L. Yen, and G. S. Chang, 2011: The Constellation Observing System for Meteorology Ionosphere and Climate follow-on mission. Proc. Aerospace Conf., Big Sky, MT, IEEE, 1–7, https://doi.org/10.1109/AERO.2011.5747291.

    • Crossref
    • Export Citation
  • Dee, D. P., and Coauthors, 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553597, https://doi.org/10.1002/qj.828.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dickinson, M., and J. Molinari, 2002: Mixed Rossby–gravity waves and western Pacific tropical cyclogenesis. Part I: Synoptic evolution. J. Atmos. Sci., 59, 21832196, https://doi.org/10.1175/1520-0469(2002)059<2183:MRGWAW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dong, J., M. Xue, and K. Droegemeier, 2011: The analysis and impact of simulated high-resolution surface observations in addition to radar data for convective storms with an ensemble Kalman filter. Meteor. Atmos. Phys., 112, 4161, https://doi.org/10.1007/s00703-011-0130-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dunkerton, T. J., and F. X. Crum, 1995: Eastward propagating ~2- to 15-day equatorial convection and its relation to the tropical intraseasonal oscillation. J. Geophys. Res., 100, 25 78125 790, https://doi.org/10.1029/95JD02678.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • English, S. J., R. J. Renshaw, P. C. Dibben, A. J. Smith, P. J. Rayer, C. Poulsen, F. W. Saunders, and J. R. Eyre, 2000: A comparison of the impact of TOVS arid ATOVS satellite sounding data on the accuracy of numerical weather forecasts. Quart. J. Roy. Meteor. Soc., 126, 29112931, https://doi.org/10.1002/qj.49712656915.

    • Search Google Scholar
    • Export Citation
  • Evensen, G., 1994: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res., 99, 10 14310 162, https://doi.org/10.1029/94JC00572.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gaspari, G., and S. Cohn, 1999: Construction of correlation functions in two and three dimensions. Quart. J. Roy. Meteor. Soc., 125, 723757, https://doi.org/10.1002/qj.49712555417.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Geer, A. J., and P. Bauer, 2011: Observation errors in all-sky data assimilation. Quart. J. Roy. Meteor. Soc., 137, 20242037, https://doi.org/10.1002/qj.830.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Haertel, P. T., and G. N. Kiladis, 2004: Dynamics of 2-day equatorial waves. J. Atmos. Sci., 61, 27072721, https://doi.org/10.1175/JAS3352.1.

  • Hong, S.-Y., Y. Noh, and J. Dudhia, 2006: A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Wea. Rev., 134, 23182341, https://doi.org/10.1175/MWR3199.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hou, A. Y., and Coauthors, 2014: The Global Precipitation Measurement mission. Bull. Amer. Meteor. Soc., 95, 701722, https://doi.org/10.1175/BAMS-D-13-00164.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Iacono, M. J., J. S. Delamere, E. J. Mlawer, M. W. Shephard, S. A. Clough, and W. D. Collins, 2008: Radiative forcing by long-lived greenhouse gases: Calculations with the AER radiative transfer models. J. Geophys. Res., 113, D13103, https://doi.org/10.1029/2008JD009944.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kiladis, G. N., M. C. Wheeler, P. T. Haertel, K. H. Straub, and P. E. Roundy, 2009: Convectively coupled equatorial waves. Rev. Geophys., 47, RG2003, https://doi.org/10.1029/2008RG000266.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kirchgessner, P., L. Nerger, and A. Bunse-Gerstner, 2014: On the choice of an optimal localization radius in ensemble Kalman filter methods. Mon. Wea. Rev., 142, 21652175, https://doi.org/10.1175/MWR-D-13-00246.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kursinski, E. R., G. Hajj, J. Schofield, R. Linfield, and K. Hardy, 1997: Observing Earth’s atmosphere with radio occultation measurements using the global positioning system. J. Geophys. Res., 102, 23 42923 465, https://doi.org/10.1029/97JD01569.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lei, L., and J. S. Whitaker, 2017: Evaluating the trade-offs between ensemble size and ensemble resolution in an ensemble-variational data assimilation system. J. Adv. Model. Earth Syst., 9, 781789, https://doi.org/10.1002/2016MS000864.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Li, J., W. W. Wolf, W. P. Menzel, W. Zhang, H. Huang, and T. H. Achtor, 2000: Global soundings of the atmosphere from ATOVS measurements: The algorithm and validation. J. Appl. Meteor., 39, 12481268, https://doi.org/10.1175/1520-0450(2000)039<1248:GSOTAF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lim, K.-S. S., and S.-Y. Hong, 2010: Development of an effective double-moment cloud microphysics scheme with prognostic cloud condensation nuclei (CCN) for weather and climate models. Mon. Wea. Rev., 138, 15871612, https://doi.org/10.1175/2009MWR2968.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lorenz, E. N., 1963: Deterministic nonperiodic flow. J. Atmos. Sci., 20, 130141, https://doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Madden, R. A., and P. R. Julian, 1971: Detection of a 40–50 day oscillation in the zonal wind in the tropical Pacific. J. Atmos. Sci., 28, 702708, https://doi.org/10.1175/1520-0469(1971)028<0702:DOADOI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Madden, R. A., and P. R. Julian, 1972: Description of global-scale circulation cells in the tropics with a 40–50 day period. J. Atmos. Sci., 29, 11091123, https://doi.org/10.1175/1520-0469(1972)029<1109:DOGSCC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mannucci, A. J., J. Dickson, C. Duncan, and K. Hurst, 2010: GNSS geospace constellation (GGC): A Cubesat space weather mission concept. California Institute of Technology Jet Propulsion Laboratory Rep., 5 pp.

  • Melhauser, C., and F. Zhang, 2012: Practical and intrinsic predictability of severe and convective weather at the mesoscales. J. Atmos. Sci., 69, 33503371, https://doi.org/10.1175/JAS-D-11-0315.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Meng, Z., and F. Zhang, 2008: Tests of an ensemble Kalman filter for mesoscale and regional-scale data assimilation. Part III: Comparison with 3DVAR in a real-data case study. Mon. Wea. Rev., 136, 522540, https://doi.org/10.1175/2007MWR2106.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Minamide, M., and F. Zhang, 2017: Adaptive observation error inflation for assimilating all-sky satellite radiance. Mon. Wea. Rev., 145, 10631081, https://doi.org/10.1175/MWR-D-16-0257.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Miyoshi, T., E. Kalnay, and H. Li, 2013: Estimating and including observation-error correlations in data assimilation. Inverse Probl. Sci. Eng., 21, 387398, https://doi.org/10.1080/17415977.2012.712527.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nieman, S. J., W. P. Menzel, C. M. Hayden, D. Gray, S. Wanzong, C. S. Velden, and J. Daniels, 1997: Fully automated cloud-drift winds in NESDIS operations. Bull. Amer. Meteor. Soc., 78, 11211134, https://doi.org/10.1175/1520-0477(1997)078<1121:FACDWI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Parrish, D. F., and J. C. Derber, 1992: The National Meteorological Center’s spectral statistical-interpolation analysis system. Mon. Wea. Rev., 120, 17471763, https://doi.org/10.1175/1520-0493(1992)120<1747:TNMCSS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Periáñez, A., H. Reich, and R. Potthast, 2014: Optimal localization for ensemble Kalman filter systems. J. Meteor. Soc. Japan, 92, 585597, https://doi.org/10.2151/jmsj.2014-605.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Reale, A. L., 2001: NOAA operational sounding products from Advanced-TOVS polar orbiting environmental satellites. NOAA Tech. Rep. NESDIS 102, 59 pp.

  • Reynolds, C. A., P. J. Webster, and E. Kalnay, 1994: Random error growth in NMC’s global forecasts. Mon. Wea. Rev., 122, 12811305, https://doi.org/10.1175/1520-0493(1994)122<1281:REGING>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ruf, C. S., and Coauthors, 2016: New ocean winds satellite mission to probe hurricanes and tropical convection. Bull. Amer. Meteor. Soc., 97, 385395, https://doi.org/10.1175/BAMS-D-14-00218.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schwartz, C. S., G. S. Romine, K. R. Smith, and M. L. Weisman, 2014: Characterizing and optimizing precipitation forecasts from a convection-permitting ensemble initialized by a mesoscale ensemble Kalman filter. Wea. Forecasting, 29, 12951318, https://doi.org/10.1175/WAF-D-13-00145.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Selz, T., and G. C. Craig, 2015: Upscale error growth in a high-resolution simulation of a summertime weather event over Europe. Mon. Wea. Rev., 143, 813827, https://doi.org/10.1175/MWR-D-14-00140.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smith, E. K., and S. Weintraub, 1953: The constants in the equation for atmospheric refractivity index at radio frequencies. J. Res. Natl. Bur. Stand. (U.S.), 50, 3941, https://doi.org/10.6028/jres.050.006.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sun, Y. Q., and F. Zhang, 2016: Intrinsic versus practical limits of atmospheric predictability and the significance of the butterfly effect. J. Atmos. Sci., 73, 14191438, https://doi.org/10.1175/JAS-D-15-0142.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tao, D., and F. Zhang, 2015: Effects of vertical wind shear on the predictability of tropical cyclones: Practical versus intrinsic limit. J. Adv. Model. Earth Syst., 7, 15341553, https://doi.org/10.1002/2015MS000474.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tavolato, C., and L. Isaksen, 2015: On the use of a Huber norm for observation quality control in the ECMWF 4D-Var. Quart. J. Roy. Meteor. Soc., 141, 15141527, https://doi.org/10.1002/qj.2440.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Velden, C. S., and K. M. Bedka, 2009: Identifying uncertainty in determining satellite-derived atmospheric motion vector height attribution. J. Appl. Meteor. Climatol., 48, 450463, https://doi.org/10.1175/2008JAMC1957.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Velden, C. S., C. Hayden, S. Nieman, W. Menzel, S. Wanzong, and J. Goerss, 1997: Upper-tropospheric winds derived from geostationary satellite water vapor observations. Bull. Amer. Meteor. Soc., 78, 173195, https://doi.org/10.1175/1520-0477(1997)078<0173:UTWDFG>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, B. R., X. Y. Liu, and J. K. Wang, 2013: Assessment of COSMIC radio occultation retrieval product using global radiosonde data. Atmos. Meas. Tech., 6, 10731083, https://doi.org/10.5194/amt-6-1073-2013.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, S., A. H. Sobel, F. Zhang, Y. Q. Sun, Y. Yue, and L. Zhou, 2015: Regional simulation of the October and November MJO events observed during the CINDY/DYNAMO field campaign at gray zone resolution. J. Climate, 28, 20972119, https://doi.org/10.1175/JCLI-D-14-00294.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wheeler, M. C., and G. N. Kiladis, 1999: Convectively coupled equatorial waves: Analysis of clouds and temperature in the wavenumber–frequency domain. J. Atmos. Sci., 56, 374399, https://doi.org/10.1175/1520-0469(1999)056<0374:CCEWAO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Whitaker, J. S., and T. M. Hamill, 2002: Ensemble data assimilation without perturbed observations. Mon. Wea. Rev., 130, 19131924, https://doi.org/10.1175/1520-0493(2002)130<1913:EDAWPO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ying, Y., and F. Zhang, 2017: Practical and intrinsic predictability of multiscale weather and convectively coupled equatorial waves during the active phase of an MJO. J. Atmos. Sci., 74, 37713785, https://doi.org/10.1175/JAS-D-17-0157.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yunck, T. P., E. J. Fetzer, A. M. Mannucci, C. O. Ao, W. Irion, B. D. Wilson, and G. J. Manipon, 2009: Use of radio occultation to evaluate atmospheric temperature data from spaceborne infrared sensors. Terr. Atmos. Ocean. Sci., 20, 7185, https://doi.org/10.3319/TAO.2007.12.08.01(F3C).

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zeng, X., and A. Beljaars, 2005: A prognostic scheme of sea surface skin temperature for modeling and data assimilation. Geophys. Res. Lett., 32, L14605, https://doi.org/10.1029/2005GL023030.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, C., J. Gottshalck, E. D. Maloney, M. W. Moncrieff, F. Vitart, D. E. Waliser, B. Wang, and M. C. Wheeler, 2013: Cracking the MJO nut. Geophys. Res. Lett., 40, 12231230, https://doi.org/10.1002/grl.50244.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, F., and J. A. Sippel, 2009: Effects of moist convection on hurricane predictability. J. Atmos. Sci., 66, 19441961, https://doi.org/10.1175/2009JAS2824.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, F., C. Snyder, and R. Rotunno, 2002: Mesoscale predictability of the “surprise” 24–25 January 2000 snowstorm. Mon. Wea. Rev., 130, 16171632, https://doi.org/10.1175/1520-0493(2002)130<1617:MPOTSS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, F., C. Snyder, and R. Rotunno, 2003: Effects of moist convection on mesoscale predictability. J. Atmos. Sci., 60, 11731185, https://doi.org/10.1175/1520-0469(2003)060<1173:EOMCOM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, F., C. Snyder, and J. Sun, 2004: Impacts of initial estimate and observation availability on convective-scale data assimilation with an ensemble Kalman filter. Mon. Wea. Rev., 132, 12381253, https://doi.org/10.1175/1520-0493(2004)132<1238:IOIEAO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, F., N. Bei, R. Rotunno, C. Snyder, and C. C. Epifanio, 2007: Mesoscale predictability of moist baroclinic waves: Convection-permitting experiments and multistage error growth dynamics. J. Atmos. Sci., 64, 35793594, https://doi.org/10.1175/JAS4028.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, F., M. Minamide, and E. E. Clothiaux, 2016: Potential impacts of assimilating all-sky infrared satellite radiances from GOES-R on convection-permitting analysis and prediction of tropical cyclones. Geophys. Res. Lett., 43, 29542963, https://doi.org/10.1002/2016GL068468.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, F., S. Talaphdar, and S. Wang, 2017: The role of global circumnavigating mode in the MJO initiation and propagation. J. Geophys. Res. Atmos., 122, 58375856, https://doi.org/10.1002/2016JD025665.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, Y., F. Zhang, D. J. Stensrud, and Z. Meng, 2016: Intrinsic predictability of the 20 May 2013 tornadic thunderstorm event in Oklahoma at storm scales. Mon. Wea. Rev., 144, 12731298, https://doi.org/10.1175/MWR-D-15-0105.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhen, Y., and F. Zhang, 2014: A probabilistic approach to adaptive covariance localization for serial ensemble square root filters. Mon. Wea. Rev., 142, 44994518, https://doi.org/10.1175/MWR-D-13-00390.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 2492 1962 35
PDF Downloads 248 40 10