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WWLLN (World Wide Lightning Location Network)

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[1] WWLLN is a global network of VLF (very low frequency) electric field receivers, operated in collaboration by universities and government labs, and used to detect and locate lightning anywhere on earth. Presently there are 60+ receiving sites located globally (see http://wwlln.net). With the availability of microsecond GPS timing and with the internet for fast communication, it is possible to achieve accurate lightning location by analyzing the received VLF lightning sferic waveform to determine the group arrival time for the sferic wave packet. These group arrival times are transmitted to a pair of redundant central computers for a time of arrival analysis to determine lightning locations in near real time. WWLLN lightning location data have been used in many diverse research studies from Transient Gamma Flashes (TGFs), Ionospheric Plasmas, tropocal cyclones, thunderstorms, and lightning climatology (see references listed below and also see http://wwlln.net/climate ).


How WWLLN Works

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Electric field receivers, sensitive in the range from 1kHz to 24 kHz, detect lightning-generated electromagnetic noise bursts, called ‘sferics’, and a local computer at each host site determines the TOGA (time of group arrival, see Dowden et al, 2002) of the sferic wave packet. With the help of a local GPS (Global Positioning Satellite) clock, the TOGA is determined, for each sferic, to within a few microseconds, and this accurate time is immediately sent over the internet to two, redundant, central processing computers on two different continents. The central processors calculate lightning locations using this continuous flow of TOGAs. Lightning locations are determined to a spatial accuracy of about 3.5 km (less than the wavelength of the peak lightning sferic energy frequency (7 to 18 kHz), and with a time accuracy better than 1 microsecond. The more energetic lightning strokes are located most easily by this method, since the VLF energy must travel thousands of km to be detected by five or more of the present 60+ WWLLN sensors. Studies have shown that WWLLN is most sensitive to lightning strokes with a peak current greater than 30 kA (see references below). The detection efficiency (DE) for lightning has steadily increased as new sensors have been added, from an early measured DE rate of just about 1% of total lightning (Lay et al, 2004) to a present estimate of 30 to 50% of all strokes over 40 kA and ~12% overall. While the probability that WWLLN detects any single lightning event is nt high, nevertheless, the probability that WWLLN detects any given lightning producing thunderstorm is nearing 100% (Jacobson et al, 2006).

History of WWLLN. The initial idea for what has become WWLLN was demonstrated by Dowden et al (2002) in a small lightning network, called the TOGA network, involving a several stations in the southern Pacific area. Subsequently the network became a global one beginning in mid-2003 and presently involves over stations with several new ones projected to join in 2008. WWLLN is a collaboration among scientists who agree to host a WWLLN lightning receiving station. WWLLN is managed by the University of Washington under direction of Prof. Robert Holzworth, in the Earth and Space Sciences Department. The main website is http://wwlln.net where a complete list of present hosts is available. LIST of STATIONS

Availability of the WWLLN data: Contact Prof. Robert Holzworth, University of Washington, Seattle, WA 98195-1310 (email: bobholz@uw.edu ). Commercial use data are available from our commercial partners Weather Decisions Technology (http://www.wdtinc.com) and Earth Networks (http://EarthNetworks.com)


References: When it was still called the 'TOGA' network: 0. Dowden, R. L. and J.B. Brundell, Improvements relating to the location of lightning discharges, Australian Patent Office, patent number AU 200071483 Al, Application Date 2000.11.08, Publication date:2001.05.17. 1.4MB PDF ... patent link

1. VLF lightning location by time of group arrival (TOGA) at multiple sites Dowden, R.L., Brundell, J.B.; Rodger, C.J. Source: Journal of Atmospheric and Solar-Terrestrial Physics, v 64, n 7, May 2002, p 817-30 PDF of text (0.6MB)

After WWLLN got its name:

2. WWLL global lightning detection system: Regional validation study in Brazil Lay, E.H. (Dept. of Earth & Space Sci., Washington Univ., Seattle, WA, USA); Holzworth, R.H.; Rodger, C.J.; Thomas, J.N.; Pinto, O., Jr.; Dowden, R.L. Source: Geophysical Research Letters, v 31, n 3, 16 Feb. 2004, p 5 pp. PDF of text (2.7 MB)

3. Rodger, C. J., J. B. Brundell, R. L. Dowden, and N. R. Thomson, 2004: Location accuracy of long distance VLF lightning location network. Ann. Geophys., 22, 747-758. PDF of text (4.7 MB)

4. Balloon observations of temporal variation in the global circuit compared to global lightning activity, Holzworth, R.H. (Earth & Space Sci., Univ. of Washington, Seattle, WA, USA); Bering, E.A., III; Kokorowski, M.F.; Lay, E.H.; Reddell, B.; Kadokura, A.; Yamagishi, H.; Sato, N.; Ejiri, M.; Hirosawa, H.; Yamagami, T.; Torii, S.; Tohyama, F.; Nakagawa, M.; Okada, T.; Dowden, R.L. Source: Advances in Space Research, v 36, n 11, 2005, p 2223-8 PDF of text (0.3MB)

5. Rodger, C. J., J. B. Brundell, and R. L. Dowden, 2005: Location accuracy of VLF World Wide Lightning Location (WWLL) network: Post-algorithm upgrade. Ann. Geophys., 23, 277-290. PDF of text (4.9 MB)

6. Yair, Y., C. Price, B. Ziv, P. L. Israelevich, D. D. Sentman, F. T. Sao-Sabbas, A. D. Devir, M. Sato, C. J. Rodger, M. Moalem, E. Greenberg, and O. Yaron, Space Shuttle observation of an unusual transient atmospheric emission, Geophys. Res. Lett., 32(2), 10.1029/2004GL021551, 2005. PDF of text (0.3 MB)

7. Collier, A. B., A. R. W. Hughes, J. Lichtenberger, and P. Steinbach, Seasonal and diurnal variation of lightning activity over southern Africa and correlation with European whistler observations, Annales Geophysicae, 24, 529 - 542, 2006. PDF of text (1.7 MB)

8. Performance assessment of the World Wide Lightning Location Network (WWLLN), using the Los Alamos Sferic Array (LASA) array as ground-truth, Abram R. Jacobson Robert H. Holzworth Jeremiah Harlin Richard L. Dowden Erin H. Lay, (Journal of Atmospheric and Oceanic Technology (AMS), V.23, pp. 1082-92, (August 2006). PDF of text (1.0 MB)

9. Local Time Variation in Land/Ocean Lightning Count Rates as Measured by the World Wide Lightning Location Network, Erin H. Lay, Abram R. Jacobson, Robert H. Holzworth, Craig J. Rodger, Richard L. Dowden, for J. Geophys. Res.,JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112, D13111, doi:10.1029/2006JD007944, 2007 PDF 0.3 MB

10. Detection efficiency of the VLF World-Wide Lightning Location Network (WWLLN): Initial case study, Craig J. Rodger, Simon Werner, James B. Brundell, Erin H. Lay, Neil R. Thomson, Robert H. Holzworth, Richard L. Dowden Ann. Geophys., 24, 3197–3214, 2006 PDF (6.4MB )

11. A Very Active Sprite-Producing Storm Observed Over Argentina, J. N. Thomas et al, EOS, Transactions, American Geophysical Union, Vol. 88, No. 10, 6 March 2007, pp. 117-128. PDF (1.1 MB)

12. Lightning activity analyses with respect to the SPCZ location, P. Ortega and T. Guignes, Geophys. Res. Lett., Vol. 34, L11807, doi:10.1029/2007GL029730, 2007. PDF of text (0.4 MB)

13. Simultaneous Imaging and ELF/VLF Measurements of a Sprite-Halo Driven by a Negative Lightning Discharge over Argentina, M.J. Taylor, M. Bailey, P.-D. Pautet, S. A. Cummer, N. Jaugey, J. N. Thomas, N.N. Solorzano, S. Sao Sabbas, R. Holzworth, Pinto and N. Schuch, for GRL (if it fits, else JGR) (2007)

14. East African lightning as a precursor of Atlantic hurricane activity, Colin Price, Yoav Yair, and Mustafa Asfur, Geophys. Res. Lett., Vol. 34, L09805, doi:10.1029/2006GL028884, 2007 PDF text (1.0 MB)

15. A Three Magnetic Direction Finder Network for a Local Warning Device, P. Orgega, Journal of Lightning Research, V. 2, PP. 18-27, 2007 PDF text 0.5 MB

16. Kumar, S. (Univ. of the South Pacific, Suva, Fiji); Anil, D.; Kishore, A.; Ramachandran, V., Whistlers observed at low-latitude ground-based VLF facility in Fiji, Journal of Atmospheric and Solar-Terrestrial Physics, v 69, n 12, Aug. 2007, 1366-76

17. GLOBAL STUDIES OF TROPICAL CYCLONES USING THE WORLD WIDE LIGHTNING LOCATION NETWORK, Natalia N. Solorzano, Jeremy N. Thomas, and Robert H. Holzworth, Paper presented at AMS 2008 meeting in New Orleans (January 2008) Solorzano et al 0.2MB

18. Seeking sprite-induced signatures in remotely sensed middle atmosphere NO2, E. Arnone, A. Kero, B. M. Dinelli, C.-F. Enell, N. F. Arnold, E. Papandrea, Craig J. Rodger, M. Carlotti, M. Ridolfi, and E. Turunen, GEOPHYSICAL RESEARCH LETTERS, VOL. 35, L05807, doi:10.1029/2007GL031791, 2008 Arnone et al, (0.2MB)

19. Rare measurements of a sprite with halo event driven by a negative lightning discharge over Argentina, M. J. Taylor, M. A. Bailey, P. D. Pautet, S. A. Cummer, N. Jaugey, J. N. Thomas, N. N. Solorzano, F. Sao Sabbas, R. H. Holzworth, O. Pinto, and N. J. Schuch, GEOPHYSICAL RESEARCH LETTERS, VOL. 35, L14812, doi:10.1029/2008GL033984, 2008 ( PDF text 0.2 MB)

20. Investigating Lightning-to-Ionosphere Energy Coupling Based on VLF Lightning Propagation Characterization, Erin H. Lay, PhD Dissertation, Physics Dept. Univ. of Washington, 2008. ( PDF 2.6MB)

21. Lightning stroke distance estimation from single station observation and validation with WWLLN data, V. Ramachandran, J. N. Prakash, A. Deo, and S. Kumar, Ann. Geophys., 25, 1509–1517, 2007 ( PDF Text 0.6MB )

22. Subionospheric early VLF perturbations observed at Suva: VLF detection of red sprites in the day?, Sushil Kumar,1 Abhikesh Kumar,1 and Craig J. Rodger, JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, A03311, doi:10.1029/2007JA012734, 2008. ( PDF Text 4.3MB )

23.Rodger, C J, J B Brundell, R H Holzworth, and E H Lay, Growing Detection Efficiency of the World Wide Lightning Location Network, Am. Inst. Phys. Conf. Proc., Coupling of thunderstorms and lightning discharges to near-Earth space: Proceedings of the Workshop, Corte (France), 23-27 June 2008, 1118, 15-20, DOI:10.1063/1.3137706, 2009. ( PDF text 0.3 MB )

24. B. J. Hazelton, B. W. Grefenstette, D. M. Smith, J. R. Dwyer, X.-M. Shao, S. A. Cummer, T. Chronis, E. H. Lay, and R. H. Holzworth, Spectral dependence of terrestrial gamma-ray flashes on source distance, GEOPHYSICAL RESEARCH LETTERS, VOL. 36, L01108, doi:10.1029/2008GL035906, 2009 ( PDF 0.2MB )

25. E.Williams, W. Lyons, Y. Hobara, V. Mushtak, N. Asencio, R. Boldi, J. Bor, S. Cummer, E. Greenberg, M. Hayakawa, R. Holzworth, V. Kotroni, J. Li, C. Morales, T. Nelson, C. Price, B. Russell, G. Satori K. Shirahata, Y. Takahashi, K. Yamashita, Ground-Based Detection of Sprites and their Parent Lightning Flashes over Africa during the 2006 AMMA Campaign, Quarterly Journal of the Royal Meteorological Society, (accepted) 2009 ( PDF 1MB )

26. E Arnone, A Kero, C-F Enell, M Carlotti, Craig J Rodger, E Papandrea, N F Arnold, B M Dinelli, M Ridolfi and E Turunen, Seeking sprite-induced signatures in remotely sensed middle atmosphere NO2: latitude and time variations, IOP PUBLISHING Plasma Sources Sci. Technol. 18 (2009) 034014 (10pp) doi:10.1088/0963-0252/18/3/034014 ( PDF 0.8 MB )

27. Robert Cifelli, Timothy Lang, Steven A. Rutledge, Nick Guy, Edward J. Zipser, Jon Zawislak, and Robert Holzworth, Characteristics of an African Easterly Wave Observed During NAMMA, Journal of Atmospheric Science (JAS) (accepted and in press), 2009. ( manuscript PDF 2.4 MB )

28. Sushil Kumar, Anil Deo, and V. Ramachandran, Nighttime D-region equivalent electron density determined from tweek sferics observed in the South Pacific Region, Earth Planets Space, 61, 905-911, 2009 ( PDF (0.3MB)

29. Colin Price, Mustafa Asfur and Yoav Yair, Maximum hurricane intensity preceded by increase in lightning frequency, Nature Geoscience Letters, Published Online: 6 APRIL 2009 | DOI: 10.1038/NGEO477 PDF 0.4 MB

30. Jeremy N. Thomas, Natalia N. Solorzano, Steven A. Cummer, and Robert H. Holzworth, Polarity and energetics of inner core lightning in three intense North Atlantic hurricanes, J. Geophysical Research, Oct 30, 2009, J. Geophys. Res. (2009JA014777) PDF 1.1MB

31. Eric J. Bucsela, Kenneth E. Pickering, Tabitha L. Huntemann, Ronald C. Cohen, Anne Perring, James F. Gleason, Richard J. Blakeslee, Rachel I. Albrecht, Robert Holzworth, James P. Cipriani, Dylana Vargas-Navarro, Ileana Mora-Segura, Alexia Pacheco-Hernandez, Sadi Lporte-Molina, Lightning-generated NOx seen by OMI during NASAs TC4 experiment, J. Geophys, Res (atmospheres) 2009JD013118R (accepted and in press), 2010 2.7 MB pdf

32. Orit Altaratz, Ilan Koren, Yoav Yair, and Colin Price, Lightning response to smoke from Amazonian fires, GEOPHYSICAL RESEARCH LETTERS, VOL. 37, L07801, doi:10.1029/2010GL042679, 2010 PDF 0.4MB

33. Sergio F. Abarca, Kristen L. Corbosiero and Thomas J. Galarneau Jr., An evaluation of the Worldwide Lightning Location Network (WWLLN) using the National Lightning Detection Network (NLDN) as ground truth, JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115, D18206, doi:10.1029/2009JD013411, 2010 PDF 1.2MB

34. Beirle, S., Huntrieser, H. and Wagner, T.: Direct satellite observation of lightning-produced NOx, Atmos. Chem. Phys., 10(22), 10965-10986, 2010. PDF 8.5MB

35. Abarca, S. F., K. L. Corbosiero, The World Wide Lightning Location Network and Convective Activity in Tropical Cyclones, Monthly Weather Review, V. 139, p. 175, 2011. PDF 5.5MB

36. D. Abreu, D. Chandan, R. H. Holzworth, and K. Strong, Atmos. Meas. Tech., 3, 1143-1153, 2010 (Copernicus Publications for EGU) PDF (1.5MB)

37. V. Connaughton, M. S. Briggs, R. H. Holzworth, M. L. Hutchins, G. J. Fishman, C. A. Wilson-Hodge, V. L. Chaplin, P. N. Bhat, J. Greiner, A. von Kienlin, R. M. Kippen, C. A. Meegan, W. S. Paciesas, R. D. Preece, E. Cramer, J. R. Dwyer, and D. M. Smith, Associations between Fermi Gamma-ray Burst Monitor terrestrial gamma ray flashes and sferics from the World Wide Lightning Location Network, JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115, A12307, doi:10.1029/2010JA015681, 2010 PDF (6.9MB)

38. Kumar, V. V, M.L.Parkinson, P.L.Dyson and G.B.Burns, Thunderstorm-associated responses in the vertical motion of the mid-latitude F-region ionosphere, Journal of Atmospheric and Solar-Terrestrial Physics,71 (2009), pp.787-793 PDF 0.6 MB

39. Holzworth, R. H., M.P. McCarthy, R. F. Pfaff, A. R. Jacobson, W. L. Wilkerson and D. E. Rowland, Lightning-generated whistler waves observed by probes on the Communication/Navigation Outage Forecast System satellite at low latitudes, J. Geophys. Res., 116, A06306,doi:10.1029/2010JA016198, 2011. PDF 1.3MB

40. Serge Soula, Oscar van der Velde, Joan Montanya, Patrice Huet, Christelle Barthe, and Jozsef Bor, Gigantic Jets produced by an isolated tropical thunderstorm near Reunion Island, J. Geophysical Res., V.116,D19103, doi:10.1029/2010JD015581, 2011 PDF 3.7MB

41. PAN LunXiang, QIE XiuShu, LIU DongXia, WANG DongFang, and YANG Jing, The lightning activities in super typhoons over the Northwest Pacific, Sci China Earth Sci, 2010, 53: 1241-1248, doi: 10.1007/s11430-010-3034-z, PDF 1.0 MB

42. Smith, D. M., B. J. Hazelton, B. W. Grefenstette, J. R. Dwyer, R. H. Holzworth, and E. H. Lay, Terrestrial gamma ray flashes correlated to storm phase and tropopause height, J. of Geophysical Research, Vol. 115, A00E49, doi:10.1029/2009JA014853, 2010 PDF 0.6MB

43. Virts, Katrina S., Joel A. Thornton, John M. Wallace, Michael L. Hutchins, Robert H. Holzworth, and Abram R. Jacobson, Daily, seasonal, and intraseasonal relationships between lightning and NO2 over the Maritime Continent, Geophys. Res. Lett., doi:10.1029/2011GL048578 (in press), 2011 PDF 0.9 MB and Supplemental Material 0.8 MB

44. Collier, A. B., T. Gjesteland, and N. Øtgaard (2011), Assessing the power law distribution of TGFs, J. Geophys. Res., 116, A10320, doi:10.1029/2011JA016612 PDF 1MB

45. Singh, Rajesh, B. Veenadhari, Ajeet K. Maurya, Morris B. Cohen, Sushil Kumar, R. Selvakumaran, P. Pant, Abhay K. Singh and Umran S. Inan, D-region ionosphere response to the total solar eclipse of 22 July 2009 deduced from ELF/VLF tweek observations in the Indian sector, J. Geophys. Res., V. 116, A10301, doi:10.1029/2011JA016641, 2011. PDF 2.9MB

46. Gjesteland, T.; stgaard, N.; Collier, A. B.; Carlson, B. E.; Cohen, M. B.; Lehtinen, N. G. Confining the angular distribution of terrestrial gamma ray flash emission J. Geophys. Res., Vol. 116, No. A11, A11313 PDF 0.4MB

47. Burgesser, Rodrigo E., Maria G. Nicora and Eldo E. Avila, Characterization of the lightning activity of "Relampago del Catatumbo", JASTP, Accepted and in press, 2012. PDF 1.1MB

48.Collier, A. B., Delport, B., Hughes, A. R. W., Lichtenberger, J., Steinbach, P., Oster, J., and Rodger, C. J. Correlation between global lightning and whistlers observed at Tihany, Hungary. Journal of Geophysical Research, 114, A07210. doi:10.1029/2008JA013863,2009 PDF 1.4MB

49. Oster, J., Collier, A. B., Hughes, A. R. W., Blomberg, L. G., & Lichtenberger, J. Spatial correlation between lightning strikes and whistler observations from Tihany, Hungary. South African Journal of Science, 105(5-6), 234-237, 2009. PDF 0.5MB

50. Collier, A. B., Bremner, S., Lichtenberger, J., Downs, J. R., Rodger, C. J., Steinbach, P., & McDowell, G. (2010). Global lightning distribution and whistlers observed at Dunedin, New Zealand. Annales Geophysicae, 28(2), 499-513. doi:10.5194/angeo-28-499-2010 PDF 6.1MB

51. Collier, A. B., Lichtenberger, J., Clilverd, M. A., Steinbach, P., & Rodger, C. J., Source Region for Whistlers Detected at Rothera, Antarctica. Journal of Geophysical Research, 116, A03219. doi:10.1029/2010JA016197, 2011. PDF 2.5MB

52. Hutchins, M.L., R. H. Holzworth, C. J. Rodger and J. B. Brundell, Far field power of lightning strokes as measured by the World Wide Lightning Location Network, JTech (J. Atmos. and Ocean. Tech. (AMS), V.29,1102-1110, 2012. JTech paper (9 MB PDF)

53. Gjesteland, T.; Øtgaard, N.; Collier, A. B.; Carlson, B. E.; Eyles, C.; Smith, D. M. A new method reveals more TGFs in the RHESSI data, Geophys. Res. Lett., Vol. 39, No. 5, L05102, 07 March 2012 PDF 0.4MB

54. Bovalo, C., Barthe, C., and Bègue, N.: A lightning climatology of the South-West Indian Ocean, Nat. Hazards Earth Syst. Sci., 12, 2659-2670, doi:10.5194/nhess-12-2659-2012, 2012. Full Article

55. Hutchins, M. L., R. H. Holzworth, J. B. Brundell, and C. J. Rodger, Relative Detection Earthciency of the World Wide Lightning Location Network, Radio Science, 2012RS005049, (accepted Oct 26, 2012), 2012 accepted MS, 14MB (pdf)

56. Briggs, M.S., G. S. Fishman, V. Connaughton, P. N. Bhat, W. S. Paciesas, R. D. Preece1, C. Wilson-Hodge, V. L. Chaplin, R. M. Kippen, A. von Kienlin, C. Meegan, E. Bissaldi, J. R. Dwyer, D. M. Smith, R. H. Holzworth, J. E. Grove and A. Chekhmann, First results on terrestrial gamma ray flashes from the Fermi Gamma-ray Burst Monitor, J. Geophys. Res, V. 115, A07323, doi:doi:10.1029/2009JA015242, 2010. 0.9MB (pdf)

57. Briggs, M. S. et al (25 authors), Terrestrial Gamma-ray Flashes in the Fermi Era: Improved Observations and Analysis Methods, J. Geophys. Res, (in press) 2012. 7.2 MB (pdf)

58. Connaughton, V., (24 authors), Radio signals from electron beams in Terrestrial Gamma-ray Flashes, Geophys. Res. Letters, (accepted), 2012. 0.6MB (pdf)

59. Ajeet K. Maurya, B.Veenadhari, Rajesh Singh, Sushil Kumar, M. B. Cohen, R Selvakumaran, Sneha Gokani, P. Pant, A. K. Singh, Umran S Inan, Nighttime D-region electron density measurements from ELF-VLF tweek radio atmospherics recorded at low latitudes, J. Geophys. Res., In press, 2012 5.2MB (pdf)

60. Virts, Katrina S., John M. Wallace, Michaale L. Hutchins, and Robert H. Holzworth, A new ground-based, hourly global lightning climatology, BAMS (AMS), In press, 2012. 2.6MB (pdf)

61. Solorzano, N.N., J. N. Thomas, J. A. Weinman*, W. Keane, M. L. Hutchins and R. H. Holzworth, WWLLN lightning and satellite microwave radiometrics at 37 to 183 GHz: Implications for convection and thundercloud charging in the broad tropics, (submitted) J. Geophys. Res. August 2012. 0.9 MB (pdf)

62. S. Xiong, M. S. Briggs, V. Connaughton, G. J. Fishman, D. Tierney, G. Fitzpatrick, S. Foley, S. Guiriec, R. H. Holzworth, and M. L. Hutchins, Location prediction of electron TGFs, J. Geophys., Res., V.117, A02309, doi:10.1029/2011JA017085, 2012., 6.2MB (pdf)

63. Michael A. Haddad, Vladimir A. Rakov, and Steven A. Cummer, New measurements of lightning electric fields in Florida: Waveform characteristics, interaction with the ionosphere, and peak current estimates, J. Geophys. Res., V. 117, D10101, doi:10.1029/2011JD017196, 2012. 2.5MB (pdf)

64. Kucienska, B., G. B. Raga, and R. Romero-Centeno, High lightning activity in maritime clouds near Mexico, Atmos. Chem. Phys. Discuss., 12, 2817-2852, 2012 (Under review), PDF or link.

65. De Boer, A. M., Collier, A. B., Caballero, R., 2013, Processes driving thunderstorms over the Agulhas Current, J. of Geophysical Research - Atmosphere. DOI:10.1002/jgrd.50238. PDF (3.4MB)

(Links to references available at http://wwlln.net/publications )