On the use of Bayesian quantile regression method to explore the historical trends in extreme precipitation and their connections with large-scale climate patterns over the contiguous USA

  • Bhikhari TharuEmail author
  • Nirajan Dhakal
Original Paper


The probability distribution function (PDF) of precipitation is expected to change under a warmer climate. The existing studies have not been able to detect trends in different thresholds of the PDF of extreme precipitation series for the contiguous USA. In this study, a fresh statistical approach (the Bayesian quantile regression method) was employed to analyze trends of annual daily maximum (ADM) and monthly maximum (MM) precipitation indices at different quantile levels and their teleconnections with large-scale climate patterns over the contiguous USA. Historic precipitation time series over the period of 65 years (1950–2014) for 1108 sites was used for the analysis. To investigate the relations between precipitation and large-scale climate patterns, two major oscillations [the El Niño–Southern Oscillation (ENSO) and the North Atlantic Oscillation (NAO)] were used as covariates in the Bayesian quantile regression model. Our results show that changes in upper quantiles of the distributions of the extreme precipitation (for both ADM and MM) have occurred at a much higher rate than previously believed as compared to the lower quantiles mainly in the coastal regions in the eastern half of the country. Variability in the spatial distribution of significant trends was observed when either ENSO or NAO index was used as a covariate in the Bayesian quantile regression model. However, for many regions of the USA, a stronger teleconnection between climate indices and precipitation indices for upper quantile level was observed as compared to lower quantile levels for both ADM and MM. The trends detected using the Bayesian quantile regression method were undetected or overlooked by other previously used approaches for trend detection. Such results are particularly useful for water managers who are more concerned with extreme values rather than the averaged one.



The authors express their gratitude to the anonymous reviewers and the editor; their comments and suggestions greatly improved the paper.

Supplementary material

704_2019_3054_MOESM1_ESM.pdf (5.7 mb)
Figure S1 Spatial patterns of linear regression trend coefficients and posterior mean trend coefficients (mm year−1) of MM derived from Bayesian quantile regression for different quantiles (τ = 0.1, 0.2, 0.8, 0.9). (PDF 5848 kb)
704_2019_3054_MOESM2_ESM.pdf (3.3 mb)
Figure S2 Spatial patterns of posterior mean trend coefficients (mm year−1) developed using the daily time series data. (PDF 3394 kb)


  1. Alhamzawi R (2018) Package ‘Brq’: an R package for Bayesian quantile regressionGoogle Scholar
  2. Andersen TK, Marshall Shepherd J (2013) Floods in a changing climate. Geogr Compass 7:95–115. CrossRefGoogle Scholar
  3. Aryal YN, Villarini G, Zhang W, Vecchi GA (2018) Long term changes in flooding and heavy rainfall associated with North Atlantic tropical cyclones: roles of the North Atlantic Oscillation and El Niño-Southern Oscillation. J Hydrol 559:698–710. CrossRefGoogle Scholar
  4. Barbosa SM (2008) Quantile trends in Baltic Sea level. Geophys Res Lett 35.
  5. Barlow M, Nigam S, Berbery EH (1998) Evolution of the north American monsoon system. J Clim 11:2238–2257.<2238:EOTNAM>2.0.CO;2 CrossRefGoogle Scholar
  6. Barnston AG, Livezey RE (1987) Classification, seasonality and persistence of low-frequency atmospheric circulation patterns. Mon Weather Rev 115:1083–1126.<1083:CSAPOL>2.0.CO;2 CrossRefGoogle Scholar
  7. Capotondi A, Wittenberg AT, Newman M et al (2014) Understanding ENSO diversity. Bull Am Meteorol Soc 96:921–938. CrossRefGoogle Scholar
  8. Colbert AJ, Soden BJ (2011) Climatological variations in North Atlantic tropical cyclone tracks. J Clim 25:657–673. CrossRefGoogle Scholar
  9. Czajkowski J, Simmons K, Sutter D (2011) An analysis of coastal and inland fatalities in landfalling US hurricanes. Nat Hazards 59:1513–1531. CrossRefGoogle Scholar
  10. Degaetano AT (2009) Time-dependent changes in extreme-precipitation return-period amounts in the continental United States. J Appl Meteorol Climatol 48:2086–2099. CrossRefGoogle Scholar
  11. Dhakal N (2019) Changing impacts of North Atlantic tropical cyclones on extreme precipitation distribution across the Mid-Atlantic United States. Geosciences:9CrossRefGoogle Scholar
  12. Dhakal N, Tharu B (2018) Spatio-temporal trends in daily precipitation extremes and their connection with North Atlantic tropical cyclones for the Southeastern United States. Int J Climatol. CrossRefGoogle Scholar
  13. Easterling DR, Peterson TC, Karl TR (1996) On the development and use of homogenized climate datasets. J Clim 9:1429–1434.<1429:OTDAUO>2.0.CO;2 CrossRefGoogle Scholar
  14. Elsner JB, Bossak BH, Niu X-F (2001) Secular changes to the ENSO-U.S. hurricane relationship. Geophys Res Lett 28:4123–4126. CrossRefGoogle Scholar
  15. Elsner JB, Liu K, Kocher B (2000) Spatial variations in major U.S. hurricane activity: statistics and a physical mechanism. J Clim 13:2293–2305.<2293:SVIMUS>2.0.CO;2 CrossRefGoogle Scholar
  16. Gan TY, Gobena AK, Wang Q (2007) Precipitation of southwestern Canada: wavelet, scaling, multifractal analysis, and teleconnection to climate anomalies. Journal of Geophysical Research: Atmospheres 112.
  17. Goly A, Teegavarapu RSV (2014) Individual and coupled influences of AMO and ENSO on regional precipitation characteristics and extremes. Water Resour Res 50:4686–4709. CrossRefGoogle Scholar
  18. Groisman PY, Knight RW, Karl TR (2001) Heavy precipitation and high Streamflow in the contiguous United States: trends in the twentieth century. Bull Am Meteorol Soc 82:219–246.<0219:HPAHSI>2.3.CO;2 CrossRefGoogle Scholar
  19. Higgins RW, Kousky VE (2013) Changes in observed daily precipitation over the United States between 1950–79 and 1980–2009. J Hydrometeorol 14:105–121CrossRefGoogle Scholar
  20. IPCC (2012) Managing the risks of extreme events and disasters to advance climate change adaptation. In: Field CB, Barros V, Stocker TF, Qin D, Dokken DJ, Ebi KL, Mastrandrea MD, Mach KJ, Plattner G-K, Allen SK, Tignor M, Midgley PM (eds) A special report of working. Cambridge University Press, CambridgeGoogle Scholar
  21. Karl TR, Knight RW (1998) Secular trends of precipitation amount, frequency, and intensity in the United States. Bull Am Meteorol Soc 79:231–242.<0231:STOPAF>2.0.CO;2 CrossRefGoogle Scholar
  22. Khouakhi A, Villarini G, Vecchi GA (2017) Contribution of tropical cyclones to rainfall at the global scale. J Clim 30:359–372. CrossRefGoogle Scholar
  23. Kim J-S, Jain S (2011) Precipitation trends over the Korean peninsula: typhoon-induced changes and a typology for characterizing climate-related risk. Environ Res Lett 6:34033. CrossRefGoogle Scholar
  24. Koenker R (2005) Quantile regression. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  25. Koenker RW, D’Orey V (1987) Computing regression quantiles. J R Stat Soc: Ser C: Appl Stat 36:383–393. CrossRefGoogle Scholar
  26. Kozumi H, Kobayashi G (2011) Gibbs sampling methods for Bayesian quantile regression. J Stat Comput Simul 81:1565–1578. CrossRefGoogle Scholar
  27. Kunkel KE (2003) North American trends in extreme precipitation. Nat Hazards 29:291–305. CrossRefGoogle Scholar
  28. Lausier AM, Jain, S (2018a) Diversity in global patterns of observed precipitation variability and change on river basin scales: a conditional quantile approach. Climatic Change v. 149:261–275–2018 v.149 no.2. doi: CrossRefGoogle Scholar
  29. Lausier AM, Jain S (2018) Overlooked trends in observed global annual precipitation reveal underestimated risks. Sci Rep 8:16746. CrossRefGoogle Scholar
  30. Lee K, Baek H-J, Cho C (2013) Analysis of changes in extreme temperatures using quantile regression. Asia-Pac J Atmos Sci 49:313–323. CrossRefGoogle Scholar
  31. Lee S-K, Atlas R, Enfield D et al (2012) Is there an optimal ENSO pattern that enhances large-scale atmospheric processes conducive to tornado outbreaks in the United States? J Clim 26:1626–1642. CrossRefGoogle Scholar
  32. Malik N, Bookhagen B, Mucha PJ (2016) Spatiotemporal patterns and trends of Indian monsoonal rainfall extremes. Geophys Res Lett 43:1710–1717. CrossRefGoogle Scholar
  33. Mallakpour I, Villarini G (2016) Analysis of changes in the magnitude, frequency, and seasonality of heavy precipitation over the contiguous USAGoogle Scholar
  34. Meng L, Shen Y (2013) On the relationship of soil moisture and extreme temperatures in East China. Earth Interact 18:1–20. CrossRefGoogle Scholar
  35. Mo KC, Berbery EH (2004) Low-level jets and the summer precipitation regimes over North America. Journal of Geophysical Research: Atmospheres 109. CrossRefGoogle Scholar
  36. Nogueira RC, Keim BD, Brown DP, Robbins KD (2013) Variability of rainfall from tropical cyclones in the eastern USA and its association to the AMO and ENSO. Theor Appl Climatol 112:273–283. CrossRefGoogle Scholar
  37. Petscher Y, Logan JAR (2014) Quantile regression in the study of developmental sciences. Child Dev 85:861–881. CrossRefGoogle Scholar
  38. Portis DH, Walsh JE, El Hamly M, Lamb PJ (2001) Seasonality of the North Atlantic Oscillation. J Clim 14:2069–2078.<2069:SOTNAO>2.0.CO;2 CrossRefGoogle Scholar
  39. Pryor SC, Howe JA, Kunkel KE (2009) How spatially coherent and statistically robust are temporal changes in extreme precipitation in the contiguous USA? Int J Climatol 29:31–45. CrossRefGoogle Scholar
  40. Rappaport EN (2014) Fatalities in the United States from Atlantic tropical cyclones: new data and interpretation. Bull Am Meteorol Soc 95:341–346. CrossRefGoogle Scholar
  41. Reich BJ (2012) Spatiotemporal quantile regression for detecting distributional changes in environmental processes. J R Stat Soc: Ser C: Appl Stat 61:535–553. CrossRefGoogle Scholar
  42. Ross T, Lott N (2003) A climatology of 1980-2003 extreme weather and climate eventsGoogle Scholar
  43. Smith AB, Katz RW (2013) US billion-dollar weather and climate disasters: data sources, trends, accuracy and biases. Nat Hazards 67:387–410. CrossRefGoogle Scholar
  44. Sun X, Lall U (2015) Spatially coherent trends of annual maximum daily precipitation in the United States. Geophys Res Lett 42:9781–9789. CrossRefGoogle Scholar
  45. Tan X, Gan TY, Chen S, Liu B (2018) Modeling distributional changes in winter precipitation of Canada using Bayesian spatiotemporal quantile regression subjected to different teleconnections. Clim Dyn 52(0):1–20. CrossRefGoogle Scholar
  46. Tan X, Shao D (2017) Precipitation trends and teleconnections identified using quantile regressions over Xinjiang, China. Int J Climatol 37:1510–1525. CrossRefGoogle Scholar
  47. Tareghian R, Rasmussen P (2013) Analysis of Arctic and Antarctic Sea ice extent using quantile regression. Int J Climatol 33:1079–1086. CrossRefGoogle Scholar
  48. Tootle GA, Piechota TC, Singh A (2005) Coupled oceanic-atmospheric variability and U.S. streamflow. Water Resources Research 41:
  49. Trenberth KE (2017) El Niño Southern Oscillation (ENSO). Reference Module in Earth Systems and Environmental Sciences. CrossRefGoogle Scholar
  50. Chernozhukov V, Umantsev L (2001) Conditional value-at-risk: aspects of modeling and estimation. Empir Econ 26:271–292CrossRefGoogle Scholar
  51. Villarini G, Smith JA, Baeck ML et al (2011) On the frequency of heavy rainfall for the Midwest of the United States. J Hydrol 400:103–120. CrossRefGoogle Scholar
  52. Wasko C, Sharma A (2014) Quantile regression for investigating scaling of extreme precipitation with temperature. Water Resour Res 50:3608–3614. CrossRefGoogle Scholar
  53. Wilks DS (2011) Statistical methods in the atmospheric sciences. AcademicGoogle Scholar
  54. Yu K, Moyeed RA (2001) Bayesian quantile regression. Statistics & Probability Letters 54:437–447. CrossRefGoogle Scholar
  55. Yu L, Zhong S, Pei L et al (2016) Contribution of large-scale circulation anomalies to changes in extreme precipitation frequency in the United States. Environ Res Lett 11:44003. CrossRefGoogle Scholar
  56. Zhang X, Wang J, Zwiers FW, Groisman PY (2010) The influence of large-scale climate variability on winter maximum daily precipitation over North America. J Clim 23:2902–2915. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsSpelman CollegeAtlantaUSA
  2. 2.Science CenterSpelman CollegeAtlantaUSA
  3. 3.Environmental and Health Sciences ProgramSpelman CollegeAtlantaUSA

Personalised recommendations