Theoretical and Applied Climatology

, Volume 113, Issue 1–2, pp 187–196 | Cite as

Mixed nonlinear regression for modelling historical temperatures in Central–Southern Italy

  • Nazzareno Diodato
  • Gianni Bellocchi
  • Chiara Bertolin
  • Dario Camuffo
Original Paper

Abstract

This paper has exploited, for Central and Southern Italy (Mediterranean Sub-regional Area), an unprecedented historical dataset as an attempt to model seasonal (winter and summer) air temperatures in pre-instrumental time (back to 1500). Combining information derived from proxy–documentary data and large-scale simulation, a statistical downscaling approach in the form of mixed regression model was developed to adapt larger-scale estimations (regional component) to the sub-regional temperature pattern (local component). It interprets local temperature anomalies by means of monthly based Temperature Anomaly Scaled Index in the range −5 (very cold conditions in June) to 2 (very warm conditions). The modelled response agrees well with the independent data from the validation sample (Nash–Sutcliffe efficiency coefficient, >0.60). The advantage of the approach is not merely increased accuracy in estimation. Rather, it relies on the ability to extract (and exploit) the right information to replicate coherent temperature series in historical times.

References

  1. Barriendos M, Martin-Vide J (1998) Secular climatic oscillations as indicated by catastrophic floods in the Spanish Mediterranean coastal area (14th–19th centuries). Clim Chang 38:473–491CrossRefGoogle Scholar
  2. Bates DM, Watts DG (2007) Nonlinear regression analysis and its applications. Wiley, Little FallsGoogle Scholar
  3. Box GEP, Hunter WG, Hunter JS (1978) Statistics for experimenters: an introduction. Wiley, New YorkGoogle Scholar
  4. Brázdil R, Pfister C, Wanner H, von Storch H, Luterbacher J (2005) Historical climatology in Europe—the state of the art. Clim Chang 70:363–430CrossRefGoogle Scholar
  5. Brewer S, Alleaume S, Guiot J, Nicault A (2007) Historical droughts in Mediterranean regions during the last 500 years: a data/model approach. Clim Past 3:355–366CrossRefGoogle Scholar
  6. Briffa KR, Osborn TJ, Schweingruber FH, Jones PD, Shiyatov SG, Vaganov EA (2002) Tree-ring width and density data around the Northern Hemisphere: part 1, local and regional climate signals. Holocene 12:737–757CrossRefGoogle Scholar
  7. Camuffo D, Enzi S (1992) Reconstructing the climate of northern Italy from archive sources. In: Bradley RS, Jones PD (eds) Climate since A.D. 1500. Routledge, London, pp 143–154Google Scholar
  8. Camuffo D, Bertolin C, Barriendos M, Dominguez-Castro F, Cocheo C, Enzi S, Sghedoni M, della Valle A, Garnier E, Alcoforado MJ, Xoplaki E, Luterbacher J, Diodato N, Maugeri M, Nunes MF, Rodriguez R (2010) 500-year temperature reconstruction in the Mediterranean Basin by means of documentary data and instrumental observations. Clim Chang 101:169–199CrossRefGoogle Scholar
  9. Clemente GF, Margottini C (1991) Sistema EVA: una biblioteca di dischi ottici per le catastrofi naturali del passato. Prometeo 9:22–29 (in Italian)Google Scholar
  10. Corradi A (1972) Corradi Alfonso: Annali delle epidemie occorse in Italia dalle prime memorie fino al 1850, five volumes, Società medico-chirurgica di Bologna (Ed.), Forni, Bologna, Italy (in Italian)Google Scholar
  11. Davi NK, Jacoby GC, D’Arrigo RD, Baatarbileg N, Jinbao L, Curtis AE (2008) A tree-ring-based drought index reconstruction for far-western Mongolia: 1565–2004. Int J Climatol 29:1508–1514CrossRefGoogle Scholar
  12. Derham W (1733–1734) An abstract of the Meteorological Diaries, communicated to the Royal Society, with re-marks upon them, by W. Derham, D. D. Canon of Windsor, F. R. S. [Vide Part III. In Transact. No 433.] Part IV. Philosophical Transactions (1683–1775) 38:405–412Google Scholar
  13. Diodato N (2007) Climatic fluctuations in Southern Italy since 17th century: reconstruction with precipitation records at Benevento. Clim Chang 80:411–431CrossRefGoogle Scholar
  14. Diodato N, Bellocchi G (2007) Estimating monthly (R)USLE climate input in a Mediterranean region using limited data. J Hydrol 345:224–236CrossRefGoogle Scholar
  15. Diodato N, Bellocchi G (2010) MedREM, a rainfall erosivity model for the Mediterranean region. J Hydrol 387:119–127CrossRefGoogle Scholar
  16. Diodato N, Bellocchi G (2011) Discovering the anomalously cold Mediterranean 1 winters during the Maunder minimum. Holocene 22:589–596CrossRefGoogle Scholar
  17. Diodato N, Ceccarelli M, Bellocchi G (2008) Decadal and century-long changes in the reconstruction of erosive rainfall anomalies at a Mediterranean fluvial basin. Earth Surf Proc Land 33:2078–2093CrossRefGoogle Scholar
  18. Dobrovolný P, Moberg A, Brázdil R, Pfister C, Glaser R, Wilson R, van Engelen A, Limanówka D, Kiss A, Halíčková M, Macková J, Riemann D, Luterbacher J, Böhm R (2010) Monthly, seasonal and annual temperature reconstructions for Central Europe derived from documentary evidence and instrumental records since ad 1500. Clim Chang 101:69–107CrossRefGoogle Scholar
  19. Durbin J, Watson GS (1950) Testing for serial correlation in least squares regression, I. Biometrika 37:409–428Google Scholar
  20. Durbin J, Watson GS (1951) Testing for serial correlation in least squares regression, II. Biometrika 38:159–179Google Scholar
  21. Esper J, Cook ER, Schweingruber FH (2002) Low frequency signals in long tree-ring chronologies for reconstructing past temperature variability. Science 295:2250–2253CrossRefGoogle Scholar
  22. Ferrari U (1977) Giovan Battista Moio, Gregorio Susanna: Diario di quanto successe in Catanzaro dal 1710 al 1769. Edizioni Effe Emme, Chiaravalle Centrale, ItalianGoogle Scholar
  23. García-Herrera R, Luterbacher J, Lionello P, González-Rouco F, Ribera P, Rodó X, Kull P, Zerefos C (2007) Reconstruction of past Mediterranean climate. Eos Trans Am Geophys Union 88. doi:10.1029/2007EO090010
  24. Garnier E, Daux V, Yiou P, García de Corazar-Atauri I (2011) Grapevine harvest dates in Besançon (France) between 1525 and 1847: social outcomes or climatic evidence? Clim Chang 104:703–727CrossRefGoogle Scholar
  25. Ge Q-S, Zheng J-Y, Hao Z-X, Zhang P-Y, Wang WC (2005) Reconstruction of historical climate in China: high-resolution precipitation data from Qing Dynasty Archives. B Am Meteorol Soc 86:671–679CrossRefGoogle Scholar
  26. Glaser R, Riemann D (2009) A thousand-year record of temperature variations for Germany and Central Europe based on documentary data. J Quaternary Sci 24:437–449CrossRefGoogle Scholar
  27. Grace RC (2004) Temporal context in concurrent chains: I. Terminal-link duration. J Exp Anal Behav 81:215–237CrossRefGoogle Scholar
  28. Granger CWJ, Hyung N, Jeon Y (2001) Spurious regressions with stationary series. Appl Econ 33:899–904Google Scholar
  29. Green W (2003) Econometric analysis, New York University, 5th edn. Prentice-Hall, New YorkGoogle Scholar
  30. Hair JF, Anderson RE, Tatham RL, Black WC (1998) Multivariate data analysis, 5th edn. Prentice-Hall, Upper Saddle RiverGoogle Scholar
  31. Helama S, Makarenko NG, Karimova LM, Kruglun OA, Timonen M, Holopainen J, Meriläinen J, Eronen M (2009) Dendroclimatic transfer functions revisited: Little Ice Age and Medieval Warm Period summer temperatures reconstructed using artificial neural networks and linear algorithms. Ann Geophys 27:1097–1111CrossRefGoogle Scholar
  32. Jones PD, Briffa KR, Osborn TJ, Lough JM, van Ommen TD, Vinther BM, Luterbacher J, Wahl ER, Zwiers FW, Mann ME, Schmidt GA, Ammann CM, Buckley BM, Cobb KM, Esper J, Goosse H, Graham N, Jansen E, Kiefer T, Kull C, Küttel M, Mosley-Thompson E, Overpeck JT, Riedwyl N, Schulz M, Tudhope AW, Villalba R, Wanner H, Wolff E, Xoplaki E (2009) High-resolution palaeoclimatology of the last millennium: a review of current status and future prospects. Holocene 19:3–49CrossRefGoogle Scholar
  33. Larocque SJ, Smith DJ (2005) A dendroclimatological reconstruction of climate since ad 1700 in the Mt. Waddington area, British Columbia Coast Mountains, Canada. Dendrochronologia 22:93–106CrossRefGoogle Scholar
  34. Leijonhufvud L, Wilson R, Moberg A (2008) Documentary data provide evidence of Stockholm average winter to spring temperatures in the eighteenth and nineteenth centuries. Holocene 18:333–343CrossRefGoogle Scholar
  35. Liang E, Shao X, Qin N (2008) Tree-ring based summer temperature reconstruction for the source region of the Yangtze River on the Tibetan Plateau. Glob Planet Chang 61:313–320CrossRefGoogle Scholar
  36. Lim KJ, Engel BA, Zang T, Muthukrishnan S, Choi J, Kim K (2006) Effects of calibration on L-THIA GIS runoff and pollutant estimation. J Environ Manag 78:35–43CrossRefGoogle Scholar
  37. Lionello P, Malanotte-Rizzoli P, Boscolo R (2006) Mediterranean climate variability. Developments in Earth and Environmental Sciences, Vol. 4. Elsevier, AmsterdamGoogle Scholar
  38. Luterbacher J, Xoplaki E (2003) 500-year winter temperature and precipitation variability over the Mediterranean area and its connection to the large-scale atmospheric circulation. In: Bolle H-J (ed) Mediterranean climate variability and trends. Springer, Berlin, pp 133–153CrossRefGoogle Scholar
  39. Luterbacher J, Dietrich D, Xoplaki E, Grosjean M, Wanner H (2004) European seasonal and annual temperature variability, trends and extremes since 1500. Science 303:1499–1503CrossRefGoogle Scholar
  40. Mann ME (2007) Climate over the past two millennia. Ann Rev Earth Pl Sci 35:111–136CrossRefGoogle Scholar
  41. Mann ME, Gille E, Bradley RS, Hughes MK, Overpeck J, Keimig FT, Gross W (2008) Global temperature patterns in past centuries: an interactive presentation. Earth Inter 4:1–29CrossRefGoogle Scholar
  42. Menascé DA (2008) Computing missing service demand parameters for performance models. Computer Measurement Group Conference, Las Vegas, NV, USA, 7–12 December, pp 241–248Google Scholar
  43. Mitchell T, Jones PD (2005) An improved method of constructing a database of monthly climate observations and associated high-resolution grids. Int J Climatol 25:693–712CrossRefGoogle Scholar
  44. Moberg A, Sonechkin DM, Holmgren K, Datsenko NM, Karlén W (2005) Highly variable Northern Hemisphere temperatures reconstructed from low- and high-resolution proxy data. Nature 433:613–617CrossRefGoogle Scholar
  45. Moberg A, Dobrovolny P, Wilson R, Brázdil R, Pfister C, Glaser R, Leijonhufvud L, Zorita E (2009) Quantifying uncertainty in documentary-data based climate reconstructions? Geophysical Research Abstracts 11:EGU2009-1177Google Scholar
  46. Morisette JT, Richardson AD, Knapp AK, Fisher JI, Graham EA, Abatzoglou J, Wilson BE, Breshears DD, Henebry GM, Hanes JM, Liang L (2009) Tracking the rhythm of the seasons in the face of global change: phenological research in the 21st century. Front Ecol Environ 7:253–260CrossRefGoogle Scholar
  47. Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models part I—a discussion of principles. J Hydrol 10:282–290CrossRefGoogle Scholar
  48. Oberhuber W, Kofler W (2002) Dendroclimatological spring rainfall reconstruction for an inner Alpine dry valley. Theor Appl Climatol 71:97–106CrossRefGoogle Scholar
  49. Ogilvie AEJ, Jonsson T (2001) Little Ice Age research: a perspective from Iceland. Clim Chang 48:9–52CrossRefGoogle Scholar
  50. Pauling A, Luterbacher J, Wanner H (2003) Evaluation of proxies for European and North Atlantic temperature field reconstructions. Geophys Res Lett 30:1787. doi:10.1029/2003GL017589 CrossRefGoogle Scholar
  51. Pfister C (1999) Wetternachhersage. 500 Jahre Klimavariationen und Naturkatastrophen (1496–1995). Haupt, BernGoogle Scholar
  52. Pfister C (2001) I cambiamenti climatici nella storia dell’Europa. Sviluppi e potenzialità della climatologia storica. In: Bonardi L (ed) Che tempo faceva. Variazioni del clima e conseguenze sul popolamento umano. Fonti, Metodologie e Prospettive, AngeliGoogle Scholar
  53. Ramsey EW III, Hodgson ME, Sapkota SK, Nelson GA (2001) Forest impact estimated with NOAA AVHRR and Landsat TM data related to an empirical hurricane wind-field distribution. Remote Sens Environ 77:279–292CrossRefGoogle Scholar
  54. Riedwyl N, Küttel M, Luterbacher J, Wanner H (2009) Comparison of climate field reconstruction techniques: application to Europe. Clim Dyn 32:381–395CrossRefGoogle Scholar
  55. Robertson I, Lucy D, Baxter L, Pollard AM, Aykroyd RG, Barker AC, Carter AHC, Switsur VR, Waterhouse JS (1999) A kernel-based Bayesian approach to climatic reconstruction. Holocene 9:495–500CrossRefGoogle Scholar
  56. Rodrigo FS, Gómez-Navarro JJ, Montávez Gómez JP (2011) Climate variability in Andalusia (southern Spain) during the period 1701–1850 ad from documentary sources: evaluation and comparison with climate model simulations. Clim Past Discuss 7:2297–2339CrossRefGoogle Scholar
  57. Rutherford S, Mann ME, Osborn TJ, Bradley RS, Briffa KR, Highes MK, Jones PD (2005) Proxy-based northern hemisphere surface temperature reconstructions: sensitivity to method, predictor network, target season, and target domain. J Climate 18:2308–2329CrossRefGoogle Scholar
  58. Schiano ME, Borghini M, Castellari S, Luttazzi C (2000) Climatic features of the Mediterranean Sea detected by the analysis of the longwave radiative bulk formulae. Ann Geophysicae 18:1482–1487CrossRefGoogle Scholar
  59. Shrestha DL, Solomatine DP (2008) Data-driven approaches for estimating uncertainty in rainfall-runoff modelling. Int J River Basin Manag 6:109–122CrossRefGoogle Scholar
  60. Stenseth NC, Ottersen G, Hurrell JW, Mysterud A, Lima M, Chan K-S, Yoccoz NG, Ådlandsvik B (2003) Studying climate effects on ecology through the use of climate indices: the North Atlantic Oscillation, El Niño Southern Oscillation and beyond. P Roy Soc B-Biol Sci 270:2087–2096CrossRefGoogle Scholar
  61. Tan M, Shao X, Liu J, Cai B (2009) Comparative analysis between a proxy-based climate reconstruction and GCM-based simulation of temperatures over the last millennium in China. J Quat Sci 24:547–551CrossRefGoogle Scholar
  62. Von Storch H, Zorita E, Jones J, Dimitirev Y, Gonzalez-Rouco F, Tett S (2005) Reconstructing past climate from noisy data. Science 306:679–682CrossRefGoogle Scholar
  63. Vrac M, Marbaix P, Paillard D, Caveau P (2007) Non-linear statistical downscaling of present and LGM precipitation and temperatures over Europe. Clim Past 3:669–682CrossRefGoogle Scholar
  64. Wessa P (2009) A framework for statistical software development, maintenance, and publishing within an open-access business model. Comput Stat 24:183–193CrossRefGoogle Scholar
  65. Wigley TML (1992) Future climate of the Mediterranean Basin with particular emphasis in changes in precipitation. In: Jeftic L, Milliman JD, Sestini G (eds) Climate change in the Mediterranean. Edward Arnold, London, pp 15–44Google Scholar
  66. Xoplaki E, Luterbacher J, Paeth H, Dietrich D, Steiner N, Grosjean M, Wanner H (2005) European spring and autumn temperature variability and change of extremes over the last half millennium. Geophys Res Lett 32:L15713. doi:10.1029/2005GL023424 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2012

Authors and Affiliations

  • Nazzareno Diodato
    • 1
  • Gianni Bellocchi
    • 1
    • 2
  • Chiara Bertolin
    • 3
  • Dario Camuffo
    • 3
  1. 1.MetEROBS-Met European Research Observatory, GEWEX-CEOP NetworkWorld Climate Research ProgrammeBeneventoItaly
  2. 2.Grassland Ecosystem Research UnitFrench National Institute of Agricultural ResearchClermont-FerrandFrance
  3. 3.Atmosphere and Ocean Science InstituteNational Research Council of ItalyPaduaItaly

Personalised recommendations