Climate Dynamics

, Volume 44, Issue 3–4, pp 791–806 | Cite as

Probabilistic reconstructions of local temperature and soil moisture from tree-ring data with potentially time-varying climatic response

  • S. E. Tolwinski-WardEmail author
  • M. P. Tingley
  • M. N. Evans
  • M. K. Hughes
  • D. W. Nychka


We explore a probabilistic, hierarchical Bayesian approach to the simultaneous reconstruction of local temperature and soil moisture from tree-ring width observations. The model explicitly allows for differing calibration and reconstruction interval responses of the ring-width series to climate due to slow changes in climatology coupled with the biological climate thresholds underlying tree-ring growth. A numerical experiment performed using synthetically generated data demonstrates that bimodality can occur in posterior estimates of past climate when the data do not contain enough information to determine whether temperature or moisture limitation controlled reconstruction-interval tree-ring variability. This manifestation of nonidentifiability is a result of the many-to-one mapping from bivariate climate to time series of tree-ring widths. The methodology is applied to reconstruct temperature and soil moisture conditions over the 1080–1129 C.E. interval at Methusalah Walk in the White Mountains of California, where co-located isotopic dendrochronologies suggest that observed moisture limitations on tree growth may have been alleviated. Our model allows for assimilation of both data sources, and computation of the probability of a change in the climatic controls on ring-width relative to those observed in the calibration period. While the probability of a change in control is sensitive to the choice of prior distribution, the inference that conditions were moist and cool at Methuselah Walk during the 1080–1129 C.E. interval is robust. Results also illustrate the power of combining multiple proxy data sets to reduce uncertainty in reconstructions of paleoclimate.


Bayesian hierarchical modeling Biological–statistical modeling Multiproxy paleoclimate reconstruction Tree-ring width Time-varying climate-paleodata relationship 



This work was supported in part by Grants NSF ATM-0724802, NSF ATM-0902715, NSF DMS-1204892, NSF AGS 1304309, and NOAA NA060OAR4310115. We thank Steve Leavitt for lending his isotope data as well as insights on their interpretation, Chris Daly and the PRISM project for making their work freely available, and Benno Blumenthal for making the PRISM data easily accessible on the IRI Data Library. We are also grateful for insightful comments from Chris Paciorek and one other anonymous reviewer, which substantially improved the final version of this paper.

Supplementary material

382_2014_2139_MOESM1_ESM.pdf (118 kb)
Supplementary material 1 (f 117 KB)


  1. Bale R, Robertson I, Salzer M, Loader N, Leavitt S, Gagen M, Harlan T, McCarroll D (2011) An annually resolved bristlecone pine carbon isotope chronology for the last millennium. Quatern Res 76(1):22–29. doi: 10.1016/j.yqres.2011.05.004 CrossRefGoogle Scholar
  2. Bradley R (1999) Paleoclimatology: reconstructing climates of the quaternary. Academic Press, San Diego, CAGoogle Scholar
  3. Bradley R (2011) High-resolution paleoclimatology. In: Hughes M, Swetnam T, Diaz H (eds) Dendroclimatology: progress and prospects, developments in paleoecological research, Chapter 1. Springer, BerlinGoogle Scholar
  4. Brazdil R, Pfister C, Wanner H, Von Storch H, Luterbacher J (2005) Historical climatology in Europe: the state of the art. Clim Change 70:363–430. doi: 10.1007/s10584-005-5924-1 CrossRefGoogle Scholar
  5. Breitenmoser P, Brönnimann S, Frank D (2013) Forward modelling of tree-ring width and comparison with a global network of tree-ring chronologies. Clim Past Discuss 9(4):4065–4098. doi: 10.5194/cpd-9-4065-2013.
  6. Chiles J, Delfiner P (1999) Geostatistics: modeling spatial uncertainty. Wiley Series in Probability and Statistics, New York, NYCrossRefGoogle Scholar
  7. Christiansen B, Ljungqvist F (2011) Reconstruction of the extratropical NH mean temperature over the last millennium with a method that preserves low-frequency variability. J Clim 24:6013–6034. doi: 10.1175/2011JCLI4145.1 CrossRefGoogle Scholar
  8. Cook E, Kairiukstis L (1990) Methods of Dendrochronology: applications in the environmental sciences. Kluwer Academic Publishers, DordrechtCrossRefGoogle Scholar
  9. Cook E, Seager R, Heim R, Vose R, Herweijer C, Woodhouse C (2009) Megadroughts in North America: placing IPCC projections of hydroclimatic change in a long-term paleoclimate context. J Quat Sci 25:48–61. doi: 10.1002/jqs.1303 CrossRefGoogle Scholar
  10. Crowley T, Lowery T (2000) How warm was the medieval warm period? AMBIO 29:51–54. doi: 10.1639/0044-7447(2000 Google Scholar
  11. Csillery K, Blum M, Gaggiotti O, Fracois O (2010) Approximate Bayesian computation (ABC) in practice. Trends Ecol Evol 25:410–418. doi: 10.1016/j.tree.2010.04.001 CrossRefGoogle Scholar
  12. Daly C, Halbleib M, Smith J, Gibson W, Doggett M, Taylor G, Curtis J, Pasteris P (2008) Physiographically sensitive mapping of climatological temperature and precipitation across the coterminous United States. Int J Climatol 28:2031–2064. doi: 10.1002/joc.1688.
  13. D’Arrigo R, Kaufmann R, Davi N, Jacoby G, Laskowski C, Myneni R, Cherubini P (2004) Thresholds for warming-induced growth decline at elevational treeline in the Yukon Territory. Glob Biogeochem Cycles 18. doi: 10.1029/2004GBO02249
  14. D’Arrigo R, Wilson R, Jacoby G (2006) On the long-term context for late twentieth century warming. J Geophys Res 111. doi: 10.1029/2005JD006352
  15. Evans M, Tolwinski-Ward S, Thompson D, Anchukaitis K (2013) Applications of proxy system modeling in high resolution paleoclimatology. Quat Sci Rev 76(0):16–28. doi: 10.1016/j.quascirev.2013.05.024.
  16. Farquhar G, O’Leary MH, Berry JA (1982) On the relationship between carbon isotope discrimination and the intercellular carbon dioxide concentration in leaves. Aust J Plant Physiol 9:121–37CrossRefGoogle Scholar
  17. Fritts HC (2001) Tree rings and climate. The Blackburn Press, New YorkGoogle Scholar
  18. Fritts HC, Smith DG, Cardis JW, Budelsky C (1965) Tree-ring characteristics along a vegetation gradient in northern Arizona. Ecology 46:394–401.
  19. Garetta V, Guiot J, Mortier F, Chadoef J, Hely C (2012) Pollen-based climate reconstruction: calibration of the vegetation–pollen processes. Ecol Mod 235–236:81–94. doi: 10.1016/j.ecolmodel.2012.03.031 CrossRefGoogle Scholar
  20. Gelman A, Rubin D (1992) Inference from iterative simulation using multiple sequences. Stat Sci 7(4):457–472. doi: 10.1214/ss/1177011136 CrossRefGoogle Scholar
  21. Gelman A, Carlin J, Stern H, Rubin D (2003) Bayesian data analysis. Chapman and Hall, Boca Raton, FLGoogle Scholar
  22. Gilks W, Richardson S, Spiegelhalter D (1996) Markov chain Monte Carlo in practice. Chapman & Hall/CRC, Boca RatonGoogle Scholar
  23. Graham N, Hughes M (2007) Reconstructing the Mediaeval low stands of Mono Lake, Sierra Nevada, California USA. Holocene 17(8):1197–1210. doi: 10.1177/0959683607085126 CrossRefGoogle Scholar
  24. Guiot J, Torre F, Jolly D, Peyron O, Boreaux J, Cheddadi R (2000) Inverse vegetation modeling by monte carlo sampling to reconstruct palaeoclimates under changed precipitation seasonality and CO2 conditions: application to glacial climate in Mediterranean region. Ecol Model 127:119–1140CrossRefGoogle Scholar
  25. Guiot J, Wu V Garreta, HB, Hatte C, Magny M (2009) A few prospective ideas on climate reconstruction: from a statistical single proxy approach towards a multi-proxy and dynamical approach. Clim Past 5:571–583.
  26. Haslett J, Whiley M, Bhattacharya S, Salter-Townshend M, Wilson S, Allen J, Huntley B, Mitchell F (2006) Bayesian paleocolimate reconstruction. J R Stat Soc 169(3):395–438. doi: 10.1111/j.1467-985X.2006.00429.x CrossRefGoogle Scholar
  27. Huang J, van den Dool HM, Georgankakos KP (1996) Analysis of model-calculated soil moisture over the United States (1931–1993) and applications to long-range temperature forecasts. J Clim 9:1350–1362CrossRefGoogle Scholar
  28. Hughes M, Funkhouser G (1998) Extremes of moisture availability reconstructed from tree rings for recent millennia in the Great Basin of Western North America. In: Beniston M, Innes J (eds) The impacts of climate variability on forests. Springer, Berlin, pp 99–107CrossRefGoogle Scholar
  29. Hughes MK, Ammann CM (2009) The future of the past: an earth system framework for high resolution paleoclimatology—editorial essay. Clim Change 94:247–259. doi: 10.1007/s10584-009-9588-0 CrossRefGoogle Scholar
  30. Jansen E, Overpeck J, Briffa K, Duplessy J, Joos F, Masson-Delmotte V, Olago D, Otto-Bliesner B, Peltier W, Rahmstorf S, Ramesh R, Raynaud D, Rind D, Solomina O, Villalba R, Zhang D (2007) Paleoclimate, Chap 6. In: Solomon S, Qin D, Manning M, Chen Z, Marquis M, Averyt K, Tignor M, Miller H (eds) Climate change 2007: the physical science basis. Contribution of working group I to the fourth assessment report of the intergovernmental panel on climate change. Cambridge University Press, CambridgeGoogle Scholar
  31. Jones P, Briffa K, Barnett T, Tett S (1998) High-resolution paleoclimatic records for the last millennium: interpretation, integration and comparison with general circulation model control-run temperatures. Holocene 8:455–471. doi: 10.1191/095968398667194956 CrossRefGoogle Scholar
  32. Kobashi T, Severinghaus JP, Brook EJ, Barnola JM, Grachev AM (2007) Precise timing and characterization of abrupt climate change 8200 years ago from air trapped in polar ice. Quat Sci RevsGoogle Scholar
  33. LaMarche V (1974) Paleoclimatic inferences from long tree-ring records. Science 183(4129):1043–1088CrossRefGoogle Scholar
  34. Leavitt S (1994) Major wet interval in White Mountains medieval warm period evidenced in \(\delta ^{13}\)C of bristlecone pine tree rings. Clim Change 26:299–307CrossRefGoogle Scholar
  35. Li B, Nychka D, Ammann C (2010) The value of multiproxy reconstructions of past climate. J Am Stat Assoc 105(491):883–895Google Scholar
  36. Luterbacher J, Dietrich D, Xoplaki E, Grosjean M, Wanner H (2004) European seasonal and annual temperature variability, trends, and extremes since 1500. Science 303(5663):1499–1503. doi: 10.1126/science.1093877 CrossRefGoogle Scholar
  37. Mann ME, Zhang Z, Hughes MK, Bradley RS, Miller SK, Rutherford S, Ni F (2008) Proxy-based reconstructions of hemispheric and global surface temperature variations over the past two millennia. Proc Natl Acad Sci USA 105:13,252–13,257. doi: 10.1073/pnas.0805721105 CrossRefGoogle Scholar
  38. McCarroll D, Loader N (2004) Stable isotopes in tree rings. Quat Sci Rev 23:771–801. doi: 10.1016/j.quascirev.2003.06.017 CrossRefGoogle Scholar
  39. Moberg A, Sonechkin D, Holmgren K, Datsenko N, Karlen W (2005) Highly variable Northern Hemisphere temperatures reconstructed from low- and high-resolution proxy data. Nature 433:613–617. doi: 10.1038/nature03265 CrossRefGoogle Scholar
  40. Murray I, Ghahramani Z, MacKay DJC (2006) MCMC for doubly-intractable distributions. In:Proceedings of the 22nd Annual Conference on Uncertainty in Artificial Intelligence (UAI-06), pp 359–366Google Scholar
  41. Parnell A, Haslett J, Allen J, Buck C, Huntley B (2008) A flexible approach to assessing synchroneity of past events using Bayesian reconstructions of sedimentation history. Quat Sci Rev 27(19–20):1872–1885. doi: 10.1016/j.quascirev.2008.07.009 CrossRefGoogle Scholar
  42. Robert C (2007) The bayesian choice: from decision-theoretic foundations fo computational implementation. Springer Texts in Statistics, ParisGoogle Scholar
  43. Salzer M, Bunn A, Graham N, Hughes M (2013) Five millennia of paleotemperature from tree-rings in the Great Basin, USA. Clim Dyn 1–10. doi: 10.1007/s00382-013-1911-9
  44. Salzer MW, Hughes MK, Bunn AG, Kipfmueller KF (2009) Recent unprecedented tree-ring growth in bristlecone pine at the highest elevations and possible causes. Proc Natl Acad Sci USA 106:20,348–20,353. doi: 10.1073/pnas.0903029106 CrossRefGoogle Scholar
  45. Shashkin A, Vaganov E (1993) Simulation model of climatically determined variability of conifers annual increment (on the example of common pine in the steppe zone). Rus J Ecol 24(5):275–280Google Scholar
  46. Smerdon J (2012) Climate models as a test bed for climate reconstruction methods: pseudoproxy experiments. WIREs Clim Change 3:63–77. doi: 10.1002/wcc.149 CrossRefGoogle Scholar
  47. Stanhill G, Cohen S (2001) Global dimming: a review of the evidence for a widespread and significant reduction in global radiation with discussion of its probable causes and possible agricultural consequences. Agric For Meteorol 107:255–278. doi: 10.1016/S0168-1923(00)00241-0 CrossRefGoogle Scholar
  48. Stine S (1990) Late Holocene fluctuations in Mono lake, eastern California. Paleogeography, paleoclimatology, palaeoecology 78:333–381. doi: 10.1016/0031-0182(90)90221-R CrossRefGoogle Scholar
  49. Stine S (1994) Extreme and persistent drought in California and Patagonia during Mediaeval time. Nature 369:546–549. doi: 10.1038/369546a0 CrossRefGoogle Scholar
  50. Stokes M, Smiley T (1968) An introduction to tree-ring dating. University of Chicago Press, ChicagoGoogle Scholar
  51. Tingley M, Huybers P (2010a) A Bayesian algorithm for reconstructing climate anomalies in space and time. Part I: development and applications to paleoclimate reconstruction problems. J Clim 23:2759–2781. doi: 10.1175/2009JCLI3015.1 CrossRefGoogle Scholar
  52. Tingley M, Huybers P (2010b) A Bayesian algorithm for reconstructing climate anomalies in space and time. Part II: comparison with the regularized expectation-maximization algorithm. J Clim 23:2782–2800. doi: 10.1175/2009JCLI3016.1 CrossRefGoogle Scholar
  53. Tingley M, Huybers P (2013) Recent temperature extremes at high northern latitudes unprecedented in the past 600 years. Nature 496(7444):201–205. doi: 10.1038/nature11969 CrossRefGoogle Scholar
  54. Tingley M, Craigmile P, Haran M, Li B, Mannshardt-Shamseldin E, Rajaratnam B (2012) Piecing together the past: statistical insights into paleoclimatic reconstructions. Quat Sci Rev 35:1–22. doi: 10.1016/j.quascirev.2012.01.012 CrossRefGoogle Scholar
  55. Tolwinski-Ward S, Evans M, Hughes M, Anchukaitis K (2011) An efficient forward model of the climate controls on interannual variation in tree-ring width. Clim Dyn doi: 10.1007/s00382-010-0945-5
  56. Tolwinski-Ward S, Anchukaitis K, Evans M (2013) Bayesian parameter estimation and interpretation for an intermediate model of tree-ring width. Clim Past 9:1481–1493. doi: 10.5194/cp-9-1481-2013 CrossRefGoogle Scholar
  57. Vaganov E, Hughes M, Kirdyanov A, Schweingruber F, Silkin P (1999) Influence of snowfall and melt timing on tree growth in subarctic Eurasia. Nature 400:149–151. doi: 10.1038/22087 CrossRefGoogle Scholar
  58. Vaganov E, Hughes M, Shashkin A (2006) Growth dynamics of conifer tree rings: images of past and future environments. Springer Ecol. Stu. 183, New YorkGoogle Scholar
  59. Wahl E, Diaz H, Ohlwein C (2011) A pollen-based reconstruction of summer temperature in central North America and implications for circulation patterns during medieval times. Glob Planet Change. doi: 10.1016/j.gloplacha.2011.10.005
  60. Yu S, Kang Z, Zhou W (2012) Quantitative palaeoclimate reconstructions as an inverse problem: A Bayesian inference of late-Holocene climate on the eastern Tibetan Plateau from a peat cellulose \(\delta ^{18}\)O record. Holocene 22(405). doi: 10.1177/0959683611425544

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • S. E. Tolwinski-Ward
    • 1
    Email author
  • M. P. Tingley
    • 2
  • M. N. Evans
    • 3
  • M. K. Hughes
    • 4
  • D. W. Nychka
    • 5
  1. 1.AIR Worldwide CorporationBostonUSA
  2. 2.Department of Meteorology and StatisticsPennsylvania State UniversityUniversity ParkUSA
  3. 3.Department of GeologyUniversity of MarylandCollege ParkUSA
  4. 4.Laboratory of Tree-Ring ResearchUniversity of ArizonaTucsonUSA
  5. 5.Institute for Mathematics Applied to GeosciencesNational Center for Atmospheric ResearchBoulderUSA

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