Across the Northern Hemisphere, the synchronization of summer peak temperatures of the Medieval Climate Anomaly (MCA, roughly 900–1300 CE) and the Little Ice Age (LIA, roughly 1300–1850 CE) increases with the spatial and temporal scale at which the epochs are measured: timing spreads among proxy-based reconstructions shrink from century-scale at individual sites to a few decades at continental scale when the longest running-mean windows of the analyzed 51–351-year range (251–351 years) are used. It remains unexplained how much of this scale-dependent coherency is a statistical artifact of averaging — temporal and spatial smoothing mechanically reduce the effective spatial degrees of freedom of a randomly varying field — and how much reflects genuinely coherent climate variability driven by external forcing or internal climate modes. This problem asks for a quantitative, uncertainty-aware account of the scale-dependent MCA/LIA peak-temperature synchronization: (1) a decomposition separating the smoothing-artifact contribution from the externally forced and internally generated contributions; (2) propagation of reconstruction timing uncertainties (tree-ring low-frequency spectral biases, proxy-network coverage gaps, methodological choices) into continental-scale peak timing and its coherency; and (3) attribution of the coherency across these spatial scales and window lengths to specific forcings and internal modes (Atlantic versus Pacific multidecadal variability). The methodological building blocks exist separately but have not been combined for this question; the problem remains open.

Background

The Medieval Climate Anomaly (MCA) and the Little Ice Age (LIA) are the two canonical climate epochs of the preindustrial Common Era (the past two thousand years): a generally warm interval centered near 900–1300 CE and a generally cold interval near 1300–1850 CE. Our knowledge of them comes from proxy-based temperature reconstructions — time series of temperature-sensitive natural archives such as tree rings (ring width and maximum latewood density, the density of the last-formed cells of a growth ring), ice-core oxygen-isotope ratios, corals, and sediments — compiled into local, regional, and continental series by efforts such as the PAGES 2k Consortium (Past Global Changes 2k, a global paleoclimate-proxy working group), and into gridded field reconstructions such as those of Neukom and colleagues. A long-standing concern is whether these epochs were globally or hemispherically synchronous. Mann and colleagues (2009) used a coupled model and reconstructions to argue for global, dynamically coherent LIA and MCA signals tied substantially to volcanic and solar forcing. By contrast, Neukom and colleagues (2019) found, using global field reconstructions, no evidence for globally coherent warm and cold periods over the preindustrial Common Era when epochs are defined with 51-year windows: the coldest epoch of the last millennium occurred in the fifteenth century in the central and eastern Pacific, in the seventeenth century in northwestern Europe and southeastern North America, and in the mid-nineteenth century elsewhere — timing differences of up to about a century between regions. A companion study (also Neukom and colleagues, 2019) showed that global-mean multidecadal variability is nevertheless coherent across reconstructions and consistent with forced model simulations, with volcanic aerosol forcing the dominant driver at those timescales, so the asynchrony question is manifestly scale-dependent.

Wang and colleagues (2022, Climate Dynamics) made this scale dependence explicit for the Northern Hemisphere. Their operational measure of epoch timing is the center-year of the single warmest (for the MCA) or coldest (for the LIA) running-mean interval of a given length, evaluated for window lengths from 51 to 351 years; synchronization is measured by the spread of these center-years across sites, regions, and continents. They found that the spread decreases systematically with larger spatial averaging domains and longer windows, that this holds for both the MCA maximum and the LIA minimum, and that the pattern is reproduced across three families of reconstructions (composite means of retained tree-ring and ice-core records, PAGES 2k continental reconstructions, and the Neukom et al. field reconstructions). They interpreted the large-scale coherence as consistent with the spatially coherent Northern Hemisphere response to external forcing — variations in incoming solar irradiance, sequences of large volcanic eruptions, and long-term greenhouse-gas changes — and the small-scale incoherence as the signature of internally generated variability such as Atlantic and Pacific multidecadal oscillations (ocean-basin-scale, decades-to-centuries variations of North Atlantic and North Pacific sea-surface temperature).

The interpretation, however, rests on an inference the authors themselves flag as incomplete. Temporal smoothing with long running means and spatial averaging over continental domains mechanically filter out localized, high-frequency fluctuations and reduce the effective spatial degrees of freedom (ESDOF) of the temperature field — roughly, the number of statistically independent spatial samples it contains; Kunz and Laepple (2024) show from instrumental data that this ESDOF reduction with timescale is a real and substantial property of natural surface temperature variability. Averaging alone can therefore manufacture apparent agreement in peak timing even when no physical synchronization process operates. Because the synchronization analysis of Wang and colleagues does not include a formal decomposition, an intervention experiment, or a detection-and-attribution test, the observed scale-dependent coherency has never been quantitatively split into (a) the mechanical ESDOF-reduction artifact, (b) the externally forced component, and (c) the internally generated component. Moreover, the precise timing of continental-scale MCA maxima and LIA minima is itself uncertain — tree-ring records can underestimate low-frequency (multicentennial) variability, proxy coverage is spatially and temporally biased, and different reconstruction methodologies displace the identified peak years — and this uncertainty has not been propagated through the synchronization analysis. Finally, paleoclimate data assimilation (a technique that optimally combines proxy observations with climate-model simulations to reconstruct past climate fields, as in the Last Millennium Reanalysis) and last-millennium model ensembles such as the Community Earth System Model Last Millennium Ensemble (CESM-LME) and the past1000 last-millennium simulations of the Paleoclimate Modelling Intercomparison Project Phase 4 (PMIP4) now exist as tools, but neither has been used to attribute the scale-dependent coherency to specific forcings or to Atlantic versus Pacific multidecadal variability. Reviews of Common Era temperature reconstructions (Anchukaitis and Smerdon 2022) and of the LIA concept itself (Collet and colleagues 2025) confirm that the synchrony question remains contested rather than settled.

Problem Statement

Explain, quantitatively and with propagated uncertainties, why the synchronization of Northern Hemisphere summer peak temperatures across the Medieval Climate Anomaly (MCA) and the Little Ice Age (LIA) increases with spatial and temporal scale, by determining: (1) how much of the observed increase in coherency — measured, as defined in the Background, by the spread of the center-years of the warmest (MCA) or coldest (LIA) running-mean interval — between local and continental spatial scales and between 51- and 351-year running-mean windows arises mechanically from the reduction of effective spatial degrees of freedom produced by temporal and spatial smoothing, and how much reflects physically coherent climate variability; (2) how the timing of continental-scale MCA maximum and LIA minimum temperatures, and the coherency of that timing, change once reconstruction uncertainties are propagated through the synchronization analysis, including tree-ring underestimation of low-frequency variability, spatial and temporal biases in proxy network coverage, and methodological choices among large-scale reconstruction approaches; and (3) what the relative contributions of specific external forcings (solar, volcanic, greenhouse-gas) and internal modes of variability (Atlantic versus Pacific multidecadal variability) to the coherency are across the local, regional, and continental spatial scales and the 51- to 351-year running-mean windows. These three components serve one overarching objective: a quantified, uncertainty-aware, mechanistic account of whether the terms MCA and LIA describe genuinely synchronized hemispheric-scale climate epochs, and if so, why their synchronization is scale-dependent. The question is posed at this generality — Northern Hemisphere, both epochs, the full hierarchy of spatial scales from local to continental and window lengths from multidecadal to multicentennial — rather than for a single scale, region, reconstruction, or mechanism.

References

  1. Wang, J., Yang, B., Fang, M., Wang, Z., Liu, J., & Kang, S. (2022). Synchronization of summer peak temperatures in the Medieval Climate Anomaly and Little Ice Age across the Northern Hemisphere varies with space and time scales. Climate Dynamics. DOI: 10.1007/s00382-022-06524-6. https://doi.org/10.1007/s00382-022-06524-6
  2. Neukom, R., Steiger, N., Gómez-Navarro, J. J., Wang, J., & Werner, J. P. (2019). No evidence for globally coherent warm and cold periods over the preindustrial Common Era. Nature. DOI: 10.1038/s41586-019-1401-2. https://doi.org/10.1038/s41586-019-1401-2
  3. Neukom, R., Barboza, L. A., Erb, M. P., Shi, F., Emile-Geay, J., Evans, M. N., Franke, J., Kaufman, D. S., Lücke, L., Rehfeld, K., Schurer, A., Zhu, F., Brönnimann, S., Hakim, G. J., Henley, B. J., Ljungqvist, F. C., McKay, N., Valler, V., & von Gunten, L. (2019). Consistent multidecadal variability in global temperature reconstructions and simulations over the Common Era. Nature Geoscience, 12, 643–649. DOI: 10.1038/s41561-019-0400-0. https://doi.org/10.1038/s41561-019-0400-0
  4. Mann, M. E., Zhang, Z., Rutherford, S., Bradley, R. S., Hughes, M. K., Shindell, D., Ammann, C., Faluvegi, G., & Ni, F. (2009). Global Signatures and Dynamical Origins of the Little Ice Age and Medieval Climate Anomaly. Science. DOI: 10.1126/science.1177303. https://doi.org/10.1126/science.1177303
  5. Anchukaitis, K. J., & Smerdon, J. E. (2022). Progress and uncertainties in global and hemispheric temperature reconstructions of the Common Era. Quaternary Science Reviews. DOI: 10.1016/j.quascirev.2022.107537. https://doi.org/10.1016/j.quascirev.2022.107537
  6. Kuhl, I., Esper, J., Schneider, L., Trouet, V., Kunz, M., Klippel, L., Büntgen, U., & Hartl, C. (2024). Revising Alpine summer temperatures since 881 CE. Climate Dynamics. DOI: 10.1007/s00382-024-07195-1. https://doi.org/10.1007/s00382-024-07195-1
  7. Collet, D., White, S., Bremer, S., Brenna, B., Glørstad, H., Gundersen, I. M., Huhtamaa, H., Krüger, K., Linderholm, H. W., Ljungqvist, F. C., Ogilvie, A. E. J., Svarva, H. L., & Þórsson, B. (2025). The Little Ice Age: The History and Future of a Traveling Concept. WIREs Climate Change. DOI: 10.1002/wcc.70023. https://doi.org/10.1002/wcc.70023
  8. Kunz, T., & Laepple, T. (2024). Effective Spatial Degrees of Freedom of Natural Temperature Variability as a Function of Frequency. Journal of Climate. DOI: 10.1175/jcli-d-23-0040.1. https://doi.org/10.1175/jcli-d-23-0040.1
  9. Cleveland Stout, R., Proistosescu, C., & Roe, G. (2023). Fingerprinting Low-Frequency Last Millennium Temperature Variability in Forced and Unforced Climate Models. Journal of Climate. DOI: 10.1175/jcli-d-22-0810.1. https://doi.org/10.1175/jcli-d-22-0810.1
  10. Miao, J., Ge, Y., & Jiang, D. (2024). Changes of Atlantic Multidecadal Variability During the Medieval Climate Anomaly and Little Ice Age and Associated Causes. Journal of Geophysical Research: Atmospheres. DOI: 10.1029/2023jd039966. https://doi.org/10.1029/2023jd039966
  11. Miao, J., Wang, T., & Wang, H. (2026). Volcanic Forcing Overwhelmed AMV's Influence on Eurasian Winter Temperatures During the Little Ice Age. Geophysical Research Letters. DOI: 10.1029/2025gl119282. https://doi.org/10.1029/2025gl119282
  12. Wang, Z., Li, L., Wang, J., & Li, K. (2026). Contrasting seasonal roles of external forcing and internal variability in East Asian temperature. npj Climate and Atmospheric Science. DOI: 10.1038/s41612-026-01505-6. https://doi.org/10.1038/s41612-026-01505-6
  13. Fang, M., Zheng, J., Wang, J., Zhu, H., & Zhang, X. (2022). Assimilating an expanded tree ring dataset to reconstruct the millennial air temperature fields for the Northern Hemisphere. International Journal of Climatology. DOI: 10.1002/joc.7528. https://doi.org/10.1002/joc.7528
  14. Wang, Z., Wang, J., Jia, J., Shi, X., Wang, S., & Pan, C. (2022). Detection and attribution of summer temperature changes in China during the last millennium. International Journal of Climatology. DOI: 10.1002/joc.7595. https://doi.org/10.1002/joc.7595
  15. Yang, B., Li, X., He, M., Wang, F., Zhao, Y., Zhang, P., & Wang, J. (2024). The influence of proxy selection on global annual mean temperature reconstructions during the Common Era. Science China Earth Sciences. DOI: 10.1007/s11430-024-1348-3. https://doi.org/10.1007/s11430-024-1348-3
  16. Fang, M., Wang, J., & Chang, H. (2026). Reconstruction of Holocene Northern Hemisphere precipitation fields using paleoclimate data assimilation. Scientific Data. DOI: 10.1038/s41597-026-06551-6. https://doi.org/10.1038/s41597-026-06551-6
  17. Michel, S. L. L., Swingedouw, D., & Mignot, J. (2026). Reconstruction of last millennium sea surface temperature on 1° grid using a random forest algorithm. Global and Planetary Change. DOI: 10.1016/j.gloplacha.2025.105279. https://doi.org/10.1016/j.gloplacha.2025.105279