Fig 1.
Flow chart illustrating the MDVM method developed in this study for the extratropical Northern Hemisphere temperature reconstruction.
Table 1.
Statistics of split validation results for the pseudo-proxy experiment.
Exp-A: 851–1500 AD for calibration and 1501–2000 AD for validation; Exp-B: 1501–2000 AD for calibration and 851–1500 AD for validation; LF-Std-Ratio: the ratio of standard deviation of reconstructed centennial variability to simulated counterpart; Uncer-LF: the uncertainty of variability on centennial scale.
Fig 2.
Comparison of power spectral analysis for the original model ensemble mean series and PPE reconstructed series with different SNR levels (0.1, 0.25, 0.5 and 1.0) over the common period 851–2000 AD.
The red line indicated the red noise spectrum, and the blue (green) line indicated the 95% (90%) confidence level.
Table 2.
Statistics of leave-one-out cross-validation results for the reconstructed composite series with CRU during the common period 1850–2000 AD.
The threshold values at 95% significance level were estimated using 5000 member Monte Carlo simulations.
Fig 3.
Spatial distribution of the screened tree-ring database used for the extratropical Northern Hemisphere temperature reconstruction during the last millennium on decadal (a), multi-decadal (b) and centennial (c) scale, respectively, as well as the distribution of total database (d) used on the three timescales.
The total amount of tree-ring records was also given under each subgraph, and the number in brackets denoted the amount for the continental North America (NA) and Eurasia (Eu), respectively.
Fig 4.
(a) Comparison between the benchmark series (CRU NH mean temperature and Moberg05-LF) and the reconstruction based on MDVM method. (b) Comparison of the reconstructions using different continental data for the extratropical Northern Hemisphere mean temperature. (c) The number of chronologies used for the reconstruction.
All the smoothed series were 11-year running averaged. Temperatures were expressed as anomalies with respect to 1961–1990 AD.
Table 3.
The top 3 coldest and warmest decades indicated by MDVM reconstruction for the extratropical Northern Hemisphere temperature anomaly with respect to the period 1961–1990 AD.
Fig 5.
Comparison between MDVM reconstructed temperature (red lines) and the variations of external forcing.
(a) Reconstructed total solar irradiance variations (blue line) obtained from the references [49, 50]. The smoothed lines were 30-year low-pass filtered and shadings denoted the timing of great solar minima. (b) Variations of reconstructed total stratospheric volcanic sulfate aerosol injection (blue bars) in Northern Hemisphere obtained from the references [57].
Fig 6.
Comparison of extratropical Northern Hemisphere temperature reconstructions over the last millennium utilizing three statistical approaches, i.e. PCR, EIV, and MDVM, respectively.
Temperatures were expressed as anomalies with respect to 1951–1980 AD. Bold lines were smoothed by 11-year moving average.
Fig 7.
Comparison of MDVM reconstruction in this study with previous reconstructions for Northern Hemisphere mean temperature.
All reconstructions were 30-year low-pass filtered, and scaled to the smoothed instrumental series by the variance and mean over the common period 1865–1973 AD.
Fig 8.
Color map of the correlation coefficient matrix for Northern Hemisphere temperature reconstructions (30-year low-pass filtered) over the common period 1000–1973 AD.
Fig 9.
Comparison of MDVM reconstruction in this study with mode simulated Northern Hemisphere temperatures for the last millennium.
All series were 30-year low-pass filtered, and scaled by the mean over the common period 850–1850 AD.