A new dataset of surface temperature over North America has been constructed by merging climate model results and empirical tree-ring data through the application of an optimal interpolation algorithm. Errors of both the Community Climate System Model version 4 (CCSM4) simulation and the tree-ring reconstruction were considered to optimize the combination of the two elements. Variance matching was used to reconstruct the surface temperature series. The model simulation provided the background field, and the error covariance matrix was estimated statistically using samples from the simulation results with a running 31-year window for each grid. Thus, the merging process could continue with a time-varying gain matrix. This merging method (MM) was tested using two types of experiment, and the results indicated that the standard deviation of errors was about 0.4 °C lower than the tree-ring reconstructions and about 0.5 °C lower than the model simulation. Because of internal variabilities and uncertainties in the external forcing data, the simulated decadal warm–cool periods were readjusted by the MM such that the decadal variability was more reliable (e.g., the 1940–1960s cooling). During the two centuries (1601–1800 AD) of the preindustrial period, the MM results revealed a compromised spatial pattern of the linear trend of surface temperature, which is in accordance with the phase transition of the Pacific decadal oscillation and Atlantic multidecadal oscillation. Compared with pure CCSM4 simulations, it was demonstrated that the MM brought a significant improvement to the decadal variability of the gridded temperature via the merging of temperature-sensitive tree-ring records.
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This study was supported by the National Natural Science Foundation of China (Grants 41175066, 41275076), China Meteorological Administration Special Public Welfare Research Fund (GYHY201306019), National Basic Research Program of China (2010CB950102), and China Postdoctoral Science Foundation (Grant 2014M550711). We acknowledge the International Tree-Ring Data Bank (ITRDB) from where we obtained the tree-ring data of North America (http://www.ncdc.noaa.gov/data-access/paleoclimatology-data/datasets/tree-ring). We thank all the data contributors and related scholars. The CRUTEM4v data were obtained from http://www.cru.uea.ac.uk/cru/data/temperature/, the Mlost data were from NOAA’s National Climatic Data Center (NCDC): ftp://ftp.ncdc.noaa.gov/pub/data/paleo/reconstructions/pcn/instrumental/MLOST/, Gistemp data were from http://data.giss.nasa.gov/gistemp/, and the CCSM4 simulation data were from http://www.cesm.ucar.edu/experiments/cesm1.0/#paleo.
The variables mentioned in Section 2.4 are listed and defined explicitly. First, we assume that the background field (referred to as the climate model-simulated gridded data) has N grids. Second, as the number of tree-ring sites is a dependent variable from grid to grid (as stated in Section 2.4), only those chronologies within the prescribed range are available, and thus, M chronologies at some time point can be assumed.
T a i : surface temperature of final analysis results at grid i.
T b i : surface temperature of background at grid i.
W: optimal weight matrix with N × M elements.
R: observation error covariance matrix. In this study, only diagonal elements are preserved, indicating that the errors of different tree rings are noncorrelated.
B: background error covariance matrix. This is computed from the covariance calculations based on a moving time window ensemble.
H: observation operator. In this study, it is used to interpolate the data in the grids at the tree-ring sites using a bilinear method; it can be regarded as a linear operator.
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Chen, X., Xing, P., Luo, Y. et al. Surface temperature dataset for North America obtained by application of optimal interpolation algorithm merging tree-ring chronologies and climate model output. Theor Appl Climatol 127, 533–549 (2017). https://doi.org/10.1007/s00704-015-1634-4
- Pacific Decadal Oscillation
- Error Covariance Matrix
- Atlantic Multidecadal Oscillation
- Merging Method
- Optimal Interpolation Scheme