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Large-scale climate history of the past millennium reconstructed solely from tree-ring data is prone to underestimate the amplitude of low-frequency variability. In this paper, we aimed at solving this problem by utilizing a novel method termed "MDVM", which was a combination of the ensemble empirical mode decomposition (EEMD) and variance matching techniques. We compiled a set of 211 tree-ring records from the extratropical Northern Hemisphere (30-90°N) in an effort to develop a new reconstruction of the annual mean temperature by the MDVM method. Among these dataset, a number of 126 records were screened out to reconstruct temperature variability longer than decadal scale for the period 850-2000 AD. The MDVM reconstruction depicted significant low-frequency variability in the past millennium with evident Medieval Warm Period (MWP) over the interval 950-1150 AD and pronounced Little Ice Age (LIA) cumulating in 1450-1850 AD. In the context of 1150-year reconstruction, the accelerating warming in 20th century was likely unprecedented, and the coldest decades appeared in the 1640s, 1600s and 1580s, whereas the warmest decades occurred in the 1990s, 1940s and 1930s. Additionally, the MDVM reconstruction covaried broadly with changes in natural radiative forcing, and especially showed distinct footprints of multiple volcanic eruptions in the last millennium. Comparisons of our results with previous reconstructions and model simulations showed the efficiency of the MDVM method on capturing low-frequency variability, particularly much colder signals of the LIA relative to the reference period. Our results demonstrated that the MDVM method has advantages in studying large-scale and low-frequency climate signals using pure tree-ring data.

Summer temperature extremes over the global land area were investigated by comparing 26 models of the fifth phase of the Coupled Model Intercomparison Project (CMIP5) with observations from the Goddard Institute for Space Studies (GISS) and the Climate Research Unit (CRU). Monthly data of the observations and models were averaged for each season, and statistics were calculated for individual models before averaging them to obtain ensemble means. The summers with temperature anomalies (relative to 1951-1980) exceeding 3σ (σ is based on the local internal variability) are defined as "extremely hot". The models well reproduced the statistical characteristics evolution, and partly captured the spatial distributions of historical summer temperature extremes. If the global mean temperature increases 2°C relative to the pre-industrial level, "extremely hot" summers are projected to occur over nearly 40% of the land area (multi-model ensemble mean projection). Summers that exceed 5σ warming are projected to occur over approximately 10% of the global land area, which were rarely observed during the reference period. Scenarios reaching warming levels of 3°C to 5°C were also analyzed. After exceeding the 5°C warming target, "extremely hot" summers are projected to occur throughout the entire global land area, and summers that exceed 5σ warming would become common over 70% of the land area. In addition, the areas affected by "extremely hot" summers are expected to rapidly expand by more than 25%/°C as the global mean temperature increases by up to 3°C before slowing to less than 16%/°C as the temperature continues to increase by more than 3°C. The area that experiences summers with warming of 5σ or more above the warming target of 2°C is likely to maintain rapid expansion of greater than 17%/°C. To reduce the impacts and damage from severely hot summers, the global mean temperature increase should remain low.