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Results from the fully and biogeochemically coupled simulations in which CO2 increases at a rate of 1%yr-1 (1pctCO2) from its preindustrial value are analyzed to quantify the magnitude of carbon-concentration and carbon-climate feedback parameters which measure the response of ocean and terrestrial carbon pools to changes in atmospheric CO2 concentration and the resulting change in global climate, respectively. The results are based on 11 comprehensive Earth system models from the most recent uncertain over land than over ocean as has been seen in existing studies. These values and their spread from 11 CMIP6 models have not changed significantly compared to CMIP5 models. The absolute values of feedback parameters are lower for land with models that include a representation of nitrogen cycle. The transient climate response to cumulative emissions (TCRE) from the 11 CMIP6 models considered here is 1.77±0.37 ° C EgC-1 and is similar to that found in CMIP5 models (1.63±0.48 °C EgC-1) but with somewhat reduced model spread. The expressions for feedback parameters based on the fully and biogeochemically coupled configurations of the 1pctCO2 simulation are simplified when the small temperature change in the biogeochemically coupled simulation is ignored. Decomposition of the terms of these simplified expressions for the feedback parameters is used to gain insight into the reasons for differing responses among ocean and land carbon cycle models.

Realistic projection of future climate-carbon (C) cycle feedbacks requires better understanding and an improved representation of the C cycle in permafrost regions in the current generation of Earth system models. Here we evaluated 10 terrestrial ecosystem models for their estimates of net primary productivity (NPP) and responses to historical climate change in permafrost regions in the Northern Hemisphere. In comparison with the satellite estimate from the Moderate Resolution Imaging Spectroradiometer (MODIS; 246 ± 6 g C m−2 yr−1), most models produced higher NPP (309 ± 12 g C m−2 yr−1) over the permafrost region during 2000–2009. By comparing the simulated gross primary productivity (GPP) with a flux tower-based database, we found that although mean GPP among the models was only overestimated by 10% over 1982–2009, there was a twofold discrepancy among models (380 to 800 g C m−2 yr−1), which mainly resulted from differences in simulated maximum monthly GPP (GPPmax). Most models overestimated C use efficiency (CUE) as compared to observations at both regional and site levels. Further analysis shows that model variability of GPP and CUE are nonlinearly correlated to variability in specific leaf area and the maximum rate of carboxylation by the enzyme Rubisco at 25°C (Vcmax_25), respectively. The models also varied in their sensitivities of NPP, GPP, and CUE to historical changes in climate and atmospheric CO2 concentration. These results indicate that model predictive ability of the C cycle in permafrost regions can be improved by better representation of the processes controlling CUE and GPPmax as well as their sensitivity to climate change.

A realistic simulation of snow cover and its thermal properties are important for accurate modelling of permafrost. We analyse simulated relationships between air and near-surface (20 cm) soil temperatures in the Northern Hemisphere permafrost region during winter, with a particular focus on snow insulation effects in nine land surface models, and compare them with observations from 268 Russian stations. There are large cross-model differences in the simulated differences between near-surface soil and air temperatures (ΔT; 3 to 14 °C), in the sensitivity of soil-to-air temperature (0.13 to 0.96 °C °C-1), and in the relationship between ΔT and snow depth. The observed relationship between ΔT and snow depth can be used as a metric to evaluate the effects of each model's representation of snow insulation, hence guide improvements to the model's conceptual structure and process parameterisations. Models with better performance apply multilayer snow schemes and consider complex snow processes. Some models show poor performance in representing snow insulation due to underestimation of snow depth and/or overestimation of snow conductivity. Generally, models identified as most acceptable with respect to snow insulation simulate reasonable areas of near-surface permafrost (13.19 to 15.77 million km2). However, there is not a simple relationship between the sophistication of the snow insulation in the acceptable models and the simulated area of Northern Hemisphere near-surface permafrost, because several other factors, such as soil depth used in the models, the treatment of soil organic matter content, hydrology and vegetation cover, also affect the simulated permafrost distribution.

A significant portion of the large amount of carbon (C) currently stored in soils of the permafrost region in the Northern Hemisphere has the potential to be emitted as the greenhouse gases CO2 and CH4 under a warmer climate. In this study we evaluated the variability in the sensitivity of permafrost and C in recent decades among land surface model simulations over the permafrost region between 1960 and 2009. The 15 model simulations all predict a loss of near-surface permafrost (within 3 m) area over the region, but there are large differences in the magnitude of the simulated rates of loss among the models (0.2 to 58.8 × 103 km2 yr−1). Sensitivity simulations indicated that changes in air temperature largely explained changes in permafrost area, although interactions among changes in other environmental variables also played a role. All of the models indicate that both vegetation and soil C storage together have increased by 156 to 954 Tg C yr−1 between 1960 and 2009 over the permafrost region even though model analyses indicate that warming alone would decrease soil C storage. Increases in gross primary production (GPP) largely explain the simulated increases in vegetation and soil C. The sensitivity of GPP to increases in atmospheric CO2 was the dominant cause of increases in GPP across the models, but comparison of simulated GPP trends across the 1982–2009 period with that of a global GPP data set indicates that all of the models overestimate the trend in GPP. Disturbance also appears to be an important factor affecting C storage, as models that consider disturbance had lower increases in C storage than models that did not consider disturbance. To improve the modeling of C in the permafrost region, there is the need for the modeling community to standardize structural representation of permafrost and carbon dynamics among models that are used to evaluate the permafrost C feedback and for the modeling and observational communities to jointly develop data sets and methodologies to more effectively benchmark models.

Soil temperature (Ts/change is a key indicator of the dynamics of permafrost. On seasonal and interannual timescales, the variability of Ts determines the activelayer depth, which regulates hydrological soil properties and biogeochemical processes. On the multi-decadal scale, increasing Ts not only drives permafrost thaw/retreat but can also trigger and accelerate the decomposition of soil organic carbon. The magnitude of permafrost carbon feedbacks is thus closely linked to the rate of change of soil thermal regimes. In this study, we used nine process-based ecosystem models with permafrost processes, all forced by different observation-based climate forcing during the period 1960-2000, to characterize the warming rate of Ts in permafrost regions. There is a large spread of Ts trends at 20 cm depth across the models, with trend values ranging from 0.010 ± 0.003 to 0.031 ± 0.005 °C yr-1. Most models show smaller increase in Ts with increasing depth. Air temperature (Ta/and longwave downward radiation (LWDR) are the main drivers of Ts trends, but their relative contributions differ amongst the models. Different trends of LWDR used in the forcing of models can explain 61 % of their differences in Ts trends, while trends of Ta only explain 5 % of the differences in Ts trends. Uncertain climate forcing contributes a larger uncertainty in Ts trends (0.021 ± 0.008 °C yr-1, mean ± standard deviation) than the uncertainty of model structure (0.012 ± 0.001 °C yr-1/, diagnosed from the range of response between different models, normalized to the same forcing. In addition, the loss rate of near-surface permafrost area, defined as total area where the maximum seasonal active-layer thickness (ALT) is less than 3 m loss rate, is found to be significantly correlated with the magnitude of the trends of Ts at 1 m depth across the models (R D-0:85, P = 0:003), but not with the initial total nearsurface permafrost area (R =-0:30, P = 0:438). The sensitivity of the total boreal near-surface permafrost area to Ts at 1 m is estimated to be of-2.80 ± 0.67 million km2 °C-1. Finally, by using two long-term LWDR data sets and relationships between trends of LWDR and Ts across models, we infer an observation-constrained total boreal near-surface permafrost area decrease comprising between 39 ± 14 × 103 and 75 ± 14 × 103 km2 yr-1 from 1960 to 2000. This corresponds to 9-18 % degradation of the current permafrost area.

Soil temperature (Ts/change is a key indicator of the dynamics of permafrost. On seasonal and interannual timescales, the variability of Ts determines the activelayer depth, which regulates hydrological soil properties and biogeochemical processes. On the multi-decadal scale, increasing Ts not only drives permafrost thaw/retreat but can also trigger and accelerate the decomposition of soil organic carbon. The magnitude of permafrost carbon feedbacks is thus closely linked to the rate of change of soil thermal regimes. In this study, we used nine process-based ecosystem models with permafrost processes, all forced by different observation-based climate forcing during the period 1960-2000, to characterize the warming rate of Ts in permafrost regions. There is a large spread of Ts trends at 20 cm depth across the models, with trend values ranging from 0.010 ± 0.003 to 0.031 ± 0.005 °C yr-1. Most models show smaller increase in Ts with increasing depth. Air temperature (Ta/and longwave downward radiation (LWDR) are the main drivers of Ts trends, but their relative contributions differ amongst the models. Different trends of LWDR used in the forcing of models can explain 61 % of their differences in Ts trends, while trends of Ta only explain 5 % of the differences in Ts trends. Uncertain climate forcing contributes a larger uncertainty in Ts trends (0.021 ± 0.008 °C yr-1, mean ± standard deviation) than the uncertainty of model structure (0.012 ± 0.001 °C yr-1/, diagnosed from the range of response between different models, normalized to the same forcing. In addition, the loss rate of near-surface permafrost area, defined as total area where the maximum seasonal active-layer thickness (ALT) is less than 3 m loss rate, is found to be significantly correlated with the magnitude of the trends of Ts at 1 m depth across the models (R D-0:85, P = 0:003), but not with the initial total nearsurface permafrost area (R =-0:30, P = 0:438). The sensitivity of the total boreal near-surface permafrost area to Ts at 1 m is estimated to be of-2.80 ± 0.67 million km2 °C-1. Finally, by using two long-term LWDR data sets and relationships between trends of LWDR and Ts across models, we infer an observation-constrained total boreal near-surface permafrost area decrease comprising between 39 ± 14 × 103 and 75 ± 14 × 103 km2 yr-1 from 1960 to 2000. This corresponds to 9-18 % degradation of the current permafrost area.

Soil is currently thought to be a sink for carbon; however, the response of this sink to increasing levels of atmospheric carbon dioxide and climate change is uncertain. In this study, we analyzed soil organic carbon (SOC) changes from 11 Earth system models (ESMs) under the historical and high radiative forcing (RCP 8.5) scenarios between 1850 and 2100. We used a reduced complexity model based on temperature and moisture sensitivities to analyze the drivers of SOC losses. ESM estimates of SOC change over the 21st century (2090–2099 minus 1997–2006) ranged from a loss of 72 Pg C to a gain 253 Pg C with a multi-model mean gain of 63 Pg C. All ESMs showed cumulative increases in both NPP (15% to 59%) and decreases in SOC turnover times (15% to 28%) over the 21st century. Most of the model-to-model variation in SOC change was explained by initial SOC stocks combined with the relative changes in soil inputs and decomposition rates (R2 = 0.88,p