Improving the joint estimation of CO₂ and surface carbon fluxes using a Constrained Ensemble Kalman Filter in COLA (v1.0)

Atmospheric inversion of carbon dioxide (CO2) measurements to understand carbon sources and sinks has made great progress over the last two decades. However, most of the studies, including four-dimension variational (4D-Var), Ensemble Kalman filter (EnKF), and Bayesian synthesis approaches, obtains directly only fluxes while CO2 concentration is derived with the forward model as post-analysis. Kang et al. (2012) used the Local Ensemble Transform Kalman Filter (LETKF) that updates the CO2, surface carbon fluxes (SCF), and meteorology field simultaneously. Following this track, a system with a short assimilation window and a long observation window was developed (Liu et al., 2019). However, this system faces the challenge of maintaining global carbon mass. To overcome this shortcoming, here we introduce a Constrained Ensemble Kalman Filter (CEnKF) approach to ensure the conservation of global CO2 mass. After a standard LETKF procedure, an additional assimilation process is applied to adjust CO2 at each model grid point and to ensure the consistency between the analysis and the first guess of global CO2 mass. In the context of observing system simulation experiments (OSSEs), we show that the CEnKF can significantly reduce the annual global SCF bias from ~0.2 gigaton to less than 0.06 gigaton by comparing between experiments with and without it. Moreover, the annual bias over most continental regions is also reduced. At the seasonal scale, the improved system reduced the flux root-mean-square error from priori to analysis by 48–90 %, depending on the continental region. Moreover, the 2015–2016 El Nino impact is well captured with anomalies mainly in the tropics.

Modeling and Simulation of Vacuum Low Pressure Carburizing Process in Gear Steel

A combination of simulation and experimental approaches to optimize the vacuum carburizing process is necessary to replace the costly experimental trial-and-error method in time and resources. In order to accurately predict the microstructure evolution and mechanical properties of the vacuum carburizing process, a multi-field multi-scale coupled model considering the interaction of temperature, diffusion, phase transformation, and stress was established. Meanwhile, the improved model is combined with the heat treatment software COSMAP to realize the simulation of the low-pressure vacuum carburizing process. The low-pressure vacuum carburizing process of 20CrMo gear steel was simulated by COSMAP and compared with the experimental results to verify the model. The results indicated that the model could quantitatively obtain the carbon concentration distribution, Fe-C phase fraction, and hardness distribution. It can be found that the carbon content gradually decreased from the surface to the center. The surface carbon concentration is relatively high only after the carburizing stage. With the increase in diffusion time, the surface carbon concentration decreases, and the carburized layer depth increases. The simulated surface carbon concentration results and experimental results are in good agreement. However, there is an error between calculations and observations for the depth of the carburized layer. The error between simulation and experiment of the depth of carburized layer is less than 6%. The simulated surface hardness is 34 HV lower than the experimental surface hardness. The error of surface hardness is less than 5%, which indicates that the simulation results are reliable. Furthermore, vacuum carburizing processes with different diffusion times were simulated to achieve the carburizing target under specific requirements. The results demonstrated that the optimum process parameters are a carburizing time of 42 min and a diffusion time of 105 min. This provides reference and guidance for the development and optimization of the vacuum carburizing process.