Abstract.Bubbling is an important pathway of methane emissions from wetland ecosystems.However the concentration-based threshold function approach in current biogeochemistry models of methane is not sufficient to represent the complex ebullition process. Here we revise an extant process-based biogeochemistry model, the Terrestrial Ecosystem Model into a multi-substance model (CH 4 , O 2 , CO 2 and N 2 ) to simulate methane production, oxidation, and transport (particularly ebullition) with different model complexities. When ebullition is modeled with a concentrationbased threshold function and if the inhibition effect of oxygen on methane production and the competition for oxygen between methanotrophy and heterotrophic respiration are retained, the model becomes a two-substance system. Ignoring the role of oxygen, while still modeling ebullition with a concentration-based threshold function, reduces the model to a one-substance system. These models were tested through a group of sensitivity analyses using data from two temperate peatland sites in Michigan. We demonstrate that only the four-substance model with a pressure-based ebullition algorithm is able to capture the episodic emissions induced by a sudden decrease in atmospheric pressure or by a sudden drop in water table. All models captured the retardation effect on methane efflux from an increase in surface standing water which results from the inhibition of diffusion and the increase in rhizospheric oxidation. We conclude that to Correspondence to: J. Tang (tang16@purdue.edu) more accurately account for the effects of atmospheric pressure dynamics and standing water on methane effluxes, the multi-substance model with a pressure-based ebullition algorithm should be used in the future to quantify global wetland CH 4 emissions. Further, to more accurately simulate the pore water gas concentrations and different pathways of methane transport, an exponential root distribution function should be used and the phase-related parameters should be treated as temperature dependent.

Bubbling is an important pathway of methane emissions from wetland ecosystems; however the concentration-based threshold function approach in current biogeochemistry models of methane is not sufficient to represent the complex ebullition process. Here we revise an extant process-based biogeochemistry model, the Terrestrial Ecosystem Model into a multi-substance model (CH₄, O₂, CO₂ and N₂) to simulate methane production, oxidation, and transport (particularly ebullition) with different model complexities. When ebullition is modeled with a concentration-based threshold function and if the inhibition effect of oxygen on methane production and the competition for oxygen between methanotrophy and heterotrophic respiration are retained, the model is a two-substance system. Ignoring the role of oxygen, while still modeling ebullition with a concentration-based threshold function, reduces the model to a one-substance system. These models were tested through a group of sensitivity analyses at two temperate peatland sites in Michigan. We demonstrate that only the four-substance model with a pressure-based ebullition algorithm is able to capture the episodic emissions induced by a sudden decrease in atmospheric pressure. All models captured the retardation effect on methane efflux from an increase in surface standing water which results from the inhibition of diffusion and the increase in rhizospheric oxidation. We conclude that to more accurately account for the effects of atmospheric pressure dynamics and standing water on methane effluxes, the multi-substance model with a pressure-based ebullition algorithm should be used in the future to quantify global wetland CH₄ emissions. Further, to more accurately simulate the pore water gas concentrations and different pathways of methane transport, an exponential root distribution function should be used and the phase-related parameters should be treated as temperature dependent

Propagating correlations between on-line and off-line state variables in the problem of sequential inversion of surface fluxes for atmospheric CH<sub4</sub> is investigated with the fixed-lag Kalman smoother, the fixed-lag ensemble square root Kalman smoother and the fixed-lag square root sigma-point Kalman smoother. The formulae for the fixed-lag Kalman smoother in Bruhwiler et al. (2005) are further developed with a more concise representation of the posterior covariance. Extension to the fixed-lag ensemble square root Kalman smoother and fixed-lag square root sigma-point Kalman smoother allows us to treat nonlinear observation operators easily. To constrain the posterior fluxes within their feasible ranges, the constrained fixed-lag Kalman smoother is also presented, and the variable transform technique is implemented for the other two smoothers. Results with synthetic inversion of CH<sub4</sub> fluxes indicate that our developed methods are good alternatives to existing methods for conducting sequential inversion of atmospheric trace gases. It is also shown that the benefit of including the correlation between on-line and off-line state variables is case dependent

Abstract. A large amount of soil carbon in northern temperate and boreal regions could be emitted as greenhouse gases in a warming future. However, lacking detailed microbial processes such as microbial dormancy in current biogeochemistry models might have biased the quantification of the regional carbon dynamics. Here the effect of microbial dormancy was incorporated into a biogeochemistry model to improve the quantification for the last century and this century. Compared with the previous model without considering the microbial dormancy, the new model estimated the regional soils stored 75.9 Pg more C in the terrestrial ecosystems during the last century and will store 50.4 and 125.2 Pg more C under the RCP8.5 and RCP2.6 scenarios, respectively, in this century. This study highlights the importance of the representation of microbial dormancy in earth system models to adequately quantify the carbon dynamics in the northern temperate and boreal natural terrestrial ecosystems.

Abstract. The scheme to propagate correlations between online and off-line state variables in atmospheric inversions using the fixed-lag Kalman smoother proposed in Bruhwiler et al. (2005) is explained as a process to impose a balanced constraint on the on-line state variables. It is then extended to the fixed-lag ensemble square root Kalman smoother and fixed-lag square root sigma-point Kalman smoother, allowing us to treat nonlinear observation operators easily. Further, to constrain the posterior fluxes within their feasible ranges, the constrained fixed-lag Kalman smoother is presented and the variable transform technique is proposed for the other two smoothers. Comparisons between various methods and observational data are conducted using a synthetic inversion of atmospheric CH 4 fluxes. The results indicate that our developed methods are good alternatives to existing methods for conducting sequential inversion of atmospheric trace gases. It is also shown that the benefit to include the correlations between on-line and off-line state variables is case dependent.