Radiocarbon Reconstruction Evaluated by the E3SM Land Model

Radiocarbon (¹⁴C) is a powerful tracer of the global carbon cycle that is commonly used to assess carbon cycling rates in various Earth system reservoirs and as a benchmark to assess climate model performance. Therefore, it has been recommended that Earth System Models (ESMs) participating in the Coupled Model Intercomparison Project Phase 6 (CMIP6) report predict ¹⁴C values for relevant carbon pools. However, a detailed representation of ¹⁴C dynamics may be an impractical burden on model developers. In a recent Journal of Advances in Modeling Earth Systems (JAMES) paper, Metzler et al. (2020), scientists presented an alternative approach to compute ¹⁴C values from the numerical output of an ESM that does not explicitly represent these dynamics. Researchers evaluated their approach using the E3SM land model (ELMv1) (Chen et al., 2019; Zhu et al., 2019; Riley et al., 2018).

Background

Terrestrial ecosystems, and soils in particular, are important global carbon (C) reservoirs but have large uncertainties in the size of the stock, process rates, and their representation in Earth System Models. The dynamics of ¹⁴C in various components of terrestrial ecosystems can be used to interpret the rates at which (1) CO₂ is removed from the atmosphere into plants through photosynthesis, (2) CO₂ moves from vegetation into soils through litter fall and mortality, and (3) CO₂ cycles back to the atmosphere via respiration. As a result, ¹⁴C has been used in many empirical studies to evaluate rates of soil C cycling and, more recently, as a tool for model evaluation (Ahrens et al., 2015; Chen et al., 2019; Dwivedi et al., 2017) and intercomparison (He et al., 2016).

Linear response theory suggests that the impulse response function of a particular model can be used to compute isotope dynamics without explicitly simulating the isotope within the model but rather using the response function to convolve the isotope tracers (Thompson & Randerson, 1999). Therefore, it may not be necessary to explicitly represent isotope dynamics a priori in a model; rather, they can be obtained a posteriori through the convolution procedure. However, linear response theory relies on assumptions of steady‐state and model linearity, which are not met for the type of transient simulations performed with ESMs.

Metzler et al. (2018) recently developed a method to obtain a mathematical object, the state‐transition matrix, which generalizes response function theory for nonlinear models out of equilibrium. This approach removes previous assumptions that prevented the use of the linear response approach for the computation of isotope and tracer dynamics a posteriori from simulations. Therefore, the state‐transition matrix approach offers an opportunity to compute isotope dynamics from models that do not explicitly represent them and could be applied to models participating in CMIP6, for example. Since output from these models is provided in discrete time steps often much larger than the internal model time step, it is a challenge to translate the state‐transition‐matrix approach from the continuous to the discrete case. In the recently-published Metzler et al. (2020) paper, however, scientists extended the Metzler et al. (2018) method to the discrete‐time case and applied it to reconstruct tracer and isotope dynamics from model output.

Approach

Carbon cycle models are subject to the law of mass conservation and therefore can be represented as compartmental systems. The JAMES paper approach required computed ¹²C stocks and fluxes among all carbon pools for a particular simulation of the model. From this output, a time‐dependent linear compartmental system was computed with its respective state‐transition matrix. Using transient atmospheric ¹⁴C values as inputs, the state‐transition matrix was then applied to compute ¹⁴C values for each pool, the average value for the entire system, and component fluxes.

Researchers demonstrated the approach with ELMv1‐ECA, an alternative version of E3SM’s land model that explicitly represents ¹²C and ¹⁴C in seven soil pools and 10 vertical layers, making it an appropriate test case to evaluate the proposed method.

Δ¹⁴C values in the different pools aggregated for all depths through time (Lines: ELMv1‐ECA; dots: DTA using 10‐day time step). Sites (top to bottom): boreal, temperate, and tropical forests. CWD is coarse woody debris. Litters 1, 2, and 3 denote metabolic, cellulose, and lignin litters. Soils 1, 2, and 3 are fast, intermediate, and passive soil pools. Atmospheric Δ¹⁴C values (blue) increase in response to nuclear bomb testing in the 1960s. Faster cycling pools respond more rapidly to the atmospheric Δ¹⁴C changes. Slower cycling pools show a lagged and damped response. Differences in DTA and ELMv1‐ECA modeled values are imperceptible in this figure.

Relative error in ¹⁴C values for coarse woody debris (CWD), aggregated litter, and soil pools over time for the temperate forest site. ¹⁴C relative error is approximately two orders of magnitude larger than ¹²C error but is always small in comparison to model uncertainty and spatial heterogeneity (Chen et al., 2019; Lawrence et al., 2019). The largest biases in the litter pool follow the bomb spike in atmospheric ¹⁴C concentrations and vary seasonally.

Results

Results from the proposed method are highly accurate (relative error <0.01%) compared with the ELMv1‐ECA ¹²C and ¹⁴C predictions, demonstrating the potential to use this approach in CMIP6 and other model simulations that do not explicitly represent ¹⁴C. Since comparisons against observations indicate that ESM land models inaccurately predict soil carbon (C) turnover, this approach provides a framework to improve process representations affecting these biases.

Publication

• Metzler, H., Zhu, Q., Riley, W., Hoyt, A., Müller, M., & Sierra, C. (2020).  Mathematical Reconstruction of Land Carbon Models From Their Numerical Output: Computing Soil Radiocarbon From C Dynamics. Journal of Advances in Modeling Earth Systems, 12(1). https://doi.org/10.1029/2019ms001776.

Additional References

• Holm, J. A., R. G. Knox, A. J. N. Lima, C. D. Koven, M. Longo, W. J. Riley, R. I. Negron-Juarez, A. C. d. Araujo, A. Manzi, L. M. Kueppers, P. R. Moorcroft, N. Higuchi, and J. Q. Chambers (2020), The Central Amazon forest sink under current and future atmospheric CO₂: Predictions from big-leaf and demographic vegetation models, JGR-Biogeosciences, https://doi.org/10.1029/2019JG005500.
• Zhu, Q., W. J. Riley, C. M. Iversen, and J. Kattge (2020), Assessing impacts of plant stoichiometric traits on terrestrial ecosystem carbon accumulation using the E3SM land model, J. of Advances in Modeling Earth Systems, https://doi.org/10.1029/2019MS001841.
• Chen, J., Q. Zhu, W. J. Riley, Y. He, J. T. Randerson, and S. E. Trumebore (2019), Comparison with Global Soil Radiocarbon Observations Indicates Needed Carbon Cycle Improvements in the E3SM Land Model, JGR-Biogeosciences, https://doi.org/10.1029/2018JG004795.
• Zhu, Q., W. J. Riley, J. Y. Tang, J. R. Randerson, N. Collier, F. M. Hoffman, X. Yang, and G. Bisht (2019), Representing nitrogen, carbon, and phosphorus interactions in the ELMv1-ECA Land Model: Model development and global benchmarking, J. of Advances in Modeling Earth Systems, https://doi.org/10.1029/2018MS001571.
• Riley, W. J., Q. Zhu, and J. Y. Tang (2018), Weaker land-climate feedbacks from nutrient uptake during photosynthesis-inactive periods, Nature Climate Change, https://doi.org/10.1038/s41558-018-0325-4.

Funding

• The U.S. Department of Energy Office of Science, Biological and Environmental Research supported this research as part of the Earth System Model Development program area through the Energy Exascale Earth System Model (E3SM) project. Additional funding came from the Regional & Global Model Analysis program area through the Reducing Uncertainty in Biogeochemical Interactions through Synthesis and Computation (RUBISCO) Scientific Focus Area (SFA)

Contact

• William J. Riley, Lawrence Berkeley National Laboratory