A New Inverse Modeling Tool for Understanding Plant Drought Stress using Atmospheric ¹³C of CO₂ Measurements

B. Rastogi¹, C. Alden^1,2 and J.B. Miller³

¹Cooperative Institute for Research in Environmental Sciences (CIRES), University of Colorado, Boulder, CO 80309; 707-567-8793, E-mail: bharat.rastogi@noaa.gov
²LongPath Technologies, Inc., Boulder, CO 80309
³NOAA Global Monitoring Laboratory (GML), Boulder, CO 80305

Feedbacks related to exchanges of water and carbon between the atmosphere and the terrestrial biosphere are key uncertainties in our understanding of Earth’s climate. Of particular importance for climate projections is the response of diverse biomes to moisture stress due to increasing vapor pressure deficit and changing precipitation regimes, as well as responses to increasing atmospheric CO₂. The ¹³C:¹²C ratio of CO₂ (denoted as δ¹³C) is a proxy for plant water stress, since most plants favor the assimilation of ¹²CO₂ during photosynthesis by about 2%, and this “discrimination” is reduced under periods of moisture stress. While discrimination has been observed at the leaf and ecosystem scales for decades, recent studies have shown that atmospheric δ¹³C is sensitive to changes in plant response to water stress at regional to global scales. However, few studies have tried to formally assimilate δ¹³C within the context of an atmospheric inverse model to constrain regional-scale plant water stress. Here, we first examine the fundamental requirements that allow δ¹³C to constrain discrimination using a simple physical model that links observed changes in d¹³C to net ecosystem exchange, discrimination, and atmospheric mixing. We then present a novel and rigorous regional data assimilation system and test it using synthetic measurements from a network of highly calibrated CO₂ and δ¹³Catm measurements. The model simultaneously solves for net ecosystem exchange of CO₂ and discrimination fluxes that are optimally consistent with pseudo-measurements. We find that the model can resolve signals that are considerably smaller than the limits of the simple physical model. However, this improvement is contingent on the analytical uncertainty of measurements. We find that a dense network of highly calibrated measurements of δ¹³Catm can constrain regional-scale linkages between carbon and water fluxes between terrestrial ecosystems and the atmosphere.

Figure 1. A simple physical model showing the sensitivity of atmopsheric δ¹³C measurements to changing photosynthetic discrimination at a tall tower site in Maine. Here, different colors indicate different values of Net ecosytem exchange of CO₂ (NEE), and the shading represents variability in sensitivity to total surface flux (i.e., "footprints"). The model shows that the the sensitivity of atmopsheric δ¹³C to photosynthetic discrimination is additionally contingent on the mgnitude of NEE. Finally the dotted horizontal line shows a typical value of analytical uncertainty for the measurements.