Inverse estimation of Vcmax, leaf area index, and the Ball-Berry parameter from carbon and energy fluxes

Canopy fluxes of CO2 and energy can be modeled with high fidelity using a small number of environmental variables and ecosystem parameters. Although these ecosystem parameters are critically important for modeling canopy fluxes, they typically are not measured with the same intensity as ecosystem fluxes. We developed an algorithm to estimate leaf area index (LAI), maximum carboxylation velocity (Vc(max)), the Ball-Berry parameter (m), and substrate-dependent ecosystem respiration rate (beta(A)) by inverting a commonly used modeling paradigm of canopy CO2 and energy fluxes. To test this algorithm, fluxes of sensible heat (H), latent heat (LE), and CO2 (Fc) were measured with eddy covariance techniques in a pristine grassland-forb steppe site in northern Kazakhstan. We applied the algorithm to these data and identified ecosystem characteristics consistent with data across a time series of meteorological drivers from the Kazakhstan data. LAI was calculated by fitting the model to measured H + LE, Vc(max) and beta(A) were solved simultaneously by fitting the model to measured CO2 fluxes, and m was calculated by varying the partitioning of available energy between H and LE. Seasonal changes in LAI ranged from 2.0 to 2.4, Vc(max) declined from 20 to 5 mu mol CO2 m(-2) s(-1), respiration as a percentage of assimilation ranged from 0.5 to 0.75, and m varied from 17 to 24. Our results with the Kazakhstan data showed that LAI, Vc(max), ecosystem respiration, and m can be solved to accurately predict (R-2 = 80 to 95%) carbon and energy fluxes with nonsignificant bias at 20-min and daily timescales. The ecosystem characteristics calculated in our study were consistent with independent measurements of the seasonal dynamics of a shortgrass steppe in Kazakhstan and with values published in the literature. These characteristics were closely linked to mean daily fluxes of CO2 but were not dependent on the environmental drivers for the periods they were measured. We conclude that process model inversion has potential for comparing CO2 and energy fluxes among different ecosystems and years and for providing important ecosystem parameters for evaluating climatic influences on CO2 and energy fluxes.