Assimilation of multiple data sets with the ensemble Kalman filter to improve forecasts of forest carbon dynamics.

The ensemble Kalman filter (EnKF) has been used in weather forecasting to assimilate observations into weather models. In this study, we examine how effectively forecasts of a forest carbon cycle can be improved by assimilating observations with the EnKF. We used the EnKF to assimilate into the terrestrial ecosystem (TECO) model eight data sets collected at the Duke Forest between 1996 and 2004 (foliage biomass, fine root biomass, woody biomass, litterfall, microbial biomass, forest floor carbon, soil carbon, and soil respiration). We then used the trained model to forecast changes in carbon pools from 2004 to 2012. Our daily analysis of parameters indicated that all the exit rates were well constrained by the EnKF, with the exception of the exit rates controlling the loss of metabolic litter and passive soil organic matter. The poor constraint of these two parameters resulted from the low sensitivity of TECO predictions to their values and the poor correlation between these parameters and the observed variables. Using the estimated parameters, the model predictions and observations were in agreement. Model forecasts indicate 15 380-15 660 g C/ m2 stored in Duke Forest by 2012 (a 27% increase since 2004). Parameter uncertainties decreased as data were sequentially assimilated into the model using the EnKF. Uncertainties in forecast carbon sinks increased over time for the long-term carbon pools (woody biomass, structure litter, slow and passive SOM) but remained constant over time for the short-term carbon pools (foliage, fine root, metabolic litter, and microbial carbon). Overall, EnKF can effectively assimilate multiple data sets into an ecosystem model to constrain parameters, forecast dynamics of state variables, and evaluate uncertainty.

Learning in multilevel games with incomplete information. I.

A model is presented of learning automata playing stochastic games at two levels. The high level represents the choice of the game environment and corresponds to a group decision. The low level represents the choice of action within the selected game environment. Both of these decision processes are affected by delays in the information state due to inherent latencies or to the delayed broadcast of state changes. Analysis of the intrinsic properties of this Markov process is presented along with simulated iterative behavior and expected iterative behavior. The results show that simulation agrees with expected behavior for small step lengths in the iterative map. A Feigenbaum diagram and numerical computation of the Lyapunov exponents show that, for very small penalty parameters, the system exhibits chaotic behavior.

Learning in multilevel games with incomplete information. II.

Multilevel games are abstractions of situations where decision makers are distributed in a network environment. In Part I of this paper, the authors present several of the challenging problems that arise in the analysis of multilevel games. In this paper a specific set up is considered where the two games being played are zero-sum games and where the decision makers use the linear reward-inaction algorithm of stochastic learning automata. It is shown that the effective game matrix is decided by the willingness and the ability to cooperate and is a convex combination of two zero-sum game matrices. Analysis of the properties of this effective game matrix and the convergence of the decision process shows that players tend toward noncooperation in these specific environments. Simulation results illustrate this noncooperative behavior.