Application of a dual unscented Kalman filter for simultaneous state and parameter estimation in problems of surface‐atmosphere exchange

Abstract

A dual unscented Kalman filter (UKF) was used to assimilate net CO2 exchange (NEE) data measured over a spruce‐hemlock forest at the Howland AmeriFlux site in Maine, USA, into a simple physiological model for the purpose of filling gaps in an eddy flux time series. In addition to filling gaps in the measurement record, the UKF approach provides continuous estimates of model parameters and uncertainty. The process explicitly recognizes uncertainty in the measurement data and model structure, providing approximate, effectively optimal state and parameter estimates with less subjectivity than in many previous gap‐filling methods. The dual UKF is a recursive predictor‐corrector estimation method whereby noisy measurement data are used to continuously update nonlinear process model predictions of the desired states, in this case net ecosystem exchange, among others. Two parallel filters are run simultaneously in the dual approach, one for state and the other for parameter estimation. The unscented transformation employs a deterministic sampling of “sigma points” from the joint density that captures the first two moments of the distribution to the second order. Nonlinear process models are applied to these sigma points to propagate the joint density within the filter framework. The UKF estimate of annual NEE in 2000 at the Howland Forest totaled −296.4 ± 2.4 g carbon m−2 (mean ± standard deviation) using nocturnal data when the square root of the momentum flux (u*) exceeded 0.25 m s−1. This NEE value is about 9% higher than a previous estimate where gaps were filled by physiological models fitted to monthly, seasonal, and annual data. Model estimates are sensitive to the threshold set for accepting or rejecting nocturnal flux data (“u* threshold”), and we show that uncertainty in annual estimates is dominated by the choice of u* threshold.