A simple net ecosystem productivity model for gap filling of tower-based fluxes: An extension of Landsbergʹs equation with modifications to the light interception term

Net ecosystem productivity (NEP) is a key ecological variable in forestry and carbon sequestration sciences. Advances in eddy-covariance instrumentation in recent years have improved the accuracy to which productivity in ecosystems can be measured. However, equipment failure, power outages, system maintenance shutdowns, and inclement weather frequently introduce gaps in the measurement data stream, which can reduce the integrity, usefulness, and interpretation of the data. To compensate for these limitations, a simple NEP model with few automatically adjustable parameters is developed to improve gap filling of discontinuous time series. Initial model formulation and parameter-value determination are founded on 2004 growing-season NEP measurements collected at eight Fluxnet-Canada (FCRN) stations (i.e., eight ecosystems) from across Canadaʹs southern commercial forest zone. A preliminary inter-equation comparison of three commonly used flux equations, all with photosynthetically active radiation (PAR) as the independent variable, revealed that the three equations provided similar mean description of NEP. In this paper, we use Landsbergʹs equation [Landsberg, J.J., 1977. Some useful equations for biological studies. Exp. Agric. 13, 272–286] in modelling NEP. Initial parameter values of the Landsbergʹs equation were shown to depend on forest species composition, stand age, and existing site conditions. Further analysis indicated that on average for a 9-day period for the Atlantic Maritime balsam fir site in New Brunswick, Landsbergʹs equation represented mean NEP very well for cloudy days, but performed poorly when light conditions deviated from average conditions. We hypothesized that variation in the level of diffuse and direct radiation contributed to differences in light response. As Landsbergʹs equation does not explicitly address (i) light quality, i.e., level of diffuse to direct illumination, and (ii) vertical canopy structure, a simple NEP model combining Landsbergʹs equation with a two big-leaf (sunlit versus shade leaf model concept) and multiple-layer canopy light transmission formulation was developed for modelling the day-to-day variation in NEP and for gap filling. Results from these enhancements captured more of the NEP peaks (coefficient of determination, r2 = 0.70) than were previously modelled with the unaltered form of Landsbergʹs equation (r2 = 0.63). Model sensitivity analysis suggested partitioning the canopy in four canopy layers provided the best overall improvement in NEP calculations; beyond four layers, model improvement was minor.