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Stochastic Diffusion Model for Estimating Trace Gas Emissions with Static Chambers

^a Department of Biostatistics, University of Aarhus, Vennelyst Boulevard 6, DK-8000 Aarhus C, Denmark
^b Department of Crop Physiology and Soil Science, Danish Institute of Agricultural Sciences, Research Centre Foulum, P. O. Box 50, DK-8830 Tjele, Denmark

View larger version (6K): [in a new window]   Fig. 1. (a) An example of the deterministic diffusion model. (b) An arbitrary simulated trajectory from the stochastic extension of the model in (a). (c) Simulated trace gas concentrations extracted from the trajectory in (b)

View larger version (13K): [in a new window]   Fig. 2. Linear regression systematically underestimates the true emission rate when the concentration curve exhibits declining gradients. Unfortunately, the nonlinearity cannot be detected by means of R2, when only three measurement time points are used. For the fictive data in the plot,

View larger version (24K): [in a new window]   Fig. 3. Measured N2O concentrations (µL L-1 N2O) against time (minutes) since deployment. The number (1–5) at each curve is for identification

View larger version (9K): [in a new window]   Fig. 4. Model evaluation for the chamber Low GWL-3 in the September data set. (a) The solid curve is the estimated expected values for Eq. [8], and the slopes of the lines are the emission rates estimated by linear regression (dashed) and the method based on Eq. [8] (dotted). (b) Quantile plot of the estimated uniform residuals. If Eq. [8] is a valid model for the data, the points should be scattered unsystematically around the identity line

View larger version (13K): [in a new window]   Fig. 5. An arbitrary simulated trajectory from Eq. [8] with parameter values given by the average of the values for the 10 plots in the two data sets. The solid line is the corresponding deterministic model curve given by Eq. [1]. Time is measured in minutes since deployment, and the concentration is measured in µL L-1 N2O

View larger version (15K): [in a new window]   Fig. 6. Estimated N2O emission rates (Table 2) plotted against water-filled pore space at 5- to 10-cm depth