Inference of emission rate using the inverse-dispersion method for the multi-source problem

The inverse-dispersion method (IDM) has been widely used to infer the emission rate of a spatially homogeneous and well-defined source (referred to as the single-source problem). To infer the emission rate of a spatially heterogeneous source (referred to as the multi-source problem), a large number of downwind concentration measurements usually need to be conducted. In this paper, with the evapotranspiration (ET) data obtained in a field-scale experiment, we evaluated the feasibility and accuracy of IDM for multi-source strength inference with only two downwind concentration measurements. Field ET in this experiment exhibited typical multi-source characteristics due to sequential irrigation plot by plot. Under such conditions, large errors existed in the ET estimation via conventional methods, such as the gradient method. This heterogeneous ET was inferred by IDM with two assumptions: (1) the magnitude of the plot ET decays exponentially with the date after irrigation, having a characteristic decay timescale τ; (2) the daily variation pattern of ET obeys normal distribution with an expectation μ and a standard deviation σ. The accuracy of the inferred ET was validated by the measured water vapor fluxes via eddy covariance system. Then, sensitivity analysis on τ and σ was conducted. We found that only σ had an obvious effect on the accuracy of the ET inference. Moreover, our analysis showed that it was better to make accurate measurements on the upwind concentration, which was essential to the reliability of the implementation of IDM.