Abstract. We present top-down constraints on global monthly N 2 O emissions for 2011 from a multi-inversion approach and an ensemble of surface observations. The inversions employ the GEOS-Chem adjoint and an array of aggregation strategies to test how well current observations can constrain the spatial distribution of global N 2 O emissions. The strategies include (1) a standard 4D-Var inversion at native model resolution (4 • × 5 • ), (2) an inversion for six continental and three ocean regions, and (3) a fast 4D-Var inversion based on a novel dimension reduction technique employing randomized singular value decomposition (SVD). The optimized global flux ranges from 15.9 Tg N yr −1 (SVDbased inversion) to 17.5-17.7 Tg N yr −1 (continental-scale, standard 4D-Var inversions), with the former better capturing the extratropical N 2 O background measured during the HIAPER Pole-to-Pole Observations (HIPPO) airborne campaigns. We find that the tropics provide a greater contribution to the global N 2 O flux than is predicted by the prior bottomup inventories, likely due to underestimated agricultural and oceanic emissions. We infer an overestimate of natural soil emissions in the extratropics and find that predicted emissions are seasonally biased in northern midlatitudes. Here, optimized fluxes exhibit a springtime peak consistent with the timing of spring fertilizer and manure application, soil thawing, and elevated soil moisture. Finally, the inversions reveal a major emission underestimate in the US Corn Belt in the bottom-up inventory used here. We extensively test the impact of initial conditions on the analysis and recommend formally optimizing the initial N 2 O distribution to avoid biasing the inferred fluxes. We find that the SVD-based approach provides a powerful framework for deriving emission information from N 2 O observations: by defining the optimal resolution of the solution based on the information content of the inversion, it provides spatial information that is lost when aggregating to political or geographic regions, while also providing more temporal information than a standard 4D-Var inversion.
Permutation entropy (PE), as one of the powerful complexity measures for analyzing time series, has advantages of easy implementation and high efficiency. In order to improve the performance of PE, some improved PE methods have been proposed through introducing amplitude information and distance information in recent years. Weighted-permutation entropy (W-PE) weight each arrangement pattern by using variance information, which has good robustness and stability in the case of high noise level and can extract complexity information from data with spike feature or abrupt amplitude change. Dispersion entropy (DE) introduces amplitude information by using the normal cumulative distribution function (NCDF); it not only can detect the change of simultaneous frequency and amplitude, but also is superior to the PE method in distinguishing different data sets. Reverse permutation entropy (RPE) is defined as the distance to white noise in the opposite trend with PE and W-PE, which has high stability for time series with varying lengths. To further improve the performance of PE, we propose a new complexity measure for analyzing time series, and term it as reverse dispersion entropy (RDE). RDE takes PE as its theoretical basis and combines the advantages of DE and RPE by introducing amplitude information and distance information. Simulation experiments were carried out on simulated and sensor signals, including mutation signal detection under different parameters, noise robustness testing, stability testing under different signal-to-noise ratios (SNRs), and distinguishing real data for different kinds of ships and faults. The experimental results show, compared with PE, W-PE, RPE, and DE, that RDE has better performance in detecting abrupt signal and noise robustness testing, and has better stability for simulated and sensor signal. Moreover, it also shows higher distinguishing ability than the other four kinds of PE for sensor signals.
The task of image reconstruction for an electrical capacitance tomography (ECT) system is to determine the permittivity distribution and hence the phase distribution in a pipeline by measuring the electrical capacitances between sets of electrodes placed around its periphery. In view of the nonlinear relationship between the permittivity distribution and capacitances and the limited number of independent capacitance measurements, image reconstruction for ECT is a nonlinear and ill-posed inverse problem. To solve this problem, a new image reconstruction method for ECT based on a least-squares support vector machine (LS-SVM) combined with a self-adaptive particle swarm optimization (PSO) algorithm is presented. Regarded as a special small sample theory, the SVM avoids the issues appearing in artificial neural network methods such as difficult determination of a network structure, over-learning and under-learning. However, the SVM performs differently with different parameters. As a relatively new population-based evolutionary optimization technique, PSO is adopted to realize parameters’ effective selection with the advantages of global optimization and rapid convergence. This paper builds up a 12-electrode ECT system and a pneumatic conveying platform to verify this image reconstruction algorithm. Experimental results indicate that the algorithm has good generalization ability and high-image reconstruction quality.
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