How well can inverse analyses of high-resolution satellite data resolve heterogeneous methane fluxes? Observing system simulation experiments with the GEOS-Chem adjoint model (v35)

We perform observing system simulation experiments (OSSEs) with the GEOS-Chem adjoint model to test how well methane emissions over North America can be resolved using measurements from the TROPOspheric Monitoring Instrument (TROPOMI) and similar high-resolution satellite sensors. We focus analysis on the impacts of (i) spatial errors in the prior emissions and (ii) model transport errors. Along with a standard scale factor (SF) optimization we conduct a set of inversions using alternative formalisms that aim to overcome limitations in the SF-based approach that arise for missing sources. We show that 4D-Var analysis of the TROPOMI data can improve monthly emission estimates at 25 km even with a spatially biased prior or model transport errors (42 %–93 % domain-wide bias reduction; R increases from 0.51 up to 0.73). However, when both errors are present, no single inversion framework can successfully improve both the overall bias and spatial distribution of fluxes relative to the prior on the 25 km model grid. In that case, the ensemble-mean optimized fluxes have a domain-wide bias of 77 Gg d−1 (comparable to that in the prior), with spurious source adjustments compensating for the transport errors. Increasing observational coverage through longer-timeframe inversions does not significantly change this picture. An inversion formalism that optimizes emission enhancements rather than scale factors exhibits the best performance for identifying missing sources, while an approach combining a uniform background emission with the prior inventory yields the best performance in terms of overall spatial fidelity – even in the presence of model transport errors. However, the standard SF optimization outperforms both of these for the magnitude of the domain-wide flux. For the common scenario in which prior errors are non-random, approximate posterior error reduction calculations (derived via gradient-based randomization) for the inversions reflect the sensitivity to observations but have no spatial correlation with the actual emission improvements. This demonstrates that such information content analysis can be used for general observing system characterization but does not describe the spatial accuracy of the posterior emissions or of the actual emission improvements. Findings here highlight the need for careful evaluation of potential missing sources in prior emission datasets and for robust accounting of model transport errors in inverse analyses of the methane budget.

How well can inverse analyses of high-resolution satellite data resolve heterogeneous methane fluxes? Observation System Simulation Experiments with the GEOS-Chem adjoint model (v35)

We perform Observation System Simulation Experiments (OSSEs) with the GEOS-Chem adjoint model to test how well methane emissions over North America can be resolved using measurements from the TROPOspheric Monitoring Instrument (TROPOMI) and similar high-resolution satellite sensors. We focus analysis on the impacts of i) spatial errors in the prior emissions, and ii) model transport errors. Along with a standard scale-factor (SF) optimization we conduct a set of inversions using alternative formalisms that aim to overcome limitations in the SF-based approach that arise for missing sources. We show that 4D-Var analysis of the TROPOMI data can improve monthly emission estimates at 25 km even with a spatially biased prior or model transport errors (42–93 % domain-wide bias reduction; R increases from 0.51 up to 0.73). However, when both errors are present, no single inversion framework can successfully improve both the overall bias and spatial distribution of fluxes relative to the prior on the 25 km model grid. In that case, the ensemble-mean optimized fluxes have a domain-wide bias of 77 Gg/d (comparable to that in the prior), with spurious source adjustments compensating for the transport errors. Increasing observational coverage through longer-timeframe inversions does not significantly change this picture. An inversion formalism that optimizes emission enhancements rather than scale factors exhibits the best performance for identifying missing sources, while an approach combining a uniform background emission with the prior inventory yields the best performance in terms of overall spatial fidelity—even in the presence of model transport errors. However, the standard SF optimization outperforms both of these for the magnitude of the domain-wide flux. For the common scenario in which prior errors are non-random, approximate posterior error reduction calculations for the inversions reflect the sensitivity to observations but have no spatial correlation with the actual emission improvements. This demonstrates that such information content analysis can be used for general observing system characterization but does not describe the spatial accuracy of the posterior emissions or of the actual emission improvements. Findings here highlight the need for careful evaluation of potential missing sources in prior emission datasets and for robust accounting of model transport errors in inverse analyses of the methane budget.

On the use of inverse modeling to improve subsurface drainage simulations

<p>The application of inverse modeling approaches has been expanded to the field of hydrology this last decade. Here, the inverse modeling has been used to adjust the input parameters of a new agricultural subsurface drainage model (SIDRA-RU) using observations of the model output. SIDRA-RU is a semi-conceptual and semi-analytical model that transforms the rainfall into a daily drainage discharge. The model is divided into two modules. The first one consists of a conceptual reservoir that converts the net rainfall into recharge; the second module simulates the drainage discharge and the water table level above the mid-drains, based on the resolution of the Boussinesq equation.</p><p>The adjoint model of SIDRA-RU has been successfully generated by means of the automatic differentiation tool (TAPENADE). First, this adjoint model is used to explore the local and global adjoint sensitivities of the valuable function defined over the drainage discharge simulations (model output), with respect to the model input parameters. Next, the most influential parameters are estimated using both the classical calibration algorithm (PAP-GR) and the variational data assimilation method (4D-VAR). For the latter method, a simple stochastic procedure has been proposed to avoid trapping the minimization process in the local minimum points.</p><p>Our results have shown that the quality of the drainage discharge simulations obtained using the 4DVAR method is better than the ones performed by the PAP-GR calibration algorithm, in terms of the water balance in particular. Indeed, less than 5 mm of the cumulative discrepancy was registered between simulated and observed water volume based on the five-year daily drainage discharge data of the Chantemerle agricultural field. However, some numerical tests, conducted to investigate the convergence of the variational calibration method, indicate the potential presence of the equifinality issues. This could be highlighted by the self-compensation of the physical soil parameters (K<sub>sat</sub> and µ) and those managing the conceptual SIDRA-RU reservoir (S<sub>inter</sub> and SSDI). The performed sensitivity analysis has shown that the parameters having the most impact on the drainage discharge are those controlling the nervousness and recession of the water level in soils followed by those managing the start of the drainage season.</p>

High-resolution hybrid inversion of IASI ammonia columns to constrain US ammonia emissions using the CMAQ adjoint model

Ammonia (NH3) emissions have large impacts on air quality and nitrogen deposition, influencing human health and the well-being of sensitive ecosystems. Large uncertainties exist in the “bottom-up” NH3 emission inventories due to limited source information and a historical lack of measurements, hindering the assessment of NH3-related environmental impacts. The increasing capability of satellites to measure NH3 abundance and the development of modeling tools enable us to better constrain NH3 emission estimates at high spatial resolution. In this study, we constrain the NH3 emission estimates from the widely used 2011 National Emissions Inventory (2011 NEI) in the US using Infrared Atmospheric Sounding Interferometer NH3 column density measurements (IASI-NH3) gridded at a 36 km by 36 km horizontal resolution. With a hybrid inverse modeling approach, we use the Community Multiscale Air Quality Modeling System (CMAQ) and its multiphase adjoint model to optimize NH3 emission estimates in April, July, and October. Our optimized emission estimates suggest that the total NH3 emissions are biased low by 26 % in 2011 NEI in April with overestimation in the Midwest and underestimation in the Southern States. In July and October, the estimates from NEI agree well with the optimized emission estimates, despite a low bias in hotspot regions. Evaluation of the inversion performance using independent observations shows reduced underestimation in simulated ambient NH3 concentration in all 3 months and reduced underestimation in NH4+ wet deposition in April. Implementing the optimized NH3 emission estimates improves the model performance in simulating PM2.5 concentration in the Midwest in April. The model results suggest that the estimated contribution of ammonium nitrate would be biased high in a priori NEI-based assessments. The higher emission estimates in this study also imply a higher ecological impact of nitrogen deposition originating from NH3 emissions.

Development of four-dimensional variational assimilation system based on the GRAPES–CUACE adjoint model (GRAPES–CUACE-4D-Var V1.0) and its application in emission inversion

In this study, a four-dimensional variational (4D-Var) data assimilation system was developed based on the GRAPES–CUACE (Global/Regional Assimilation and PrEdiction System – CMA Unified Atmospheric Chemistry Environmental Forecasting System) atmospheric chemistry model, GRAPES–CUACE adjoint model and L-BFGS-B (extended limited-memory Broyden–Fletcher–Goldfarb–Shanno) algorithm (GRAPES–CUACE-4D-Var) and was applied to optimize black carbon (BC) daily emissions in northern China on 4 July 2016, when a pollution event occurred in Beijing. The results show that the newly constructed GRAPES–CUACE-4D-Var assimilation system is feasible and can be applied to perform BC emission inversion in northern China. The BC concentrations simulated with optimized emissions show improved agreement with the observations over northern China with lower root-mean-square errors and higher correlation coefficients. The model biases are reduced by 20 %–46 %. The validation with observations that were not utilized in the assimilation shows that assimilation makes notable improvements, with values of the model biases reduced by 1 %–36 %. Compared with the prior BC emissions, which are based on statistical data of anthropogenic emissions for 2007, the optimized emissions are considerably reduced. Especially for Beijing, Tianjin, Hebei, Shandong, Shanxi and Henan, the ratios of the optimized emissions to prior emissions are 0.4–0.8, indicating that the BC emissions in these highly industrialized regions have greatly reduced from 2007 to 2016. In the future, further studies on improving the performance of the GRAPES–CUACE-4D-Var assimilation system are still needed and are important for air pollution research in China.

Analysis of the Influence of Trace Point Step-Jump Behavior

To explore the influence of the trace point step-jump behavior on a terminal guidance system, an analysis is performed from the line-of-sight rate (LOS rate) and guidance accuracy views for designing an anti-step-jump guidance law. First, the linear terminal guidance model under the trace point jump circumstance is constructed, and then the fundamental reason for the miss distance is investigated by deriving the upper bound of the LOS rate at the initial step-jump moment. Following this, the novel proposed analytical differential adjoint model is established with the adjoint method, and its validity is demonstrated comparing with the numeric derivative model. Based on the adjoint model, the effects of the ratio coefficient, the time constant, and the jump amplitude on the guidance accuracy are explored. Finally, a novel anti-step-jump guidance law is designed to shorten the recovery time of the overload. The simulations have shown that the faster recovery time and higher accuracy are achieved in comparison with the proportional navigation guidance, optimal guidance, and adaptive sliding mode guidance.