When solving inverse modeling problems (including emission sources identification problems), measurement operators link variables of the mathematical model of the considered processes with the measured values. Along with linear measurement operators (e.g. in situ point measurements of concentrations, integral measurements in time, total column measurements, etc.), nonlinear measurement operators are also used in air quality assessment and forecasting problems. In particular, such operators arise in remote sensing data processing. The objective of the work is to demonstrate the extension of the approach based on sensitivity operators and adjoint ensembles to the inverse problems with nonlinear measurement operators.
Three-dimensional models allow realistic modeling of atmospheric transport and transformation processes, but at the same time require a large amount of a priori data to set model parameters and significant computational resources to solve inverse modeling tasks. Emission sources identification problem is a key inverse modeling task for the air quality studies. In the paper we numerically evaluate in a realistic regional scenario an emission source identification algorithm based on sensitivity operators and adjoint equations solution ensembles for a three-dimensional case and image-type concentration measurements.
KEYWORDS: Data modeling, Inverse problems, Atmospheric modeling, Atmospheric chemistry, Algorithm development, Reconstruction algorithms, Chemical elements, Chemical species
Data assimilation algorithms are an important part of modern air quality modeling techniques. To study the real-time operation mode features of the data assimilation algorithms we numerically compare its performance to the solution in the “inverse problem mode”, when the same set of data is available “at once”. The objective of the paper is to compare the gradient-based (variational) and derivative-free solvers in the data assimilation mode to the solution of the reference inverse problem of reconstructing unobservable chemical species concentrations for the atmospheric chemistry model with a derivative-free solver.
KEYWORDS: Data modeling, Inverse problems, Atmospheric chemistry, Atmospheric modeling, Algorithm development, Chemical elements, Data acquisition, Process modeling, Mathematical modeling
The development of efficient data assimilation algorithms for atmospheric chemistry models is an important part of modern air quality studies. In the data assimilation framework considered, the identification of the chosen model parameters is used to continue the model state function to the unobservable part of the domain. This continuation problem is solved sequentially on the set of time intervals called the data assimilation windows. The framework is illustrated on a low-dimensional atmospheric chemistry model.
We discuss the issues of solving a wide range of environmental forecasting and design problems, which are formulated as mathematical continuation problems. Our approach's main idea is that we improve the quality of state function recovery by applying sensitivity theory methods, solving inverse problems, and data assimilation problems. This approach is demonstrated for the urban air quality problem in the example of the city of Novosibirsk.
The algorithm for source identification and concentration field reconstruction problems for an atmospheric chemistry transport and transformation model is tested with combined in situ and remote sensing data. It is based on the ensembles of the adjoint problem solutions and the sensitivity operators. Novosibirsk city traffic emissions inverse modeling scenario is used to test the algorithm.
KEYWORDS: In situ metrology, Remote sensing, Air contamination, Data modeling, Inverse problems, Atmospheric modeling, Atmospheric chemistry, Systems modeling, Chemical analysis
The results of the inverse source problem solution for an atmospheric chemistry transport and transformation model for in situ and remote sensing measurement data are compared. The algorithm based on the ensembles of the adjoint problem solutions is applied to solve the inverse problem. The solutions are compared in the Novosibirsk city inverse modeling scenario.
The efficiency of the variational chemical data assimilation algorithm is evaluated in a scenario for the city of Novosibirsk. In the algorithm the data assimilation is carried out quasi-independently on the different stages of the splitting scheme of the chemical transport model. RADM2 chemical reaction scheme is selected as the atmospheric chemistry reaction mechanism. Monitoring data is available in the limited number of the monitoring sites and for the limited number of species.
KEYWORDS: Data modeling, Atmospheric modeling, Atmospheric chemistry, Inverse problems, Mathematical modeling, Chemical elements, Algorithms, Systems modeling, Reconstruction algorithms, Algorithm development
The algorithm of source identification for atmospheric chemistry transformation models with the measurement data in the form of time series is tested numerical in the scenario with the second generation regional acid deposition model chemical mechanism. The algorithm is based on the sensitivity operator that is constructed from the ensemble of the adjoint equation solutions. This operator allows to apply algorithms for the solution of nonlinear operator equations for the solution of the inverse problem. The objective of the paper is to numerically evaluate the ability of the algorithm to solve the realistic inverse source problems with the mechanism.
The variational data assimilation algorithm for the atmospheric chemistry transport and transformation model is applied to the airborne sensing profiles of chemical substances concentration. The data assimilation is performed quasiindependently on the separate stages of the splitting scheme. For the linear transport stage the direct algorithm is used. In the nonlinear transformation stage an iterative gradient-type one is applied. In the numerical experiment the realistic scenario of vertical ozone concentration profiles assimilation has been considered.
The verification of the results of numerical simulation of the distribution of anthropogenic emissions of the Norilsk industrial zone using the WRF-CHEM model using airborne sounding data carried out in 13 August 2004 was carried out. The results of numerical modelling of the distribution of the concentration of sulphur dioxide, ozone and mass concentration of aerosol reproduce qualitatively the distributions obtained during airborne sounding. Quantitative estimates showed that the root-mean-square error for sulphur dioxide, the mass concentration of aerosol PM2.5 and ozone, calculated for all three flights, was 36 ppb, 3.4 μg/m3, 7.7 ppb, respectively.
Calculation results with algorithm reconstitution of vertical ozone source profile, shows that in inside daily period, in background areas of West Siberia, photo-chemical ozone formation prevailing above ozone inflow process from overlying stratum.
The performance of variational data assimilation algorithm for in situ concentration measurements for transport and transformation model of atmospheric chemical composition is studied numerically in the case of indirect measurements. The algorithm is based on decomposition and splitting methods with direct solution of data assimilation problems for splitting stages. This design allows avoiding iterative processes and working in real-time. In the numerical experiments we study the sensitivity of data assimilation results to variations of measurement data quality and quantity.
Atmospheric chemistry dynamics is studied with convection-diffusion-reaction model. The numerical Data Assimilation algorithm presented is based on the additive-averaged splitting schemes. It carries out ''fine-grained'' variational data assimilation on the separate splitting stages with respect to spatial dimensions and processes i.e. the same measurement data is assimilated to different parts of the split model. This design has efficient implementation due to the direct data assimilation algorithms of the transport process along coordinate lines. Results of numerical experiments with chemical data assimilation algorithm of in situ concentration measurements on real data scenario have been presented. In order to construct the scenario, meteorological data has been taken from EnviroHIRLAM model output, initial conditions from MOZART model output and measurements from Airbase database.
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