Sensitivity Operator Framework for Analyzing Heterogeneous Air Quality Monitoring Systems
Abstract
:1. Introduction
2. Materials and Methods
2.1. Chemical Transport Model
- We suppose that only a given set of species is emitted. For the rest of species , .
- The emission sources are supposed to be constant in time ().
- We do not require the emission sources to be positive since variables unconsidered in the model, chemical transformations, various land types, and meteorological conditions, such as rains and snowfalls, can act as sinks for the specific chemicals.
- In the Inverse problem, the uncertainty function has to be identified from the partial information (“measurement data”) about , described in Section 2.3.
2.2. Sensitivity-Operator Based Representation of Measurement Data
2.3. Measurement Data Types
- “Timeseries”: time series of concentrations of the specific species in the specific points. In the state function terms:Projection system:For any element of , the parameter ranges from 0 to . The number of the frequencies is the parameter of the projection system. This parameter is responsible for the temporal resolution of the considered data. Hence the total number of projection functions corresponding to the Timeseries is
- “Pointwise”: Pointwise concentration measurements of the specific species at specific moments and specific points. In the state function terms:Projection system:The projection system is naturally defined by the measurement points. Hence the total number of the projection functions is . In the case of a large number of points, these data can be aggregated.
- “Integral”: Integrals of concentrations over the time interval of the specific species in the specific points. In the state function terms:Projection system:Here . Integral measurements are equivalent to “Timeseries” measurements with .
- “Snapshot”: specific species concentration fields images at specific moments in time. In the state function terms:Projection system:The projection system has two parameters: and , which define the spatial resolution of the considered data. For any image, and range in and , respectively. Hence .
2.4. Sensitivity-Operator-Based Analysis of Measurement System
2.4.1. Inverse Problem Solution
- (1)
- The “exact” solution is given. In our case, this is the location and capacity of the emission sources.
- (2)
- The “exact” solution is then used to simulate the “measurement data“. This “measurement data” is used in the algorithm to solve the inverse problem.
- (3)
- The result of the algorithm is compared with the “exact” solution. In this case, both the reconstruction of the source is estimated, and the convergence parameters of the algorithm are analyzed.
2.4.2. Sensitivity Operator Properties Analysis
2.5. Inverse Modeling Scenario
- Geographical domain.
- Monitoring system characteristics: locations and accuracy.
- Main emission sources to construct the “exact” solution.
- Chemical transformation mechanism, initial, and boundary conditions.
- Meteorological conditions, determining CTM model coefficients.
3. Results
3.1. Heterogeneous Measurements
3.2. Specific Measurement Types
3.3. Accuracy of the Reconstruction’s Prediction
- Red: Section 3.1, “realistic” source case;
- Green: Section 3.1, “single” source case;
- Blue: Section 3.1, “unified” source case;
- Black: Section 3.2, Timeseries experiment;
- Cyan: Section 3.2, Pointwise experiment;
- Magenta: Section 3.2, Snapshot experiment.
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
BNT | Baikal Natural Territory |
SVD | Singular value decomposition |
COSMO | Consortium for Small-scale Modeling |
CTM | Chemical transport model |
Appendix A. Newton–Kantorovich-Type Algorithm
Algorithm A1 Newton–Kantorovich-type Algorithm |
|
Appendix B. Projection Equivalence
Appendix C. Chemical Transformation Model (Leighton Relationship-Based)
Appendix D. The Description of the Meteorological Scenario
- 23.07 Rain zone in the foothills of the Altai, in the Kuzbass. The cold front from the west offset to the east. There is practically no leading stream. Weak variable wind in the west of Lake Baikal.
- 24.07 Rain zone in the foothills of Altai-Sayan (Khakassia), Western Sayan (Daily precipitation HMS 29698 Nizhneudinsk-57mm). With the approach of a cold front from the west, the wind is mainly south-easterly.
- 25.07 The rain zone encircles the Western Sayans from the north. Cold front, offset to the east, the wind weakens and changes direction to mainly western.
- 26.07 The cold front approaches the Hangar from the west. Baikal, in the warm sector orographically cut off in the south (baric depression, thunderstorms south and north of Lake Baikal).
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Type | Description | ||
---|---|---|---|
Pointwise | 60 | 60 | |
Timeseries | 60 | 6 | |
Integral | 5 | 5 | |
Snapshot | 625 | 1 | |
Composite | 750 | Sum of the above |
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Penenko, A.; Penenko, V.; Tsvetova, E.; Gochakov, A.; Pyanova, E.; Konopleva, V. Sensitivity Operator Framework for Analyzing Heterogeneous Air Quality Monitoring Systems. Atmosphere 2021, 12, 1697. https://doi.org/10.3390/atmos12121697
Penenko A, Penenko V, Tsvetova E, Gochakov A, Pyanova E, Konopleva V. Sensitivity Operator Framework for Analyzing Heterogeneous Air Quality Monitoring Systems. Atmosphere. 2021; 12(12):1697. https://doi.org/10.3390/atmos12121697
Chicago/Turabian StylePenenko, Alexey, Vladimir Penenko, Elena Tsvetova, Alexander Gochakov, Elza Pyanova, and Viktoriia Konopleva. 2021. "Sensitivity Operator Framework for Analyzing Heterogeneous Air Quality Monitoring Systems" Atmosphere 12, no. 12: 1697. https://doi.org/10.3390/atmos12121697
APA StylePenenko, A., Penenko, V., Tsvetova, E., Gochakov, A., Pyanova, E., & Konopleva, V. (2021). Sensitivity Operator Framework for Analyzing Heterogeneous Air Quality Monitoring Systems. Atmosphere, 12(12), 1697. https://doi.org/10.3390/atmos12121697