Ассимиляция данных в имитационном моделировании экологических процессов методом минимизации корректирующих возмущений

Александр Григорьевич Топаж; Евгений Павлович Митрофанов

doi:10.21638/11701/spbu10.2017.309

Authors

Александр Григорьевич Топаж Bureau Hyperborea, 40, Podvoisky ul., St. Petersburg, 193312, Russian Federation
Евгений Павлович Митрофанов Agrophysical Research Institute, 14, Grazhdanskiy pr., St. Petersburg, 195220, Russian Federation

DOI:

https://doi.org/10.21638/11701/spbu10.2017.309

Abstract

The on-line correction of the vector of a dynamic model state variable by direct or indirect measurements is a well-known problem of the theory of automatic control. It is called the problem of data assimilation. Ecological models require specific approaches to this problem in comparison to traditional methods used in hydrometeorology. The main difference is that there are only rare observations on a limited number of indirect characteristics. The paper presents an original approach to data assimilation for such cases. The main idea is inclusion an additional term to the initial system, which describes the random external influences that are not counted in the ideal model. Further, one can find a form of these perturbations that minimizes the weighted sum of their integrated power and the norm of deviations of the observed and theoretical characteristics at moments of measurement. Then the choice of weighting factor allows us for comparative confidence to be reflected between the theoretical model and actual measurements. Thus, the formal statement of the problem is written down as a problem of optimal control. Examples of application of the proposed method for several simple models are given. In the problem of the uniform motion of a material point, an analytical solution can be obtained which, nonetheless, yields rather interesting results. The problem of data assimilation for the Lotka—Volterra model has been solved numerically. It is shown that the proposed method of “minimal perturbation” leads to the least “traumatic” correction of the ideal model in comparison with the available alternative approaches; i. e., adaptive parameter identification or backdating adjustment of the initial state. Refs 7. Figs 2.

Keywords:

assimilation of data, minimization of corrective disturbances, ecology, simulation modeling

Downloads

Download data is not yet available.

References

Литература

Брыксин В. М., Евтюшкин А. В., Хворова Л. А. Разработка программного комплекса оценки урожайности зерновых культур с использованием математического моделирования и данных дистанционного зондирования Земли // Материалы Всерос. конференции (с международным участием) «Математические модели и информационные технологии в сельскохозяйственной биологии: итоги и перспективы», 14–15 октября 2010 г. СПб.: АФИ, 2010. С. 76–80.

Клещенко А. Д., Найдина Т. А. Использование данных дистанционного зондирования для моделирования физиологических процессов растений в динамических моделях прогнозирования урожая // Современные проблемы дистанционного зондирования Земли из космоса. 2011. Т. 8, № 1. C. 170–178.

Шутяев В. П. Операторы управления и итерационные алгоритмы в задачах вариационного усвоения данных. М.: Наука, 2001. 240 с.

Kalnay E. Atmospheric modeling, data assimilation and predictability. Cambridge: Cambridge University Press, 2003. 341 p.

Olioso A., Inoue Y., Ortega-Farias S., Brisson N. Future directions for advanced evapotranspiration modeling: Assimilation of remote sensing data into crop simulation models and SVAT models // Irrigation and Drainage Systems. 2005. Vol. 19. P. 377–412.

Тихонов А. Н., Арсенин В. Я. Методы решения некорректных задач. М.: Наука, 1974. 223 с.

Medvedev S., Topaj A. Crop simulation model registrator and polyvariant analysis // IFIP Advances in Information and Communication Technology (AICT). 2011. Vol. 359. P. 295–301.

References

Bryksin V. M., Evtiushkin A. V., Khvorova L. A. Razrabotka programmnogo kompleksa otsenki urozhainosti zernovykh kul’tur s ispol’zovaniem matematicheskogo modelirovaniia i dannykh distantsionnogo zondirovaniia Zemli [Development of a software system for assessing crop yields using mathematical modeling and remote sensing data from the Earth]. Proceeding of Russian Conference “Mathematical models and information technologies in agricultural biology: results and prospects”. October 14–15, 2010. Saint Petersburg, ARI Press, 2010, pp. 76–80. (In Russian)

Kleshchenko A. D., Naidina T. A. Ispol’zovanie dannykh distantsionnogo zondirovaniia dlia modelirovaniia fiziologicheskikh protsessov rastenii v dinamicheskikh modeliakh prognozirovaniia urozhaia [The use of remote sensing data to model the physiological processes of plants in dynamic crop forecasting models]. Sovremennyie problemy distantsionnogo zondirovaniia Zemli iz kosmosa [Modern problems of remote sensing of the Earth from space], 2011, vol. 8, no. 1, pp. 170–178. (In Russian)

Shutiaev V. P. Operatory upravleniia i iteratsionnye algoritmy v zadachakh variatsionnogo usvoeniia dannykh [Operators of control and iterative algorithms in problems of variational data assimilation]. Moscow, Nauka Publ., 2001, 240 p. (In Russian)

Kalnay E. Atmospheric Modeling, Data Assimilation and Predictability. Cambridge, Cambridge University Press, 2003, 341 p.

Olioso A., Inoue Y., Ortega-Farias S., Brisson N. Future directions for advanced evapotranspiration modeling: Assimilation of remote sensing data into crop simulation models and SVAT models. Irrigation and Drainage Systems, 2005, vol. 19, pp. 377–412.

Tikhonov A. N., Arsenin V. Ia. Metody resheniia nekorrektnykh zadach [Methods for solving illposed problems]. Moscow, Nauka Publ., 1974, 223 p. (In Russian)

Medvedev S., Topaj A. Crop simulation model registrator and polyvariant analysis. IFIP Advances in Information and Communication Technology (AICT), 2011, vol. 359, pp. 295–301.