A Concept of Environmental Forecasting and Variational Organization of Modeling Technology

1. A Concept of Environmental Forecasting and Variational Organization of Modeling Technology Vladimir Penenko Institute of Computational Mathematics and Mathematical Geophysics SD RAS

2. Challenges of environment forecasting: • Predictability of climate-environment system? • Stability of climatic system? • sensitivity to perturbations of forcing • Features of environment forecasting: uncertainty • in the long-term behavior of the climatic system; • in the character of influence of man-made factors • in the conditions of changing climate

3. Uncertainty • Discrepancy between models and real phenomena • insufficient accuracy of numerical schemes and algorithms • lack and errors of input data

4. A CONCEPT OF ENVIRONMENTAL FORECASTING • Basic idea: we use inverse modeling technique to assess risk and vulnerability of territory (object) with respect to harmful impact in addition to traditional forecasting the state functions variability by forward methods

5. Theoretical background • The methodologyis based on: • control theory, • sensitivity theory, • risk and vulnerability theory, • variational principles in weak-constrained formulation, • combined use of models and observed data, • forward and inverse modeling procedures, • methodology for description of links between regional and global processes ( including climatic changes) by means of orthogonal decomposition of functional spaces for analysis of data bases and phase spaces of dynamical systems

6. Basic elements for concept implementation: • models of processes • data and models of measurements • global and local adjoint problems • constraints on parameters and state functions • functionals: objective, quality, control, restrictions etc. • sensitivity relations for target functionals and constraints • feedback equations for inverse problems

7. Mathematical model of processes

8. Model of atmospheric dynamics

9. Transport and transformationof humidity

10. Transport and transformation model of gas pollutants and aerosols Operators of transformation

11. Variational form of model’s set: hydrodynamics+ chemistry+ hydrological cycle

12. Variational form of convection-diffusion operators boundary conditions on

13. Model of observations Variational form

14. Functionals for generalized description of information links in the system

15. Variational principle Augmented functional for computational technology Algorithms for construction of numerical schemes

16. The universal algorithm of forward & inverse modeling

17. Some elements of optimal forecasting and design The main sensitivity relations Algorithm for calculation of sensitivity functions

18. Algorithms for uncertainty calculation based on sensitivity analysis and data assimilation: in models of processes in initial state in model parameters and sources in models of observations

19. Fundamental role of uncertainty functions • integration of all technology components • bringing control into the system • regularization of inverse methods • targeting of adaptive monitoring • cost effective data assimilation

20. Optimal forecasting and design • Optimality is meant in the sense that estimations of the goal functionals do not depend on the variations : • of the sought functions in the phase spaces of the dynamics of the physical system under study • of the solutions of corresponding adjoint problems that generated by variational principles • of the uncertainty functions of different kinds which explicitly included into the extended functionals

21. Construction of numerical approximations • variational principle • integral identity • splitting and decomposition methods • finite volumes method • local adjoint problems • analytical solutions • integrating factors

22. 4DVar real time data assimilation algorithm Basic elements in frames of splitting and decomposition schemes: p - number of stages - operator of the model,

23. Scenario approach for environmental purposes • Inclusion of climatic data via decomposition of phase spaces on set of orthogonal subspaces ranged with respect to scales of perturbations • Construction of deterministic and deterministic-stochastic scenarios on the basis of orthogonal subspaces • Models with leading phase spaces

24. Leading basis subspace for geopotential for 56 years

25. Leading basis subspace for horizontal velocities for 56 years

26. Leading orthogonal subspaces 36 years, 26.66% 46 years, 26.63% 56 years,26.34%

27. Risk/vulnerability assessmentSome scenarios for receptorsin Siberia

28. Ekaterinburg Yakutsk Khanti-Mansiisk Krasnoyarsk Tomsk Mondy Ulan-Ude Tory Ussuriisk “climatic” April

29. Long-term forecasting for Lake Baikal regionRisk function Surface layer, climatic October

30. Conclusion • Algorithms for optimal environmental • forecasting and design are proposed • The fundamental role of uncertainty is highlighted

31. Thank you for your time!

32. Eigenvalues of Gram matrix as a measure of informativeness of orthogonal subspaces Separation of scales : climate/weather noise 36 years 46 years 56 years

33. Risk assesment for Lake Baikal region

34. Volcano Schiveluch ( Kamchatka, Russia) eruption19-21.05.2001. Forward problem. Surface layer aerosol concentrations ( <2 mkm)