Institute of Computational Mathematics and Mathematical Geophysics SD RAS, Novosibirsk Mathematical models for ecological prognosis, design and monitoring V.V. Penenko

What is the role of atmospheric chemistry in amplifying or damping climate change? How will human activities transform the dynamical and chemical properties of the future atmosphere? How will quality of life change?

System organization of environmental modeling Models of processes hydrodynamics transport and transformation of pollutants Data bases Models of observations Functionals Quality, observations, restrictions, control, cost,etc. extended: functional +model as integral identity Solution of forward problemsSolution of adjoint problems Calculation of sensitivity functions and variations of functionals Analysis of sensitivity relations risk/vulnerability, observability, sources System of decision making, design Identification of parameters, decrease of uncertainties, data assimilation, monitoring

Analysis of the climatic system for construction of long-term scenarios: Extraction of multi- dimentional and multi-component factors from data bases Classification of typical situations with respect to main factors Investigation of variability Formation of “leading” spaces Approaches and tools

Scenario approach Models of hydrodynamics Models of transport and transformation of pollutants (gases and aerosols) Sensitivity and observability algorithms Combination of forward and inverse techniques Joint use of models and data Nested models and domains

Model of hydrodynamics

Transformation of moisture and pollutants Gases and aerosols interaction with underlying surface dry and wet deposition condensation and evaporation coagulation Model of atmospheric chemistry Model of aerosol dynamics Model of moisture transformation water vapour cloud water rain water

is the function of pressure

Model of aerosol dynamics - concentration of particles in volume - coagulation kernel; - rates of condensation and evaporation; - coefficients of diffusive change of particles; - removal parameter; -source term; -parameters of collective interaction of particles

Hydrological cycle of atmospheric circulation for studying aerosols If supersaturation -->condensation - content of water vapor, cloud water and rain water in respectively Notations: - autoconversion of cloud water to rain water (*dt) - accretion of cloud droplets by rain drops (*dt) - evaporation of rain water(*dt) - condensation (evaporation)(*dt)

Hydrological cycle no yes no yes output input no yes

Functionals of measurements

The structure of the source term source power source shape reference point of the source Particular case

Functionals for assessment of source parameters

The main sensitivity relations The algorithm for calculation of sensitivity functions are the sensitivity functions are the parameter variations The feed-back relations

Factor analysis ( global scale). Reanalysis hgt 500, june

West Siberia region E, N June,

West Siberia, 97% Global, 17% Eigenfunction N1, June,

Novosibirsk

East Siberia Region E, N June,

Global, 17% East Siberia, 97% Eigenvectors N1, June,

Irkutsk

. June г

Sensitivity relation for estimation of risk/vulnerability and observability

Sensitivity function for estimation of risk/vulnerability domains for Lake Baikal

Conclusion Combination of forward and inverse modeling factor and principle component analysis sensitivity theory on the base of variational principles gives the possibility for coordinated solution of the variety of environmental problems, such as diagnosis prognosis monitoring (mathematical background) design