Nikolay N. Zavalishin http://ifaran.ru e-mail: nickolos@ifaran.ru - PowerPoint PPT Presentation

Russian Academy of Sciences A.M. Obukhov Institute of atmospheric physics Laboratory of mathematical ecology Nikolay N. Zavalishin http://ifaran.ru e-mail: nickolos@ifaran.ru Биотический круговорот в болотных ландшафтах южной и средней тайги Западной Сибири при изменениях климата и хозяйственных воздействиях Biotic turnover in peatland landscapes of southern and middle taiga in Western Siberia under climate and anthropogenic changes ENVIROMIS-2016 Томск , 11 - 16 июля 2016 Поддержано проектом РФФИ № 16-07-0201- а

Классы моделей биотического круговорота в экосистемах Классы моделей биотического круговорота Детальные имитационные на Качественные « минимальные » малых масштабах времени на больших масштабах ( минуты , часы , сутки , декады ) времени ( месяц , год и более ) Модели промежуточной сложности Biological turnover model classes Qualitative «minimal» on long Simulation models on short time time scales (month, year et. al.) scales (minutes, hours, days, (Hilbert et al, 2000; Frolking, decades) (Wetland-DNDC) 2001; McGill et al., 2010) Models of intermediate complexity

“Simple” models of biological turnover in peatlands in context of the model system COMBOLA (COmplex MOdel of BOg LAndscapes) H 2 O tree layer CO 2 CH 4 shrub-grass layer aerobic zone moss layer roots layer litter water table depth peat anaerobic zone

Universal scheme of a biotic turnover in terrestrial ecosystems Carbon and nitrogen flows in an ecosystem: G D+D’ Ph+Z photosynthesis, respiration, denitrification and nitrogen fixation consumption, Pr V+L+{ Slh } Mo+F+ Sph litterfall, excretion accumulation in real increment, import and export, abiotic oxidation, translocation Sln R Reservoirs : G – green phytomass, Pr – perennial phytomass, R – living roots, D + D’ - dead standing phytomass, Simulation models V + L +{ Slh } – dead roots + litter + {humus}, Ph + Z – phyto- and zoophagues, Mo + F + Sph – microorganisms+fungi+saprophages, “Minimal” models Sln – soil reserve nutrients.

Aggregation of static schemes for biotic turnover schemes in minimal models G D+D’ Ph+Z Pr V+L+{ Slh } Mo+F+ Sph Sln R q 1 q 2 f 12 C 1 C 2 C q 1 N y 1 y 2 y 1 G+Pr+R N y 2 f 32 C y 1 N q 2 f 13 f 23 C f 12 N f 31 C q 2 Ph+Z+F+Mo q 3 N f 12 +Sph C 3 Storages : C C N y 2 f 13 f 13 C f 32 C C 1 , N 1 - phytomass; C 2 , N 2 – q 3 y 3 N N f 32 f 23 C N f 23 phytophages and destructors q 3 D+D’+L+V+Sln (animals, fungi, bacteria); C 3 , C y 31 N 3 – dead organic matter of C N y 32 y 31 litter and root-based peat layer

Minimal aggregated compartment schemes of particular and combined cycles in peatland ecosystems C q 1 N y 1 NPP q 2 f 12 G+Pr+R N y 2 C 1 C 2 C y 1 N q 2 C f 12 y 1 y 2 NPP N f 31 C q 2 f 32 Ph+Z+F+Mo N f 12 f 13 f 23 +Sph C C y 2 N f 13 f 13 C f 32 C q 3 q 3 N N C 3 f 32 f 23 C N f 23 q 3 D+D’+L+V+Sln y 3 C y 31 C N y 32 y 31 Storage : C 1 , N 1 – P hytomass; C 2 , N 2 – D ead O rganic M atter of NPP NPP the root layer Run-off Consumption Run-off Consumption P C 1 , N 1 C 1 Consumption Litterfall Decay Litterfall Decay Input Run-off Input Run-off DOM C 2 , N 2 C 2 Peat formation Peat formation Mineralization

Simplest aggregated models of carbon cycle: feedbacks and critical flows Primary productivity NPP Run-off Respiration Run-off Consumption Living OM Phytomass C 1 C 1 NPP functional form: Consumption NPP = C ( C ) 1 1 Litterfall Decay Litterfall Decay Input Run-off Dead OM Input Run-off Dead OM C 2 C 2 Peat formation Peat formation Dynamic equations for the 2-component scheme: Dynamic equations for the 2-component scheme with feedback: = dC / dt C ( C ) m C C 1) 1 1 1 1 1 12 1 = dC / dt C ( C ) m C C 1) + γ 21 С 1 С 2 1 1 1 1 1 12 1 2) = + dC 2 / dt q m C C = + C 2 2 2 12 1 dC 2 / dt q m C C 2) - γ 21 С 1 С 2 2 2 2 12 1

NPP-phytomass relation in terrestrial ecosystems dC 1 = - carbon balance equation for vegetation C C C NPP y f y 12 12 11 dt NPP C y 12 C y 11 = C C NPP q y - net primary productivity C 1 1 11 NPP const ( C ) NPP 1 C 1 1 C y 23 C f 12 = lim NPP const C y 22 C q 2 C C 2 1 C y 21 In any mathematical model of biological turnover in terrestrial ecosystems on any time scale the equation for carbon balance of vegetation is strongly determined by functional form of the Net Primary Productivity - the difference between gross photosynthesis and autotrophic respiration.

NPP-phytomass relation in peatland ecosystems Forest peatlands of Western Siberia Forest peatlands of Western Siberia: Least-squared approximation by rational 180,00 function in MatLab: 160,00 140,00 p x R 2 = 0.8937 = 0 f ( x ) 120,00 NPP, gС/m2/year + 1 r x 100,00 1 Forest peatlands 80,00 Peatlands of Western Siberia: 60,00 Least-squared approximation by rational 40,00 function in MatLab : 20,00 + x ( p p x ) 0,00 = 0,00 5000,00 10000,00 15000,00 20000,00 25000,00 0 1 f ( x ) Phytomass, gС/m2 + + R 2 = 0.7481 2 1 r x r x 1 2 Peatlands by Siberian Peatlands works NPP functional form: 1400,00 Peatlands by Basilevich s 1200,00 database = = 0 а ) NPP C C ( C ) 1 + 1 1 1 NPP, gС/m2/year 1 r C 1000,00 1 1 800,00 + s s C = = б ) 0 1 1 NPP C C ( C ) 600,00 1 + + 1 2 1 2 1 r C r C 1 1 2 1 400,00 200,00 0,00 Data from (Efremov et al., 2007; Basilevich, 0,00 2000,00 4000,00 6000,00 8000,00 10000,00 12000,00 Titlyanova, 2008; Golovatskaya et al., 2009; Phytomass, gС/m2 Kosykh et al., 2010).

Simplest aggregated models of carbon cycle: feedbacks and critical flows Primary productivity NPP Run-off Respiration Run-off Consumption Living OM Phytomass C 1 C 1 Consumption NPP functional form: Litterfall Decay s Litterfall Decay = = 0 NPP C C ( C ) а ) 1 + 1 1 1 1 r C 1 1 Input Run-off Dead OM Input Run-off Dead OM + s s C C 2 = = б ) 0 1 1 NPP C C ( C ) C 2 1 + + 1 2 1 2 1 r C r C 1 1 2 1 Peat formation Peat formation Dynamic equations for 2-component scheme: Dynamic equations for 2-component scheme with feedback: s = dC / dt C 0 m C C 1) s 1 1 1 1 12 1 + 1 r C = dC / dt C 0 m C C 1) 1 1 1 1 1 1 12 1 + 1 r C + s s C 2) 1 1 = 0 1 1 dC / dt C m C C + s s C 1 1 + + 1 1 12 1 2 1 r C r C 2) = 0 1 1 dC / dt C m C C 1 1 2 1 1 1 + + 1 1 12 1 2 1 r C r C = + dC 2 / dt q m C C 1 1 2 1 2 2 2 12 1 = + dC 2 / dt q m C C 2 2 2 12 1

Simplest aggregated models of carbon cycle: equilibria and stability NPP C q 1 Equilibrium [0; q 2 / m 2 ] belongs to all models C C C y 11 y 12 y 12 C y 11 C 1 C 1 C f 21 C y 24 C f 12 C f 12 C C q 2 y 22 C y 22 C q 2 C 2 C 2 C y 21 C y 21 1) Up to two non-zero equilibria from a quadratic equation 1) The only non-zero equilibrium for C 1* 2) Up to two non-zero equilibria from a quadratic 2) Up to three non-zero equilibria by qubic equation for C 1* equation for C 1* Jacobi matrix for non-zero equilibria: Jacobi matrix for non-zero equilibria : NPP NPP m 0 + m C C C C = J 1 12 C = J 1 12 12 1 2 21 1 2 C 1 1 m C m C 12 2 12 21 2 2 21 1 Neutrality condition (Hopf bifurcation): Stability condition for models 1) и 2): NPP + + + = + * * m C m C NPP 2 21 1 1 12 21 2 C < m + Node condition (saddle-node bifurcation): 1 1 12 C NPP 1 + = * * * ( m )( m C ) ( C ) C 1 12 2 21 2 12 21 2 21 1 C 1

Two-component schemes of carbon cycle in peatland ecosystems of southern taiga in Western Siberia C - y 11 C =150.4 NPP=q 1 C - y 11 C =350.1 NPP=q 1 C 1 = 1204.8 C 1 = 2985.9 C =5.7 C = 23 f 12 f 12 C = 20 q 2 C =20 q 2 C =111 f 13 C 2 C =134.7 C 2 f 13 C f 23 C f 23 C =121.6 y 2 C =140.1 C =0 y 2 q 3 C = 0 q 3 C - f 32 C = 14.7 f 23 C - f 32 C = 106.5 f 23 C 3 = 1826.6 C 3 = 2430.26 C =8 y 31 C =8 y 31 C = 112 C - f 23 C + y 2 C = 156.3 y 32 f 32 C = 21 C - f 23 C + y 2 C = 236.2 y 32 f 32 Oligotrophic pine-shrub-sphagnum Oligotrophic low pine-shrub-sphagnum C - y 11 C =192.6 NPP=q 1 C - y 11 C =269.4 NPP=q 1 C 1 = 1068 C 1 = 465.8 C =8.4 f 12 C =27.3 f 12 C =8 q 2 C =20 q 2 C =184.2 f 13 C 2 C 2 C =242.1 f 13 C f 23 C 43.6 y 2 C f 23 C =45.7 y 2 C =15 q 3 C =0 q 3 C - f 23 C =87.2 f 32 C - f 32 C =132.1 f 23 C 3 = 2157.5 C 3 = 1534.4 C =8 C =10 y 31 y 31 C = 102 C - f 23 C + y 2 C = 130.8 y 32 f 32 C - f 23 C - q 2 C + y 2 C = 157.8 f 32 C = 102 y 32 Oligotrophic sedge-sphagnum fen Eutrophic fen Storages - g C /m 2 , flows - g C /m 2 · year. Data from (Golovatskaya, Dyukarev, 2009; Golovatskaya, 2010).

Dynamics of carbon cycle in southern taiga peatlands of Western Siberia s 0 / ε 1 s 1 / ε 1 4 2 TC - 2,3 2 TC + 2,3 1.5 1.5 2 3 2 TC 1,2 1 1 1 0.5 1 0.5 r 1 5 10 15 20 25 30 r 1 5 10 15 20 25 30 Stability domains s 1 / ε 1 s 0 / ε 1 H 1+ 5 5 H 1+ 2 2 4 4 7 TC + 2,3 1.5 TC + 2,3 1.5 6 3 3 1 6 1 H 1- 2 2 H 1- 0.5 0.5 1 1 γ 21 γ 21 0.05 0.1 0.15 0.2 0.25 0.3 0.05 0.1 0.15 0.2 0.25 0.3