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Nikolay N. Zavalishin http://ifaran.ru e-mail: nickolos@ifaran.ru - - PowerPoint PPT Presentation
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
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“Simple” models of biological turnover in peatlands in context of the model system COMBOLA (COmplex MOdel of BOg LAndscapes)
tree layer shrub-grass layer moss layer litter roots layer peat water table depth anaerobic zone aerobic zone H2O CO2 CH4
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Carbon and nitrogen flows in an ecosystem: photosynthesis, respiration, denitrification and nitrogen fixation consumption, litterfall, excretion accumulation in real increment, import and export, abiotic
- xidation,
translocation
Universal scheme of a biotic turnover in terrestrial ecosystems
Reservoirs: G – green phytomass, Pr – perennial phytomass, R – living roots, D+D’- dead standing phytomass, V+L+{Slh} – dead roots + litter + {humus}, Ph+Z – phyto- and zoophagues, Mo+F+Sph – microorganisms+fungi+saprophages, Sln – soil reserve nutrients.
G Ph+Z Pr D+D’ R
V+L+{Slh} Mo+F+Sph
Sln
Simulation models “Minimal” models
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G+Pr+R Ph+Z+F+Mo +Sph
D+D’+L+V+Sln
y1
C
f12
C
f13
C
q2
C
y2
C
f32
C
y31
C
q3
C
f23
C
q1
C
y1
N
q2
N
f12
N
f13
N
f31
N
f32
N
q3
N
f23
N
y32
C
y31
N
y2
N
G Ph+Z Pr D+D’ R
V+L+{Slh} Mo+F+Sph
Sln
C1 C2 C3 y1 f12 f13 q2 y2 f32 q3 f23 q1 y3
Aggregation of static schemes for biotic turnover schemes in minimal models
Storages : C1, N1 - phytomass; C2, N2 – phytophages and destructors (animals, fungi, bacteria); C3, N3 – dead organic matter of litter and root-based peat layer
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G+Pr+R Ph+Z+F+Mo +Sph
D+D’+L+V+Sln
y1
C
f12
C
f13
C
q2
C
y2
C
f32
C
y31
C
q3
C
f23
C
q1
C
y1
N
q2
N
f12
N
f13
N
f31
N
f32
N
q3
N
f23
N
y32
C
y31
N
y2
N
NPP
C1 C2
NPP Litterfall Run-off Consumption Input Run-off Decay Peat formation
C1 C2 C3 y1 f12 f13 q2 y2 f32 q3 f23
NPP
y3
Minimal aggregated compartment schemes of particular and combined cycles in peatland ecosystems
Storage : C1, N1 – Phytomass; C2, N2 – Dead Organic Matter of the root layer P C1, N1 DOM C2, N2
Litterfall Run-off NPP Consumption Input Run-off Decay Consumption Peat formation Mineralization
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Dynamic equations for the 2-component scheme with feedback: 1) +γ21С1С2 2) - γ21С1С2
1 12 1 1 1 1 1
) ( / C C m C C dt dC =
1 12 2 2 2 2 /
C C m q dt dC
C
+ =
Dynamic equations for the 2-component scheme: 1) 2)
1 12 1 1 1 1 1
) ( / C C m C C dt dC =
1 12 2 2 2 2 /
C C m q dt dC + =
Simplest aggregated models of carbon cycle: feedbacks and critical flows
NPP functional form:
) (
1 1
C C NPP =
Phytomass
C1
Dead OM
C2
NPP Litterfall Run-off Consumption Input Run-off Decay Peat formation
Living OM
C1
Dead OM
C2
Primary productivity Litterfall Run-off Respiration Input Run-off Consumption Peat formation Decay
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- carbon balance equation for vegetation
C C C
y f y NPP dt dC
11 12 12 1 =
- net primary productivity
C C
y q NPP
11 1
=
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.
) (
1
C const NPP
1 1C
NPP
C1 C2
y11
C
f12
C
y12
C
y21
C
q2
C
NPP y22
C
y23
C
NPP-phytomass relation in terrestrial ecosystems
const NPP
C
=
1
lim
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Peatlands of Western Siberia:
Least-squared approximation by rational function in MatLab: R2 = 0.7481
2 2 1 1
1 ) ( ) ( x r x r x p p x x f + + + =
NPP-phytomass relation in peatland ecosystems
Data from (Efremov et al., 2007; Basilevich, Titlyanova, 2008; Golovatskaya et al., 2009; Kosykh et al., 2010).
Forest peatlands of Western Siberia
0,00 20,00 40,00 60,00 80,00 100,00 120,00 140,00 160,00 180,00 0,00 5000,00 10000,00 15000,00 20000,00 25000,00
Phytomass, gС/m2
NPP, gС/m2/year Forest peatlands
Peatlands
0,00 200,00 400,00 600,00 800,00 1000,00 1200,00 1400,00 0,00 2000,00 4000,00 6000,00 8000,00 10000,00 12000,00 Phytomass, gС/m2 NPP, gС/m2/year Peatlands by Siberian works Peatlands by Basilevich database
NPP functional form: а) б)
) ( 1
1 2 1 2 1 2 1 1 1 1 1
C C C r C r C s s C NPP = + + + =
) ( 1
1 1 1 1 1 1
C C C r s C NPP = + =
Forest peatlands of Western Siberia:
Least-squared approximation by rational function in MatLab: R2 = 0.8937
x r x p x f
1
1 ) ( + =
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Dynamic equations for 2-component scheme: 1) 2)
1 12 1 1 1 1 1 1
1 / C C m C r s C dt dC + =
1 12 1 1 2 1 2 1 1 1 1 1 1
1 / C C m C r C r C s s C dt dC + + + =
1 12 2 2 2 2 /
C C m q dt dC + =
Dynamic equations for 2-component scheme with feedback: 1) 2)
1 12 1 1 1 1 1 1
1 / C C m C r s C dt dC + =
1 12 1 1 2 1 2 1 1 1 1 1 1
1 / C C m C r C r C s s C dt dC + + + =
1 12 2 2 2 2 /
C C m q dt dC + =
Phytomass
C1
Dead OM
C2
NPP Litterfall Run-off Consumption Input Run-off Decay Peat formation
Living OM
C1
Dead OM
C2
Primary productivity Litterfall Run-off Respiration Input Run-off Consumption Peat formation Decay
Simplest aggregated models of carbon cycle: feedbacks and critical flows
NPP functional form: а) б)
) ( 1
1 2 1 2 1 2 1 1 1 1 1
C C C r C r C s s C NPP = + + + =
) ( 1
1 1 1 1 1 1
C C C r s C NPP = + =
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Jacobi matrix for non-zero equilibria: Stability condition for models 1) и 2):
=
2 12 12 1 1
m m C NPP J
12 1 1
+ < m C NPP
1) Up to two non-zero equilibria from a quadratic equation for C1* 2) Up to three non-zero equilibria by qubic equation for C1*
C1 C2
y11
C
f12
C
y12
C
y21
C
q2
C
q1
C
y22
C
y24
C
C1 C2 y11
C
f12
C
y12
C
y21
C
q2
C
NPP y22
C
f21
C
1) The only non-zero equilibrium 2) Up to two non-zero equilibria from a quadratic equation for C1* Equilibrium [0; q2/m2] belongs to all models Jacobi matrix for non-zero equilibria : Neutrality condition (Hopf bifurcation): Node condition (saddle-node bifurcation):
+ =
1 21 2 2 21 12 2 1 21 2 1 12 12 1 1
C m C C C C C m C NPP J
* 2 21 1 12 1 * 1 21 2
C C NPP m C m + = + + +
* 1 21 * 2 21 12 * 2 21 2 12 1 1
) ( ) )( ( C C C m m C NPP = +
Simplest aggregated models of carbon cycle: equilibria and stability
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Oligotrophic pine-shrub-sphagnum Oligotrophic low pine-shrub-sphagnum
Two-component schemes of carbon cycle in peatland ecosystems of southern taiga in Western Siberia
C1 = 2985.9 C2 C3 = 2430.26
f12
C = 23
f13
C=111
q2
C = 20
y2
C=140.1
f32
C-f23 C+y2 C = 236.2
y31
C=8
q3
C = 0
f23
C
y32
C = 21
NPP=q1
C-y11 C=350.1
f23
C - f32 C = 106.5
C1 = 1204.8 C2 C3 = 1826.6
f12
C=5.7
f13
C=134.7
q2
C=20
y2
C=121.6
f32
C-f23 C+y2 C = 156.3
y31
C=8
q3
C=0
f23
C
y32
C = 112
NPP=q1
C-y11 C=150.4
f23
C - f32 C = 14.7
Storages - gC/m2, flows - gC/m2·year. Oligotrophic sedge-sphagnum fen
C1 = 465.8 C2 C3 = 1534.4
f12
C=27.3
f13
C=242.1
q2
C=20
y2
C=45.7
f32
C-f23 C-q2 C+y2 C = 157.8
y31
C=8
q3
C=0
f23
C
y32
C = 102
NPP=q1
C-y11 C=269.4
f23
C - f32 C =132.1
C1 = 1068 C2 C3 = 2157.5
f12
C=8.4
f13
C=184.2
q2
C=8
y2
C43.6
f32
C-f23 C+y2 C = 130.8
y31
C=10
q3
C=15
f23
C
y32
C = 102
NPP=q1
C-y11 C=192.6
f32
C - f23 C =87.2
Eutrophic fen
Data from (Golovatskaya, Dyukarev, 2009; Golovatskaya, 2010).
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Dynamics of carbon cycle in southern taiga peatlands of Western Siberia
1 2 TC1,2 r1 s0/ε1
2 0.5 1 1.5 5 10 15 20 25 30
TC-2,3 TC+2,3 3 4 r1 s1/ε1
2 0.5 1 1.5 5 10 15 20 25 30
1 2 Stability domains H1+ H1- 5 3 4 γ21 s0/ε1
2 0.5 1 1.5 0.05 0.1 0.15 0.2 0.25 0.3
1 2 6 TC+2,3 H1+ H1- 5 3 4 γ21 s1/ε1
2 0.5 1 1.5 0.05 0.1 0.15 0.2 0.25 0.3
1 2 6 TC+2,3 7
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LOM C1, N1 DOM C2, N2
Litterfall Run-off NPP Consumption Input Run-off Decay Consumption
Carbon and nitrogen interaction is provided by two mechanisms (Logofet, Alexandrov, 1984): 1) intensity of litterfall (f12C) is proportional to the C1/N1 ratio in the living phytomass that reflects nitrogen starvation of plants; 2) decay rate for dead organic matter decreases with the increase of C3/N3 ratio.
Modelling a combined carbon-nitrogen turnover in peatland ecosystems: biological mechanisms
LOM – living organic matter without consumers, DOM – dead organic matter
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Modelling a combined carbon-nitrogen turnover in ecosystems: mathematical form
LOM C1, N1 DOM C2, N2
Litterfall Run-off NPP Consumption Input Run-off Decay Consumption
Mathematical form for coupled N-C flows (Alexandrov et al., 1994): 1) Litterfall :
- carbon flow: , nitrogen flow:
2) Decomposition of dead organic matter:
- carbon flow: , - nitrogen flow:
3) nitrogen uptake from soil by plants: 4) NPP functional form:
1 2 1 12 12
N C f
C C =
1 12 12
C f
N N =
2 2 2 2 21
C N d y
N N =
2 2 21
N d y
C C =
1 2 2 2 21 21
C C N f
N N =
) , ( ) (
2 2 21 1 1
N C f C C NPP
N
=
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Dynamic model of combined carbon-nitrogen turnover : + = + = + = =
2 2 2 2 1 2 2 2 21 1 21 2 2 2 2 1 2 1 12 2 2 2 2 2 2 1 2 2 2 21 1 12 1 13 1 1 1 1 1 12 13 2 2 2 21 1 1 1
/ / / ) ( / C N d C C N C N m q dt dN N C N d C m q dt dC C C N C N N m dt dN N C C N C C dt dC
N N N N N C C C C N N N N C C N
Modelling a combined carbon-nitrogen turnover: dynamic equations
Climate change scenarios from the global climate model IPSL (CMIP5): RCP-2.6 (softly warm) – +0,9 … 2,3 ºC up to 2100 globally, +1,0 … 1,5 ºC locally RCP-8.5 (extremely warm) - +3,2 … 5,4 ºC up to 2100 globally, +2,8 … 4,0 ºC locally
C1, N1 C2, N2
y12
C
f12
C
y13
C
y21
C
q2
C
NPP y12
N
f12
N
f21
N
q2
N
y22
C
y23
C
y21
N
y22
N
y13
N
y23
N
Temperature dependent model parameters: NPP = NPP(Ca)- NPP of vegetation increases under atmospheric CO2 content Ca; m2С =m2С(T) – peat formation intensity; d2С = d2С(T,H) – intensity of decay for dead organic matter depend on the annual air temperature and total precipitation in a polynomial form.
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Two-component schemes of carbon and nitrogen cycles in peatland ecosystems of middle and southern taiga in Western Siberia
Oligotrophic pine-shrub- sphagnum peatland (ryam)
Data from (Kosykh, Mironycheva-Tokareva, Parshina, 2010; Makhatkov, Kosykh, Romantsev, 2007; Makhatkov, Kosykh, 2010; Basilevich, Titlyanova, 2008).
C1=1242.4 N1=15.07 C2 = 4348.1 N2 = 27.4
y12
C = 20.9
f12
C=430.2
y21
C = 124.2
q2
C = 1.4
NPP=q1
C-y11 C = 457.5
y12
N = 0.5
f12
N= 5.74
f21
N = 6.24
q2
N=0.3
y22
C = 307
y21
N=1.65
y22
N = 4.39
13
Storages - gC/m2, gN/m2, flows - gC/m2·year, gN/m2year.
C1=907.4 N1=12.8 C2 = 3256.6 N2 = 17.6
y12
C = 30
f12
C=529
y21
C = 149.2
q2
C = 5
NPP=q1
C-y11 C = 562.7
y12
N = 2.4
f12
N= 6.3
f21
N = 8.7 2 N=0.03
y22
C = 285
y21
N=4.0
y22
N = 0.3
3.7
Mesotrophic sedge-sphagnum fen
C1=940.5 N1=13.3 C2 = 1043.1 N2 = 18.5
y12
C = 28.9
f12
C=560.6
y21
C = 360
q2
C = 6.4
NPP=q1
C-y11 C = 589.5
y12
N = 4.7
f12
N= 5.3
f21
N = 9
q2
N=1.5
y22
C = 170
y21
N=2.5
y22
N = 0.3
Mesotrophic sedge-shrub-sphagnum fen
Middle taiga Southern taiga
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Climate change by the IPSL global climate model with scenarios:
- RCP-8.5
- RCP-2.6
Границы устойчивости равновесий биотического круговорота болот средней и южной тайги Западной Сибири
Южная тайга
,NPP intensity, gС/gN/год
Средняя тайга
Stability boundaries for steady states in models of a biotic turnover in peatlands of middle and southern taiga in Western Siberia
Stability domains of stationary dynamic regime of the biological turnover:
Southern taiga Middle taiga
1 – oligotrophic pine-shrub-sphagnum mire (“high ryam”); 2 – oligotrophic pine- shrub-sphagnum mire (“low ryam”); 3 – mesotrophic fen; 4 – oligotrophic fen; 5 – pine forest; 6 – eutrophic fen
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Выводы
1) For peatlands from different regions various relations between NPP and phytomass can be obtained with equal requirements. They can be approximated by rational functions determining dynamics of the simplest two-component models of biological turnover; 2) Minimal aggregated models of separate carbon cycle can demonstrate a functional form impact for flow dependency but limited in estimation of turnover dynamics and equilibria although the model with feedback shows oscillatory dynamic regimes; 4) «Soft» climatic scenario RCP-2.6 of the IPSL model can transform oligo- and mesotrophic fens into forested states (“ryams”) while “ryams” can perform into forests under a century time interval; 5) Under the «hard» climate change scenario RCP-8.5 of the IPSL model forested
- ligotrophic peatlands of middle and southern taiga can be transformed into fen state
due to increased precipitation except “high ryam” of the middle taiga that can become forest due to sufficient nitrogen availability. 3) Nitrogen cycle inclusion even into the simplest scheme of the turnover allows to make calculation and interpretation of equilibria more effective and realize some feedbacks in the system;
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