Russian Academy of Sciences A.M. Obukhov Institute of Atmospheric - - PowerPoint PPT Presentation

SLIDE 1

Nikolay N. Zavalishin Russian Academy of Sciences A.M. Obukhov Institute of Atmospheric Physics Laboratory of Mathematical Ecology

Supported by the RFBR project 10-05-00265a and the Program “Physical and chemical processes in atmosphere and cryosphere determining climate and environmental change”

Reaction of the biotic cycle in southern taiga forest and peatland ecosystems of European part of Russia to the climate change and human perturbations

e-mail: nickolos@ifaran.ru

SLIDE 2

Oligotrophic Mesotrophic Eutrophic

Formed under high humidity conditions and a lack of nutrient load that is realized

• nly by atmospheric
• precipitation. A typical

feature is small number of plant species and a cover of sphagnum mosses. Nutrient-water regime is carried out by underground water or rivers with high content of mineral elements. Vegetation cover has a high biodiversity, species richness and structural complexity. Formed under the mixed type of nutrient-water regime by atmospheric precipitation, input from adjacent ecosystems, as well as underground water. Vegetation can include both oligotrophic and eutrophic species, and has higher level of biodiversity.

Mires and forests of southern taiga take an important part in regulating biogeochemical cycles of carbon, nitrogen, water and mineral elements both at regional and at the global levels. Carrying out an active matter exchange with the environment they can be sources or stocks for green-house gases under the climate change and human economic and resource-mining activities. Due to structural complexity and lack of knowledge on functioning mechanisms, mathematical modelling of main ecosystem biogeochemical cycles is necessary for forecasting reactions and dynamic behavior of those ecosystems to extern al perturbations.

Elements of bog ecosystems classification

Peatland and forest ecosystems of the southern taiga in European part of Russia

by nutrient-water regime by vegetation cover

forest forest-fen fen

SLIDE 3

Biogeochemical cycles in different types of peatland ecosystems

Oligotrophic, mesotrophic, eutrophic peatland ecosystems in the southern taiga, European part of Russia (Novgorod region): carbon, nitrogen and mineral element biotic cycles (Bazilevich and Tishkov, 1982, 1986; Alexandrov et al., 1994) Local low-parametric dynamic model of coupled carbon-nitrogen cycles with climatic parameterization and steady states corresponding to the bog ecosystems classification

?

Photos are from (Bazilevich and Titlyanova, 2008)

SLIDE 4

Biogeochemical cycles in adjacent forest ecosystems

Spruce-bilberry ecosystem in the southern taiga, European part of Russia (Novgorod region): carbon, nitrogen and mineral element biotic cycles (Bazilevich et al., 1986)

?

A steady state for the local low-parametric dynamic model of coupled carbon- nitrogen cycles in bog ecosystems with climatic parameterizations

Main problems (how to…?): 1) Aggregation of a multi-compartment scheme; 2) Low-parametric dynamic model design from some static balanced or disbalanced diagrams.

SLIDE 5

Aggregation principles and techniques for compartment schemes

G Ph+Z Pr D+D’ R

V+L+{Slh} Mo+F+Sph

Sln

Aggregation principles: 1) division of living and dead organic matter;

2) division of above- and underground living organic matter; 3) consumers (Ph+Z) and destructors (Mo+F+Sph) are aggregated into separate units independently on where they live. Carbon flows in ecosystems: photosynthesis, respiration, consumption, death, excretion, litterfall fixation in actual growth, input, output, abiotic oxidation translocation Reservoires: G – green phytomass, Pr – perennial phytomass, R – living roots, D+D’- standing dead phytomass, V+L+{Slh} – dead roots + litter + organic matter in soil, Ph+Z – phytophages+zoophages, Mo+F+Sph – microorganisms+fungi+saprophages, Sln – soil reserve of nutrients.

SLIDE 6

Reservoires: C1, N1 - carbon and nitrogen in living organic matter (LOM), C2, N2 – carbon and nitrogen in consumers and destructors, C3, N3 – carbon and nitrogen in litter and other dead organic matter (DOM).

Aggregated scheme of carbon and nitrogen cycles in ecosystems

Input and output flows: q1

C – carbon assimilation from atmosphere,

q3

C – carbon input from adjacent ecosystems

(abcent in oligotrophic case), q2

N – fixation of

atmospheric nitrogen by microorganisms, q3

N –

nitrogen input with surface water and precipitation, y1

C, y2 C – respiration and

consumption by phytophages of another ecosystems, y2

N – denitrification, y3 C – peat

formation, carbon output with streams, abiotic

• xidation, y3

N – peat formation and nitrogen

• utput.

Intercompartment flows:

,f12

C, f12 N– consumption of biomass by

phytophages, f13

C, f13 N – litterfall, f23 C –

death of consumers and microorganisms, f31

N –nitrogen consumption from soil

resource by roots, and translocation, f32

C –

destruction of dead organic matter, f23

N –

excretion by microorganisms and consumers.

C1 = 8490, N1=26.3 C2=35.2, N2=0.1 C3=8835, N3=78.9

y1

C=598.5

f12

C=38.49

f13

C=342.7

q2

C=0

y2

C=296.6

f32

C= 621.8

y3

C=114.3

q3

C

f23

C=363.21

q1

C=987.5

5 y1

N=0.083

q1

N=0.9

f12

N=0.756

f13

N= 6.16

f31

N= 5.635

f23

N=0.13

q3

N=0.825

y3

N=1.58

q2

N=0.41

f32

N=0.7

Units: storages C - in g/m2 of dry weight, flows C in g/m2·year of dry weight; storages N – in gN/m2, flows N – in gN/m2·year.

SLIDE 7

fki ( xk , xi )

x k ( t ) x i ( t ) x 1 ( t )

yk ( xk ) qk ( t ) qi ( t )

yi ( xi ) q1( t )

y1( x1 )

fik (xi , xk )

xk=3.5

xi=70 x1= 180

yk = 0.8 qk = 0.5

f k i = 15

q i = 8

yi = 3

q1 = 30 y1 = 10

f k i = 8.5

?

General problem of a dynamic model design by a given «storage-flow» diagram for a single biogeochemical cycle

a set of compartment schemes for time moments t0, t1,…, collected from the field studies dynamic model for storages in reservoires

Dynamic equations in general form: ∑ − + − =

≠ = n i k k ik ki i i i

f f y q dt dx

, 1

) ( f(x) y(x) q(x) x + − = dt d

q - vector of input flows from the environment; y - vector of output flows to the environment; fki - intercompartment flow from i to j

The main problem: how to make dynamic model from one flow-balanced diagram?

SLIDE 8

5) intercompartment flow control types: a) fki = donor; b) fki = recipient; c) fki = Lotka-Volterra

j i ij

x x γ

i ijx

α

j ijx

β

Modified method for a single-cycle dynamic system design

Main assumptions (1-5c) for given stationary schemes:

;

* *

x y m

i i i =

;

* *

x f

i ki ki =

β

;

* *

x f

k ki ki =

α

;

* * *

x x f

k i ki ki =

γ

Coefficients of flow functions are calculated from the given scheme: cis

. γ γ

is si −

= =

bi

s

. , ; ), ( s i s i m

is si ik i k ki i

≠ − = − ∑ + −

≠

β α α β

1) q* + f* = y* - at least one of the given diagrams is a dynamic equilibrium; 2) fki = fki (xk, xi); fik = fik(xi, xk) – intercompartment flows depend only on participating storages; 3) qi = const – input flows can have only constant form; 4) yi = mixi – output flows are linear; 5d) additional control types with saturation:

,

i ki i k ki ki

x L x x K g + =

,

k ki i k ki ki

x L x x K g + =

) )( (

i ki k ki i k ki ki

x N x L x x K g + + = Coefficients of flow functions with saturation are calculated from several given schemes or by special calibration procedures

Dynamic compartment model:

∑

= = =

− + ∑ + ∑ + − =

n s is si n s s is i n s s i s i i i i

g g x c x x b x m q dt dx

1 1 1

) ( ) ( ) ,..., ( /

1

x x x q x G C x x diag B dt d

n

+ + + =

i,s = 1,…n

SLIDE 9

Modelling a coupled carbon-nitrogen cycle: dynamic mechanisms

Carbon and nitrogen interaction is provided by two mechanisms (Logofet, Alexandrov, 1985): 1) N/C decrease in living organic matter results in an increment of total litterfall, due to weakness of plants under nitrogen starvation; 2) N/C increase in dead organic matter results in an increment of the DOM decomposition rate. Dynamic equations of the coupled model:

i = 1,…,3 ∑ − + − =

≠ = 3 , 1

) (

i k k C ik C ki C i C i i

f f y q dt dC ∑ − + − =

≠ = 3 , 1

) (

i k k N ik N ki N i N i i

f f y q dt dN Mathematical form of coupled N-C flows (Alexandrov, 1994): 1) Litterfall :

• carbon flow: , nitrogen flow:

2) Decomposition of dead organics:

• carbon flow: , - nitrogen flow:

1 2 1 13 13

N C f

C C

α =

1 13 13

C f

N N

α =

2 3 2 3 31 31

C N C f

N N

α =

2 3 32 32

C N f

C C

γ =

Another intercompartment flow functions: f12

C=γ12 CC1 C2 ; f12 N=γ12 NN1C2; f23 C=α23 CC2 ;

f23

N=α23 NN2; f32 N=γ32 NN3C2;

Carbon assimilation flux is approximated by a saturation function:

1 01 1 01 1

C L C K qC + =

The main purpose: to investigate stability and bifurcations of steady states as a reaction of the carbon cycle to climatic and human perturbations.

SLIDE 10

Stability domains of coupled cycles and external perturbations

Carbon assimilation by plants, g/m2 year dry weight

Specific intensity of run-off and peat formation

peat mining or melioration atmospheric CO2 increase due to the climate change Living organic matter decrease due to fires

Partial stability boundaries of stationary dynamic regimes of coupled cycles functioning : 1 –mesotrophic forest-fen; 2 – a mesotrophic (oligotrophic under q3

C=0) sphagnum

pine forest; 3 – a eutrophic fen (oligotrophic under q3

C=0); 4 – multistability of a fen

and forest-fen; 5 – a spruce forest; 6 – a water basin without LOM

SLIDE 11

Conclusions

1) method of dynamic compartment model design by static “storage-flow” schemes helps in constructing coupled models of carbon-nitrogen cycle functioning based on two most important connections: litterfall dependence on N/C relation in living

• rganic matter and increase of decomposition rate under N/C increase in dead
• rganic matter;

2) current carbon-nitrogen cycles functioning in the mesotrophic peatland can lose stability both under doubling atmospheric CO2 increase, and in the opposite case. In the former, a mesotrophic forest-fen tends to the forest state – sphagnum pinery or spruce forest, while in the latter it is transformed into oligotrophic or eutrophic fen; 3) including nitrogen cycle in the model of ecosystem functioning allows to reflect biologically possible states of bog and forest more adequately than it was for only carbon cycle model, although not all steady states appear under the particular set of

• coefficients. More detailed bifurcation analysis would make the picture of bog-forest

relationship under climate change more clear.

SLIDE 12

Problems of modelling biogeochemical cycles in ecosystems

1) What basis can be found for algorithm of flow functions choice in both single- and multiple cycles dynamic models: stability requirements, optimal principles, thermodynamic rules ? 2) How should be accounted for uncertainty in storage-flow values ? It’s important because dynamic models with symmetries may (and most often are) structurally unstable; 3) “Upscaling” problem: algorithms are needed for spreading geographically local modelling results on large territories with estimating their correctness (the simplest method is trivial multiplying on area occupied by ecosystems of that type, but it can result in essential errors); 4) Cutting non-desirable bifurcation surfaces: how should we construct the system to minimize a number of complex stability boundaries which give intractable dynamic regimes difficult to be interpreted ?; 5) What new observations and data should be collected for better understanding connections between climate change and biogeochemical cycles in different ecosystem types?; 6) Many more…

Thank you for attention !

SLIDE 13

Different types of bog ecosystems in the parameter space

Specific intensity of run-off and peat formation Carbon assimilation by plants, g/m2 year dry weight Mesotrophic bogs: Oligotrophic bogs: North-West of European Russia Western Siberia Mean-temperature-related model parameters: q1

C = q1 C(C1)- carbon assimilation by vegetation

depends on its biomass and linearly grows under the atmospheric СО2 increase; m3

C =m3 C(T)– intensity of peat formation depends

• n T – air mean annual temperature;

γ32 =γ32(T) – dead organic matter decomposition rate depends on the mean annual temperature

SLIDE 14

56,5 24,6

18,9

15,6 34,2

26,1

10 20 30 40 50 60 70 80 90 100 (1) (2) Олиготрофные Мезотрофные Эвтрофные

Оценки долей площади болотных провинций, занимаемых основными типами болот, при изменениях климата по сценариям удвоения СО2 в атмосфере Современные оценки долей площади болотных провинций, занимаемых основными типами болот (Вомперский, 2005)

68,2 17,6

14,2

13,4 38,6

24,8

10 20 30 40 50 60 70 80 90 100 (1) (2) Олиготрофные Мезотрофные Эвтрофные

Оценка изменений отношения типов болот при изменениях климата по сценарию удвоения CO2 в атмосфере

(1) – северо-запад России: Ладожско-Ильменская провинция; (2) – Западносибирская южной тайги Классификация болотных провинций (Кац, 1970) и оценка площади, занятой каждым типом болот по провинциям (Вомперский, 2005)

Вомперский С.Э., Сирин А.А., Цыганова О.П., Валяева Н.А., Майков Д.А., Болота и заболоченные земли России: попытка анализа пространственного распределения и разнообразия. Известия РАН, серия географическая, 2005, №5, с. 39-50.

SLIDE 15

Coupled biogeochemical cycles with climatic parameterization

Классификация болотных провинций (Кац, 1970) и оценка площади, занятой каждым типом болот по провинциям (Вомперский, 2005)

Вомперский С.Э., Сирин А.А., Цыганова О.П., Валяева Н.А., Майков Д.А., Болота и заболоченные земли России: попытка анализа пространственного распределения и разнообразия. Известия РАН, серия географическая, 2005, №5, с. 39-50.

C1, N1, W1 C2, N2 C3, N3, W3

y1

C

f12

C

f13

C

q2

C

y2

C

f32

C

y3

C

q3

C

f23

C

q1

C

q1

W

y1

W

y1

N

q1

N

f12

N

f13

N

f31

N

f13

W

f31

W

f23

N

q3

W

y3

W

q3

N

y3

N

q2

N

q1W – осадки, q3W – приток с соседних экосистем и с грунтовыми водами (отсутствует в олиготрофном случае), y1W – транспирация и испарение с растительного покрова, y3W – испарение с непокрытой поверхности и сток, f13W – сток части осадков, f31W – потребление воды растительностью из почвы,

SLIDE 16

Periodic and chaotic dynamics after CO2 atmospheric increase

Limit cycle Γ1

(4) as a result of Hopf

bifurcation for the given equilibrium. q1=1010 g/(m2year), m4=0.012986. Initial conditions: x0=[8550 1.8 36 8900]. Limit cycles Γ2

(4) and Γ4 (4) as a result of

period doubling bifurcation for the cycle Γ1

(4). q1=1018 g/(m2 year) and q1=1025.25

g/(g2 year). Strange attractor after the period-doubling bifurcation. q1=1027.6 g/(m2 year).

SLIDE 17

Steady states of the carbon cycle model and interpretation

] 6 . 8835 ; 246 . 36 ; 5 . 8830 [

) 3 (

=

−

x

Multistability of of steady regimes: convergence of time plots to steady states x(2) and x(3+).

a fen or raised bog a measured mesotrophic bog sphagnum pine forest or a meadow and a mesotrophic bog )] ) ( ( 1 ; ; [

13 1 13 1 3 4 13 1 1 ) 1 (

α α α + + + = m q q m m q x

]; ; ; [

3 2 1 ) 3 ( ± ± ± ± =

x x x x