modeling biogeochemical cycles: dynamical climatology gerrit lohmann 2. june 2005, 15.15 o‘clock...

Modeling Biogeochemical Cycles: Dynamical Climatology

Gerrit Lohmann2. June 2005, 15.15 o‘clock

• Biogeochemical cycles• Clocks 14-C• Thermohaline Circulation• Some homework

Modeling Biogeochemical Cycles:

Turnover Time, renewal time

M content if a substance in the reservoir

S total flux out of the reservoir

MS=kMQ

single reservoir with source flux Q, sink flux S, and content M

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The turnover time of carbon in biota in the ocean surface water is3 x 1015/(4+36) x 1015yr ≈ 1 month

The equation describing the rate of change of the content of a reservoir can be written as


If the reservoir is in a steady state (dM/dt = 0) then the sources (Q) and sinks (S) must balance.

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If material is removed from the reservoir by two or more separate processes, each with a flux Si, then turnover times with respect to each process can be defined as:

Since ∑ Si = S, these time scales are related to the turnover time of the reservoir,

In fluid reservoirs like the atmosphere or the ocean, the turnover time of a tracer is also related to the spatial and temporal variability of its concentration within the reservoir.


Fig. 4-2 Inverse relationship between relative stand-dard deviation of atmospheric concentration and turnover time for important trace chemicals in thetroposphere. (Modified from Junge (1974) with per-mission from the Swedish Geophysical Society.)

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In fluid reservoirs like the atmosphere or the ocean, the turnover time of a tracer is also related to the spatial and temporal variability of its concentration within the reservoir.


Atmosphere 725(Annual increase ~3)

Surface waterDissolved inorg. 700

Dissolved org. 25(Annual increase ~ 0,3)

Surface biota3

Intermediate andDeep water

Dissolved inorg. 36,700Dissolved org. 975

(Annual increase ~ 2,5)

Short-lived biota~110

Long-lived biota ~450(Annual decrease ~1)

Litter~60

Soil 1300 - 1400(Annual decrease ~1)

Peat (Torf)~160

Fossil fuelsoil, coal, gas

5,000 - 10,000

Respiration &decomposition

~36

Primaryproduction

~40

Detritus~4

Detritus decomposition

54-50

~40 ~38

5

2 - 5

2 - 5

~15~40

~120~60~90~93Deforestation

~1

‹1

‹1

~15~1

Fig. 4-3 principal reservoirs and fluxes in the carbon cycle. Units are 1015 g(Pg) C (burdens)and PgC/yr (fluxes). (From Bolin (1986) with permission from John Wiley and Sons.)

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The residence time is the time spent in a reservoir by an individual atom or molecule. It is also theage of a molecule when it leaves the reservoir. PDF

PDF of residence times be denoted by ø ( )

The (average) residence time

The (average) age of atoms in a reservoir is given by[PDF is always decreasing ]

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lake

exponential decay238 U

removal is biasedtowards young particles"short circuit" case:Sink close to the source

Modeling Biogeochemical Cycles: The adjustment process is

e-folding time

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The flux Fij from reservoir i to reservoir j is given by

The rate of change of the amount Mi in reservoir i is thus

where n is the total number of reservoirs in the system. This system of differential equationscan be written in matrix form as

where the vector M is equal to (M1, M2,... Mn) and the elements of matrix k are linear combinationsof the coefficients kij

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Modeling Biogeochemical Cycles: 4 - 6


where and are the eigenvectors of the matrix k. In our case we have

or, in component form and in terms of the initial conditions:

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response time

cycle 1k12 k21

turnover times of the two reservoirs

cycle

1

01

1

02

1


?


ATMOSPHERE (dust)

SURFACE OCEAN

SEDIMENTS

2812

0.00009

1.29X108

DEEP OCEAN

MINE-RABLE

P

323-645

6460OCEAN BIOTA

87.5Land (upper 60 cm of soil)

96.9

LAND BIOTA

1.6 - 4.032.2

0.11

1.870.58 1.4

0.690.600.39

0.02 0.010.140.106.06.0

The global phosphorus cycle. Values shown are in Tmol and Tmol/yr. (T=10^12)The mass of P in each reservoir and rates of exchange. Phosphate PO4(3-)

33.6

0.03

0.10

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Table 4-1 Response of phosphorus cycle to mining output. Phosphorus amounts are given inTg P (1Tg=1012g). In addition, a pertubation is introduced by the flux from reservoir 7 (mineablephosphorus), which is given by 12 exp(0.07t) in units of Tg P/yr

Tcycle = 5300 years

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Q T

S1 S2

1 2

Example: An open two-reservoir system

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Simplified model of the carbon cycle. Ms represents the sum of all forms ofdissolved carbon , , and

CO2

H 2 HCO3

HCO3

,

CO 22

Atmosphere

M A

Terrestrial System

M T

Ocean surfaceDiss C= CO2,HCO3,H2CO3

M S

Deep layers of ocean

M D

F TA

F AT

F SA F AS

F SDF DS

Non-linear System: Simplified model of the biogeochemical carbon cycle. (Adapted from Rodhe and Björkström (1979) with the permission of the Swedish Geophysical Society.)

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where the exponent SA (the buffer, or Revelle factor) is about 9. The buffer

factor results from the equilibrium between CO2(g) and the more prevalent forms of

dissolved carbon. As a consequence of this strong dependence of FSA on MS,

a substantial increase in CO2 in the atmosphere is balanced by a small increase of MS.

FSA kSAM S

SA

FAT K AT M AAT

FAT K AT M AAT

atmosphere to the terrestial system

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uptake of atmospheric CO2 by terrestrial biota

with MTB being the content of carbon in terrestrial biota and D, a Michaelis constant.Mass MTB may grow without bounds. To avoid such a mathematical explosion, Williams(1987) suggested that the factor MTB in Equation (33) be replaced by


Fig. 4.13 Calculated and observed annual wet deposition of sulfur in mgS/m2 per year.

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ThermodynamicEquation

Equationsof Motion

TurbulenceParameterization

SaltEquation

Sea Ice


HydrologicEquation

Vegetation

Land Ice

OCEAN LAND

TurbulenceParameterization

Equationsof Motion

Radiation


WaterConservation

Equation

CloudParameterization

ATMOSPHERE

Sensible Heat

Radiation

Runoff

WindStress

Sensible Heat

Radiation

Evaporation

Precipitation

Evaporation

Precipitation

Schematic diagram showing the components of a global climate model (GCM).

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organized fluid motion molecular diffusion

continuity of tracer mass

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Eddy correlation technique, eddy diffusivity


Fig 4-15 Orders of magnitude of the average vertical molecular or turbulent diffusivity(which is largest) through the atmosphere, oceans, and uppermost layer of ocean sediments.

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modeling biogeochemical cycles: dynamical climatology gerrit lohmann 2. june 2005, 15.15 o‘clock...

Documents

modeling biogeochemical

reservoir j

reservoir stotal

n reservoir i

turnover time of carbon

time scales

average residence time

kmq single reservoir