Modeling Biogeochemical Cycles: Dynamical Climatology Gerrit Lohmann 2. June 2005, o‘clock Biogeochemical cycles Clocks 14-C Thermohaline Circulation Some homework

Modeling Biogeochemical Cycles: Turnover Time, renewal time Mcontent if a substance in the reservoir Stotal flux out of the reservoir M S=kMQ single reservoir with source flux Q, sink flux S, and content M The turnover time of carbon in biota in the ocean surface water is 3 x /(4+36) x yr ≈ 1 month The equation describing the rate of change of the content of a reservoir can be written as

Modeling Biogeochemical Cycles: If the reservoir is in a steady state (dM/dt = 0) then the sources (Q) and sinks (S) must balance If material is removed from the reservoir by two or more separate processes, each with a flux S i, then turnover times with respect to each process can be defined as: Since ∑ S i = 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.

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

Modeling Biogeochemical Cycles: Atmosphere 725 (Annual increase ~3) Surface water Dissolved inorg. 700 Dissolved org. 25 (Annual increase ~ 0,3) Surface biota 3 Intermediate and Deep water Dissolved inorg. 36,700 Dissolved org. 975 (Annual increase ~ 2,5) Short-lived biota ~110 Long-lived biota ~450 (Annual decrease ~1) Litter ~60 Soil (Annual decrease ~1) Peat (Torf) ~160 Fossil fuels oil, coal, gas 5, ,000 Respiration & decomposition ~36 Primary production ~40 Detritus ~4 Detritus decomposition ~40 ~ ~15 ~40 ~120~60~90~93 Deforestation ~1 ‹1 ~15 ~1 Fig. 4-3 principal reservoirs and fluxes in the carbon cycle. Units are g(Pg) C (burdens) and PgC/yr (fluxes). (From Bolin (1986) with permission from John Wiley and Sons.) 4 - 3

Modeling Biogeochemical Cycles: The residence time is the time spent in a reservoir by an individual atom or molecule. It is also the age 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 ] lake exponential decay 238 U removal is biased towards young particles "short circuit" case: Sink close to the source

Modeling Biogeochemical Cycles: The adjustment process is e-folding time 4 - 5

Modeling Biogeochemical Cycles: The flux F ij from reservoir i to reservoir j is given by The rate of change of the amount M i i n reservoir i is thus where n is the total number of reservoirs in the system. This system of differential equations can be written in matrix form as where the vector M is equal to (M 1, M 2,... M n ) and the elements of matrix k are linear combinations of the coefficients k ij 4 - 6

Modeling Biogeochemical Cycles: 4 - 6

Modeling Biogeochemical Cycles: 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: 4 - 6

Modeling Biogeochemical Cycles: response time turnover times of the two reservoirs

Modeling Biogeochemical Cycles: ?

ATMOSPHERE (dust) SURFACE OCEAN SEDIMENTS X10 8 DEEP OCEAN MINE- RABLE P OCEAN BIOTA 87.5 Land (upper 60 cm of soil) 96.9 LAND BIOTA 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-)

Modeling Biogeochemical Cycles: Table 4-1 Response of phosphorus cycle to mining output. Phosphorus amounts are given in Tg P (1Tg=10 12 g). In addition, a pertubation is introduced by the flux from reservoir 7 (mineable phosphorus), which is given by 12 exp(0.07t) in units of Tg P/yr T cycle = 5300 years 4 - 8

Modeling Biogeochemical Cycles: QT S1S1 S2S2 12 Example: An open two-reservoir system 4 - 9

Modeling Biogeochemical Cycles: Simplified model of the carbon cycle. M s represents the sum of all forms of dissolved carbon,, and Atmosphere M A Terrestrial System M T Ocean surface Diss C= CO 2,HCO 3,H 2 CO 3 M S Deep layers of ocean M D F TA F AT F SA F AS F SD F 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.)

Modeling Biogeochemical Cycles: where the exponent  SA (the buffer, or Revelle factor) is about 9. The buffer factor results from the equilibrium between CO 2 (g) and the more prevalent forms of dissolved carbon. As a consequence of this strong dependence of F SA on M S, a substantial increase in CO 2 in the atmosphere is balanced by a small increase of M S. atmosphere to the terrestial system

Modeling Biogeochemical Cycles: uptake of atmospheric CO 2 by terrestrial biota with M TB being the content of carbon in terrestrial biota and D, a Michaelis constant. Mass M TB may grow without bounds. To avoid such a mathematical explosion, Williams (1987) suggested that the factor M TB in Equation (33) be replaced by

Modeling Biogeochemical Cycles:

Fig Calculated and observed annual wet deposition of sulfur in mgS/m 2 per year

Modeling Biogeochemical Cycles: Thermodynamic Equation Equations of Motion Turbulence Parameterization Salt Equation Sea Ice Thermodynamic Equation Hydrologic Equation Vegetation Land Ice OCEANLAND Turbulence Parameterization Equations of Motion Radiation Thermodynamic Equation Water Conservation Equation Cloud Parameterization ATMOSPHERE Sensible Heat Radiation Runoff Wind Stress Sensible Heat Radiation Evaporation Precipitation Evaporation Precipitation Schematic diagram showing the components of a global climate model (GCM)

Modeling Biogeochemical Cycles: organized fluid motionmolecular diffusion continuity of tracer mass

Modeling Biogeochemical Cycles: Eddy correlation technique, eddy diffusivity

Modeling Biogeochemical Cycles: 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

Modeling Biogeochemical Cycles: