ATS 621 Fall 2012 Lecture 5

Back to the Box Model…. Example: strat-trop exchange

How are sinks represented? Wet and dry deposition: Chemistry: Notice these are all first-order losses (rate = constant x M)

The simplified box model M M Q S If not in steady state, and if we have an initial condition, we can solve the equation and examine approach to new steady state (assumes first order loss process)

M0M0 M0M0 Q0Q0 S 0 = k M 0 M1M1 M1M1 Q1Q1 S 1 = k M 1

SPECIAL CASE: SPECIES WITH CONSTANT SOURCE, 1 st ORDER SINK Steady state solution (dm/dt = 0) Initial condition m(0) Characteristic time  = 1/k for reaching steady state decay of initial condition If S, k are constant over t >> , then dm/dt  0 and m  S/k: "steady state"

TWO-BOX MODEL defines spatial gradient between two domains m1m1 m2m2 F 12 F 21 Mass balance equations: If mass exchange between boxes is first-order:  system of two coupled ODEs (or algebraic equations if system is assumed to be at steady state) (similar equation for dm 2 /dt)

Illustrates long time scale for interhemispheric exchange; can use 2-box model to place constraints on sources/sinks in each hemisphere

TWO-BOX MODEL (with loss) m1m1 m2m2 T Lifetimes: If at steady state sinks=sources, so can also write: S1 S2 Q Now if define:  =T/Q, then can say that: Maximum  is 1 (all material from reservoir 1 is transferred to reservoir 2), and therefore turnover time for combined reservoir is the sum of turnover times for individual reservoirs. For other values of , the turnover time of the combined reservoir is reduced. m o = m 1 +m 2

EXAMPLE OF TWO-BOX MODEL (S cycle) T Lifetimes: S1 S2 Q Now if define:  =T/Q, then can say that: m o = m 1 +m 2

Atmospheric Lifetime of Fossil Fuel Carbon Dioxide Annual Review of Earth and Planetary Sciences Vol. 37: (Volume publication date May 2009) First published online as a Review in Advance on January 26, 2009 DOI: /annurev.earth David Archer,1 Michael Eby,2 Victor Brovkin,3 Andy Ridgwell,4 Long Cao,5 Uwe Mikolajewicz,3 Ken Caldeira,5 Katsumi Matsumoto,6 Guy Munhoven,7 Alvaro Montenegro,2 and Kathy Tokos6 CO2 released from combustion of fossil fuels equilibrates among the various carbon reservoirs of the atmosphere, the ocean, and the terrestrial biosphere on timescales of a few centuries. However, a sizeable fraction of the CO2 remains in the atmosphere, awaiting a return to the solid earth by much slower weathering processes and deposition of CaCO3. Common measures of the atmospheric lifetime of CO2, including the e-folding time scale, disregard the long tail. Its neglect in the calculation of global warming potentials leads many to underestimate the longevity of anthropogenic global warming. Here, we review the past literature on the atmospheric lifetime of fossil fuel CO2 and its impact on climate, and we present initial results from a model intercomparison project on this topic. The models agree that 20–35% of the CO2 remains in the atmosphere after equilibration with the ocean (2–20 centuries). Neutralization by CaCO3 draws the airborne fraction down further on timescales of 3 to 7 kyr.

Hydrological cycle Evap: 75% water, 25% land or transpiration Average lifetime until conversion to droplet: 10 days

Oxygen budget

Note these balance, and work on relatively fast time scales Fossil fuel combustion is a sink of O 2 ; but if we burned it all, would use a few percent of atmos O 2 If photosynthesis stopped, we’d lose a source of O 2 ; all surface organic matter would be consumed in ~20 years, but impact on O 2 still small…. Only this reservoir is big enough to matter for O2 budget

Tropospheric ozone cycle

Tropospheric ozone cycle, continued Note this is an important source of OH  !

Global sulfur cycle

THE GLOBAL SULFUR CYCLE SO 2 H 2 S volcanoes coal combustion oil refining smelters SO 2 CS 2 SO 4 2- OCEAN 1.3x10 21 g S  10 7 years deposition runoff SO 4 2- plankton COS (CH 3 ) 2 S microbes vents FeS 2 uplift ATMOSPHERE 2.8x10 12 g S  1 week SEDIMENTS 7x10 21 g S  10 8 years (sources in Tg S y -1 )

Source Regions for DMS Lana, A., et al. (2011), An updated climatology of surface dimethlysulfide concentrations and emission fluxes in the global ocean, Global Biogeochem. Cycles, 25, GB1004, doi: /2010GB

Ocean currents (sources of upwelling)

Winds blowing across the ocean surface often push water away from an area. When this occurs, water rises up from beneath the surface to replace the diverging surface water. This process is known as “upwelling.” Subsurface water that rises to the surface as a result of upwelling is typically colder, rich in nutrients, and biologically productive. Therefore, good fishing grounds typically are found where upwelling is common. For example, the rich fishing grounds along the west coasts of Africa and South America are supported by year-round coastal upwelling. Seasonal upwelling and downwelling also occur along the West Coast of the United States. In winter, winds blow from the south to the north, resulting in downwelling. During the summer, winds blow from the north to the south, and water moves offshore, resulting in upwelling along the coast. This summer upwelling produces cold coastal waters in the San Francisco area, contributing to the frequent summer fogs. (Duxbury, et al, 2002.)

The CLAW Hypothesis Charlson, R. J., Lovelock, J. E., Andreae, M. O. and Warren, S. G. (1987). "Oceanic phytoplankton, atmospheric sulphur, cloud albedo and climate". Nature 326 (6114): 655–661.

EXTRA SLIDES (not part of “official” course materials) : More on Models from Prof. Colette Heald  these were included at end of posted Lecture 4