1. Develop an approach to analyzing large data sets.
2. Using linear least least squares regressions to predict changes in a single variable based on changes in other variables.

• greenhouse warming
• gas exchange
• photosynthesis
• respiration
• partial pressure
• saturation concentration
• apparent oxygen utilization

Introduction:
    Over the last 50 years a dramatic change in the atmospheric CO₂ has been documented. This increase in CO₂ may act to change the heat balance caused by build up of greenhouse gases in the atmosphere resulting in warming of the earth by trapping infrared radiation in a process known as greenhouse warming. One of the main sinks of atmospheric CO₂ is the ocean through gas exchange where CO₂ gas diffuses into the ocean because of concentration gradients. Thus, in areas where the surface ocean concentration of CO₂ ([CO₂]) is lower than that of the atmosphere there is a net flux of CO₂ into the ocean. Because atmospheric CO₂ is continually rising as we burn more fossil fuel, there is a globally averaged net flux of CO₂ into the ocean. Despite the net flux of CO₂ into the ocean there are still many areas of the ocean that act as sources due to high concentrations of CO₂ in the ocean. To properly quantify the how much CO₂ is going into the ocean it is important to understand what mechanisms are controlling the surface ocean concentration of CO₂.

Mechanisms that control CO₂ concentration in the surface ocean:

1. Biological processes
• Photosynthesis:
• CO₂ + H₂O + light +nutrients --> O₂ + organic matter (CH₂O)
• In this process CO₂ is taken up by plants to produce O₂ and organic matter (CH₂O).
• Because the photosynthetic process also involves the uptake of NO3 the ratio that cell usually take up CO₂ and give off O₂ is anywhere from 1-1.4. This ratio is known as the photosynthetic quotient.
• Respiration:
• organic matter (CH₂O) + O₂ --> H₂O + CO₂ + nutrients
• This a process that is mediated by bacteria and breaks down organic matter to produce CO₂
• CaCO₃ production and dissolution
• CO₂ + CaCO₃ + H₂O <---> 2HCO₃^- + Ca²⁺
• Production of CaCO₃ to produce shells will cause the above reaction to go to the left and will result in a increasing of CO₂ concentration. Dissolution of CaCO₃ forming animals will decrease the surface ocean CO₂ concentrations; thus, biological processes involving CaCO₃ will counteract the effect of photosynthesis and respiration on the the concentration of CO₂.
2. Gas exchange
• This is the process where gases at the surface of the ocean are exchanged with gas in the atmosphere. This process tends towards an equilibrium where the where the partial pressure of gases in the surface waters is equal to that in the atmosphere.
• With no photosynthesis or respiration water at the surface will tend to be at equilibrium with the atmospheric CO₂ and O₂.
• The concentration of CO₂ in the atmosphere is only ~370 ppm and thus the equilibrium concentration in water for CO₂ is proportional to the partial pressure of CO₂ (pCO₂) in the atmosphere by the solubility constant, a,  for CO₂ in water at insitu temperature and salinity. Thus,

[CO₂]_sw=a * pCO₂
- the partial pressure of an ideal gas is the percent composition of that gas in air (thus, pCO₂ in air is equal to ~370 matm)
- because CO₂ combines with water to form carbonic acid and its dissociation products bicarbonate and carbonate:

CO_2(g) + H₂O <-->H₂CO_3(aq) <--> H⁺ + HCO_3(aq)^-  <-->H⁺ + CO_3(aq)^2-

a reservoir of CO₂ gas is stored up as dissociation products and thus the time that it takes for CO₂ in surface waters to equilibrate with the atmosphere is much longer than O₂.

• Oxygen makes up ~21% (210000 ppm) of the atmospheric gas by volume. When the partial pressure of O₂  in the atmosphere comes to equilibrium with that in the atmosphere (~21 matm) the oxygen concentration in water (which is proportional to the solubility constant, a, for oxygen) is at saturation concentration. To normalize O₂ concentrations in the surface waters to the saturation concentration we use a term called apparent oxygen utilization (AOU):
 
AOU=(Saturation concentration of oxygen in sea water at insitu temperature and salinity)-[O₂]
• The AOU indicates how far out of equilibrium oxygen is at the surface:
• Positive values indicate that O₂ gas has been taken out of the water by respiration or that recent cooling has increased the saturation concentration but gas exchange has not had enough time to bring the oxygen back to equilibrium value.
• Negative values indicate that O₂ has been has been added to the water by photosynthesis or that recent warming  has decreased the saturation concentration but gas exchange has not had enough time to bring the oxygen back to equilibrium value.
3. Upwelling and horizontal advection of water masses

• The surface ocean concentration of O₂ may also change as result of upwelling and consequential horizontal advection of water masses which will bring have different initial values of CO₂ and O₂. This means that changes in oxygen or AOU due to upwelling or horizontal advection will not have the same effect on the concentration of CO₂.
• Salinity and temperature can often be thought as tracers of water masses. The combination of these two variables can be used to calculate the density of sigma_t=1000*(density-1).

References:
DeGrandpre, M. D., T. R. Hammar, C. D. Wirick, 1998. Short-term pCO2 and O2 dynamics in California coastal waters. Deep-Sea Research II 45, 1557-1575