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In these two lectures, we will be developing and exploring a class of models aimed at simulating the seasonal behavior of dissolved gases in the upper ocean. This approach can be more generally applied to any other shallow water column properties (including bio-optical modeling, particle dynamics, etc.) with very minor modifications. The model we will be discussing is a derivation of the Price-Weller-Pinkel (1986, J. Geophys. Res.91, 8411-8427) which was augmented to incorporate gas exchange and used to model oxygen (Musgrave et al., 1988: J. Geophys. Res.93, 15,679-15,700) and then extended to other gases (Spitzer and Jenkins, 1989: J. Mar. Res.47, 169-196).
There are two general types of upper ocean models (although there are hybrids of these two as well). There are the Bulk Mixed Layer Models which, as the name suggests, treat the mixed layer as a homogeneous, well mixed box, within which properties, including chemical species and physical momentum, are uniformly distributed. The other class is referred to as the turbulence closure models which attempt to explicitly model the detailed turbulent processes occurring within the mixed layer. Because the time scales are so short (often seconds to minutes), very complex, and small scale, these models are computationally very "expensive" and hard to formulate and run. We will be dealing with the simpler, bulk models here, although it must be recognized that if our focus were on more detailed behavior in the mixed layer, particularly on short time scales, we would need to turn to the more demanding models. As you will sense as we proceed, however, we have our hands full with the simple models.
You may ask why bother with all this physics stuff? We're glad you asked. The main goal is to understand the nature and rates of biogeochemical processes. Nature provides us with a dynamic laboratory in the upper ocean where we observe the biogeochemical response to changing forcing, and the observation of that response is a fundamental signal that we can use to figure out what mechanisms and rates are behind that response. The challenge, however, is to separate the physical phenomena from the biogeochemical effects, and that is where the model comes in. In some sense, we are makeing the supposition that if the model moves some things around in a believable (and testable) fashion, then it must move other things, in particular biogeochemically affected substances in a realistic fashion.
Bear in mind, that models are fundmentally abstractions of reality. We do not have the data, knowledge or computational power to construct a computer calculation that incorporates all physical/chemical/biological processes at all space and time scales. What we have to do is deliberately simplify the problem to the point where we can construct a model that contains just enough detail, and just enough relevant processes to capture the bulk behavior of the system. This is obviously a fuzzy, philosophical issue, and you have to be very careful that you don't throw away important mechanisms in the simplification process, or more likely, that you parametrize unresolved processes correctly. Further, you may get yourself in a situation of having the model successfully mimic the observations for all the wrong reasons! Thus you should be your own harshest critic when you get into this area, for models often produce convincing and believable results that look close enough to reality to convince you of the wrong things. There is a school of thought which claims that you only learn something from a model when it fails. In other words, when a model seems to be working right, it may be two (or more) "wrongs" making a "right".
The history of the specific example we will be discussing begins with an attempt to resolve the primary production controversy that was started by aphotic zone oxygen utilization rate estimates. What happened was that certain tracer-related measurements can be used to estimate ventilation rates of water masses, etc., and through those rates, calculate in situ oxygen consumption rates in the water column below the euphotic (lighted) zone of the ocean. Oxygen is consumed in the aphotic part of the water column by bacterial oxidation of organic carbon, either from dissolved phase (DOC) or from particles rained down from above (POC). Knowing the stoichiometic ratio between the oxygen consumed and the carbon oxidized (see for example Takahashi et al, 1985, J. Geophys. Res. 90, 6907-6924) one can estimate the rate of carbon being oxidized in the water column. Now the source of this carbon is ultimately carbon fixed by new primary production, so by integrating the total water column demand for oxygen we can estimate the total flux of carbon being supplied to the water column, and hence the new primary production. Since one is dealing with water masses with ages of years to decades, the estimate of new production thus obtained is an average over years to decades.
The trouble is, this estimate of new production turns out to be about a factor of 5 to 10 larger than conventional biological determinations based on C-14 incubations and estimates of recycling rates for oligotrophic waters. How do we arbitrate this dispute? One approach would be to look at some other part of the production "machine". Primary production is powered by photosynthesis, and the other side of the "photosynthetic coin" is oxygen production. This, in fact has been observed in the open ocean, when a classic paper by Shulenberger and Reid (1981, Deep-Sea Res. 28, 901-920) reported on and interpreted a shallow oxygen maximum that develops within the seasonal thermocline in subtropical waters during the summer. Serious questions were raised about the interpretation, however: could the oxygen maximum be produced by physical processes? One could picture bubble trapping creating a supersaturation, for example. Another possibility is that temperature changes due to the seasonal heating cycle, although they don't change the absolute oxygen concetration, may produce an apparent supersaturation in the gas.
Well, these effects can be tested. Nature has been kind enough to provide us with an abiogenic analog of oxygen with argon. Ar is chemically and biologically inert, and has physical characteristics (molecular diffusivity and solubility) very close to that of oxygen. Thus if physical processes were drastically affecting the oxygen distribution, it would show up in the argon concentrations as well. Craig and Hayward (1987, Science 235, 199-202) measured argon at a location in the subtropical Pacific, and found a much smaller effect in the Ar than in the oxygen. They concluded that the biological effects were 4 times larger than the physical. That is, 75% of the oxygen signal must be biological.
This is all well and good, but how do you go from qualitative observations of the summertime development of an oxygen and argon maxima to quantitative estimates of oxygen (and from that primary) production rates? The problem is complicated, because not only are things changing with time (on a seasonal basis), the upper part of the water column is "lossy" in that gases are lost to (or gained from) the atmosphere by a gas exchange process which is time, wind and temperature dependent. Further, possible vertical mixing processes may play a role in moving gases around in a way which we cannot quantify. Some "back of the envelope" types of calculations (Jenkins and Goldman, 1985, J. Mar. Res., 43, 465-490) indicate that the oxygen production rate is more consistent with the aphotic zone oxygen consumption rate estimated productivity but we need a more quantitative model to do a better job.
We want to construct a simple physical model which emulates the seasonal to annual structure of the upper ocean at a time series site, in this case near Bermuda. In particular, we need to simulate the mixed layer depth and temperature, as well as vertical mixing processes. We'll incorporate some simple, but realistic physics and drive the model with climatological "forcing" (heat flux, sunlight, wind stress, etc). The reason why we use the climatology rather than actual observed forcing is that we are interested in the average water column response. Furthermore, short term variations may not be balanced by local vertical processes, whereas we know that on the average the upper ocean is more-or-less in local balance. This is, parenthically, the primary weakness of one-dimensional models.
Once we have a physical model which behaves (temperature and mixed layer depth-wise) well enough to simulate observed temperature trends, we put in inert gases. This involves parameterizing the gas exchange processes at the sea surface, and ultimately matching some inert gas observations, especially Ar, which is a close analog of oxygen, against the model. This gives us a model which moves gases around right. Now we put in oxygen, with some specified oxygen productivity profiles and see what kind of productivity is required to explain the observations.
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