Upper Ocean 1-D Seasonal Models
File last modified 16 November 1998
19.3d Adding Gases to the Model: Comparing Results
It seems enough that we've run the model, but now we have to look at the results? How do we compare the results to "reality"? What features do we look for in making this comparison? Right off the bat, the problem becomes much more difficult than matching the temperature climatology. Instead of simply matching the temperature field, we have three new parameters that are somehow adjustable, and need to be matched to observations: gas exchange rates (how we scale the Liss-Merilvat formulation), air injection rates (how we scale the Keeling formulation), and partial/complete trapping fractions. Let's first look at an example run (a three year run starting from solubility equilibrium, using typical values for the adjustable parameters) for Ar and He. Below we plot the two gases as saturation anomalies (i.e. percentage difference from solubility equilibtrium). We could show you the gas concentrations instead, because that's actually what is calculated in the model (never model concentration anomalies, model concentrations, because that's what nature moves around!), but it's the anomalies which are interesting.
We can see the seasonal evolution of the Ar saturation anomaly, which stabilizes into a pattern of slight supersaturation in the winter time, then a pronounced supersaturation in the seasonal thermocline (just below the mixed layer) in the summertime. This is a result of the fact that the ocean is trying to breath Ar in response to the seasonal thermal cycling (Ar is less soluble in warmer water), but cannot keep up with the heating/cooling cycle. Thus an Ar maximum occurs every summer below the mixed layer.
The He saturation anomaly cycle looks rather different, because it is responding to different processes. Because it is very insoluble, it is driven by air injection, so it is at a minimum in the summer, when winds (and hence bubble injection processes) are smaller due to lower wind speeds, and it is at a maximum in the winter, when wind speeds are high. It is the opposite of Ar. Moreover, it is very ragged looking, since it directly responds to wind (rather than thermal) forcing, and the model is driven by stochastic winds. Our little model has wind bursts (storms) which can spike the He concentration, but has little effect on the Ar. Careful inspection reveals that the Ar sections exhibit some variation as well, but this is probably more an artifact of mixed layer thickness variations induced by the bulk Ri No. readjustments. Note one other thing in the He section: the 1% contour is gradually moving downward as the run progresses. This is the slow relaxation of the deep water as the model spins up. Since the winter mixed layer He anomalies are gradually building to a value of about 2.5 to 3% in this case, it is clear that we have to "throw away" the first year's model data because we started at the wrong initial He values: we should have started at about 3.5 to 3% supersaturation, rather than 0%.
Another interesting way to look at the results is to plot the mixed layer saturation anomalies of the gases as a function of time. We've included the gases He, Ne, Ar, Kr, Xe and abiotic O2 in the plot. Don't try to find the O2, it almost perfectly overlays the Ar curve (quelle surprise!).
There appear to be two groups of gases. He and Ne anomalies look pretty much alike: they are maximal in the winter, and minimal in the summer, like we said before. They are driven by air injection balanced by gas exchange. The other group consists of Ar, Kr, and Xe, which are driven by thermal cycling (controlled by vertical mixing) balanced by gas exchange. These gas anomalies are maximal in the summer, and minimal in the winter. In fact there is a definite trend of increasing amplitude as you go "down" the column in the periodic table. This is a result of the increasing temperature slope in solubility, and decreasing molecular diffusivity (and hence gas exchange rate). In fact, Kr and Xe anomalies go negative in the winter, because they are trying to catch up with the ingassing side of the "breathing" cycle.
We can (and will) approach the problem from the view of reducing the chi-square of the match between the data (He, Ne and Ar observations) and the model as a function of the parameters. Before doing this, it is worthwhile exploring those features of the data which are most diagnostic of the different processes. Spitzer and Jenkins (1989) identified several critical features of the observations that were sensitive to (and hence diagnostic of) certain processes and hence parameters. The discussion of these features can be rather long, so we will be very terse in our discussion, and rely on your reading the literature. We'll organize these by parameters:
So why do we bother with this kind of "analysis"? Well, it gives us some insight into the behavior of the model/real ocean, and suggests something about the shape of the chi-square hypersurface in parameter space. Further, it allows us to make some educated guesses as to the approximate ranges of parameters that are consistent with the key observations. Having established these ranges, then we can construct simple, linearized relationships describing the relation between the parameters (as unknowns) and the data-model chi-squared, and solve for optimal values which minimize the chi-squared.
We won't repeat this work here, because it was done by Spitzer and Jenkins, but we will add a little bit about He:Ne effects. This was not treated in that paper because the data were not available then. He:Ne ratios are most sensitive to the complete/partial trapping fractions. As we mentioned before, this is important if we are to scale our determination of air injection rates from He up to Ar (and hence O2). The mixed layer concentration history shown above is for an equal mixture of complete and partial trapping. The pictures shown below are for all complete trapping
Notice that the Ne anomalies are larger than the He anomalies in this case. This is because although the gases are pumped in at roughly equal rates, the Ne is more slowly equilibrated back to the atmosphere via gas exchange, and hence accumulates more in the mixed layer. This is the opposite case for partial trapping:
If we correlate the He and Ne anomalies in the model for the upper 50m (using the last two years of the model runs only, because of the spin-up problem) we observe a characteristic slope. We plot this slope as a function of complete/partial trapping fractions below for two sets of runs (each with individual stochastic wind forcing, and with different levels of forcing):
so one sees the same effect that we noted for the mixed layer.
Now what Spitzer and Jenkins did was to run the model many times, and to measure the specific criteria ( e.g. the magnitude of the subsurface argon maximum) as a function of model parameteres. They then set up a system of linear equations with these empirical relations on the left side, and with the observed values on the right. These equations were then solved in an overdetermined, least squares fashion using SVD, to obtain the best estimates of parameters.
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