Nonlinear, time dependent model sensitivity to initial conditions poses a
challenging problem when attempting to initialize such a model. In order to
initialize a chemical-physical model of the upper several hundred meters of the
North Atlantic, we have calculated the initial concentrations of several
chemical species from three estimation methods by a combination of the
Climatological Atlas of the World Ocean (Levitus, 1982) and the TTO
north, and tropical, Atlantic study databases. A 
grid of the average initial concentrations over the mixed layer depth was
generated for the method of preference and added to the initialization data
base of the model. Contour maps of this calculated initial concentration set
are presented and comparisons with the other methods and actual data are made.
Knowledge of the distribution of chemical variables in the sea is a principal goal of ocean chemists. For many years problems of technique, whether in analysis or in sampling, hampered progress. This, and the continuous challenge of determining new chemical species, has resulted in a fragmented data set which only recently has become in any way assimilable in the manner that large scale physical data sets are commonly treated.
Within the deep ocean the chemical conditions are, with the exception of the artifacts introduced by man, in approximate steady state, so that a simple compilation of data laboriously produced over many years would eventually yield a map or atlas of chemical properties. In the upper ocean, however, (viewed here as approximately extending to the maximum depth of wintertime mixing) steady state conditions can not apply and chemical data obtained from diverse cruises are badly biased in time. It is quite unlikely that we will ever achieve synoptic sampling of the entire ocean, so that some kind of model or data treatment will have to be applied in order to uncover realistic seasonal chemical signals.
In this paper we explore the problem further, and attempt to compute some wintertime surface chemical properties for the North Atlantic ocean by manipulating expedition data greatly biased in time and comparing them, where possible, to actual winter observations.
The choice of a late wintertime signal is significant. Operationally winter cruises are difficult to conduct, so that data sets generally result from fair-weather seasons. More importantly, winter forcing sets chemical boundary conditions for the upper ocean that are critical in the initialization of seasonal models. Jensen (1987) provides a review of how sensitive even simple nonlinear systems are to initial conditions.
The data sets we choose cover the distributions of PO
, NO
,
SiO
and alkalinity, since these are master variables of ocean chemistry.
The rapidly exchanging gases (such as O
, etc.) are normally set
close to atmospheric equilibrium in winter. However, the exceptionally slow
exchange time for CO
(Bolin, 1960 and Broecker and Peng, 1982) raises the
possibility of treatment similar to that proposed here for the nutrient
species; we plan to address this in a later paper. The strategy for
non-gaseous species is quite general and many other chemical properties (
e.g. trace metals) are potentially treatable in the same way.
Most ocean chemists have a general belief that wintertime properties can be estimated in some way from wintertime mixed layer depths and chemical profiles, but there appears to be a distinct lack of formalism in the concept. Woods (1985) gives one expression of this process by developing a theory explaining the regional variation of the annual maximum depth of the mixed layer. Following from this, Woods (1985) gives an equation for the nutrient balance within the seasonally varying mixed layer depth.
In this paper estimated winter surface concentrations were obtained by three methods applied to each station profile considered. The first method was by interpolation to the base of the average wintertime mixed layer depth (MLD) ( extrapolation method). The second method involved integrating and averaging over this same depth interval ( integral method). The third method was employed largely to demonstrate the necessity of information about the wintertime mixed layer depth, by interpolation to the base of the seasonal mixed layer ( seasonal method) at the time of observation. The first two methods require some a priori knowledge of physical forcing while the last is a worst case example, applying to situations when only the fair-weather station data are available. Analysis of some limited time series data and comparisons with actual wintertime cruise data (also limited) provided a means to choose a preferred method.
Aside from the motivation we received from the initialization problem of our model, additional incentives exist. The Global Ocean Flux Study (GOFS) is currently in the process of planning time series stations and cruise tracks for the world oceans (U.S. GOFS Report 2, 1986). Maps of the sort derived in this paper provide an important insight into the structure and variability of the biologically active upper several hundred meters of the ocean. Knowledge of what the ocean looks like during the summer (fair-weather) can be contrasted with estimates of its condition during the winter (foul weather). Another incentive is the sensitivity of inverse methods to initial conditions. Wunsch (1987) shows that, while solving the governing equations backwards in time and upstream in space, one is moving in an inherently unstable direction; the end point of these calculations (the initial conditions) can have a strong effect on the outcome of the model. Although Wunsch (1987) deals with the problems stemming from the initialization of an inverse model applied to transient tracers, the success we experienced in finding the initial conditions of tracers, that admittedly are in steady state on an annual time scale, leads us to believe that a similar treatment of transient tracer data also may be successful.