DISCUSSION: WALVIS PARADOX AND PHASE RELATIONSHIPS

Modular plots allow a simple visualization of phase relationships for selected climatic cycles, such as the 41-k.y. cycle extracted by Fourier analysis. By isolating the 41-k.y. cycle hidden within the original data, phase relationships can be explored, as illustrated above (Fig. F7B). Modular plots differ from a simple cycle extraction in that the individual cycles are combined to get an average cycle for a given interval, such as an entire core. All the cycles within such an interval are stacked and averaged; thus, a modular plot represents an internal stack of a selected cycle or period. (For a description of the method, see Berger et al., 1993.)

Modular plots comparing the various proxies with ¹⁸O C. wuellerstorfi were created for the following elements: sand, coarse sand, EDA, BF/g, U/g, and ¹³C of C. wuellerstorfi. Modular plots were generated for Core 175-1085A-7H, where signals were strong within the bandwidth surrounding 41 k.y. and where there are five cycles to stack. Because of the amplitude of the dominant cycle and the number of cycles, Core 175-1085A-7H is presumed to show relationships most clearly for all of the indices. Core 175-1085A-8H modular plots (not shown) were created from patched isotope data using only three 41-k.y. cycles and are much less trustworthy. Cores 175-1085A-9H and 10H have very weak 41-k.y. signals (six times weaker than those of Core 7H). Therefore, only Core 175-1085A-7H is considered as yielding reliable patterns worth discussing (Fig. F8).

On the whole, in Core 175-1085A-7H, the state of climate is more important than the change in conditions (Fig. F8). The proxies, in essence, follow ¹⁸O C. wuellerstorfi isotopic cycles, with the exception of EDA. The carbon isotope signal is seen to be slightly offset, showing a lag with respect to the oxygen isotope record. (The discrepancy of this result with the zero lag shown in Fig. F4A suggests differences in asymmetries with respect to sine-shaped cycles between the ¹⁸O and ¹³C 41-k.y. cycles.)

EDA abundance in Core 175-1085A-7H was quite low, as were (estimated) amplitudes in the fluctuations in abundance. Thus, whereas EDA has a reverse relationship to ¹⁸O compared with expectations if diatom supply goes parallel to productivity, it is equally valid to say that EDA simply does not change very much, no matter what the state. The low amplitude of variation does not preclude the determination of phase, however. This situation is quite similar to the one reported off Angola for the late Quaternary (Schneider, 1991; Berger et al., 1994).

The modular plot analysis shows that EDA is almost as much correlated to change as to state of climate, unlike the other variables. In particular, the phases of BF/g and U/g suggest that organic matter supply is at maximum during fully glacial conditions (Fig. F8A, F8C), whereas EDA peaked more than 90° earlier and is on its way down toward a minimum at the very end of the glacial. Maximum productivity during glacial conditions, as seen in the benthic foraminifers, is also in agreement with other evidence in this region, even on Walvis Ridge (Oberhänsli, 1991). On Walvis Ridge, as mentioned, diatoms and radiolarians are likewise more abundant during interglacials (Diester-Haass et al., 1992), than during periods of high productivity.

The paradox represented by the contrary phase of silica has been discussed by a number of authors (Diester-Haass et al., 1992; Hay and Brock 1992; Berger and Wefer 1996; Berger et al., 1998). We must consider the possibility that the silicate content of the upper thermocline, from which silica for diatom frustules is derived during upwelling, changes through the glacial-interglacial cycles. This has been demonstrated for the North Pacific (Berger et al., 1997). When comparing the phosphate and silicate contents of subsurface waters, one finds that phosphate content is highly correlated with Si/P, that is, silicate is reduced more rapidly than phosphate when nutrients are extracted and it is released back more slowly to the water from sinking particles within the upper water layers (Berger and Lange, 1998). It is possible therefore, in principle, to increase productivity through upwelling in a given area without increasing diatom production. To do this, phosphate has to be brought to the site within thermocline water with a low Si/P ratio, that is, waters with low nutrient content. To overcome the handicap in quality, the upwelling and mixing has to be that much more vigorous, that is, the wind stress has to be increased greatly if productivity is to remain high despite the supply of "poor" water (Berger and Lange, 1998).

Whenever intensity of mixing of surface waters and nutrient content of subsurface waters are anticorrelated, diatom production will go through an optimum that is phase-shifted from the maximum of upwelling toward the maximum of nutrient concentration. Using this conceptual approach, we can attempt to reconstruct the (presumed) driver of mixing and upwelling, that is, "wind stress," at least qualitatively. For this purpose, we use BF/g as a proxy for productivity and we take EDA/(BF/g) as a proxy for Si/P in the water and, hence, of the quality of the upwelled water.

We then write the following:

Productivity = (wind-driven upwelling rate)
x (nutrient concentration in upwelled water).

By proxy,

BF/g = wind x EDA/(BF/g),

so that

wind = (BF/g)²/EDA.

This qualitative reconstruction is illustrated in Figure F9.

The rate of mixing and upwelling (wind) is seen to be at maximum late during glacial time, with productivity peaking early in glacial time, when nutrients have not yet reached their low point. Thus, regarding productivity, it seems that early glaciation is a privileged time, when both nutrient supply (decreasing) and wind (increasing) combine for an optimum period of productivity. Also, the modular plot (Fig. F9) suggests that intensity of mixing, in essence, has to override the effects of the low glacial nutrient supply. Apparently, it is able to do so more efficiently for phosphate and nitrate (which stimulates organic matter supply) than for silicate (which stimulates diatom growth). Presumably, this is due to nutrient stratification in the thermocline, with silicate peaking at greater depth than either phosphate or nitrate (Berger and Lange, 1998).

It would be very interesting to test the hypothesis of decreased nutrient supply in upwelling waters during glacial conditions. However, the available data appear insufficient to do this. In particular, the ¹³C values available for C. wuellerstorfi and Uvigerina pertain to conditions at the seafloor at 1700-m depth. In any case, our results support the concept of nutrient depletion in the glacial thermocline (Berger and Lange, 1998), whether through increased vertical fractionation (Boyle, 1988) or through increased lockup in more focused upwelling regions (Berger et al., 1994), or both.