Broecker Box Model

In the Broecker Box model, the total amount of water in the ocean is assumed to remain constant over time. In other words, the evaporation rate and burial of water in the sediments is equal to the rate of water input from river runoff and precipitation. The sizes of the surface- and deep-water reservoirs are also assumed to remain constant over time. This requires the global rate of upwelling to equal the global rate of downwelling. 

The Broecker Box model also assumes that materials enter the ocean only through river and groundwater runoff. This is a realistic assumption as all the other sources, such as atmospheric fallout and hydrothermal emissions, supply negligible amounts of... 

Regardless of the degree of its accuracy, the Broecker Box model can be used to obtain further insights into the relative importance of the biological pump. For example, we note that the surface-water volume is 10 times smaller than the deepwater. Since the rates of downwelling and upwelling are equal, seawater must spend one-tenth of its time in the surface-water box. The residence time of surface water is then 1/10 x 1000, or lOOy. Since the volume of surfece water is small, as is for the biolimiting ele-... 

Table 9.1 Broecker Box Model unlimited Elements. Ratios and Recycling Efficiencies for Representative Biolimiting, Biointermediate, and Bio-... 

Nutrients are carried back to the sea surface by the return flow of deep-water circulation. The degree of horizontal segregation exhibited by a biolimiting element is thus determined by the rates of water motion to and from the deep sea, the flux of biogenic particles, and the element s recycling efficiency (/and from the Broecker Box model). If a steady state exists, the deep-water concentration gradient must be the result of a balance between the rates of nutrient supply and removal via the physical return of water to the sea surface. 

Preformed phosphate represents an important component of the dissolved phosphate reservoir. This is seen in the relatively low ratio of remineralized to preformed phosphate, which ranges from 0.36 to 0.70. Based on the Broecker Box model presented in Chapter 9, only about 1% of the phosphate escapes from the ocean on any given mixing cycle to become buried in the sediments. So to a first approximation, only 36 to 70% of the phosphate in a deepwater mass originates from remineralization. (The wide range in percentage reflects geographic variability related to the age of the water... 

Box model for the biolimiting elements. Source From Broecker, W. S. (1974). Chemical Oceanography, Harcourt, Brace and Jovanovich Publishers, pp. 14-15. 

In terms of organic carbon generation, the coccolithophorids are a minor player, representing only 6 to 8% of global marine primary production. But their detrital remains contribute disproportionately to the burial of carbon in marine sediments. This is due to near complete loss of POC via remineralization as the detrital hard and soft parts settle to the seafloor. As estimated from Broecker s Box model in Chapter 9, only about 1% of the POM that sinks out of the surfece water is buried in marine sediments. In comparison, about 20% of the biogenic PIC survives to become buried in the sediments. 

Primary outputs are produced essentially by sedimentation and (to a much lower extent) by emissions in the atmosphere. The steady state models proposed for seawater are essentially of two types box models and tube models. In box models, oceans are visualized as neighboring interconnected boxes. Mass transfer between these boxes depends on the mean residence time in each box. The difference between mean residence times in two neighboring boxes determines the rate of flux of matter from one to the other. The box model is particularly efficient when the time of residence is derived through the chronological properties of first-order decay reactions in radiogenic isotopes. For instance, figure 8.39 shows the box model of Broecker et al. (1961), based on The ratio, normal-... 

Example 4.13. Carbon-14 as a Tracer for Oceanic Mixing In a simplified two-box model of the ocean, the warm waters and the cold waters may tie subdivided into two well-mixed reservoirs—an upper one a few hundred meters in depth and a lower one of 3200 m depth. The Cj content of the upper and lower reservoirs (corresponding to the Pacific) are, respectively, 1.98 x 10 mol liter and 2.44 x 10 mol liter, whereas the C/C ratios for uppsr and lower reservoirs are, respectively, 0.92 x 10 and 0.77 x 10 mol/ mol. Estimate from this information the rate of vertical mixing and the residence time of the water in the deep sea (Broecker, 1974). 

Broecker s model is shown in Figure 15.16. The ocean is divided into two boxes—an upper one of a few hundred meters depth and a lower one of... 

Figure 4.18. Two-box steady-state model for the cycle of water, carbon, and C between the surface and deep sea. (See Example 4.13) (After Broecker, 1974).

Figure 15.16. Broecker s (1974) idealized kinetic model for the marine cycles of biologically fixed elements. volume of river water entering the ocean per year expressed as volume per unit sea area (m m yr or m yr ) = 0.1 m yr Chv, concentration of an element in average river water (mol m ) x Cnv, input flux (mol yr ) Fmix. volume of water sinking into deep water box = volume of water rising to surface water box (volume m yr ) = 2(X) m yr Q...

Figure 3 Results from a simple three-box ocean carbon cycle model, (a) The physical circulation and modeled radiocarbon (A C) values, (b) The model biogeochemical fields, ocean DIG, and phosphate PO4) and atmospheric pCOa. From Toggweiler JR and Sarmiento JL, Glacial to inter-glacial changes in atmospheric carbon dioxide The critical role of ocean surface waters in high latitudes, The Carbon Cycle and Atmospheric CO2. Natural Variations Archean to Present, Sundquist ET and Broecker WS (eds.), pp. 163-184, 1985, Copyright [1985]. American Geophysical Union. Adapted by permission of American Geophysical Union.

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