Using a simple box mixing model, we show that ventilation rate estimates obtained from tracer box models may be significantly smaller than fluid replacement rates. The degree to which a tracer ventilation estimate approaches the actual (fluid) ventilation rate depends on the surface boundary condition for that tracer. Ventilation rates for rapidly exchanging tracers (e.g. 3He) are close to the fluid ventilation rate while tracers with limited surface exchange (e.g. tritium) ventilate more slowly. For box mixing models, the ratio of ventilation rates for limited surface exchange tracers to rapidly exchanging tracers approaches the ratio of summer to winter mixed layer depths. Further, the distribution of rapidly equilibrating tracers more accurately tracks climatological fluctuations in water mass formation rates. Limited surface exchange tracers show a damping proportional to the ratio of summer to winter mixed layer depths. To compare model results with observations, we calculate 3He and tritium ventilation rates from data taken in 1979 in the eastern subtropical North Atlantic. In calculating the tritium ventilation rates, we modify a North Atlantic tritium “source function” (time history of-surface water tritium concentrations), extending previous work using recent data. On shallow density surfaces (σ < 27.0), the computed tritium ventilation rates are 2–3 times slower than those for 3He, in agreement with climatological ratio of summer to winter mixed layer depths. Deeper in the thermocline, the two tracer estimated ventilation rates converge. This trend may be related to the decreasing effectiveness of 3He gas exchange in equilibrating the deeper winter mixed layers of the more northerly isopycnal outcrops. We conclude that box models using limited surface exchange tracers (e.g. 14C and tritium) can under predict oxygen utilization rates (OUR) by up to 3 times due to differences in tracer boundary conditions, while a tracer like 3He may overestimate OUR by 10–20%.
Doney, Scott C., and William J. Jenkins. 1988. "The effect of boundary conditions on tracer estimates of thermocline ventilation rates." Journal of Marine Research 46, (4). https://elischolar.library.yale.edu/journal_of_marine_research/1919