Turnover times

The turnover time is the ratio between the content (M) of a reservoir and the total flux out of it (S)  

The turnover time may be thought of as the time it would take to empty the reservoir if the sink (S) remained constant while the sources were zero (To S = M). In fluid reservoirs like the atmosphere or 

If material is removed from the reservoir by two or more separate processes, each with a flux S one can define turnover times with respect to each such process as  

Since 2S, = S, these time-scales are related to the turnover time of the reservoir, tq, by 

The equation describing the rate of change of the content of a reservoir can be written as  

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Acetylcholine serves as a neurotransmitter. Removal of acetylcholine within the time limits of the synaptic transmission is accomplished by acetylcholinesterase (AChE). The time required for hydrolysis of acetylcholine at the neuromuscular junction is less than a millisecond (turnover time is 150 ps) such that one molecule of AChE can hydrolyze 6 105 acetylcholine molecules per minute. The Km of AChE for acetylcholine is approximately 50-100 pM. AChE is one of the most efficient enzymes known. It works at a rate close to catalytic perfection where substrate diffusion becomes rate limiting. AChE is expressed in cholinergic neurons and muscle cells where it is found attached to the outer surface of the cell membrane. 

Turnover time. The turnover time of a reservoir is the ratio of the content M of the reservoir to the sum of its sinks S or the ratio of M to the sources Q. The turnover time is the time it will take to empty the reservoir in the absence of sources if the sinks remain constant. It is also a measure of the average time spent by individual molecules or atoms in the reservoir (more about this will be presented in Chapter 4). 

Time Scales and Single Reservoir Systems 4.2.1 Turnover Time... 

The turnover time may be thought of as the time it would take to empty the reservoir if the sink (S) remained constant while the sources were zero (tqS = M). This time scale is also sometimes referred fo as "renewal time" or "flushing fime." In the common case when the sink is proportional to the reservoir content (S = kM), the turnover time is the inverse of the proportionality constant (k ), which is analogous to first-order chemical kinetics. 

In fluid reservoirs like fhe afmosphere or the ocean, the turnover time of a tracer is also related to the spatial and temporal variability of ifs concentration within the reservoir a long turnover time corresponds to a small variability and vice versa (Junge, 1974 Hamrud, 1983). Figure 4-2 shows a plot of measured trace gas variability in the atmosphere versus turnover time estimated by applying budget considerations as indicated by Equation (1). An inverse relation is obvious, but the scatter in the data... 

As an application of the turnover time concept, let us consider the model of the carbon cycle shown in Fig. 4-3. This diagram is different from the one used in the chapter on the carbon cycle (Chapter 11), because it serves our purposes better for this chapter. The values given for fhe various fluxes and burdens are very similar to the corresponding figure in Chapter 11 (Fig. 11-1). 

The turnover time of carbon in biota in the ocean surface water is 3 x 10 /(4 + 36) x lO yr 1 month. The turnover time with respect to settling of detritus to deeper layers is considerably longer 9 months. Faster removal processes in this case must determine the turnover time respiration and decomposition. 

Fig. 4-2 Inverse relationship between relative standard deviation of atmospheric concentration and turnover time for important trace chemicals in the troposphere. (Modified from Junge (1974) with permission from the Swedish Geophysical Society.)...

It can be shown that for a reservoir in steady state. To is equal to t, i.e. the turnover time is equal to the average residence time spent in the reservoir by individual particles (Eriksson, 1971 Bolin and Rodhe, 1973). This may seem to be a trivial result but it is actually of great significance. For example, if tq can be estimated from budget considerations by comparing fluxes and burdens in Equation (1) and if the average transport velocity (V) within the reservoir is known, the average distance (L = Vxr) over which the transport takes place in the reservoir can be estimated. 

Consider a single reservoir, like the one shown in Fig. 4-1, for which the sink is proportional to the content (S = kM) and which is initially in a steady state with fluxes Qo = So and content Mq. The turnover time of this reservoir is... 

This means that the observed change in M mainly reflects a change in the source flux Q or the sink function. As an example we may take the methane concentration in the atmosphere, which in recent years has been increasing by about 0.5% per year. The turnover time is estimated to be about 10 years, i.e., much less than Tobs (200 years). Consequently, the observed rate of increase in atmospheric methane is a direct consequence of a similar rate of increase of emissions into the atmosphere. (In fact, this is not quite true. A fraction of the observed increase is probably due to a decrease in sink strength caused by a decrease in the concentration of hydroxyl radicals responsible for the decomposition of methane in the atmosphere.)... 

In situations where Tobs is comparable in magnitude to tq, a more complex relation prevails between Q, S, and M. Atmospheric CO2 falls in this last category although its turnover time (3 years, cf. Fig. 4-3) is much shorter than Tobs (about 300 years). This is because the atmospheric CO2 reservoir is closely coupled to the carbon reservoir in the biota and in the surface layer of the oceans (Section 4.3). The effective turnover time of the combined system is actually several hundred years (Rodhe and Bjdrk-strom, 1979). 

It is seen that in the steady state the total mass is distributed between the two reservoirs in proportion to the sink coefficients (in reverse proportion to the turnover times), independent of the initial distribution. 

The response time in this simple model will depend on the turnover times of both reservoirs and will always be shorter than the shortest of the two turnover times. If tqi is equal to T02, then Tcycle will be equal to half of this value. 

In general, if the removal flux is dependent upon the reservoir content raised to the power a (a 1), i.e., S = BM, the adjustment process will be faster or slower than the steady-state turnover time depending on whether a is larger or smaller than unity (Rodhe and Bjorkstrdm, 1979). 

Calculate the turnover time of carbon in the various reservoirs given in Fig. 4-3. 

What is the relation between the turnover time To the average transit time and the average age ta, in a reservoir where all particles" spend an equal time in the reservoir ... 

Consider the water balance of a lake with a constant source flux Q. The outlet is the "threshold" type where the sink is proportional to the mass of water above a threshold value Mi S = k(M — Ml). Calculate the turnover time of water at steady state and the response time relative to changes in Q. 

Rodhe, H. (1978). Budgets and turnover times of atmospheric sulfur compounds. Atmos. Environ. 12,671-680. 

Fig. 6-3 Global water balance. Storages in km fluxes in km /yr. Turnover times calculated as storage divided by total annual inflow. (Data from Shiklomanov and Sokolov, 1983.)...

Average turnover time (defined as storage volume divided by annual inflow or outflow volume, assuming steady state) is a measure of... 

The enormous volume of the oceans results in an average turnover time of more than 2600 years, compared to less than 10 days for atmospheric water. Although the reservoir is much smaller than the oceans, the cryosphere has the longest turnover time due to the small input flux. Average turnover times for all seven reservoirs, calculated from the data in Fig. 6-3, are shown in Table 6-3. 

Many hydrologic reservoirs can be further subdivided into smaller reservoirs, each with a characteristic turnover time. For example, water resides in the Pacific Ocean longer than in the Atlantic, and the oceans surface waters cycle much more quickly than the deep ocean. Similarly, groundwater near the surface is much more active than deep reservoirs, which may cycle over thousands or millions of years, and water frozen in the soil as permafrost. Typical range in turnover times for hydrospheric reservoirs on a hillslope scale (10-10 m) are shown in Table 6-4 (estimates from Falkenmark and Chapman, 1989). Depths are estimated as typical volume averaged over the watershed area. 

Patricia C. Henshaw, Robert J. Charlson, and Stephen j. Burges Table 6-4 Hillslope scale turnover times... 

Assuming an input flux equal to oceanic evaporation, this would give a turnover time of about 750 years. The turnover time analysis is not strictly correct since freshwater resides in a number of interconnected reservoirs however. 

The turnover time of water vapor in the atmosphere obviously is a function of latitude and altitude. In the equatorial regions, its turnover time in the atmosphere is a few days, while water in the stratosphere has a turnover time of one year or more. Table 7-1 Qunge, 1963) provides an estimate of the average residence time for water vapor for various latitude ranges in the troposphere. Given this simple picture of vertical structure, motion, transport, and diffusion, we can proceed to examine the behavior of... 

The concept of average residence time, or turnover time, provides a simple macroscopic approach for relating the concentrations in ocean reservoirs and the fluxes between them. For the single box ocean in Fig. 10-17 the rate of change of the concentration of component n can be expressed as... 

The content of the material in a carbon reservoir is a measure of that reservoir s direct or indirect exchange rate with the atmosphere, although variations in solar also create variations in atmospheric content activity (Stuiver and Quay, 1980, 1981). Geologically important reservoirs (i.e., carbonate rocks and fossil carbon) contain no radiocarbon because the turnover times of these reservoirs are much longer than the isotope s half-life. The distribution of is used in studies of ocean circulation, soil sciences, and studies of the terrestrial biosphere. 

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