17.8: Residence Time

Essential to Know

• Substances, including water, move through different parts of the oceans, atmosphere, and biosphere at different rates.
• The concentration of a substance in a part of the ocean, atmosphere, or biosphere is determined by how fast, on average, a molecule of the substance moves from input to output within that particular segment of the environment. This rate is measured as a residence time.
• Residence time is calculated by dividing the total quantity of a substance within an environmental segment (or “box”) by the rate of either its input or its removal from the segment.
• Residence time can be used to estimate the concentration increases that will result from increased discharges of a substance into a segment of the ocean. It is particularly useful for pollution assessments in estuaries and coastal waters. Long residence time and small water volume lead to high concentrations of a contaminating substance.
• In certain situations, we can use residence times to estimate the relative magnitudes of inputs to, or outputs from, a particular ocean segment without measuring them directly.

Understanding the Concept

Marine and atmospheric sciences involve the study of the movement of elements, water, and other substances within the oceans and atmosphere, and between the oceans, atmosphere, biosphere, and Earth’s mantle and crust. These movements are components of complex biogeochemical cycles (Chap. 5). The complexity of chemical movements within these cycles makes it very difficult, if not impossible, to study a cycle as a whole. Accordingly, the environment must be divided into segments for most studies.

A segment of the environment is chosen by a characteristic that distinguishes it from adjacent segments in some way. A segment, which, for convenience, is usually called a “box” or “compartment,” can be defined as almost any part of the Earth, ocean, or atmosphere. For example, a box could be defined as the entire world ocean, a single basin such as the Mediterranean Sea, or a simple square section of open ocean that is identified only by boundaries defined by an oceanographer. A box could also be the entire ocean biomass or the members of a particular fish species within a specified geographic area. Boxes are often defined to investigate the residence times of substances.

The substance of interest enters a box through certain identifiable pathways (inputs) and leaves through other identifiable pathways (outputs). Substances passing through the box can move quickly from input to output, or remain within the box for a long period before exiting. The average time that an atom or molecule of a relevant substance remains in the box is an important characteristic of the system and is expressed as its residence time.

To calculate the residence time in a defined box, one must measure the total quantity of the substance in the box, and either its rate of input to or its rate of output from the box. For example, if we want to determine the residence time of sodium in the Mediterranean Sea, we estimate the total quantity of sodium by measuring the sodium ion concentration at different places, averaging the result, and multiplying by the Mediterranean Sea’s volume. The rate at which sodium is entering or leaving the Mediterranean must also be measured. All of the sea’s inputs or outputs must be considered, including river runoff, atmospheric fallout and rain, and exchange of water between the Mediterranean and the Atlantic Ocean through the Straits of Gibraltar, between the Mediterranean and the Black Sea through the Bosporus, and between the Mediterranean and the Red Sea through the Suez Canal. We could determine the residence time of the water itself by measuring the total quantity of water and its inputs and outputs from the Mediterranean in the same way, but in this case, we would have to consider an additional output: evaporation.

Once we know the total amount of the substance of interest in the box and the rate of its input or output, we can calculate a residence time if we assume that the system we are studying is in a steady state (in other words, if we assume that the amount of substance in the box remains stable over time). Because the Earth’s biogeochemical cycles have had billions of years to reach equilibrium, we can usually accept that assumption when we are studying large boxes, such as an entire ocean basin. However, the smaller the box, the less likely the assumption is to be true. Although the Earth’s biogeochemical cycles are in approximate steady state when averaged globally, these processes can vary substantially at any one place and time because of such changes as variations in the year-to-year rate of river flow.

If the total amount of substance in the box remains stable over time, the rate of input must equal the rate of output (Fig. CC8-1). The residence time is calculated as the total quantity of the substance in the box divided by either the output or input rate. Measured in years or another time unit, residence time is the time it would take for the outputs to remove all the substance from the box if all inputs were stopped, and vice versa.

Figure CC8-1. This simple model shows how we calculate residence time by dividing the mass of the substance in the environmental segment (“box” or “compartment”) by either the rate of input or the rate of removal (output) of the substance from the box.

The concept of residence time has many uses. First, it provides a method of estimating the rates of some processes that are difficult to measure directly. For example, if we can measure the concentration of a particular element in Mediterranean seawater and the rate of input of this element from rivers and adjacent seas, we can calculate the rate at which this element is being removed to the sediment. We did not include sedimentation (or evaporation and salt precipitation) in our preceding examination of sodium cycling in the Mediterranean because, for sodium (as opposed to other elements), the rate of removal to the sediment is extremely slow at present, so it is negligible in relation to other inputs and outputs.

A second use of residence time is to determine the probable fate of contaminants released to the oceans. If we release contaminants with long residence times, they will remain in the oceans for a long time and may cause pollution. If contaminants have short residence times, human additions to the oceans will be quickly removed (usually to the ocean sediment). Residence times of the elements in the world oceans are discussed in Chapter 5.

One important characteristic of biogeochemical cycles is that mechanisms for the removal of a substance from a box are generally related to the concentration of the substance in the box. If the concentration increases, the output rate will also increase. For example, if the concentration of a substance in the Mediterranean is increased, the rate of loss of the substance from the Mediterranean will increase as seawater flows out of this sea to an adjacent sea. Similarly, higher concentrations lead to faster uptake by biota and faster removal to sediment, although there is often not a simple linear relationship in these instances.

An increase in the input rate to a box generally raises the concentration in the box until the output rate matches the elevated input rate. If the expected increase in input is known, the resulting increase in concentration can sometimes be calculated and predicted. This method is extremely important in determining the potential of rivers, bays, or segments of the coastal ocean to be affected by contaminant inputs. A hypothetical example illustrates how this assessment can be made. Figure CC8-2 shows the equations we could use for an estuary into which is discharged river water that carries a natural concentration (C) of a substance. An industrial complex is proposed that will discharge additional amounts of this substance to the estuary. For simplicity, we will assume that the substance of interest is not removed to sediment within the estuary and that it can leave the estuary only dissolved in seawater. From the calculations in Figure CC8-2, we see that the change in concentration (δC) that can be expected to occur in the estuary after the additional input (δI) begins is easily estimated if the residence time, volume of the estuary, and magnitude of δI are known. The important observation to be made about this result is that the concentration increase caused by an increased input of a contaminant substance is greater if the residence time (T) in the discharge water body is long in relation to its volume (V).

Figure CC8-2. A calculation, which is based on the residence time of a substance in an estuary or similar water mass, can be used to predict the effects of a new source of contamination that increases the input rate of the substance to a defined segment of the environment, or “box.”

This finding is important because some water bodies, particularly estuaries, may have long residence times and small volumes. Such locations are not good choices for waste discharge. San Francisco Bay is a particularly good example. It has two segments: South San Francisco Bay, which has a water residence time of weeks to months; and North Bay, which has a similar volume but a water residence time of only a day or two. Inputs of treated municipal wastewater to South San Francisco Bay have caused serious water quality problems, whereas much larger inputs of treated municipal wastewater and industrial wastewater to North Bay have caused comparatively minor problems. The difference is the longer residence time in South San Francisco Bay.

Residence time calculations can be more complicated when there are multiple, separated inputs or outputs in the area of interest. For example, the calculation in Figure CC8-2 is more complicated if a fraction of the contaminant is removed to sediments within the estuary. Nevertheless, residence time observations and calculations can be useful tools in such situations. If we can measure only the inputs and the contaminant concentrations in the estuary shown in Figure CC8-2, the calculated residence time will not tell us how much of the substance is flushed out to the ocean or how much is removed to the estuary sediment. We need not perform the relevant calculations here, but if we measure the inputs of the substance, its concentrations, and the residence time of water (not the residence time of the substance) in the estuary, we can calculate how much of the substance is removed with the water to the ocean and how much is retained in the estuary sediments and/or biota.