Lake retention time (also called the

residence time The residence time of a fluid parcel is the total time that the parcel has spent inside a control volume (e.g.: a chemical reactor, a lake, a human body). The residence time of a set of parcels is quantified in terms of the frequency distribu ...

of lake water, or the water age or

flushing time The residence time of a fluid parcel is the total time that the parcel has spent inside a control volume (e.g.: a chemical reactor, a lake, a human body). The residence time of a set of parcels is quantified in terms of the frequency distribution ...

) is a calculated quantity expressing the

mean There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value ( magnitude and sign) of a given data set. For a data set, the '' ar ...

time that water (or some dissolved substance) spends in a particular

lake A lake is an area filled with water, localized in a basin, surrounded by land, and distinct from any river or other outlet that serves to feed or drain the lake. Lakes lie on land and are not part of the ocean, although, like the much large ...

. At its simplest, this figure is the result of dividing the lake volume by the flow in or out of the lake. It roughly expresses the amount of time taken for a substance introduced into a lake to flow out of it again. The retention time is especially important where

pollutant A pollutant or novel entity is a substance or energy introduced into the environment that has undesired effects, or adversely affects the usefulness of a resource. These can be both naturally forming (i.e. minerals or extracted compounds like o ...

s are concerned.

Global retention time

The global retention time for a lake (the overall mean time that water spends in the lake) is calculated by dividing the lake

volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ...

by either the mean rate of inflow of all

tributaries A tributary, or affluent, is a stream or river that flows into a larger stream or main stem (or parent) river or a lake. A tributary does not flow directly into a sea or ocean. Tributaries and the main stem river drain the surrounding drain ...

, or by the mean rate of outflow (ideally including

evaporation Evaporation is a type of vaporization that occurs on the surface of a liquid as it changes into the gas phase. High concentration of the evaporating substance in the surrounding gas significantly slows down evaporation, such as when h ...

and seepage). This metric assumes that water in the lake is well-mixed (rather than

stratified Stratification may refer to: Mathematics * Stratification (mathematics), any consistent assignment of numbers to predicate symbols * Data stratification in statistics Earth sciences * Stable and unstable stratification * Stratification, or st ...

), so that any portion of the lake water is much like any other. In reality, larger and deeper lakes are generally not well-mixed. Many large lakes can be divided into distinct portions with only limited flow between them. Deep lakes are generally stratified, with deeper water mixing infrequently with surface water. These are often better modeled as several distinct sub-volumes of water.

More specific residence times

It is possible to calculate more specific residence time figures for a particular lake, such as individual residence times for sub-volumes (e.g. particular arms), or a

residence time distribution The residence time of a fluid parcel is the total time that the parcel has spent inside a control volume (e.g.: a chemical reactor, a lake, a human body). The residence time of a set of parcels is quantified in terms of the frequency distribution ...

for the various layers of a stratified lake. These figures can often better express the

hydrodynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) a ...

of the lake. However, any such approach remains a simplification and must be guided by an understanding of the processes operating in the lake. Two approaches can be used (often in combination) to elucidate how a particular lake works: field measurements and

mathematical model A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, ...

ing. One common technique for field measurement is to introduce a tracer into the lake and monitor its movement. This can be a solid tracer, such as a float constructed to be neutrally buoyant within a particular water layer, or sometimes a liquid. This approach is sometimes referred to as using a

Lagrangian reference frame __NOTOC__ In classical field theories, the Lagrangian specification of the flow field is a way of looking at fluid motion where the observer follows an individual fluid parcel as it moves through space and time. Plotting the position of an indi ...

. Another field measurement approach, using an

Eulerian reference frame __NOTOC__ In classical field theories, the Lagrangian specification of the flow field is a way of looking at fluid motion where the observer follows an individual fluid parcel as it moves through space and time. Plotting the position of an indi ...

, is to capture various properties of the lake water (including mass movement, water temperature,

electrical conductivity Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...

and levels of dissolved substances, typically oxygen) at various fixed positions in the lake. From these can be constructed an understanding of the dominant processes operating in the various parts of the lake and their range and duration. Field measurements alone are usually not a reliable basis for generating residence times, mainly because they necessarily represent a small subset of locations and conditions. Therefore, the measurements are generally used as the input for numerical models. In theory it would be possible to integrate a system of hydrodynamic equations with variable boundary conditions over a very long period sufficient for inflowing water particles to exit the lake. One could then calculate the traveling times of the particles using a Lagrangian method. However, this approach exceeds the detail available in current hydrodynamic models and the capacity of current computer resources. Instead, residence time models developed for gas and

fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) a ...

chemical engineering Chemical engineering is an engineering field which deals with the study of operation and design of chemical plants as well as methods of improving production. Chemical engineers develop economical commercial processes to convert raw materials in ...

, and bio-hydrodynamics can be adapted to generate residence times for sub-volumes of lakes.

Renewal time

One useful mathematical model the measurement of how quickly inflows are able to refill a lake. Renewal time is a specific measure of retention time, where the focus is on 'how long does it take to completely replace all water in a lake.' This is modeling can only be done with an accurate budget of all water gained and lost by the system. Renewal time simply becomes a question how quickly could the inflows of the lake fill the entire

of the basin (this does still assume the outflows are unchanged). For example if

Lake Michigan Lake Michigan is one of the five Great Lakes of North America. It is the second-largest of the Great Lakes by volume () and the third-largest by surface area (), after Lake Superior and Lake Huron. To the east, its basin is conjoined with that o ...

was emptied, it would take 99 years for its tributaries to completely refill the lake.

List of residence times of lake water

''The residence time listed is taken from the infobox in the associated article unless otherwise specified.''

References

External links

EPA's Great Lakes Factsheet #1

* {{cite web , url = http://www.niwa.co.nz/news-and-publications/publications/all/wa/14-4/native , title = Land-locked fish and lake-residence time , author = Jody Richardson, Alistair McKerchar , date = December 2006 , access-date =22 May 2007 - relationship between residence time of lakes of New Zealand and

koaro The climbing galaxias or kōaro (''Galaxias brevipinnis'') is a fish of the family Galaxiidae found in Australia, New Zealand, and nearby islands. The name climbing galaxias is used in Australia, and koaro or kōaro in New Zealand. Further verna ...

smelt Smelt may refer to: * Smelting, chemical process * The common name of various fish: ** Smelt (fish), a family of small fish, Osmeridae ** Australian smelt in the family Retropinnidae and species ''Retropinna semoni'' ** Big-scale sand smelt ''A ...

and common bully populations. Aquatic ecology

Retention time In chemical analysis, chromatography is a laboratory technique for the separation of a mixture into its components. The mixture is dissolved in a fluid solvent (gas or liquid) called the ''mobile phase'', which carries it through a system (a ...