How to calculate the residence time

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How to calculate the residence time

#1 Post by tony1230 » Thu Jan 24, 2013 1:47 am

As we all know that the time for water staying in a semi-close sea or a bay would exerts important influence on many,like matter transport etc..I have searched in ROMS forum for this topic,but find none directly available.I have read some related papers in which they employed the approach of using dye concentration,i.e.,giving a initial constant concentration for dye over the area(e.g. 1.0 mg/m3) and to calculate the time when the concentration reach a fixed value,e.g.,0.5 mg/m3.If this is the case,the residence time near boundary would be very short and more large where far from the boundary,this seems make sence.My doubts/questions are:

1、Dye can move in and out of the area,dye concentration could be reincrease after they reach the fixed value,so how to calculate the time?

2、As for a semi-close/bay area,the residence may be one value. So,do i just to average the residence times from each grid point if i use the aforementioned way?

This is what i know to do this job and maybe you have better ones.I have nothing experience on this,if you have,plz let me know how we can reasonably calculate the residence time for a water body.

Your comments/ideas/tips would be warmly appreciated.

- Shou

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Re: How to calculate the residence time

#2 Post by rduran » Fri Jan 25, 2013 1:11 am

How about seeding some Lagrangian floats to see if any left and came back?

There is another Lagrangian technique that quite frankly I find a tremendous tool, I believe it will become a very popular with time. It might be useful in your applications since it allows you to measure total volume of water parcels exchanged in a certain time. It is restricted to a certain time-length since numerical diffusion will start causing problems at some point you will need to do some sensitivity tests to see how long the Lagrangian label technique remains useful. I found that in my application they remain meaningful up to month-long integrations, but that can vary.

It is pretty straightforward to implement, you can see early applications of this technique in

Kuebel Cervantes, B. T., J. S. Allen, and R. M. Samelson, 2004. Lagrangian characteristics of continental shelf flows forced by periodic wind stress. Nonlin. Proc. Geophys., 11, 3-16.

Kuebel, B. T., J. S. Allen, and R. M. Samelson, 2003. A modeling study of Eulerian and Lagrangian aspects of shelf circulation off Duck, North Carolina. J. Phys. Oceanogr., 33, 2070-2092.

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Re: How to calculate the residence time

#3 Post by lanerolle » Fri Jan 25, 2013 6:47 pm

I have used both a passive tracer and Lagrangian particles to calculate Residence Times. However, I think if we are to stick to strict definitions, if we use a tracer/dye, the times calculated are called Flushing Times as opposed to Residence Times. My applications involve idealized model problems and the Chesapeake Bay.

Lagrangian particles are easier to implement and count than passive tracers but a tracer has an advantage of naturally conforming to the concept of concentration levels/thresholds which go into the calculation of RTs or FTs. One of the experiments that needs to be conducted when using particles is to increase the ensemble size (e.g. 1000, 2000, 4000, 8000, 16000, etc.) and ensure that the RTs/FTs you get are ensemble size independent.

Another issue you face with particles is that, if your flow is tidal then, its possible for particles to cross a given barrier (at which we apply the exit/entrance condition) multiple times and then RTs/FTs have to be defined as "first crossing", etc. It is possible that due to tidal action, the particles may take a long time to totally cross the barrier. For tidally dominated regions therefore, it may be better to do a long simulation (1-2 years) and then calculate the residual velocities/currents and use them to evaluate your RTs/FTs via the passive tracer or Lagrangian particle path approach.

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Re: How to calculate the residence time

#4 Post by zhzhlin » Tue Jan 29, 2013 3:10 am

It is true that the dye may re-enter the domain after it's flushed out. I think a practical way to deal with it is to define residence time at each location as the time it takes for the dye concentration to FIRST go below 1/e of the initial value. The dye might get re-entrained back into the domain, and formed a second peak in concentration before declining again, but only the first drop should be used to calculate residence time (see attached figure as an example). For more detail, please refer to Figure 10 and 11 in the following reference:
Zhang Z, Falter JL, Lowe RJ, and Ivey G. (2012) The combined influence of hydrodynamic forcing and calcificationon the spatial distribution of alkalinity in a coral reef system. J. Geophys. Res. 117, C04034.
The residence times are indicated by solid circles in this figure.
The residence times are indicated by solid circles in this figure.
Fig13.png (5.45 KiB) Viewed 4854 times

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Re: How to calculate the residence time

#5 Post by zhang » Wed Jan 30, 2013 3:28 am

If you want your calculation of the residence time to be mathematically precise and also resolve its temporal and spatial variability, you should definitely look into the Constituent-oriented Age and Residence time Theory (CART; ). The forward model gives the first moment of the age distribution (i.e., mean age) and the corresponding adjoint gives the mean residence time. Both are 4 dimensional variables. The re-entry problem has also been addressed in the theory (a series of papers). The authors named the one neglecting re-entry "strict mean residence time" and other considering re-entry "exposure time". The commonly referred "flushing time" is just a spatial and temporal average of the 4 dimensional residence/exposure time. If you care only about the one-quantity flushing time, you could use tracer releases (Lagrangian or Eulerian) in a forward model to estimate, as the previous replies suggested. If you want to study the temporal and spatial variability of the residence time, tracer releases in a forward model become too expensive, and you should look into the CART theory. We have summarized the CART and applied it in the New York Bight area using the ROMS adjoint model in the following paper:
Zhang, W. G., J. L. Wilkin, and O. M. E. Schofield, 2010: Simulation of water age and residence time in New York Bight. J. Phys. Oceanogr., 40, 965-982.

Weifeng Zhang

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Re: How to calculate the residence time

#6 Post by crode1968 » Thu Jan 31, 2013 7:56 pm


you might have a quick look at
Bolin, B., & Rodhe, H. (1973). A note on the concepts of age distribution and transit time in natural reservoirs. Tellus, 25(1), 58–62. doi:10.1111/j.2153-3490.1973.tb01594.x

"A brief review is given of the concepts age distribution, transit time distribution, turn-over time, average age and average transit time (residence time) and their relations. .." ... B80.d01t03


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