Flushing salt in the summer months

The hyper-saline events build up over a period of several years. During the summer months of those years, some rain falls, the rivers rise, and some salt is flushed from the system. The problem is that not enough is flushed from the system before the winter dry period starts the salt build up again.

Now assume we made the operating rule that :-

• Whenever the lake became hyper-saline. (I.e. Significantly saltier than the sea).
• And there was sufficient natural inflow to cause outflow from the lake to the sea.

We would make a compensation release of to flush salt out of the system.

For convenience define and . Any quantity with a prime denotes the same quantity as the unprimed version, but with all I replaced by .

For flow from lake to sea we have...

At time we have...

Where....

The load at any time after is...

Where...

Denote the load including the effect of the release by . Substituting in for ...

Which after half a page of algebra simplifies to...

The load after a summer flushing release.

Thus again physically speaking the load is made up of three parts...

1. The load in the system which would have been if no release had been made.
2. The effect of any change in volume. (If was at t=0 then this second term would be 1.) Looking at the physical values, the effect of this term is very small.
3. A decay term which governs the process.

Just a small consistency check, if or is 0, then we get the same value as the original formula.

Assume the compensation release is small compared to the volume of the lake. Now use Taylor's theorem to first order to estimate the change in load due to the release.

Denote the salt concentration in the lake by .

The last term is a correction factor near 1. In the ``prevent salt influx'' scenario, the load prevented from entry was , where as here the amount flushed goes as .

Thus if the lake is hyper saline, more is achieved by flushing. Note however, one's efforts are ``watered down'' if the natural inflow continues.