Confusion about the correlation time unit in RANDOM PINK NOISE funtion

[Simplifier]

The initial and final time in my model is 1985 and 2016, and I have set TIME STEP to 0.0625. I am using RANDOM PINK NOISE function which contains correlation time. Since I want the picked up data to have a path dependency behaviour of six months, should I put 0.5 (i.e. half a year) as correlation or 6 (i.e. 6 months)? Does the correlation time in RANDOM PINK NOISE function follow the units for time that I have chosen in my model, which is year, or the TIME STEP in my model, which is 0.0625?

[Administrator]

Does the correlation time in RANDOM PINK NOISE function follow the units for time that I have chosen in my model, which is year, or the TIME STEP in my model, which is 0.0625?

It should be measured in years. TIME STEP is also in years (it's 0.0625 of a year). So the value should be 0.5, create a constant for this and give it the unit year.

You can also try changing the correlation time constant so it's measured in months. Use this in the PINK NOISE function and run the units check, it will point out the error. This is why units checks are so important.

[Simplifier]

Thanks for your clear, helpful explanation.

As long as we are on the time subject, I was wondering what adjustment time or delay means in a model and why we have to consider it while choosing the time step? Since I've been told the time step I select should be 1/3 of the smallest delay in my model. I'm still having problem with choosing the right time step as I dont know if i have or should include delay in my model.

[tomfid]

The rule of thumb for 1/3 the smallest delay is reasonable, but sometimes not sufficient. Really the rule should be 1/3 the shortest effective time constant, whether it is in a negative or positive loop, and this is not always known. The simplest thing to do is do some testing - lower the time step and see whether the model behavior changes significantly. However, in a stochastic model this too may not be definitive.

[Simplifier]

The rule of thumb for 1/3 the smallest delay is reasonable, but sometimes not sufficient. Really the rule should be 1/3 the shortest effective time constant, whether it is in a negative or positive loop, and this is not always known. The simplest thing to do is do some testing - lower the time step and see whether the model behavior changes significantly. However, in a stochastic model this too may not be definitive.

Thanks for your explanation. Because I'm using many RANDOM PINK NOISE functions in my model, changing TIME STEP changes my model behaviour, which I dont know its a bad thing or not considering what you said. I remember once you showed to me how it works:
"If you think about a run with 4 time steps, the random draws might be
Time 1 2 3 4
Value 3 8 2 6
If you halve the time step, you get
Time 0.5 1 1.5 2 2.5 3 3.5 4
Value 3 8 2 6 1 7 7 9
The value 2 now occurs at time 1.5 instead of time 2, etc."

So is it normal if the model behaviour changes when TIME STEP is changed?

[tomfid]

Correct. Behavior changes are expected with random functions, and not a bad thing, except to the extent that it makes analysis harder.

If you use the "1/3" rule, be sure to consider that the higher-order delay functions like SMOOTH3 and DELAY3 have a time constant that is (delay time)/(delay order).

If things are going horribly wrong with a high-gain positive loop, this will usually be obvious from wild overshoots or other bad behavior.

Setting the TIME STEP to a large value deliberately is often a good test of robustness - you can use it to reveal potential problems, then reduce it again for normal simulations.