Rainfall probabilities

[tomfid]

Here's a model that's close to what I had in mind (no SAMPLE IF TRUE though).

Rainfall variation is decomposed into two bits:

Long term, year-to-year variability (drought, ENSO, or whatever) is a lognormal term applied to the mean seasonal distribution.

Short term, day-to-day variation in rainfall is modeled as a Poisson distribution - i.e., rainfall is a discrete event that occurs at some frequency.

The Poisson distribution isn't really ideal, because of its discreteness and because it doesn't really capture the interday autocorrelation. However, the "prob of daily rainfall" isn't really enough information to specify that anyway.

This at least behaves fairly well with various time steps (try .0625 and .25, for example).

If you look at the behavior of "rainfall per episode" it's a bit weird. It implies that dry season rain is very rare, but very heavy when it occurs. That could be an artifact of arbitrary lookups, or an error in my formulation - I'll let you figure that out.

Tom

[LAUJJL]

Hi Richard and Tom

Tom's question about the necessity to have an idea how the soil dries between two rains to justify the utility of getting into a sort of discreet model seems fondamental.
This information being not included in the model, I do not see the utility of representing rainfall as a succession of discreet events. Representing it with a pure continuous model should be sufficient without the overhead of discreet modeling.
One other question: suppose that the drying process between two rains and its effect on the vegetation is known, is it an absolute necessity to still represent the problem with such a discreet representation?
By experience, I have noticed that it is very time consuming and unproductive to represent a phenomenon as discreet, at least in Vensim using the SD paradigms for problems that are not purely process oriented.
So would not it be possible to stay in the safe and comfortable continuous environment and still represent at least to a certain point the problem of soil drought between two rains? At least take some time to think about it.
Some ideas?
Regards.
JJ

[tomfid]

Along the lines of JJ's thinking:

Discreteness probably matters, in the sense that daily rain of 1mm is different from 30mm once a month. However, it's possible that randomness in rainfall arrival is not important, or hides insight. In that case, you could model the short-term rain process as a PULSE TRAIN. Then you could vary rain intensity and frequency to see what effect that has on drying. Then worry about the "real" stochastic process later, when you understand what matters.

Tom

[rdudley]

Soil moisture is a whole area on its own and I am trying to use a simple version. Basically water comes into the soil until it is at what is called "field capacity" after which it drains through or flows off. Field capacity varies with soil type... e.g. sandy soils hold less moisture. Drying from field capacity to the "wilting point" is basically an exponential decline highly dependent on soil type, also on the amount of organic matter etc... thus dependent on previous crops grown. There are lots of soil models and crop production models... but I am wanting to keep this part of the model simple

The time constant for moisture decline in a typical soil could be as short as .1 months so getting close to time step. But for other reasons I don't really want to go to days as the time unit.

[tomfid]

I posted a version of the Pink Noise generator that includes a :MACRO: version here: http://models.metasd.com/2010/03/pink-noise/

Tom

[rdudley]

Just a little update...

The real data approach might be worthwhile as a check, but in reality I need to have a representation of reality so I can run some long-term and sensitivity simulations.

I've ended up raising the emphasis on the yes / no variability and lowering the emphasis on the amount of rain. Now more rain occurs not just within an incident but because of more (or fewer) rainfall incidents. For my purposes this works well. I stuck with using months as the unit, and the soil moisture loss time is something like .25 months or perhaps smaller. That is a month, or probably less, without rain and the plants will be dead (depends on soil type, organic matter etc... not my interest right now). So I am using a time step of 0.015... which in reality is less than a day.