REPLY Meaning of Stock/Level (SD6972)

[SDMAIL Tom Fiddaman]

Posted by  Tom Fiddaman <tom at ventanasystems.com>

I think Jack's latest missive has clarified the debate:
> So again, it appears we have these two premises:
> 1. "any variable that can change only over time, needs to be treated as
> a stock."
> 2. "Temperature cannot change instantaneously. It can only change
> gradually, over time."
>
> Thus the conclusion follows that:
> 3. Temperature needs to be treated as a stock.

This is a good characterization of the argument, and highlights the 
problem with the first premise: a thing that can change only over time 
might be a stock (heat) or something that changes as a function of an 
underlying stock (temperature). Thus "can it change only over time?" is 
a helpful question to ask oneself when seeking the stocks in a model, 
but may not be sufficient to pin down the best representation.

> Above is the SD viewpoint. The scientific viewpoint starts with the
> definition of temperature, which is "a measure of the internal energy or
> enthalpy, that is the level of elementary motion giving rise to heat
> transfer." Note that temperature is independent of the mass of an object.
>
> This agrees with your position, that temperature should not be treated
> as a stock. I feel the same way, which is why I brought the subject up.

I would argue that the SD viewpoint is not different from the scientific 
viewpoint, or at least shouldn't be.

In the case of temperature, there's a good physical argument to make 
heat or enthalpy the underlying stock. In a system with constant mass 
and no phase transitions, treating temperature as a stock could be a 
perfectly reasonable simplification. In some cases, it might be useful 
to further simplify by ignoring the stock of heat, treating temperature 
as an auxiliary. For example, in a model of glacial cycles one might use 
and auxiliary representing the equilibrium temperature of the 
atmosphere, rather than explicitly modeling the dynamics of heat 
accumulation, because the time constant (<1yr) is so short with respect 
to the period of interest (>100,000yr).

In other cases, there isn't a clear argument for one or another 
mathematically equivalent formulation - should one model the position 
and velocity of a body, or the position and momentum? I prefer the 
latter, but either way we will have velocity and momentum, one of which 
will be a stock, the other an auxiliary related to the stock by mass, 
with neither changing instantaneously.

> Perhaps we could modify Bob's definition of a stock slightly, to this:
> "A stock is any variable whose behavior is best represented as changing
> over time, due to rates of increase and decrease." or more briefly as "A
> stock is any variable best represented as an accumulation." or even more
> briefly as "A stock is an accumulation." The last is how Sterman defines
> it, on page 192.
>
> The "best represented" aspect is why an element in one model is an
> auxiliary variable, in another model is a stock, and in yet another
> model is a constant.

Right. One could even go a bit further and describe a stock as something 
best represented by an integration, but the definition becomes a bit 
tautological. The real need is for a menu of criteria one might apply in 
order to make good choices among competing, possibly equivalent options. 
The notion of accumulation is helpful toward that end, but perhaps not 
in all cases - I don't find it particularly helpful for thinking about a 
pipeline delay (infinite order), for example. The menu might include:
- accumulation (of inflows and outflows or simply net changes)
- delay, inertia, momentum
- persistence, memory, or ergodicity (the "stop time" thought experiment)
- gradual vs. instantaneous change
- measurability (the idea that flows are uselessly noisy when viewed at 
fine time scales)
- integral vs. derivative
- units of measure
Most of this was laid out pretty clearly in Industrial Dynamics, Chapter 6.

I rather doubt that even modestly experienced modelers would get into 
protracted arguments over the fundamental nature of a particular 
variable. Where there will be disagreement is over the philosophically 
impure tradeoffs (include or neglect a stock, at what level of 
aggregation?) that need to be made in order to yield a model that is 
useful. This is generally regarded as art. I think it is an art to the 
extent that we as a field haven't really formalized a method for making 
choices efficiently. However, it's also a science in the sense that any 
given assumption can be tested against alternatives (disaggregate the 
population by gender, change the order of delays, etc.).

Tom

****************************************************
Tom Fiddaman
Ventana Systems, Inc. 
Posted by  Tom Fiddaman <tom at ventanasystems.com>
posting date  Thu, 24 Apr 2008 10:34:31 -0600