Posted by Bill Braun <bbraun@hlthsys.com>
Was Problem Solving versus Optimization (SD5227)
>>You will note that they base their scenarios on what I
>>_think_ is a system dynamics simulation called
>>Wonderland.
An application of Wonderland can be found at:
http://journal-ci.csse.monash.edu.au/ci ... rbert.html
Bill Braun
Posted by Bill Braun <bbraun@hlthsys.com>
posting date Mon, 25 Apr 2005 09:33:07 -0500
Wonderland Model (was Problem Solving versus Optimization)
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Bill Braun bbraun hlthsys.com
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Tom Fiddaman tom vensim.com
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Wonderland Model (was Problem Solving versus Optimization)
Posted by Tom Fiddaman <tom@vensim.com>
WAS Problem Solving versus Optimization (SD5227)
There's also a copy of the Wonderland model in my model library. It's the
7th item down at:
http://www.sd3.info/models/index.html#Climate
It's a replication based on the original publication about the model:
Alexandra Milik, Alexia Prskawetz, Gustav Feichtinger, and Warren C.
Sanderson, ""Slow-fast Dynamics in Wonderland,"" Environmental Modeling and
Assessment 1 (1996) 3-17.
I view the model and analysis in the original article as technically
interesting, but rather divorced from the real world. It's rather galling
that the SciAm authors bash LTG, then select a model that has serious
formulation errors of its own. A robust model should be a prerequisite to
development of robust strategy; otherwise the addition of uncertainty
merely blurs one's view of the model's problems.
In the model directory you'll find a brief critique, which I reproduce
below. I think there's actually much more to discover, and I hope others
will contribute the results of their look at the model.
>>This copy of the Wonderland model works with Vensim DSS, as I created
>>several macros to simplify the appearance of the exponential functions and
>>to prevent over/underflows. The model incorporates a fix suggested by the
>>author that prevents Natural Capital from reaching exactly 0 or 1 due to
>>roundoff error. The fix introduces an unintended side effect, i.e. that
>>the temporary natural capital (the stock in my version) rises above 1 and
>>falls below 0. There is a double-precision version of Vensim that would
>>probably work without the fix, though I haven't tried it.
>>I can replicate the dream and nightmare scenarios from the source article
>>(subject to the upper/lower bound parameter choice), though I can't get an
>>escape behavior without changing another parameter. The need for the
>>upper/lower bound on natural capital highlights what I think is the
>>problem with the model. The idea that the environment cannot be damaged if
>>it's initially pristine (NK=1) doesn't really make sense. The upper and
>>lower bounds to NK solve the problem computationally, but they don't seem
>>to have any real-world justification. I think it would be better to
>>separate the damage process (from pollution) and the regeneration process.
>>To do this, I think the concept of natural capital in the model needs to
>>be clarified.
>>The logistic expression for equation 3 (natural capital change rate)
>>suggests that natural capital means biomass of some sort. For real
>>biomass, regeneration is logistic but damage is not, so the contributions
>>of damage and regrowth should be additive, not multiplicative. If, on the
>>other hand, natural capital is meant to represent pollution, then an
>>explicit pollution stock would be clearer. In this case, the emissions and
>>uptake processes would still be additive, and uptake would be nonlinear
>>but probably not logistic. If you want both stock pollutants and biomass
>>dynamics, then it seems that the environment in the model needs to be 2nd
>>order.
>>On a related note, it seems to me that if natural capital = 0, output per
>>capita ought to be zero, rather than contracting at a constant rate.
>>Again, this depends on the meaning of natural capital. A formulation with
>>an explicit capital stock and capital-labor-natural capital production
>>function would be clearer, though more complex. This might also help to
>>clarify the processes of pollution output vs. abatement.
>>Overall, I found the analysis of the model very interesting. Some of the
>>fixes/clarifications/critiques I've listed above would make the slow-fast
>>dynamics go away (mainly by changing the logistic behavior of natural
>>capital, eliminating the attracting manifolds at NK = 0 and NK = 1). I'd
>>like to see a model that fixes some of the problems I see, but preserves
>>the interesting dynamics, esp. the 3 scenario trajectories. Tom Fiddaman, 1998
Tom
Posted by Tom Fiddaman <tom@vensim.com>
posting date Mon, 25 Apr 2005 10:23:47 -0600
WAS Problem Solving versus Optimization (SD5227)
There's also a copy of the Wonderland model in my model library. It's the
7th item down at:
http://www.sd3.info/models/index.html#Climate
It's a replication based on the original publication about the model:
Alexandra Milik, Alexia Prskawetz, Gustav Feichtinger, and Warren C.
Sanderson, ""Slow-fast Dynamics in Wonderland,"" Environmental Modeling and
Assessment 1 (1996) 3-17.
I view the model and analysis in the original article as technically
interesting, but rather divorced from the real world. It's rather galling
that the SciAm authors bash LTG, then select a model that has serious
formulation errors of its own. A robust model should be a prerequisite to
development of robust strategy; otherwise the addition of uncertainty
merely blurs one's view of the model's problems.
In the model directory you'll find a brief critique, which I reproduce
below. I think there's actually much more to discover, and I hope others
will contribute the results of their look at the model.
>>This copy of the Wonderland model works with Vensim DSS, as I created
>>several macros to simplify the appearance of the exponential functions and
>>to prevent over/underflows. The model incorporates a fix suggested by the
>>author that prevents Natural Capital from reaching exactly 0 or 1 due to
>>roundoff error. The fix introduces an unintended side effect, i.e. that
>>the temporary natural capital (the stock in my version) rises above 1 and
>>falls below 0. There is a double-precision version of Vensim that would
>>probably work without the fix, though I haven't tried it.
>>I can replicate the dream and nightmare scenarios from the source article
>>(subject to the upper/lower bound parameter choice), though I can't get an
>>escape behavior without changing another parameter. The need for the
>>upper/lower bound on natural capital highlights what I think is the
>>problem with the model. The idea that the environment cannot be damaged if
>>it's initially pristine (NK=1) doesn't really make sense. The upper and
>>lower bounds to NK solve the problem computationally, but they don't seem
>>to have any real-world justification. I think it would be better to
>>separate the damage process (from pollution) and the regeneration process.
>>To do this, I think the concept of natural capital in the model needs to
>>be clarified.
>>The logistic expression for equation 3 (natural capital change rate)
>>suggests that natural capital means biomass of some sort. For real
>>biomass, regeneration is logistic but damage is not, so the contributions
>>of damage and regrowth should be additive, not multiplicative. If, on the
>>other hand, natural capital is meant to represent pollution, then an
>>explicit pollution stock would be clearer. In this case, the emissions and
>>uptake processes would still be additive, and uptake would be nonlinear
>>but probably not logistic. If you want both stock pollutants and biomass
>>dynamics, then it seems that the environment in the model needs to be 2nd
>>order.
>>On a related note, it seems to me that if natural capital = 0, output per
>>capita ought to be zero, rather than contracting at a constant rate.
>>Again, this depends on the meaning of natural capital. A formulation with
>>an explicit capital stock and capital-labor-natural capital production
>>function would be clearer, though more complex. This might also help to
>>clarify the processes of pollution output vs. abatement.
>>Overall, I found the analysis of the model very interesting. Some of the
>>fixes/clarifications/critiques I've listed above would make the slow-fast
>>dynamics go away (mainly by changing the logistic behavior of natural
>>capital, eliminating the attracting manifolds at NK = 0 and NK = 1). I'd
>>like to see a model that fixes some of the problems I see, but preserves
>>the interesting dynamics, esp. the 3 scenario trajectories. Tom Fiddaman, 1998
Tom
Posted by Tom Fiddaman <tom@vensim.com>
posting date Mon, 25 Apr 2005 10:23:47 -0600