The Problems in Modeling Nature, With Its Unruly Natural Tendencies

[A review of]

USELESS ARITHMETIC
Why Environmental Scientists Can’t Predict the 
Future. By Orrin H. Pilkey and Linda 
Pilkey-Jarvis. 256 pages. Columbia University Press, $29.50.
Read an Excerpt <http://www.columbia.edu/cu/cup/publicity/pilkeyexcerpt.html>


By CORNELIA DEAN
Published: February 20, 2007

When coastal engineers decide whether to dredge 
sand and pump it onto an eroded beach, they use 
mathematical models to predict how much sand they 
will need, when and where they must apply it, the 
rate it will move and how long the project will 
survive in the face of coastal storms and erosion.

Orrin H. Pilkey, a coastal geologist and emeritus 
professor at Duke, recommends another approach: 
just dredge up a lot of sand and dump it on the 
beach willy-nilly. This “kamikaze engineering” 
might not last very long, he says, but projects 
built according to models do not usually last 
very long either, and at least his approach would 
not lull anyone into false mathematical certitude.

Now Dr. Pilkey and his daughter Linda 
Pilkey-Jarvis, a geologist in the Washington 
State Department of Geology, have expanded this 
view into an overall attack on the use of 
computer programs to model nature. Nature is too 
complex, they say, and depends on too many 
processes that are poorly understood or little 
monitored — whether the process is the feedback 
effects of cloud cover on global warming or the 
movement of grains of sand on a beach.

Their book, “Useless Arithmetic: Why 
Environmental Scientists Can’t Predict the 
Future,” originated in a seminar Dr. Pilkey 
organized at Duke to look into the performance of 
mathematical models used in coastal geology. 
Among other things, participants concluded that 
beach modelers applied too many fixed values to 
phenomena that actually change quite a lot. For 
example, “assumed average wave height,” a 
variable crucial for many models, assumes that 
all waves hit the beach in the same way, that 
they are all the same height and that their 
patterns will not change over time. But, the 
authors say, that’s not the way things work.

Also, modelers’ formulas may include coefficients 
(the authors call them “fudge factors”) to ensure 
that they come out right. And the modelers may 
not check to see whether projects performed as predicted.

Eventually, the seminar participants widened the 
project, concluding that erroneous assumptions, 
fudge factors and the reluctance to check 
predictions against unruly natural outcomes 
produce models with, as the authors put it, “no 
demonstrable basis in nature.” Among other 
problems, they cite much-modeled but nevertheless 
collapsed North Atlantic fishing stocks, 
poisonous pools unexpectedly produced by open pit 
mining, and invasive plants and animals that routinely outflank their modelers.

Two issues, the authors say, illustrate other 
problems with modeling. One is climate change, in 
which, they say, experts’ justifiable caution 
about model uncertainties can encourage them to 
ignore accumulating evidence from the real world. 
The other is the movement of nuclear waste 
through an underground storage site at Yucca 
Mountain in Nevada, not because it has failed — 
it has yet to be built — but because they say it 
is unreasonable to expect accurate predictions of 
what will happen far into the future — in this 
extreme case, tens or even hundreds of thousands of years from now.

Along the way, Dr. Pilkey and Ms. Pilkey-Jarvis 
describe and explain a host of modeling terms, 
including quantitative and qualitative models 
(models that seek to answer precise questions 
with more or less precise numbers, as against 
models that seek to discern environmental trends).

They also discuss concepts like model sensitivity 
— the analysis of parameters included in a model 
to see which ones, if changed, are most likely to change model results.

But, the authors say it is important to remember 
that model sensitivity assesses the parameter’s 
importance in the model, not necessarily in 
nature. If a model itself is “a poor 
representation of reality,” they write, 
“determining the sensitivity of an individual 
parameter in the model is a meaningless pursuit.”

Given the problems with models, should we abandon 
them altogether? Perhaps, the authors say. Their 
favored alternative seems to be adaptive 
management, in which policymakers may start with 
a model of how a given ecosystem works, but make 
constant observations in the field, altering 
their policies as conditions change. But that 
approach has drawbacks, among them requirements 
for assiduous monitoring, flexible planning and a 
willingness to change courses in midstream. For 
practical and political reasons, all are hard to achieve.

Besides, they acknowledge, people seem to have 
such a powerful desire to defend policies with 
formulas (or “fig leaves,” as the authors call 
them), that managers keep applying them, long 
after their utility has been called into question.

So the authors offer some suggestions for using 
models better. We could, for example, pay more 
attention to nature, monitoring our streams, 
beaches, forests or fields to accumulate 
information on how living things and their 
environments interact. That kind of data is 
crucial for models. Modeling should be 
transparent. That is, any interested person 
should be able to see and understand how the 
model works — what factors it weighs heaviest, 
what coefficients it includes, what phenomena it 
leaves out, and so on. Also, modelers should say 
explicitly what assumptions they make.

And instead of demanding to know exactly how high 
seas will rise or how many fish will be left in 
them or what the average global temperature will 
be in 20 years, they argue, we should seek to 
discern simply whether seas are rising, fish 
stocks are falling and average temperatures are 
increasing. And we should couple these models 
with observations from the field. Models should 
be regarded as producing “ballpark figures,” they 
write, not accurate impact forecasts.

“If we wish to stay within the bounds of reality 
we must look to a more qualitative future,” the 
authors write, “a future where there will be no 
certain answers to many of the important 
questions we have about the future of human interactions with the earth.”


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