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Hypoxia or Hubris?
How Computer-Models Spoil Science
and Badly Advise Government
The Error of von Neumann's Elephant.
Errors of math in predicting hypoxia in the Gulf of Mexico.

by Douglas Moreman

The Warning of von Neumann's Elephant

John von Neumann (1903-1957) has been judged to be one of the most creative mathematicians of all time. One of his many works advanced a fundamental part of the Computer Revolution we see in motion around us. When they were still very young, warning us of a specific misuse of computers, John von Neumann said to physicist Enrico Fermi:

"With four parameters I can fit an elephant,
and with five I can make him wiggle his trunk."

Sciences and economies are suffering today from a failure to perceive and understand that warning.

In some areas of science, wriggling the trunks of imaginary elephants is taken as a sign of advanced and reliable "research." Computer-models are believed to prove things. This article will show you that some do not, no matter how confidently they are presented by seeming experts.

A brief introduction to this long article

Related erroneous thinking: Beyond Science

More pages of this website.

The elephant has company - even older lessons from history have been forgotten.
Blind and double-blind methods resulted from such a lesson.
The outcomes of experiments comparing various treatment of groups were found to change according to the expectations of people measuring the groups. It became a custom, in some fields of research, to require that people, in a position to "put a thumb onto the scales of measurement," to not know which group received what treatment.
Computer modeling seems to have no safeguards against unconscious distortions that result from experimenter bias.

By studying closely one example, perhaps we can find what misunderstandings allow bad modeling to be done, be proudly published, announced to news media, and result in damaging policies of government.

A Really Good, Bad Example.
One really good example of peer-accepted, bad science is a particular model of the nearly annual Dead Zone along the coast of the Gulf of Mexico from the mouth of the Mississippi westward - some years into the waters of Texas. This model is a good example, in part, because it is presented more clearly and completely than, for example, the much more complex and costly models of the "global warming" due, in theory, to increasing atmospheric levels of carbon dioxide. The model of the Dead Zone illustrates errors that have been made in those less-accessible, more economically costly models.

Some modelers of the Dead Zone off the Gulf Coast of Louisiana have done a good thing and made yearly, testable predictions of one measure of the "size" of that Dead Zone. Here is a graph, by Michael Courtney and Joshua Courtney, showing that in half of those years, the predictions have been spectacularly wrong.
Hypoxia Predictions from Predictions Wrong Again
Failure to heed the early warning given by John von Neumann is not the only mistake easily seen in Gulf Coast sciences. In just one journal article, that we call "Scavia 2003", there are more than seven big errors. There are other big errors, you can see, in an even more foundational article, Beyond Science. Errors in the sciences of the Dead Zone of the Mississippi River illustrate patterns that can be found in other "environmental sciences" that use computer models. Bad computer-modeling is producing bad science that gives bad advice to governments.

We will examine a model, one of low-oxygen levels in part of the Gulf of Mexico, whose 22 parameters were selected to fit just 20 data items. Perhaps you think that I just made a joke. Yes, the parameters are too many for the data. The authors surely did not see them all as "parameters." But, each parameter could have been fudged at least a little bit to help the model "fit" the data. Some of the parameters lacked even approximate, pre-model measurement. Rather, the set of data to-be-explained was used to compute the same parameters that were used in the explanation of that data. This is analogous to "circular reasoning," a well known way to "prove" falsehoods. The model wiggles the elephant's trunk. But for years the model was extolled on a website of the US Government, as an example for aspiring environmental scientists. One social implication or warning of this extolling is that models with von Neumann's Elephants are esteemed in environmental sciences like idols in a strange land and provide oracular predictions to government officials.

Is it possible for nearly an entire field of academic science to be wrong? I am old enough to remember being appaled, though only very new to mathematics at the time, that Educators and many Mathematicians worked with the National Science Foundation to "reform" mathematics education in America via "The New Math." A tidal wave swept across the nation. School-teachers everywhere had to learn about "sets" or find new jobs. The wave passed from elementary through secondary schools. I remember when a new edition of a venerable college calculus text came out with a "Chapter 0" that covered "sets." That the remainder of the text, after Chapter 0, was unchanged showed (to me, at least) how silly had become the influence of the social tidal wave of New Math. I met a mathematician-educator of Harvard University (Edwin Moise), an author of a distinctive pair of mathematics texts and an actual expert in sets. He wrote, in the midst of the herd-enthusiasm, that the New Math was either going to improve mathematics education in the United States or do it great harm. Today, one can hardly find a reference to "The New Math" in all of the World Wide Web.

Science, being human, is, largely, organized into fads and some are rife with belief and delusion.

Even "settled science," even in Physics, has been wrong. In 2014 a paper came out in October that proved, the authors said, that "black holes cannot exist." Another article in October said that black holes cannot exist in the form people had assumed. How many hundreds of papers and grant-proposals had assumed, until that October, that black holes Must exist? Can you imagine what misplaced enthusiasm can run through one of the newer fields that has almost no history, as a science, and almost no solid theory, of its own, for training the minds of its participants?

If you have not yet done so, please look into "Memoirs of Extraordinary Popular Delusions and the Madness of Crowds" which has been warning us since 1841 that we humans, including, perhaps even particularly including, "intelligent" humans, are subject to judgement-blinding, collective manias.

There is enough material accumlated in the recent-most 50 years to fill many pages of "Popular Delusions among Mad Crowds of Scientists." Consider, for examples, Medicine (frontal lobotomies -- worthy of a Nobel Prize in 1949), Nutrition (dairy products), Education (New Math) and, in 2014, Physics(black holes and, Jan 2015, vanishing evidence for Big Bang).

Theories of the Dead Zone (a name that many avoid because the zone often has life, but is memorable and gets straight at the point of controversy) are belied by their most fundamental data. We shall see that this data, looked at without lenses of Belief, has been warning that an extolled model might be wrong. But the model, and its descendants and cousins, continue to advise government, as do more important models likewise based on computer models.


Size-of-Dead-Zone with respect to Nitrogen in the rivers.
Why were these most fundamental data-points
omitted from the article?
The societal success of such a flawed model is screaming a warning that all environmental "facts" based on computer models are to be dis-trusted. Some may be true, but how can anyone tell which ones, given the terrible mistakes made by so many modelers? I have worked, long hours, building computer models for the past 14 years. I would Never make the claims for my models that are regularly made by others for theirs - who seem to have never heard of Von Neumann's Elephant or of the reason for "double-blind experiments."

"Blind" and "double-blind" methods were created because researchers, perhaps unconsciously, had been fudging their processes to produce results they had hoped for or expected. Well, computer models can be fudged. I will show you how this can done in the context of Scavia 2003. Apparently

no practices, analogous to double-blinding, exist to prevent unconscious fudging of computer models.
I believe the authors of Scavia 2003 have all been honestly doing the best science they know. Three of them have been helpful to me. I will, later herein, present a theory of what I think fooled them. If they were wrong, they erred honestly and in good company.

There is a plausible assumption, a strongly held Belief for some, that the summertime "Dead Zones" of the Gulf of Mexico are caused by fertilizer washing off farmlands to the north. Fertilizer in the Gulf grows organic matter. Dead matter and wastes sink to the sea floor and rot. On the continental shelf, the rotting of fertilizer-enhanced organic matter consumes oxygen faster than other processes renew it. The water on the sea floor can become devoid of oxygen and "dead." This dead water, when it exists, lies on the bottom of some part of the continental shelf of the Gulf of Mexico - just south of Louisiana. It was, 30 years ago, a plausible belief that the size of that dead zone was larger as the amount of fertilizer coming down the river was larger. But, that belief, as can be understood via the omitted graph, is belied by its most fundamental data. And, mathematical modeling and reasoning that has been used to confirm this Belief are shown, herein, to have been faulty. Possibly, in every field of science, many models in which there are parameters not determined by measurements, are faulty. The model below may not be any worse than others, but it is the only one that I have reproduced - a labor of a few months that I am not willing to repeat.

The focus of attention below, Scavia 2003, is a paper co-authored by some of the most well-known scientists of the Dead Zone.

Predicting the response of Gulf of Mexico hypoxia to variations in Mississippi River nitrogen load. Limnol. Oceanogr.48:951-956.
By Donald Scavia, Nancy N. Rabalais, R. Eugene Turner, Dubravko Justic´, and William J. Wiseman, Jr. 2003.

This webpage is an adaptation of a long technical paper that details mistakes made in or exposed in Scavia 2003. Wishing to avoid some of the social aspects, the "politics," of science, and cringing at the prospect of harming reputations, I have withheld the paper until now, in 2014, when I see that government policies have been infected by the bad science.

Abstract

Various computer programs were written to replicate some results of Scavia 2003. While results were indeed replicated, we explain that those results are without merit, based as they are upon flawed mathematical reasoning. Furthermore, using data implicit in graphs by Scavia et al., doubt is cast on the fundamental assumption - that springtime nitrogen-loading in the Mississippi River controls the size of the hypoxic zone in the northern Gulf of Mexico. Yet, the assumption and continuingly bad models are used to lobby government to restrict the use of fertilizer in the food-producing heart of the USA.

To repair damaged Science, it will not be enough to "fix" the model. The result of a fix will be another bad model whose flaws would take event more time and labor to expose. The methods and habits that produce bad models must be fixed. The epistemology of Science must be given tools to kill bad science that results from computer-modeling.

Theory that Springtime Nitrogen Drives the Dead Zone

There is a theory that nitrogen from the Mississippi Basin controls the size of the summertime "Dead Zones" in the Gulf of Mexico. The region of these hypoxic zones extends about 10 to 60 miles out to sea and stretches from the mouths of the Mississippi westward, some years into Texas waters. The Nitrogen Theory has been stated and restated for so long by such respected researchers that is it widely regarded as equivalent to fact, and is presented as fact, and influences policies of the US government. Perhaps there will be a virtue in a review of some component of this theory by an outsider - which I am, being simply a mathematician who can implement models on computers. I also have been doing my own, mostly lone-wolf science for more than 50 years. Me

Mistake of Evidence-Bending. An often-made mistake, by people in general, is to Believe an idea and bend evidence to confirm it. Done in cliques, largely unconscious evidence-bending is a group-confirming exercise - powerfully reassuring to Believers.
When I refer to a peerclique, I will mean a clique of Believers in science who collectively control a substantial proportion of journals related to that Belief.

The map in Figure 1 shows an assumption of the Scavia Model. Does the assumption seem remotely likely to be correct?

Figure 1. The flow of the River, M, is out to sea and on the surface of that sea. But, a subsurface East-to-West current flows under the region of study of annual Dead Zones, carrying nitrogen-based nutrients from river A and river M. The plume of M can be seen in some satellite-images, extending southward, far out to sea. But, the modeling in Scavia 2003 has more than 50% of the river's nitrogen, in some form or other, reconcentrated at a point R to the north of the plume. I call this the Reconcentration Hypothesis. One of the authors stated in conversation that the dispersed nitrogen, bound in organic matter, falls from the plume then is current-carried northward along the sea-floor to R. Thus the birth of my skeptical inquiry.

Mistake of Failing to Give Falsification a Chance. Failure to use your theory to make theory-testing predictions.

In 2003, Scavia et al. announced what seemed to be the first substantial model designed to predict the response of dissolved oxygen to nitrogen from the Mississippi Basin. "Hypoxia" relates to low levels of oxygen. One might expect that an article whose title begins "Predicting ... hypoxia..." and which presents a model for that purpose would be clear about how that model computes concentrations of oxygen and would make at least one tested prediction about oxygen. The title of the article is "Predicting the response of Gulf of Mexico hypoxia to variations in Mississippi River nitrogen load". But, the article does not make even one tested prediction (curve-fitting is not prediction). Why did the "peers" not object to this?

The customs of Science demand that a finding claimed by one party be repeatable by another party. In spite of my work in replicating Scavia 2003, I judge the report to have failed to meet that demand. It ought not have been necessary for me to seek out in a vaguely referenced text the most-probable model therein that was most likely to be the one adapted to become the Scavia model, and then to be obliged to seek a value of an essential parameter totally missing from the Scavia 2003 report. But, I did. I will here report findings resulting from my repeating, by computer, some of the modeling of Scavia 2003.

Where are the data points? It seemed prudent to examine a graph of the most fundamental raw data. A graph of 17 data-points. It would surely illuminate the simple hypothesis that years with higher springtime levels of Nitrogen (in the rivers) also had larger Size of Dead Zone. Plot the yearly points (Nitrogen, Size) and you will have a more-of-less straight line that rises from left to right, right? The data-points were not given in Scavia 2003. I looked for them in other publications - in vain.

When we join the passions of religion or of politics to our science, the truth of the science suffers. It seems acceptable for, it not yet required of, researchers in some fields of environmental sciences to be "activists" trying to "save" some species or to save some part of, or the entire, planet. Some who study the Gulf of Mexico are "activists" in the sense that they actively advise governments, suggesting policies to alter the behavior of people, in particular farmers, in the watershed of the great river. Has this activism impacted scientific judgement?

Mistake of Withholding Facts. Withholding information that might cast doubt on your Believed Theory.

Unable to find the graph that would be the foundational graph of the Dead Zone idea, I decided to plot it myself. But then, I found no references to locations of the raw data. Eventually, however, I came up with the following graph:


Figure 2. Versions of this graph have, in the years since I had to make my own, been published in articles by Rabalais and by Scavia. The double digits in Figure 2 denote years - "99" denotes 1999.

Note: LARGE amounts of Nitrogen (the 13 right-most points of the graph) in the rivers are targets of reduction through political action. There are four outlier-points on the left of the graph, with SMALL values of Nitrogen. The action proposed by Scavia 2003 relates to LARGE values of Nitrogen - included among the 13 points that are clustered on the right side of the graph. These are most relevant to scientist-inspired government attempts to reduce the size of Dead Zones by forcing farmers to reduce their use of fertilizer.
The four outling points in the left side of the graph are least relevant and, being such outliers, seem likely to distort whatever process might be indicated by the 13 relevant points, on the right.
A math-less glomming of the LARGE-Nitrogen points shows there is no way to draw a respectable data-representing straight line that rises from left to right.
Studied further, with a wee bit of care and knowledge, the graph shows us clearly that

the anti-farmer policies will fail to reduce the average size of the annual Dead Zones.

Consider this defense of the omission of the fundamental graph: The graph is mis-leading, suggesting as it does that primitive methods cannot predict its data-points. But Scavia 2003 can do. Indeed, if you were to plot, along side (Nitrogen, Size), the yearly points (Nitrogen, Model's-Output-Size), you would see an uncannily good fit of the model to the measured.
But, that is a false defense because for each year there is a free parameter that fudges the Model's Size onto the Measured Size. So of course the fit is good - it is an application of von Neumann's Elephant.

The Scavia 2003 Model Does Not Substantiate the "Action Plan"

One can see pictures in clouds. I see six data-points, in the LARGE Nitrogen region, rising from left to right in almost a straight line. But, these six are flanked by seven that do not agree. Letting one's imagination run wild, one can draw families of curves from left to right, including the SMALL points, so that each data-point is near to one of the curves. And so forth. So, maybe the real world is slyly telling us something that we clever humans can figure out. That might be so, but using multiple von Neumann's elephants will, in no way, prove that your cloud-images are true.


Figure 2b. For the values, N, of Nitrogen-load of the rivers, relevant to recommended plans of "action," there is Zero Correlation of Size of Dead Zone and Nitrogen.

Mistake of Leaping beyond Science. So strongly Believing your science that you fail to properly test it before you "go beyond science" and give advice to power-wielding bureaucrats.

The Scavia article was, for years, among the "top ten" articles recommended on a NOAA website. Its lead author was, formerly, the Chief Scientist of a division of NOAA. Based partly on the authority of its authors (see Beyond Science into Policy, Rabalais et al. 2002 and see Beyond Science.) the US government began, in 1998 to plan to regulate use of nitrogen-containing fertilizer by farmers in the American Midwest, and this led to the Harmful Algal Bloom and Hypoxia Research and Control Act of 2004. Yet, studied deeply, Scavia 2003 reveals fatal flaws in its modeling, suggests that the Nitrogen Theory itself rests on a shaky foundation, and shows that a proposed "Action Plan" for ending hypoxia, discussed in Scavia 2003, will fail (Figure 2b).

For five years, I kept private my knowledge of the flaws in Dead Zone Science. Why embarrass good people? Then, in July 2013, I learned that people who Believe the bad science are suing the US EPA to restrict the freedoms of farmers in the watershed of the Mississippi. Seeing that this bad science is actually moving government, and having seen what appeared to be a deterioration in the quality of some of the science steering the EPA, I feel forced to reveal my findings about its flawed mathematics and modeling.

I will concentrate on errors in the modeling and only mention other considerations such as: there seems to be a rationale, and some experimental evidence, for suspecting that the algae deemed responsible for the Dead Zones is actually a benefit to the over-all population of fish in the Gulf of Mexico - by adding nitrogen and carbon to the system. Directly, and indirectly, algae is fish-food. So, even if attacking farming in the watershed could diminish algae, that might be a very bad thing to do. A result might be higher prices for food from both land and sea - and no practical "improvement" in the Dead Zones.

Mistake of Doing too Much with too Little. Your model is far too simple to account for its phenomena.
Omitting the Sun from your climate model might be an example. Or, omitting from your hypoxia model the fact that shading of sunlight by algae, or by suspended mud in the top part of the water, can reduce oxygen produced in lower levels.
The model of Scavia 2003 is of just one geographic dimension but is applied to "predicting" oxygen concentrations in a three dimensional volume of the Gulf.
The effect of water-temperature on the critical parameter "oxygen saturation" is not even mentioned.

Here is a preview of a main mathematical flaw of environmental modeling:
We will see that one model is selected, in effect if not in understanding, from a rectangular box in a five-dimensional space representing such models. I call that box "the Elephant's Cage" of the model. I also call it the "Parameter Box" of the model; but, I fear that few would remember that name. Having an Elephant's Cage is a bad thing. The larger it is, in number of dimensions and in edge-lengths, the worse the mistake.

An Elephant's Cage Can Lead to Mistakes
Doing any one of these is a mistake:
* Have no rationale for selecting one model over all others in the cage. The model might be, within itself, optimized against some criteria but so might have been every one of the non-chosen models.
* Derive no prediction from the selected model which might distinguish it from all, or even most, of the non-selected models.
* In spite of lack of clarity about method, and no short-range predictions having been tested, derive long range predictions.
* Then treat these predictions as likely to be true and advance them as part of a basis for government edicts that will harm some overwhelmed minority of citizens.
* Ignore even the possibility that those predictions might contradict predictions from some of those other models in the cage - models that might be of equal or superior scientific merit.
* Ignore the fact that your model is too simple and might be contradited by a more complete theory.
* Ignore the liklihood that your short-sighted actions will, for the general population, do more harm than good.

The Theory of Spring Nitrogen: “the size L of the summertime Dead Zones of the northern Gulf of Mexico is due to and predictable from the amount N of springtime nitrogen flowing down the Mississippi River Basin.” This abbreviated theory suggests that a study of the graph of the known data-points (N,L) will reveal a pattern and this pattern might be captured in a predictive model. There were, at the time of the Scavia article, a mere 17 of these points and they, in close inspection, do not support the Theory. So, the Theory might have seemed wrong, had the graph ever been published, before the Scavia computer-model was used to "predict" effects of various possible (government-induced) restrictions on fertilizer.

Foundations of the Scavia Model

The Scavia article presents a “model” which deals with hypoxia measured in the coastal waters of the Gulf of Mexico westward for nearly 600 km from “the mouth of the Mississippi.” The Scavia “model” can be called a “model-generator.” It is used in Scavia 2003 to generate a yearly model for each of the17 years, from 1985 to 2002, in which Nancy Rabalais, one of the authors, mapped a Dead Zone. The principal datums can be given in the form (Y,NM,NA,L,Np) where

Y is a year from 1985 to 2002 excepting 1989;

NM and NA are measures of nitrogen delivered to the Gulf by the rivers Mississippi, M, and Atchafalaya, A, in the spring of year Y;

L is the east-to-west length of the Dead Zone for that year; and


Np is the number of component “patches” seen in a map of that Dead Zone. Np is not correctly or completely reported in Scavia 2003

The points (Y,NM,NA,L,Np) constitute a five-dimensional parameter box, the Elephant's Cage of the Scavia model.

The modeling in Scavia 2003 rests on a simple, a too simple, pair of differential equations involving two functions. One of those functions, D(), is solved for and used in computer-modeling.

The modeling, using the D() function below, cannot produce more than Np = 2 "patches," two mutually separated zones of hypoxia. Scavia 2003 reports two or one patch for every year for which it mentions patches. In particular, it states that in 1999 there was a "single" patch. I found a map of the Dead Zone for 1999 and I counted four patches - two large and two tiny.

Rabalais et al. in Characterization of Hypoxia, 1999, give the maps of Dead Zones from 1985 through 1998. Childs et al. 2003 give 1999. Maps from 2000 are available in EPA Hypoxia Press Releases (see References below).

I attempted to replicate Np, the number of patches, using only the reported information, then replicated again using corrected information. The fudge-factors in the model allowed success in both cases!

Predicting (Badly?) for Government

The article purports to show that L can be “predicted,” for each year Y, from amounts NM and NA of nitrogen coming from the Mississippi Basin, as determined from measurements, in a couple of spring months of Y, at two points M and A, one on each of the Mississippi and the Atchafalaya rivers. The Nitrogen data comes from an agency of government.

Mandated by Federal law in 1954, a control structure north of Baton Rouge has bled, since 1977, thirty percent of the flow of the Mississippi into the Atchafalaya - which takes a steeper, shorter route to the gulf. An assumption which seems reasonable and widely used is: in summertime, the greater the amount of nitrogen made available by the rivers, the greater the mass of new algae and algae-eating organisms which grow in the ocean-plumes of the rivers then dies, sinks and rots, consuming oxygen.

The authors seem to assume that the net effect of hypoxia is bad for the fish of the Gulf of Mexico. To the contrary, it would seem that if the mass of algae in the gulf is increased due to extra Nitrogen then this is a good thing - algae is, or turns into, food for fish. While some dies sinks and rots, much is eaten. Fish abandon low-oxygen areas but proliferate in the food-rich surrounding waters. The commercially most important fish to Louisiana, the menhaden, eats algae. Have the authors ever estimated how much of the Nitrogen does not fall to the bottom in a rotting process but, rather, is food-chained up into the meats of various fish? Have they begun to compute the net commercial, or environmental if you prefer, effect of that Nitrogen? I hope they have, because they have been advising government upon the effects of agricultural Nitrogen.

Each Water-Speed Implies one Deficiency Function D()

The model-generator has a parameter v, called "advection," which represents speed of east-to-west flow of water along the bottom of the relevant region of the continental shelf. For each of the years Y, a value of v is selected and a model is generated. The main part of each yearly model is its function D( ) which can be thought of as representing "oxygen-deficit." The article does not give a full formula for D( ) and does not specify, or even clearly hint at, a method for “selecting” v. One who attempts to replicate the Scavia article, and is not personally advised by one of the authors, seems doomed to making the best guesses he can at omitted parts - some trivial and at least one of great importance. Using a computer, one can test several guesses per second.

For each positive number x, D(x) is the "oxygen deficit" at location x (kilometers) west of "the mouth" of the Mississippi." But, how can we know which of its five largest mouths is “the mouth of the Mississippi”? I presume Southwest Pass, which is by far the largest seemingly relevant mouth and is near to the longitude through another mouth, Tiger Pass (in Figure 1 these passes are the west-most two connections from the river M to the sea).

I surmise that, given a year Y and its measured values NM, NA of nitrogen, and the Dead Zone's length, L, a numerical method finds a suitable value of v and this v specifies a D( ), the general form of which is begun but not finished in Scavia. A typical D( ) is shown in Figure 3. The Scavia article contains no image of a D( ). It thereby hides an otherwise obvious implication of a physical impossibility, as we shall see. O() is, of course, what counts. The model's O() is derived from D() but only via a reference value OS - which Scavia 2003 fails to mention.

Click Figure to Enlarge.

Figure 3. Shown in black, a typical D( ) for a year whose Dead Zone had two patches. It is shown at the top of its graph that D(x) exceeds OS. This is physically impossible - because it implies that oxygen-concentration O() falls below the x-axis and is negative. Scavia 2003 omitted mentioning OS entirely; so, this false prediction of the theory was not addressed nor made available for readers to address.

The values of “x” represent distances from “the mouth of the Mississippi” westward, measured in kilometers. The bottom of the sharp dip in D() is at x = XA whose value, 220, is said to indicate “the mouth of the Atchafalaya.” The number 220 might reasonably have been replaced with 218 or with 221. If one examines a map of the region, one can see that this river, labeled “A” in Figure 1, enters a bay which connects broadly to the Gulf and the value of XA could have reasonably been given a different value - from a range of 10 or 20 kilometers wide. This is a small matter, but it hints that the Scavia modeling has hidden flexibility which might allow it to fit many possible scenarios in the real world, and not be able to prove even one of them.

The Error of the Elephant's Cage.
Flexibility in parameters allows a modeling procedure to generate models to predict a variety of different futures. The future predicted in practice is, thereby, selectable. Flexibility in parameters can create a nouveau-astrology that can endure so long as its predictions and retrodictions are confined to an untestable future or an untestable past.

Actually, history shows that a really strongly-knit community of Believers can survive its demonstrably wrong predictions. Descendants or cousins of the model in Scavia 2003 have made spectacularly wrong predictions in 2012 and again in 2013. Laudably, some (e.g. Scavia and Turner) are making actually testable predictions.

The numbers NM and NA and NM + NA are similar enough to each other, in some behaviors, that I sometimes use just NM or N = NM + NA in discussion.

Scavia 2003 suggests that its one-dimensional model "successfully" represents a three-dimensional process. But, it does not. It merely "fits" curves to a few data-points and ignores many other other implications of the theory behind the modeling. In Science, we do NOT ignore implications of our theories when they disprove those theories.

Each yearly Scavia model uses the one-dimensional number-interval [0,600] to represent the three-dimensional region containing all the Dead Zones’ waters along more than 600 kilometers of somewhat curved coastline. Figure 1 shows the part where measurements of oxygen-concentration had been taken each July by Nancy Rabalais.

The interval [0,600] is not clearly tied to the real world at either its east or its west end. On the east, we imagine "the mouth" of the Southwest Pass to be represented by some clearly defined point, or at least a longitude. Then x = 0 will be on the line of that longitude. For each x > 0, x represents the distance in kilometers to the west, measured more-or-less parallel to the curving coast. The vertical line at x = 0 is near to the east-most of the oxygen sampling stations in the yearly hypoxia maps of Rabalais, and is near to “R” in Figure 1. The only other value of x which is given some connection to the real world is x = XA, the "220" noted above - having to do with "the mouth of the Atchafalaya River.

But, lack of precise connections of "x" to geometry may not have concerned the authors because, it seems, they never intended to predict a value for oxygen-concentration at any specific location whatsoever. They could have predicted that at distances x1, x2, ..., xn from R, the values of oxygen would be O(x1),O(x2),...,O(xn). Such detailed numbers do not matter, only the grand conclusions that seem to rest on those ignored details? From what epistemology of science does that come?

When a yearly model "predicts" that the hypoxic zone will have two patches, the predicted and actual positions of those patches are ignored. That the model is way off in predicting those positions is not mentioned in Scavia 2003. The model only, for some of its years, gets the number of patches correct due to its great flexibility in the parameters.

In general, belief-confirming facts create enthusiasm in reporting - and, contradicting facts are not reported.

Since when does an entire field of "scientists" ignore clear, discrediting implications of a theory? A snide answer, that I do not believe, is: "since Government funding became important." Rather, I suspect the answer lies in "the madness of crowds," and not in venality of individuals: "everyone" in the entire field was thinking the same way: that

wiggling elephant-trunks make good models and,
the proof is that they can closely fit existing data.

Actually, of course, a computer-model that uses wiggling elephant-trunks is just a modern form of customer-awing pre-science oracle. The awing part is furthered by impenetrable jargon or by clearly stated but uncheckble assertions.

D( ) is called “the oxygen deficit.” One surmises that O(x), the oxygen-concentration at westward distance x, is computed from D(x) in some manner probably similar to that of a model in the text, Chapra 1997, referred to by Scavia 2003. We will try to surmise more properties of this function O( ), that is (unaccountably) missing from a paper about predicting low values of O( ).

"Pycnocline" Was Carefully Described then not Used.
Water from the rivers floats above the denser sea water and can be moved by sustained winds (Nan Walker, 1996). The saltier water below trends westward under the regions of Dead Zones at less than one kilometer per day. There is an abstract definition of “pycnocline” which allows us to use this word to indicate a boundary between the less salty and the denser, more salty of two layers of water. Less salty water in the layer above the pycnocline is exposed to air and is relatively high in oxygen, probably “saturated” at least in some thin film at the top.

The concept of "pycnocline" plays no part in the model. The model is of a one dimensional flow, east to west and, in particular, has no vertical component - whereas pycnocline divides a top volume from a bottom volume in the water. Such actual components are replaced, via what in Mathematics is called "hand-waving," with two parameters "a" and "b". "Pycnocline" seems to have been a part of the thinking before the model but there is nothing actually in the model to go with this statement in Scavia 2003:

Because the model simulates subpycnoclinal concentrations ...
Absent entirely from the math, "pycnocline" was used seven times in the article and three times in the abstract. Its only rationale seems to have been to convince the reader that a "3," used in the model to indicate hypoxic conditions, had a history and was to be taken seriously. But that "3" seems to have been selected as yet another fudge-factor to help the model (which has 22 other parameters) to fit the 21 data items.

By contrast, OS, oxygen-saturation at the water's surface, is critical to the model and not mentioned even once.

The article gives an “oxygen flux,” denoted by “a,” which is a coefficient in one of the two initial differential equations of the modeling and appears intended to represent a rate of transfer of dissolved oxygen from the atmosphere through the relatively oxygen-rich superpycnoclinal layer all the way to the bottom of the relatively oxygen-poor subpycnoclinal layer that abuts the rotting material on the sea floor.

The ocean’s depth in the regions of hypoxia ranges mostly from 20 to 100 feet, but depth is not a term in the two given differential equations. Since depth in the ocean is ignored, the rate of flux from top to bottom, assumed to be constant, is a mathematical fiction not determined by measurement. Indeed, Scavia 2003 says of "a" and "b":

“... the values of the first-order rate constants used for flux and consumption ... are parameterizations of many processes and thus cannot be derived from direct measurements.”

It seems that “are parameterizations of many processes” means, in practice, that the two parameters, "a" and "b," result from artful guessing. They are "selected" so that some curves will fit some data:

"...they were selected to produce the typical downstream oxygen profiles."
No such "profile" was given in the results.
The "parameterizations of many processes” are "selected" (from what options by what method?) so that some curves fit some data. These two parameters are not independently connected to Reality. This is exactly what von Neumann warned us of.

The parameter "b" is called “oxygen demand.” Each term of (a,b) is selected from a range of possible values and those ranges are not mentioned in Scavia 2003. These parameters a and b are two of the five terms called the “Parameters of Wiggling” - the five dimensions of the Elephant's Cage.

Mistake of Hiding Absurdities behind Heavy Jargon.
Giving "a" and "b" seemingly reality-related and science-derived names "oxygen flux" and "oxygen demand" does not make them real. They are not real. The careful, technical language hides artful guessing. There is no way, even in imagination, to meaningfully measure those parameters, or even to "parameterize" them from "processes" (unless that is what curve-fitting is). The field-specific language of sciences actually helps obscure enormous errors of science. Speaking for just myself, the confidence reflected in the crisp, refined, and large-worded technical language in Scavia 2003 was somewhat intimidating to me when I, an outsider, first encountered it and I was still assuming this team of experts understood everything they were doing.

The Scavia modeling process has, I surmise, three sub-processes which I name UberModel, YearlyModel, and an Extrapolation model. Each of these component modeling processes uses the form of function D( ) which is given below, but each has different parameters being fixed-in-use or being given-in-output. Modeling process UberModel, not clear in Scavia, determines values of the five Parameters for Wiggling, the five parameters of D( ).

The Necessary Parameter, OS, Was Hidden. Scavia 2003 indicates that its “model” (mainly its equation D( )) comes from a model given in Chapra 1997. Using that book (Chapra 1997, Page 390) we see that there is a number, herein called OS, that is related to oxygen-concentration when it is maximal ("saturated") at the air-water boundary. Recall that O(x) denotes "the oxygen-concentration" at westward distance x. Which is a fiction because, in our three dimensional world, a number "x" in the model does not specify an actual place. Nonetheless, in each yearly model, D(x) =  OS - O(x), so D(x) is reasonably called “the oxygen deficit” at x. High values of D() correspond to low values of O(), possibly to "hypoxic" levels. OS is used clearly in Chapra 1997 but, though central to the modeling, is not even mentioned in Scavia 2003. OS seems to represent a measure of the oxygen-concentration, assumed to be at saturation, at the air-surface of the ocean. The aforementioned "flux" is motion of oxygen from the water's surface where its concentration is OS, to the sea floor where its concentration has some value, O(x). But at what location x? And, as OS varies during the days and the weeks, one might ask when was it measured, and at what temperatures? Well, it wasn't measured. I surmise it to be the main hidden "parameterization of many processes" - the main trunk-wiggler. The question of the correctness of OS is avoided in Scavia by simply failing to even mention the existence of this Parameter of Wiggling that, according to Chapra 1997, would have been used in actual calculations.

It might appear to the weak of spirit that omission of a key term in a model would make its replication impossible. But not so. Through the massive power of computers, even the omission of the key function, O(), can be overcome.

In Chapra 1997, OS is the concentration of oxygen at saturation. A measured value of it is probably good, within a millimeter of the air-water boundary, as representative of the actual concentration of oxygen. This number varies widely over a range of plausible real-world temperatures and salinities (Chapra 1997, Page 362). I suspect that OS was "selected," in UberModel, somewhere from 6 to 9 (mg/L, milligrams per liter) with one criterion being reasonableness with respect to known real-world averages and another criterion being to fit the model-generator well-enough to three special datums, three known “advections” v, speeds of flow of the subpycnoclinal coastal water. This is what I did in replication.

The hidden number OS seems critical to the model and I include it in Parameters of Wiggling. Rather than declaring the Scavia article to be un-repeatable, I wrote a computer program which used several values for OS, from 6 to 9, in various trials. I found values of OS which gave me good fits to 17 (N,L) datums. It can been seen in Chapra 1997 that those found-values for OS were plausible with respect to being average of saturation values at possible temperatures and salinities of the surface of the Gulf Coast waters in July, the month of measuring L.

Ultimately, none of these careful details matter.

The Model Can Fit False Data as Well as True

We will see that the flexibility of the modeling allows it to “accurately simulate” invented data as well as actual data, thus mocking the certainty of

“... our ability to accurately simulate the year-to-year ...” Scavia 2003 (Page 952).

"To accurately simulate" seems to mean, to make a graph like that of my Figure 4, which, by the way, fits the data better than does theirs. People have their own styles of expression - I would never say that my Figure 4 "accurately simulates" anything.
The article, about “prediction of hypoxia,” does not actually fully say how its yearly models predict hypoxia. Hypoxia exists on the seafloor at each (fictional) location x such that D(x) > OS - 3. The supposition, or guess, that “3" comes from “2" via the pycnocline is said to have been explained in an earlier article prior to Scavia 2003. But as “3" ignores variations in depths of sea floor and depths of pycnocline, “3" must be some kind of average over these depths and over times. The "3" was probably was rounded to one digit for convenience. I denote OS - 3 by Dh. “Hypoxia” exists at x when (x,D(x)) is above the horizontal line y = Dh in Figure 3.

"The length" of the Dead Zone could reasonably be the distance from its east-most point to its west-most point. In the graph in Figure 2, this length is x4 - x1. "The length" could also have fairly been defined to be the sum (x2 - x1) + (x4 - x3). Scavia does not say which notion of “length” was used. So, in replicating the partially presented work, I had software run both versions. In Figure 3, the number Np of “patches” is 2 and these patches of hypoxia are represented by the intervals (x1, x2) and (x3, x4).

One Model for each Year's Data

In YearlyModel, for each Y, a speed v is computed so that its D( ) produces a value of x4 - x1 which is near to the Rabalais-length L for year Y. The D( ) in Figure 3 is from one of 17 yearly models generated in YearlyModel.
Repeating the core of the modeling process:
for each yearly-measured value L of Length, a speed v is computed such that L is the length of the hypoxic region (wherein D(x) < 3) for the function D() that results from using v in a formula for D().

Wrongly Defining the Oxygen-Deficit Function D()

The Scavia 2003 model-generator, used in YearlyModel, comes from a pair of differential equations given in Chapra 1997 (Page 390). These equations relate to two functions, one of them similar to Scavia’s function D( ). Even granted that one-dimensional x is used rather than (x,y,z), these functions are defined, or ought to be, on ordered pairs (x,t) where t is time. The model, in Chapra 1997, applies, for example, to the concentration in some river of some substance downstream from a source such as a sewage plant. The output of the source is reasonably steady and, so, the “steady state solution” is used. It seems, that is, that the limit of D(x,t), as t goes to eternity, is used.

Scavia 2003 imagines a coast-bound current flowing westwardly along the sea floor, like a river. It adapts the river-model in Chapra accordingly.

Occurring in terms such as exp(-at), time drops out with these terms as they get close enough to zero. What is left is D(x) rather than D(x,t). Typical Dead Zones last a few months, not eternity, and extend for a few hundred kilometers along the Gulf Coast. The speed of flow (less than 1 kilometer per day) of “subpycnoclinal” water and the distances seem to argue against “steady state.” But, the Scavia article jumps straight to its “steady state solution,” giving no explanation. I suspect this lack of clarity, about meeting sufficient condition for assuring the state-at-eternity, is inherited from Chapra 1997 (see Pages 14, 308, but also 390, 391). But, the reasons the steady-state make sense in the examples in Chapra 1997 do not apply to the northern Gulf of Mexico. So, the first modeling errors are right here at the beginning.

Scavia 2003 does not make clear how a yearly model is generated via the model-generator. For each year, there is just one parameter, v, for YearlyModel to determine. I assume that, for each year Y, a value of v is generated in YearlyModel, by an interative numerical procedure, so that the length of the Dead Zone for the D( ) determined by a particular v is acceptably near to the measured length given by Nancy Rabalais for year Y. YearlyModel outputs 17 values of v, one for each of the years. The 17 matches, of “predicted” values of L to measured lengths, given in Scavia's Fig. 3a, are not perfect. This suggests that additional constraints were used - because I obtained tighter fits in my own simulations. Or, maybe I just ran the computer harder. One of my simulations produced Figure 4, wherein it also got, unseen in the picture, the Scavia-given values of number of patches Np.


Figure 4. Measured length of Dead Zone together with a length modeled for a given oxygen-saturation, OS. Each of several trials value of OS resulted in such a graph. An artful computerist can pick the model he likes best.

Let us see how, for each of the given years Y, its hypoxia-representer D( ) can be determined. First, we select or compute numbers a, b, XA, OS and H which are to be constant over all those years. Those five numbers are the Parameters of Wiggling, output by UberModel. Scavia did not describe a method for UberModel and only barely suggests how three Parameters of Wiggling (a, b, and XA) were "selected" (how they became "parameterizations of many processes"?). Of the five Parameters of Wiggling, OS and XA are not acknowledged in Scavia 2003 as parameters yet seem to have the best chance of being connected to Elephant-defeating, independent measurements. OS and XA are each selected from its range of possibilities, and can help, to a greater or lesser extent, the modeling process fit the set of 17 (N,L) pairs. Parameter H will be covered later below. The scant attention in Scavia 2003 to getting UberModel right dooms the Scavia Modeling Processes to ultimate failure - independently of the possible failure, shown in Figure 2, of its foundational assumption, and independent of internal contradictions. Yet, Scavia 2003 was, for years, a model in government for aspiring young, environmental scientists. Perhaps influential research is now, ten years later, being done by people inspired by Scavia 2003.

For each year Y, nature gives us length L of the Dead Zone. For each year Y, nature gives us NM and NA which are measures of nitrogen coming down the Mississippi and Atchafalaya rivers, respectively, in two months presumed to be relevant. That these two, or any two, months are particularly relevant contradicts, most egregiously, another part of the modeling. We will soon see that nitrogen cannot be "advected" into place fast enough.

Recall that Dh = OS - 3 and, when D(x) > Dh, there is, by definition, "hypoxia" at distance x from "the mouth of the Mississippi."

I wrote an optimization program (actually, I wrote several) which, given Parameters of Wiggling, finds a value of parameter v so that the yearly model resulting from v approximates closely the yearly length-datum L. The output value of L equals x4 - x1 where x1 is the least number x such that D(x) = Dh (or 0 if no such x exists) and x4 is the greatest number x, distance westward from R, such that D(x) = Dh (or 0 if no such x exists).

The two rivers are the presumed sources of nitrogen-containing organic matter into the westward flowing current along the sea bottom. Neither river, we here presume, contributes rot-ables to its east.

D( ) is defined like this:

Numbers are abbreviated:
H = 0.5 (see below this parameter "H" of wiggling)
M0 = H*(0.016)*Nm, (Nitrogen entering at the Mississippi)
A0 = H*(0.016)*Na, (Nitrogen at the Atchafalaya)
u = a/(b -a) ("a" and "b" are from above).

Somehow select water-speed v (e.g. via a bisecting search in YearlyModel. In the Extrapolation model, v is V(Y)).

Abbreviate c = a/v and d = b/v.

Define M( ), (M(x) is Mississippi Nitrogen reaching distance x):

M(x) = 0, if x <= 0 and

M(x) = u*M0*(exp(-c*x) - exp(-d*x)), if 0 < x.

Letting z denote, x - XA,
A(x) = u*A0*(exp(-c*z) - exp(-d*z)) (Atchafalaya Nitrogen)

Define D( ):

D(x) = M(x), if x <= XA,

D(x) = M(x) + A(x), if XA < x.

End of definition of D( ).

Recall that XA was given the value of 220. We shall see how H was set equal to 0.5 .

Now we can see a contradiction between the model and facts in the real world.

Self-Contradiction Breaks Law #1.
Let us consider how such a model computes D(220). Scavia 2003 reports a number just less than 0.6 kilometers per day as the mean of its 17 yearly values of v. Therefore, a simple and honestly representative value for v is 0.6/day. This v is a speed at which the bottom water might flow westward along the coast, from “the mouth of the Mississippi.” The nitrogen arriving at x = 220 (in kilometers) in water from the Mississippi has been traveling for 220 / 0.6 or about a year, 366 days.
This implies a
Great Leap through Time:
the values of Nm used at x = 220 ought to be those of the previous year, Y-1. But the model calculates using Nm of this year, Y. Thus, the model contradicts itself in assuming that this year’s nitrogen exists at x = 220 but implying that this year’s nitrogen will not arrive at x = 220 for another year.

Ethically, can such a model, wrapped in however many layers of intellectually intimidating trappings of science, be used to encourage government to start a program that might, perhaps, help some fish but will certainly hurt many farmers a lot and most Americans, a little, who eat the produce of those farmers?

The nitrogen arriving at x = 110 is six months out of phase so the two months in which data is taken are not the months needed for calculating D(x) at that x. Similar problems exist for other values of x. Therefore, the assumed special worth of springtime N is thoroughly contradicted. It seems that either the subpycnoclinal current is not the main transporter of nutrients to the Dead Zones of the Gulf or the Theory of Spring Nitrogen is false.

Some flaws of method in Scavia 2003:

1) there were too few data points and too many parameters,
2) there were un-measured (and un-measurable) parameters (von Neumann's Elephant),
3) “steady state” is assumed without checking to see that its minimal conditions are met,
4) the model-generator is too flexible to result (other than by luck) in accurate predictions,
5) the yearly models make the physically impossible implication of negative concentration of oxygen (a secondary error is to ignore these implications. A related error is to not reveal these implications),
6) an assumption behind the modeling process implies the Reconcentration Hypothesis (see Figure 1) which seems unlikely to be true,
7) critical parameters and methods were omitted from the presentation,
8) given the believed rates of motion of the waters, the springtime measurements of nitrogen in the two rivers cannot be relevant to measurements across all of the Dead Zone in July, when measurements of hypoxia are made, and

Scavia 2003 has been educational and probably will lead to advances, regardless of, or even because of, its flaws. People who would make great advances risk making mistakes. But, one might judge the predictions of Scavia 2003, or of its siblings or of its cousins or of their descendants, ought not be taken seriously.

Consider the magnitude of the error made by its field of science in accepting Scavia 2003 as worthy of use in planning by government. Ought one to suspect that the entire field, unable to detect glaring flaws in Scavia 2003, is similarly flawed? Perhaps every mathematical model in Gulf Coast science ("and beyond") will be seen to contain a von Neumann's Elephant? One might wonder: missing the most elementary, higher-level, principle of scientific modeling, of what other errors is this peerclique capable?

Is the peerclique of Gulf Coast Sciences embedded in a larger, equally flawed, peerclique? How far into Environmental Sciences do these erroneous reasonings extend? How many government programs around the world are based on the resulting bad advice?

I have found a report that presents no model but seems to involve unconsciously Bending Evidence, by misconstruing simple graphs, to support a Belief. See: Graphs said to "suggest" that fertilizer from northern farms has increased the size of the zones of hypoxia in the northern Gulf of Mexico don't.

The error of von Neumann's Elephant is the big mistake in terms of lessons that generalize to other fields of science. But Scavia 2003 exemplifies many other kinds of mistake. The prevalence of similar mistakes (beyond hypoxia) in Gulf Coast sciences is suggested by Scavia 2003 ever being published, and then by the acclaim not having been publically corrected.

Beating a Dead Elephant

On the other hand, perhaps there is a way to fix the contradictions in the modeling via some simple modifications? Perhaps, contrary to rational expectations, it works! After all, Scavia asserts,

“this model is the first to successfully predict the direct effect of variable nutrient loads on the areal extent of hypoxia [in the northern Gulf of Mexico].”

But, more pessimistically, I have not found any prediction of anything in the Scavia article - in the sense of foretelling a future which was later examined before publication of the article.

The word “predict” is used in the Scavia article, until its last section, as some people might use the word “fit.” It seems correct that the model-generator can generate in YearlyModel, for each of the given 17 years, a model which fits a given data point (N,L). In the sense of “successfully” predicting the future, it had not been established in 2003 that “the model” could do that. Since 2003, there has been some evidence that, when it, or its decendants or its cousins, try to do that, they sometimes fail spectacularly.

Note on how the model could and how it is used to "predict."
To predict next year's size of Dead Zone, one could wait until the Springtime Nitrogen N is available and then measure the "advection" v in the region of dead zones and then, from N and v, compute D(). From D(), one could compute the predicted length L of the Dead Zone for that year. The absurdity of this is apparent as soon as one asks how to measure "the" advection of a zone of water whose areal extent (forget the vertical) exceeds 5,000 square miles.
So how does one escape or hide the absurdity? One uses "Monte Carlo" techniques to use the 17 or so (v,L) pairs from the existing data to, it seems magically, make predictions into the eternal future. Which seems a new level of absurdity to me, but most scientists, alas, will be intimidated by their lack of understanding of Monte Carlo. To avoid appearing to be an ignorant fool, not worthy of the peerclique, they will not voice a public doubt.

Scavia 2003 has an extrapolation-model that uses the results of the 17 yearly models. This extrapolation-model can be used to predict. It had done no tested predicting as of 2003 - when it began to influence government.

Might the extrapolation-model make correct predictions, in spite of the yearly models on which it is based being self-contradictory and too flexible? Is there a geni in the bottle of "Monte Carlo" that, rubbed 17 times, will statistically smooth out all the preceding bad reasoning?

Those who gave us Scavia 2003 have had had the years from 2003 for testing against their Dead Zones (see the EPA hypoxia press releases for some of those years, indicated in References below). I noticed in the news when relatives of Scavia 2003 led to earnestly given predictions of historically huge Dead Zones in 2012 and 2013. And I was not surprised that they did not occur - one can, in the long run, predict more accurately, I think, by always predicting the historical mean, ignoring Nitrogen. Though doomed by von Neumann's Elephant to failure, the attempts seem, laudably, to be in the spirit of science.

Too Flexible: You Can Choose the Future.

Suppose you give me two appropriate (not vertical to each other) points (u,L1) and (z,L2) and I select for you numbers m and b so that the function L(x) = mx + b passes through those two points. I hope you would not then say that I had produced a “model” which successfully “predicts” the L1 and L2? This is a badly wrong use of “to predict.”

Analogously, when the Scavia model-generator is given 17 points of the form (N,L), it selects, in some way, 17 values of its parameter water-speed, v, to “predict” the 17 yearly L-values. This is not “prediction” in the sense of seeing into the future. L is not predicted in the future, but is already known and is used to make the model. However, perhaps the Extrapolation model can see into the future, just as a straight line can be used for extrapolating into the future. One difference is that the straight line model does not directly contradict known facts and another is that the public, and average politicians, recognize and are leary of extrapolation along a line.

Suppose you give me just two appropriate points (u,v1) and (z,v2) from real measurements then I somehow determine three parameters (a,b,c) and give you function f(x) = ax2 + bx + c such that f(u) = v1 and f(z) = v2. Three parameters from two datums. Would you feel safe using this quadratic to determine your policies for the future? Would you feel safe if I asserted that my model “explains 100% of the variation in the v’s”? I hope not. Three parameters is too many for just two data-points. There exist infinitely many such functions f(x) that fit the data. A model-generating process is too flexible, when it has more parameters than calibration datums.
Scavia 2003 had 20 datums and at least 22 parameters. The process can produce mutually contradictory predictions. The statistics behind that "explaining" of some variance does not actually "explain" anything. Such use of statistics, and such misuse of what would appear to be common English, can encourage false confidence in people who do not have time to learn and check the reasoning.

Working out the Model

Extras Much of the article from here down will be removed to another file.

Ultimately, the Monte Carlo Extrapolation model, was selected, non-optimally, from an infinite, solid box of the model-determiners in the Elephant Cage.

In the Elephant's Cage are some models which fit, just as well, all the known facts used in Scavia 2003 to create its Extrapolation model. Very probably not all of these would make the same long-term predictions as does the one selected by Scavia 2003. Why ignore all the others, failing even to mention them? Perhaps one could have used numerical methods in UberModel to approximate optimal Parameters of Wiggling. That Scavia 2003 did not seek an optimum is strongly suggested by the results having only one significant digit (e.g. a = 0.003). That optimising would not have saved the enterprise from its other mistakes.

B.

The Nitrogen, in various partly known organic packages, is given less than 90 days to do the following.
The Great Nitrogen Round-up at Tiger Pass
The Mississpi Nitrogen spreads over a thousand square miles as it flows southward into the Gulf. It is taken up by algae and some of it passes into animals. The Nitrogen disperses over a thousand square miles, sinks, reverses its course in a subpycnoclinal current, and reconstitutes in a vastly lower volume (per unit of time) flow just west of "the mouth of the Mississippi River. (The arrows in Figure 1 illustrate this Reconcentration Hypothesis) At some point along the way, organic matter sinks and rots. That it sinks in deep water then makes its way back into shallow water seems unlikely, but, somewhere, it sinks.
Reconcentrated at x = 0, the Nitrogen-grown organic material flows at about 0.6 kilometers a day in a sub-surface stream westward to Texas, rotting and making hypoxia. Details of this scenario can be altered. Whatever the imagined details, the dispersed Nitrogen, reconcentrated, appears just south, and maybe a little west, of Tiger Pass, at x = 0.

Surely the authors, who all seem brilliant in other ways, know the the Great Nitrogen Round-up at Tiger Pass is ridiculous (and deserves a ridiculous name). So, what gives?

The un-worried acceptance of several obvious "approximations" to truth can be explained if the authors believed them to be of no importance given that the ultimate product "worked." Unfortunately, in this hypothesis, they believed that fitting the data constituted "success."
They believed that wiggling an elephant's trunk was a sign, not of failure, but of success.
And, being good science, a model with several obvious, even admitted, flaws, can ethically be used to advise government - because it "works". Well, it does not work.

C.

Mistake of Too Many Tuning Knobs

For (17 lengths) plus (3 advections) = (20 datums), there are (5 group) plus (17 yearly) = (22 selectable) parameters for tuning the 17 yearly models.

I count 20 datums for calibrating 22 parameters. Even if I miscount slightly, the number of data points is far too small for the number of tuning knobs in the model. This mistake is independent of the mistake of von Neumann's Elephant.

Perhaps the number of patches each year was another constraint. But this is not enough. I used that extra data and still computed nonsensical results. In particular,

I replaced the Nitrogen data with the amount of water flowing down the rivers and was still able to fit the Lengths and Patches.

In the first determining of the parameter “g” of the Theory of Universal Gravity, how many datums do you think were used? One? One cannon ball was rolled, down an incline, one time? For 22 parameters, what would be an appropriate number of datums, to achieve confidence sufficient for ethically giving policy-advice to a government?

The five Parameters of Wiggling specify the UberModel. Then, in YearlyModel, for each of the 17 years, a value of v is found, using the year’s NM and NA, such that the length L of that year’s Dead Zone is matched, well enough. It seemed likely to me that slight errors in length could have been tolerated to achieve some other match, such as number of hypoxic patches. I allowed some error in matching length in some of my programs and produced eye-pleasing fits of the 17 yearly data-points (Figure 2) while matching every Np given in Scavia 2003. Even with the extra error for meeting the constraint of number of patches, I get better matches to lengths shown in my Figure 4 than seen in Fig 3. of Scavia 2003.

Swap Some Years of Nitrogen and the Model Roles On
The model has more selectable parameters than would have been sufficient. This renders the model-generator wonderfully flexible.

It can not only fit the real data-set, but a range of false data-sets.
I have swapped the values of nitrogen for several pairs of years and found my program was still able to solve for values of v so that the computed lengths are even closer to those of the real data than are those pictured bin Scavia 2003.

Save the Gulf by Reducing the Flow of the Mississippi.
The model-generator is so flexible that it gives a nearly perfect fit to the 17 lengths when the measures NM and NA are replaced with the appropriately scaled respective rates of flow FM and FA of the two rivers. Are we to suspect that these rates-of-flow control the size of the Dead Zone? Perhaps they do, but curve-fitting does not prove it. No one will argue from my model that the Federal Government adopt an Action Plan to reduce hypoxia by reducing the flow of the Mississippi River by 45%.

Its most basic data cast doubt on fundamental assumption of Scavia 2003. Doubt falls, thereby, on many other publications about hypoxia in the Gulf of Mexico.

D.

Connect Your Model, Every Way You Can, to Observables

Scavia 2003 did the opposite, seemingly shunning obvious connections.
An imperative of Science is to follow-through on logical and reasonable empirical implications of a model. If one logical implication of Newton’s theory of gravity had been the passing, at a near future date, of a planet behind the Moon, Newton would not have said, “ignore that test, it isn’t what my model is about.” The Scavia models demand that 25% of the nitrogen-containing output of the Mississippi River pass through its algae-growing plume and then pass through “x = 0” on its rotting way to and past “x = 220.” Has anyone calculated, seen or sought such a great mass of rotting goo passing through that small region (“R” in Figure 1)? Has anyone looked for signs of the remarkable, nearly miraculous, currents demanded by the Reconcentration Hypothesis?

Theories are not proven by pretty pictures nor by mountainous loads of data. Theories are disproven by wrong predictions and by internal contradictions. Scavia 2003, and its Theory of Springtime Nitrogen, has both.

E.

Too Soon Beyond Science into Policy?

The computer-modelling seems totally useless for correctly advising governments. Is the remainder of the relevant and predictive science good?

The Theory of Springtime Nitrogen is falsified by its own data and by the Great Leap through Time it requires. Is the Nitrogen Theory (free of assumptions about when nitrogen is delivered) in danger? Why did people accept it in the first place? For readers interested in this I recommend a study of the graphs in Figure 5 of Beyond Science into Policy by Rablais et al 2002. Do the graphs support more than they undercut the Nitrogen Theory?
Graphs said to "suggest" that hypoxia is new to the northern Gulf of Mexico do the opposite.

Therein is considered: do the changes indicated by the sedimentary records shown in the graphs of Beyond Science coincide more with fertilizer-use in Mississippi Basin or with the first drilling, in the region of hypoxia, of oil wells? Hundreds of these wells were drilled beginning in 1940 and into the early 1950s and canals were cut through swamps, releasing mud to drift out over the Dead Zones.
And also considered: do the changes indicated by the sedimentary records shown in the graphs of Beyond Science coincide more with fertilizer-use in Mississippi Basin or with the abrupt drop, in 1953, of suspended sediments delivered by the Missouri River?

Possibly there was misinterpretation of graphs. When I study the graphs of Figure 5 of Beyond Science, I do NOT see the conclusions drawn in that paper by Rabalais. Increasing fertilizer seems to come after some of its supposed effects. But, the oil-development in the nearby swamps and continental shelf come before those supposed effects, as does the abrupt drop in sediments delivered by the Missouri River. Historically, cause-before-effect has been the preferred order in science.

But, I must be misreading those graphs. Surely all the experts in the relevant environmental sciences would have noticed such a simple fact. I await correction.

Scavia 2003 makes a couple of edict-related assertions which, possibly because of my ignorance as an outsider, seem over-reaching:

“An assessment of the causes and consequences of hypoxia concluded that the almost threefold increase in nitrogen load to the Gulf ... has driven the long-term increase in hypoxia since the middle of the last century ...”

I am pretty sure that hypoxia in the Gulf has not been directly or assuredly measured (well enough to determine its possible “increase”) since “the middle of last century,” but only since 1985. Furthermore, examination of the evidence, given in Scavia 2003 itself and which is based on direct measurements, suggests that there had been, by 2003,

* no increase in nitrogen in the past 18 years,
* no increase in the length-measured zone of hypoxia in the previous 10 years and
* no statistically strong, nitrogen-connected, increase in length in the entire 18 years in which there had been direct measurement of the geographical extent of hypoxia.
My personal, you can form your own, theory of the certainty of that quoted pronouncement above is peerclique mentality. But, that certainty demands an Action Plan:
“The Federal–State–Tribal Action Plan for reducing ... hypoxia in the northern Gulf ... agreed on a goal to reduce the ... hypoxic area ... [the] plan ... suggests that a 30% reduction ... [in] nitrogen load would be needed ...”
Scavia 2003 continues:
“However, the model scenarios outlined here suggest that a 30% reduction might not be sufficient ...” (Study Fig.2, Fig. 3a, and Fig. 3b of Scavia et al, 2003)

Ought a fatally flawed model be used as a basis for edicts?

Fortunately, no “model” is needed to see the correctness of the insufficiency which Scavia 2003 warns us against in that quote. That a 30% decrease in springtime nitrogen will have no effect whatsoever in reducing length of Dead Zone is strongly suggested - one might say "nearly proven" - by a plot of length of Dead Zone against river-borne nitrogen. In my Figure 2 or in Figure 5, look to the left of the Nitrogen Gap: You can see that a reduction to 4/day (i.e. by about 45%, where the units are 1000 times those in Fig. 2 of Scavia 2003) might be called for. However, the effect of even a 45% reduction in nitrogen cannot be safely predicted as there exist only four relevant data points. But, assume we proceed and lead a government agency to regulatory pastures with the shining light of just four data points. Stiputlate that about 74% of nitrogen coming down the rivers “is agricultural in origin” (Beyond Science, Page 135). Then, the pure data suggest that

to just begin reducing the size the size of Dead Zones will require a 60% decrease in the amount of nitrogen used or created by farmers (fertilizer or dung) in the Mississippi Basin.

But, how many Americans would starve to death if a 60% reduction were enforced?

References
Chapra, S. C. 1997. Surface water-quality modeling. McGraw-Hill.
Childs, C. R., N. N. Rabalais, R. E. Turner and L. M. Proctor. 2002. Sediment denitrification in the Gulf of Mexico zone of hypoxia. Mar. Ecol., Prog. Ser. 240, 285–290.
CSCOR, http://www8.nos.noaa.gov/nccos/cscor/toppubs.aspx
Rabalais, Nancy N., R. Eugene Turner, Dubravko Justic´, Quay Dortch, and William J. Wiseman, Jr. 1999. Characterization of Hypoxia: Topic 1 Report for the Integrated Assessment on Hypoxia in the Gulf of Mexico. NOAA Coastal Ocean Program Decision Analysis Series No. 15. NOAA Coastal Ocean Program, Silver Spring, MD.
Rabalais, Nancy N., R. Eugene Turner, Donald Scavia, 2002. Beyond Science into Policy: Gulf of Mexico Hypoxia and the Mississippi River. February 2002/ Vol. 52/ BioScience
Scavia, Donald, Nancy N. Rabalais, R. Eugene Turner, Dubravko Justic´, and William J. Wiseman, Jr. 2003. Predicting the response of Gulf of Mexico hypoxia to variations in Mississippi River nitrogen load. Limnol. Oceanogr.48:951-956.
EPA Hypoxia Press Release and Map. July 29, 2003; July 26, 2004; July 29, 2005.

Memoirs of Extraordinary Popular Delusions and the Madness of Crowds, by Charles MacKay. 1841.

Note to Piers Chapman: Stratification