by Mark Bakker
 

We’ve all heard the quote before “All models are wrong, butsome are useful,” which came from the pen of the famous statistician GeorgeBox, Emeritus Professor at the University of Wisconsin (Box and Draper 1987, 424).The quote gained popularity in the groundwater community some 7 years ago whenit served as the marquee for the 2006 Darcy Lecture (Poeter 2007).

Unfortunately, the whole premise of the quote is wrong,because a groundwater model cannot, in fact, be wrong (assuming an absence ofsilly input errors and an ability to actually run a code). The paramountfeature of a groundwater model is that it is a simplification of reality.Stating that all models are wrong because they don’t equal reality makes nosense. I do not even want my models to equal reality—I already have reality. IfI want to know something about reality, it is there to be measured. A model isneeded to gain understanding of how reality works and to try to makepredictions about phenomena that cannot be tested at full scale in the field.

So, if a groundwater model cannot be wrong, can it be good,or bad, or even ugly? Ugly is a judgment call. Whether a model is good or badis inherently linked to the purpose of the model. Once the purpose is defined, amodeler can make the pertinent decisions, for example, how to simplify realityinto a conceptual model, the scale and the level of detail of the model, thesolution method or computer program, the spatial variation of the parameters, thecalibration method, etc. Once the model is finished, it can still be a bad modelfor the stated purpose. It may be that the conceptual model was missing crucialprocesses or critical parts of the system. Or the quality of the input orcalibration data was poor. Or the model was overfit. Or for whatever reason, themodel was not able to simulate the calibration data with reasonable confidenceintervals.

But a model can surely be good for the stated purpose. Thisdoesn’t mean that a good model necessarily needs to be physically based. Oreven that much of any knowledge is needed about the groundwater system. For example,an artificial neural network can be suitable for

simulating groundwater dynamics (e.g., Coulibaly et al. 2001).Or a time series analysis can be used to determine the drawdown caused by awell field (e.g., Von Asmuth et al. 2008). Such models don’t even includehydraulic conductivity terms, let alone satisfy continuity. Yet they can begood models for their stated purposes.

So was George Box wrong? No. The sentence leading up to hisfamous quote reads: “The fact that [the model] is an approximation does notnecessarily detract from its usefulness because models are approximations.” Ithink the word “wrong” was an unfortunate choice. Tying this famous quote togroundwater modeling does not serve our profession well. What client wants tospend money on a model if we tell him beforehand that it will be wrong?Meteorologists are much better at advertising their abilities. They do not sayon TV that their models are wrong. Their models, like ours, are a simplificationof reality. Like us, they use their models to make predictions, often includingconfidence intervals. They happily (well, at least they smile on TV) mightpredict a 50% chance of rain and a 50% chance of sunshine. Surely this is notthe most useful prediction, but at least they are honest about it. Let us stopcalling all our models wrong. Simply state what your model can and cannot do,and leave it at that.

 
http://onlinelibrary.wiley.com/doi/10.1111/gwat.12037/abstract