There is a battle brewing between dynamical and statistical models. The winner will be determined when the current neural ENSO conditions resolve into an El Nino or not in the current months.

The International Research Institute for Climate and Society compares the predictions of ensembles of each type of model here.

Although most of the set of dynamical and statistical model predictions issued during late April and early May 2012 predict continuation of neutral ENSO conditions through the middle of northern summer (i.e., June-August), slightly more than half of the models predict development of El Nino conditions around the July-September season, continuing through the remainder of 2012. Still, a sizable 40-45% of the models predict a continuation of ENSO-neutral conditions throughout 2012.

Most of the models predicting El Nino development are dynamical, while most of those predicting persistence of neutral conditions are statistical.

The figure above shows forecasts of dynamical (solid) and statistical (hollow) models for sea surface temperature (SST) in the Nino 3.4 region for nine overlapping 3-month periods. While differences among the forecasts of the models reflect both differences in model design, and actual uncertainty in the forecast of the possible future SST scenario, the divergence between dynamical and statistical models is clear.

This question fascinates me so much, I studied it for three years “Machine learning and the problem of prediction and explanation in ecological modelling” (1992). Why is there a distinction between dynamical and statistical models? What does it mean for prediction? What does it mean if one set of models are wrong?

For example, what if ENSO remains in a neutral or even La Nina state, thus ‘disproving’ the dynamical models. These models are based in the current understanding of physics (with a number of necessary approximations). Clearly this would say that something about the understanding of the climate system is wrong.

Alternatively, what if the currently neutral ENSO resolves into an El Nino, ‘disproving’ the statistical models. These models are based in past correlative relationships between variables. It would mean that some important physical feature of the system that is missing from the correlative variable has suddenly come into play.

Why should there be a distinction between dynamical and physical models at all? I have always argued that good, robust prediction requires no distinction. More precisely , the set of predictive models is at the intersection of statistical and dynamical models.

To achieve this intersection, from a starting point of a statistical model, each of the parameters and their relationships should by physically measurable. That is, if you use a simple linear regression model, each of the coefficients need to be physically measurable and the physical relationships between them additive.

From a starting point of a dynamical model, the gross, robust features of the systems should be properly described, and if necessary statistically parameterized. This usually entails a first or second order differential equation as the model.

This dynamical/statistical model is then positioned to incorporate both meaningful physical structure, and accurate correlative relationships.

It amazes me that most research models are developed along either dynamical or statistical lines, while ignoring the other.

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