Archive for the ‘Models’ Category

Turtles all the way down

September 5, 2011 Leave a comment

In light of recent and ongoing events – the Spencer and Braswell 2011 debacle in Remote Sensing and everyone’s continued misunderstanding of climate models – I’d like to kick off this new blog with some thoughts about modelling in science.

Whether one is a chemist or a climate scientist, a soil engineer or an astrophysicist, we all use models to understand the world around us. The ideal gas law, which is sufficiently accurate for gasses close to standard temperature and pressure, assumes gas molecules are point masses with no volume and envisions all collisions as elastic. This is best described by my thesis advisor as “volume-less tennis balls flying around”. It’s an elegantly-derived model that is incredibly accurate for the atmosphere, but even though it’s a law, it’s still a model.

As we try to understand more complex systems, we must build more complex models. The current state-of-the-art climate models are some of the most complex and computationally demanding model simulations produced by humanity, and they integrate countless hours of scientific research and understanding – from aerosol processes used to model cloud physics to radiation subroutines handling absorption, scattering, and emission across so many wavelengths that they consume half of the computing time. These models, like our most simple models, are derived from basic physics – the laws of thermodynamics, conservation of momentum and mass, etc. – and empirical measurements.

But all models, whether they are a simple one-dimensional climate model or the state-of-the-art simulation, serve some utility. The big, complex models are hard for scientists to analyze – the more processes you include, the higher the resolution, the fewer simplifying assumptions you make – the more difficult it is to figure out what is going on and what is important. Not impossible, just very hard.

But the more simple the model, the less likely it will be to capture the details. A state-of-the-art simulation can represent internal variability and produce ENSO signals, while a one-dimensional model cannot. However, that does not mean that the one-dimensional model is “wrong”. Indeed, both models will tell you that as you increase the concentrations of greenhouse gases in the atmosphere, you will raise the average surface temperature of the earth.

There is nothing wrong with simple models. As Einstein said, “Make everything as simple as possible, but not simpler”. The simpler your model is, the easier it is to understand, as fundamental relationships will become more obvious. Simplify too much, though, and the model loses all utility.

Consider three models of the earth: the earth is flat, the earth is spherical, and the earth is an oblate spheroid whose diameter on the equatorial plane is wider than its diameter on the plane of its axis of rotation

The “earth is flat” model is wrong. It is too simple a model, based on sparse and simple observations and too many wrong assumptions. It is common-sense to our eyes, so long as we don’t question our logic too deeply. This model still states we exist on the surface of something, perhaps its only redeeming aspect, but it’s going to prevent us from understanding physics, especially gravity and astronomy. A bad model, a model too simplistic, is actually a detriment to our understanding. See: geocentrism.

What about “earth is a sphere”? Well, it isn’t really spherical. It’s actually a little wider on the equatorial plane than on the plane of its axis of rotation. Is this model of the earth “wrong”?

I don’t think so. As Isaac Asimov described in “The Relatively of Wrong”, there is a spectrum of “right” and “wrong”, and as humans, our models are going to fall somewhere on this spectrum.

Wrong |—-(earth is flat)——————-(earth is spherical)–(earth is an oblate spheroid)-| Right

The “earth is spherical” is mostly right, and is very close to “earth is an oblate spheroid”. The latter captures reality much better – the distance between lines of latitude on a sphere are constant (on the earth sphere, this is about 111km), but on the real earth, this varies with latitude because of the equatorial bulge. There are also implications for gravity, as well. Depending upon your application, the “earth is a sphere” may be a perfectly sufficient model to use as it simplifies calculations.

For my research, the error introduced by assuming a constant distance between latitudes is negligible compared to the orders of magnitude of the processes I want to understand. For an engineering team managing remote sensing satellites, such as GRACE which relates satellite drift to gravitational differences, the sphere assumption is too simple. It introduces enough error that it will compromise the data from the mission and hinder our understanding.

Spencer and Braswell 2011 is an example of using too simple a model with dubious assumptions based on poor evidence.

Give me a model of the earth with more than a few free parameters, and I will demonstrate that it’s turtles all the way down.