Whipping up a Storm

Art by Rebekah Pawley.

Imagine placing a ball on top of Mount Everest, and giving it a nudge. An enormous range of landing places may be achieved by only a tiny difference in the initial direction of the push. This behaviour is known as sensitive dependence—two initially almost identical trajectories will lead to completely different results. It is fiendishly difficult for scientists to model and predict, but an understanding of Chaos—as this behaviour is known—is essential to the study of many physical systems.   It is chaos that makes predicting the weather so hard.

As a weather obsessed country, we know that two sunny mornings in a row doesn’t always mean two sunny afternoons, no matter how similar the skies look at 11 am each day. The weather displays sensitive dependence, and in order to predict it, so must our best weather models.Remember Everest?  Well our ball only had one initial condition determining its future (the direction of the push), the weather has many more. Indeed, our best models have over ten million conditions factored in, and even so, they are still not perfect. It is tempting to suggest that we can build a model from scratch simply using the laws of physics. This is unfortunately not the case—in fact some argue that chaos has forced us to re-evaluate whether it is ever really possible to have a truly successful physical model of any complex system. There are approximately 10^45 molecules in the atmosphere: precise movements of each may determine the course of the weather. It is hard not to be pessimistic about the possibilities of modelling on this level!The British public still expect a forecast. Yet we are faced with model inadequacy and measurement inaccuracy. What can we do about it? To refine the model, forecasters use ‘shadows’. A shadow is a prediction that our model has generated from given data. By using data from the past we can compare the  shadow prediction to what the weather actually did. Ideally, we would like our shadow to closely follow these observations—then we can be reasonably confident that our model is a good one for predicting future weather.Early in the development of weather prediction, forecasters would run their best model once a day, get a shadow, and then call that the forecast. As computers became more powerful, the models became more complex, and the predictions became better, but fundamentally the same problems remained.

Chaotic systems such as the weather are temperamental. In some situations, an error in the initial measurements may not completely derail the predictions, but in others the system is so sensitive that even the smallest errors will render a forecast useless.  In the past, forecasters only  had one shadow to use, and the inevitable chaotic behaviour of nature meant that, even with the best possible shadow, it would sometimes do something completely unexpected. So, instead of running a complicated model once, and programming in only one weather report, current forecasters run a simpler (to save on computational time), and thus inherently less accurate model many times, each time starting the system off in a slightly different initial state. This is known as ensemble forecasting.Ensemble forecasts allow us to see possible behaviours we may have missed if we only had one shadow and, more importantly, they allow us to quantify the reliability of our forecast. If all of our shadows cluster together, it seems to suggest that our forecast is a reliable one, whereas if each sped off on a completely different course, it would be hard to put out any forecast with confidence.We might further improve our ensemble forecasts, and use several different mathematical models, each with its own forecast ensemble, and compare them all. If all our models gave similar shadows, we might hope our predictions really were close to the truth. Unfortunately, in practice we find that, although our models each individually give ensemble forecasts grouped together, the prediction the shadows group around differs from model to model. All these models suffer some form of inadequacy. Weather prediction is an immensely difficult science, and these are just a fraction of the problems that forecasters have to deal with. So next time you end up in a thunderstorm in shorts, perhaps you will have some small sympathy for the weatherman.