## A Statistical Time Series Approach to Predicting the AMOC

By Peter Challenor and the students on the ‘Statistical Modelling in Space and Time’ fourth year mathematics module

We take a different approach to the predictions from Sheffield and Oxford already presented on the blog. We do not use the wind data from 2014 to the present day to help with the prediction but make our forecasts purely from the past data. This means that our methods could be used to forecast into the future where no measurements of winds are available. Because we use statistical methods we are also able to give uncertainty estimates on our predictions.

We use two basic methods. In both cases since we are predicting quarterly means we average the original data into quarters. The first is to fit what is known as an ARIMA model. ARIMA stands for Autoregressive Integrated Moving Average. This plot shows our forecast with the associated uncertainty.

The second model we fit is known as a Dynamical Linear Model. This fits a model for the underlying state of the overturning plus seasonal component. Here is a plot of our estimate of these two components in the past:

We can now make a prediction for the overturning into the future (in this plot):

Full details of our method + the code to try your own forecasts is given here: www.rapid.ac.uk/challenge/Exeter_Rapid_prediction.pdf