## Will the RAPID team find more large amplitude overturning excursions?

*By Grant Bigg, Jose Roberto Ayala Solares and Hua-Liang Wei, University of Sheffield*

Reconstructed (blue) and predicted (red) AMOC time series. |

At the University of Sheffield we have been working to reconstruct the time-series of Atlantic Meridional Overturning Circulation (AMOC), based on a control systems modelling approach using our knowledge of changing oceanic and meteorological conditions over the North Atlantic and neighbouring seas. By developing such a model using validation with the observed AMOC series over April 2004 to March 2014 we have produced hindcasts of the monthly variability of the AMOC from April 2014 until September 2015.

Our reconstructed AMOC time-series (BLUE line) reproduces both the disturbed annual cycle and the long-term trend of a decreasing overturning, suggesting that the combination of the ocean density and atmospheric circulation fields contain the underlying forcing factors producing the AMOC.

Our reconstructed AMOC time-series includes a prediction (RED line) out to September 2015. Given the ability of the model to reproduce the previous 10 years of observations of the AMOC, we therefore make the following three predictions:

- The RAPID observations collected this autumn will show a mean overturning which is similar to that of the previous 5 years, with a value of ~ 16 Sv.
- The observations will not show a significant anomaly such as was seen in early 2010, and indeed the maximum AMOC of the collected data will occur during November-December 2014, although we also predict a late maximum in September 2015 as well.
- Despite the mean AMOC being of a similar level to recent years there will be short-lived excursions, both positive and negative, leading to maxima and minima approaching those of the previous decade’s observations. We have already given our predicted timing of the greatest positive excursion around the end of 2014 and the smallest value is expected be in mid-summer 2015. Our model suggests the latter to be ~ 80% of the mean AMOC.

#### How the predictions were made

We use Nonlinear Auto-Regressive Moving Average with eXogenous inputs (NARMAX) system identification modelling to produce a model for the observed variation of the AMOC using two large-scale environmental variables as inputs. The first use of this technique for environmental sciences can be found in Bigg et al. (2014). To represent atmospheric variability we use the North Atlantic Oscillation index, while for oceanic variability we combine a linear measure of the surface density of the northward-flowing Gulf Stream with a linear measure of the likelihood of deep-water formation through the surface density of the Labrador and Norwegian Seas. The surface densities were calculated from the GODAS ocean reanalysis sea surface temperature and salinity.

The NARMAX system identification model uses a forward regression orthogonal least squares algorithm to build models term by term from recorded datasets. This is achieved by using the Error Reduction Ratio (ERR), which shows the contribution that each selected model term makes to the variance of the dependent variable (the observed AMOC here) expressed as a percentage, taking account of the noise in the data. The NARMAX method searches through an initial library of model terms, which typically includes linear and non-linear lagged variables, and selects the most significant terms to include in the final model. The model in this instance leads to 47 terms, with those having the greatest ERR representing quadratic terms of the oceanic input with time lags between 0 and 8 months.

Bigg, G. R., H. Wei, D. J. Wilton, Y. Zhao, S. A. Billings, E. Hanna, V. Kadirkamanathan, 2014, A century of variation in the dependence of Greenland iceberg calving on ice sheet surface mass balance and regional climate change,

*Proc. Roy. Soc Ser. A*, 470, 20130662, doi:10.1098/rspa.2013.0662.
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