Limited predictability of extreme decadal changes in the Arctic Ocean freshwater content

Abstract

Predictability of extreme changes in the Arctic Ocean freshwater content and the associated release into the subpolar North Atlantic up to one decade ahead is investigated using a CMIP5-type global climate model. The perfect-model setup consists of a 500 year control run, from which selected 10 year long segments are predicted by initialized, perturbed ensemble predictions. Initial conditions for these are selected from the control run to represent large positive or negative decadal changes in the total freshwater content in the Arctic Ocean. Two different classes of ensemble predictions are performed, one initialized with the ‘observed’ ocean globally, and one initialized with the model climatology in the Arctic Ocean and with the observed ocean elsewhere. Analysis reveals that the former yields superior predictions 1 year ahead as regards both liquid freshwater content and sea ice volume in the Arctic Ocean. For prediction years two and above there is no overall gain in predictability from knowing the initial state in the Arctic Ocean and damped persistence predictions perform just as well as the ensemble predictions. Areas can be identified, mainly in the proper Canadian and Eurasian basins, where knowledge of the initial conditions gives a gain in predictability of liquid freshwater content beyond year two. Total freshwater export events from the Arctic Ocean into the subpolar North Atlantic have no predictability even 1 year ahead. This is a result of the sea ice component not being predictable and LFW being on the edge of being predictable for prediction time 1 year.

Appendix the damped persistence prediction

The first-order autoregressive, or AR(1), model for a series ${x_t}$ with zero mean value is:

$${x_t}=~{\alpha _1}{x_{t - 1}}+{u_t}~,0<{\alpha _1}<1$$

i.e. consisting of a relaxation term with constant ${\alpha _1}$, which is the lag-1 autocorrelation coefficient, and serially independent forcing anomalies $~{u_t}$. Low frequency climate variations of the ocean driven by atmospheric weather noise can often be described by an AR(1) process (Hasselmann 1976; Frankignoul and Hasselmann 1977).

The optimal prediction of an AR(1) process is the damped persistence prediction as function of the prediction time $\tau$ at a specified time $t$ is given by:

$${\hat {x}_t}\left( \tau \right)=~\alpha _{1}^{\tau }{x_t}.$$

The spread $\sigma \left( \tau \right)$ of the damped persistence prediction as function of prediction time is given by

$$\sigma \left( \tau \right)=~\sqrt {{{\left( {{x_{t+\tau }} - {{\hat {x}}_t}\left( \tau \right)} \right)}^2}} ={\sigma _x} \times \sqrt {1 - \alpha _{1}^{{2\tau }}}$$

Thus in the beginning the ensemble spread grows steadily with time, with slower growth rates for larger ${\alpha _1}$, and gradually approaches its saturation value of ${\sigma _x}$ for large prediction times.

If ${\alpha _1}$ is close to zero, the series is a white noise series, the damped persistence prediction degenerate to ${\hat {x}_t}\left( \tau \right)=0$, i.e. the climatic prediction. In this case $\sigma \left( \tau \right)$ is near constant in time. If ${\alpha _1}$ is close to unity, the series is approximately a random walk and the optimal prediction is the persistent prediction.

For details, we refer to Box and Jenkins (1979) and Von Storch and Zwiers (1999).