Short-range correlation

In this subsection the autocorrelation behaviour of the measured ice draft on time scales of up to 10 days is briefly investigated. The purpose of this analysis was to demonstrate that sea ice thickness in coastal regions has higher decorrelation times than further away from the coast. As noted by Chatfield [1984], the interpretation of autocorrelation functions requires some experience and great care. Most difficult is often the determination of the non-correlation lags, i.e. the lag at which the data become linearly independent. A value for this lag, which is frequently cited in the literature, is the lag at which the autocorrelation function first reaches a value of zero [e.g. Romanou et al., 2006]. However, this can sometimes be misleading as shown in figure 6.19.

Fig. 6.19: Four arbitrary examples of autocorrelation functions of sea ice draft for periods of 7-10 days. The horizontal dashed lines are 2σ confidence intervals for white noise [Chatfield, 1984]. The red vertical line denotes the lag at which the function first reaches a value of zero.

The first function (a) shows clear signs of a cyclic behaviour. The decorrelation time of 0.39 days is therefore not a good choice. A similar argument applies to function (b). The value of 0.96 days in function (c) also has to be regarded as critical, as obviously many values of the function lie outside the confidence limits above the decorrelation time. Some authors therefore use other measures of autocorrelation, such as "mutual information" [Strickert, 2003]. The least critical decorrelation scale is the value of 0.1 days in function (d). It shows decorrelation of the data on very small time scales, and the autocorrelation function indicates noisy data. As these examples indicate, the interpretation of the short-range autocorrelation of the ice draft would require a very thorough treatment which would be far beyond the scope of this section.

Fig. 6.20: Mean decorrelation times of selected ULS records. The means were calculated from values of 3-6 autocorrelation functions of ice draft in four seasons, respectively. Periods with data gaps were avoided. The error bars are standard deviations of the means, corrected by the t-factor for small sample sizes [Schönwiese, 1992].

The decorrelation time scales discussed in the following are intrinsic to the time-referenced ULS data and can not be readily used to gain detailed information on the characteristics of the sea ice thickness distribution. However, selected decorrelation time scales are compared to obtain some additional information which might be helpful to understand the discussed changes in sea ice thickness. There are several possible reasons for high decorrelation time scales, e.g. slow ice drift, refrozen leads, a folded drift path (i.e. repeated sampling of the same features) or a combination of these factors. Low decorrelation time scales are conceivable for weakly deformed ice with a highly varying underside, the strongly eroded underside of undeformed ice or a high degree of ice deformation and pressure ridges of different sizes.

The broad error bars in figure 6.20 indicate that the decorrelation time scale changes signifi-cantly within one season. Using the zero-crossing approach discussed above, the data at AWI 207-2 become independent after approximately 12 hours on average. The data of AWI 207-6 decorrelate somewhat earlier. However, the mean values are not significantly different from AWI 207-2, except the value for spring (SON), which may reflect the changes in the ice regime between these two records. At AWI-209 very low decorrelation time scales were found. The same values were found for AWI-208 (not shown). This indicates that the ice drafts decorrelate quickly in the centre of the Weddell gyre. In the highly dynamic boundary region at AWI-212 high decorrelation time scales indicate heavy ridging and possibly also refreezing leads. This is most obvious in autumn (MAM). The lowest of all decorrelation values were found at AWI-227 at the northern rim of the Weddell gyre. Similar values were found for AWI-229 and most of the records of AWI-231. At AWI-232 the two records with very thick ice (232-1 and 232-8) show low decorrelation time scales in autumn (MAM) compared to the other seasons.

Fig. 6.21: Decorrelation times of the ice draft at AWI 232-1 (1996) for days of slow and fast ice drift.

The daily ice draft data in 1996 decorrelate on average 2.5 hours later on days with slow ice drift.

Compared to the records of AWI 232-4-6, the record of AWI 232-8 shows high decorrelation time scales, especially in winter and spring. At AWI-233 the data show high mean decorrelation time scales in the transition times, i.e. autumn and spring. However, also the scatter of the values is very high, so that the means are not significantly different from the winter value.

To estimate the influence of the ice drift on the decorrelation time scales, an experiment was conducted using SSM/I drift data at the position of AWI-232. For all records of AWI-232 only days without data gaps were selected. Then, the days were separated into days with positive and negative ice drift anomalies, i.e. days with anomalously slow and fast westward drift in the coastal current. Next, the decorrelation time scales of the ice draft were estimated based on the zero-crossing approach (Fig. 6.21). The ice draft data of AWI-232 (all years with measurements) decorrelate on average 1.5 hours later at days with ice drift anomalies > 0, i.e.

slow westward drift, compared to days with ice drift anomalies < 0, i.e. fast westward drift.

The differences vary from year to year, e.g. for 2006 and 2007 they were found to be negligible.

A significant correlation between ice drift anomalies and decorrelation time was not found.