Robustness of the modes of variability of Indo-Pacific sea level
Using altimetry along with two ocean models we can study the relationship between sea surface height (SSH) in the Indian and Pacific Oceans and four climate modes (the Pacific Decadal Oscillation, the El Niño-Southern Oscillation, the Indian Ocean Dipole and the Southern Annular Mode), and how robust these relationships are to the length of the time series.
Figure 1: Regression patterns for SSH from altimetry from 1993-2007 related to (a) the residual trend, (b) the PDO, (c & d) two ENSO indices, (e) the IOD and (f) the SAM. Regression coefficients which are not significantly different from zero (at the 95% level) are not shown. Coloured circles indicate significant regression coefficients calculated for tide gauges. Wherever tide gauge data is available but the coefficients are not significant a cross (×) symbol is used (from ).
Figure 1 shows the SSH patterns associated with each mode of variability calculated over the altimetry period (1993-2007). We can estimate the robustness of these patterns by comparing them to the patterns found using different time periods from reanalysis products or ocean models forced with observed winds.
Window lengths of 15 years appear to be sufficient for shorter period variability such as ENSO, however it is not sufficient for distinguishing between ENSO- and IOD-related SSH variability. Anomalously large events (such as the 1997-1998 El Niño) can still dominate due to overfitting when short window lengths are used, such that there is a dependence of the regressions on the time window chosen. The residual trend and the PDO-related SSH patterns are particularly sensitive to the length and position of the window. A 15-year window is not enough to reliably separate the trend from the PDO-related SSH variability. Window lengths on the order of 50 years (or longer) are required for robust regressions of SSH on to low frequency variability such as the PDO. The recently observed SSH-PDO relationship may therefore not be representative of the longer term record.
A large part of the error when calculating PDO-related SSH variations using a window that is too short is due to the false attribution of trends in the SSH to short term trends in the PDO index during the window. This false attribution is called trend aliasing. Figure 2 shows the part of the trend in SSH that is attributed to the PDO in the 15-year window, but which remains unexplained when using a more robust measure of the SSH regression on to the PDO (calculated over the 50-year window using two different models). This unexplained part of the trend could be due to either a trend in another climate index not included here (anthropogenic forcing, for example), or to a change in behaviour of the SSH regression on to the PDO during the recent period.
Figure 2: SSH trend (in mm/yr) over 1993-2007 attributed to the PDO when using a 15-year window rather than a 50-year window in two models, (a) MOM0.25 and (b) SODA. Tide gauges are shown in circles (from ).
This lack of robustness when using short window lengths means that when estimating long term trends in spatial patterns of SSH (associated with anthropogenic climate change, for example) from the altimetry record we must take into account the fact that the patterns of 15-year trends vary considerably depending on the window and are influenced by low frequency modes of variability such as the PDO.
 Frankcombe et al. (2014), Clim. Dyn., doi:10.1007/s00382-014-2377-0.