  We study the yearly values of the length of day (LOD, 1623-2016) and its link
to the zonal index (ZI, 1873-2003), the Northern Atlantic oscillation index
(NAO, 1659-2000) and the global sea surface temperature (SST, 1850-2016). LOD
is herein assumed to be mostly the result of the overall circulations occurring
within the ocean-atmospheric system. We find that LOD is negatively correlated
with the global SST and with both the integral function of ZI and NAO, which
are labeled as IZI and INAO. A first result is that LOD must be driven by a
climatic change induced by an external (e.g. solar/astronomical) forcing since
internal variability alone would have likely induced a positive correlation
among the same variables because of the conservation of the Earth's angular
momentum. A second result is that the high correlation among the variables
implies that the LOD and INAO records can be adopted as global proxies to
reconstruct past climate change. Tentative global SST reconstructions since the
17th century suggest that around 1700, that is during the coolest period of the
Little Ice Age (LIA), SST could have been about 1.0-1.5 {\deg}C cooler than the
1950-1980 period. This estimated LIA cooling is greater than what some
multiproxy global climate reconstructions suggested, but it is in good
agreement with other more recent climate reconstructions including those based
on borehole temperature data.
