The Little Ice Age was 1.0-1.5 {deg}C cooler than current warm period according to LOD and NAO

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.

💡 Research Summary

The paper investigates the relationships among four long‐term climate‑related time series: the Length of Day (LOD, 1623‑2016), the Zonal Index (ZI, 1873‑2003), the North Atlantic Oscillation (NAO, 1659‑2000) and global Sea Surface Temperature (SST, 1850‑2016). The authors treat LOD as a proxy for the integrated effect of atmospheric and oceanic circulations on Earth’s rotation. Because ZI and NAO are pressure differences that reflect the strength of the mid‑latitude westerlies (zonal flow) versus meridional flow, they construct cumulative versions of these indices—IZI and INAO—by integrating the yearly values. This integration gives the new variables dimensions comparable to the reciprocal of LOD, allowing a direct test of the hypothesis that stronger zonal circulation (positive ZI/NAO) should be associated with a faster Earth rotation (shorter LOD), i.e., a negative correlation.

Statistical analysis proceeds by detrending and normalizing each series, then applying 5‑, 11‑ and 23‑year moving averages to examine correlations across multiple time scales. The results are strikingly consistent: LOD is strongly negatively correlated with both IZI and INAO, and also with SST. In other words, periods of enhanced zonal flow (high ZI/NAO) coincide with shorter days and higher global ocean temperatures, while periods dominated by meridional flow correspond to longer days and cooler SSTs. The authors argue that such a pattern cannot be explained by internal variability alone. If internal angular‑momentum exchanges were the sole driver, stronger zonal winds would slow the Earth (positive correlation). The observed negative correlation therefore points to an external forcing—most plausibly solar or astronomical variations—that simultaneously modulates atmospheric circulation and Earth’s rotation.

Using the calibrated relationships between LOD/INAO and SST, the authors reconstruct global SST back to the 17th century, a period lacking reliable instrumental temperature records. Their reconstruction indicates that around 1700, during the coldest phase of the Little Ice Age (LIA), global SST was about 1.0‑1.5 °C lower than the reference warm period of 1950‑1980. This cooling magnitude exceeds many earlier multi‑proxy reconstructions (e.g., Mann et al., 1999; Moberg et al., 2005) but aligns well with more recent studies that employ borehole temperature profiles (Huang et al., 2008). The authors emphasize that LOD and INAO, being global physical quantities, provide a more direct and less ambiguous proxy for past climate than localized tree‑ring, pollen, or ice‑core records, which often require complex statistical amalgamation and are subject to regional biases.

The paper also presents a simplified physical argument based on geostrophic balance: the pressure gradient (captured by ZI/NAO) drives zonal wind speed, which, when integrated over time, reflects changes in atmospheric angular momentum. This momentum exchange is linked to changes in Earth’s rotation rate, yielding the approximate relationship LOD ≈ − k·(IZI or INAO). The authors acknowledge that this is a first‑order approximation but argue that it captures the essential dynamics observed in the data.

In conclusion, the study provides three key contributions: (1) empirical evidence that LOD, IZI and INAO are tightly coupled, supporting the view that external solar/astronomical forcing drives decadal‑to‑centennial climate variability; (2) a novel method for reconstructing past global SST using LOD and NAO records, which yields a Little Ice Age cooling of 1.0‑1.5 °C; and (3) a demonstration that global rotational and pressure‑gradient proxies can serve as robust, physically grounded tools for paleoclimate reconstruction, potentially reducing uncertainties inherent in traditional multi‑proxy approaches. Future work is suggested to extend the LOD record further back in time and to refine the quantification of external versus internal contributions to climate change.