Late 19th century navigational uncertainties and their influence on sea surface temperature estimates

Dai, Chenguang, Chan, Duo, Huybers, Peter and Pillai, Natesh (2021) Late 19th century navigational uncertainties and their influence on sea surface temperature estimates. The Annals of Applied Statistics, 15 (1), 22-40. (doi:10.1214/20-AOAS1367).

Abstract

Accurate estimates of historical changes in sea surface temperatures (SSTs) and their uncertainties are important for documenting and understanding historical changes in climate. A source of uncertainty that has not previously been quantified in historical SST estimates stems from position errors. A Bayesian inference framework is proposed for quantifying errors in reported positions and their implications on SST estimates. The analysis framework is applied to data from the International Comprehensive Ocean-Atmosphere Data Set (ICOADS3.0) in 1885, a time when astronomical and chronometer estimation of position was common but predated the use of radio signals. Focus is upon a subset of 943 ship tracks from ICOADS3.0 that report their position every two hours to a precision of 0.01^∘ longitude and latitude. These data are interpreted as positions determined by dead reckoning that are periodically updated by celestial correction techniques. The posterior medians of uncertainties in celestial correction are 33.1 km (0.30^∘ on the equator) in longitude and 24.4 km (0.22^∘) in latitude, respectively. Celestial navigation uncertainties being smaller in latitude than longitude is qualitatively consistent with the relative difficulty of obtaining astronomical estimates. The posterior medians for two-hourly dead reckoning uncertainties are 19.2% for ship speed and 13.2^∘ for ship heading, leading to random position uncertainties with median 0.18^∘ (20 km on the equator) in longitude and 0.15^∘ (17 km) in latitude. Reported ship tracks also contain systematic position uncertainties relating to precursor dead-reckoning positions not being updated after obtaining celestial position estimates, indicating that more accurate positions can be provided for SST observations. Finally, we translate position errors into SST uncertainties by sampling an ensemble of SSTs from the Multiscale Ultrahigh Resolution Sea Surface Temperature (MURSST) data set. Evolving technology for determining ship position, heterogeneous reporting and archiving of position information, and seasonal and spatial changes in navigational uncertainty and SST gradients together imply that accounting for positional error in SST estimates over the span of the instrumental record will require substantial additional effort.

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Contributors

Author: Duo Chan

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