Modelling Global Mean Sea Level: estimation and uncertainty quantification for drift and acceleration
by Dr. Xavier Loizeau, Dr. Maurice Cox, Dr. Bernardo Mota, Dr. Pieter De Vis, Dr. Jonathan Mittaz, Mrs./Ms. Sajedeh Behnia, Dr. Emma Woolliams

Abstract

Sea-level is a critical essential climate variable (ECV). The rise in sea-level is one of the primary indicators of global climate change and caused by two processes: thermal expansion of water as the oceans become warmer and melting of glaciers in Greenland and Antarctica. It also has a direct impact on society, particularly in low-lying Pacific-island countries, but also on coastal cities around the world. Global mean sea level (GMSL) is defined as the average height of the ocean surface (across the entire planet) relative to a reference geoid, having been corrected for transient changes (waves, tides, etc.). One very important GMSL product is derived from satellite altimetry data, which provides a continuous, global 30-year record. The repeated measurement of GMSL, associated with a data generation model, allows the estimation of the drift and acceleration of the GMSL, and provides key insight to policy makers. In [1], the authors suggest a covariance matrix for GMSL data acquired over 25 years and averaged over 10-day periods; estimate the parameters of a linear model (including constant, linear and quadratic terms, and terms representing annual and semi-annual seasonal effects). They obtain the associated uncertainty using the Ordinary Least Squares estimator. The authors carry out this process over subsets of the data to estimate the first two derivatives (drift and acceleration) of the model. We propose an alternative method to estimate the derivatives of the GMSL, using the entire data set; investigate the use of the Generalised Least Squares estimator, take better account of the dependence structure of the data; investigate model-validation methods; propose a sparse model in a wavelet functions basis to consider the complex variation of the ocean level and estimate its parameters using a LASSO estimator. In future work on ECVs, and more generally in work that involves correlated variables, it will be vital to take dependencies into account during the estimation of key quantities. The same applies to model validation, uncertainty reporting and the trade-off between model flexibility and detail in reporting. The result will be more realistic uncertainties, clearer statements of the quantity of interest, and improved communication with policy makers. [1] Ablain et al 2019. https://doi.org/10.5194/essd-11-1189-2019