A sea-level budget (2003-2020) from a statistical, global, simultaneous inversion
Authors: Royston Samantha , Brady Aoibheann , Chuter Stephen , Ziegler Yann , Vishwakarma Bramha , Westaway Richard , Rougier Jonathan , Bamber Jonathan 
Published: March 2022

&lt;p&gt;&lt;span xml:lang=&quot;EN-GB&quot; data-contrast=&quot;auto&quot;&gt;&lt;span&gt;It is important to close the&lt;/span&gt;&lt;span&gt;&amp;#160;sea-level budget&lt;/span&gt;&lt;span&gt;&amp;#160;(SLB)&lt;/span&gt;&lt;span&gt;, to validate&amp;#160;&lt;/span&gt;&lt;span&gt;the independent observation systems of its components and to understand changes in time in those component contributions.&amp;#160;&lt;/span&gt;&lt;span&gt;Recent studies have&lt;/span&gt;&lt;span&gt;,&lt;/span&gt;&lt;span&gt;&amp;#160;&lt;/span&gt;&lt;span&gt;in turn&lt;/span&gt;&lt;span&gt;,&lt;/span&gt;&lt;span&gt;&amp;#160;&lt;/span&gt;&lt;span&gt;clos&lt;/span&gt;&lt;span&gt;ed&lt;/span&gt;&lt;span&gt;&amp;#160;the global-mean sea-level budget for the `golden era&amp;#8217; of&amp;#160;&lt;/span&gt;&lt;span&gt;highest&lt;/span&gt;&lt;span&gt;&amp;#160;&lt;/span&gt;&lt;span&gt;spatio&lt;/span&gt;&lt;span&gt;-temporal coverage&lt;/span&gt;&lt;span&gt;&amp;#160;from observations&lt;/span&gt;&lt;span&gt;&amp;#160;(from 2005&amp;#8212;2016)&lt;/span&gt;&lt;span&gt;,&amp;#160;&lt;/span&gt;&lt;span&gt;closed&amp;#160;&lt;/span&gt;&lt;span&gt;regional&amp;#160;&lt;/span&gt;&lt;span&gt;sea-level&amp;#160;&lt;/span&gt;&lt;span&gt;budgets,&amp;#160;&lt;/span&gt;&lt;span&gt;and&amp;#160;&lt;/span&gt;&lt;span&gt;extended the budget to present.&lt;/span&gt;&lt;span&gt;&amp;#160;In the&amp;#160;&lt;/span&gt;&lt;span&gt;latter&lt;/span&gt;&lt;span&gt;,&amp;#160;&lt;/span&gt;&lt;span&gt;careful consideration is needed on&amp;#160;&lt;/span&gt;&lt;span&gt;the&lt;/span&gt;&lt;span&gt;&amp;#160;treatment of the&lt;/span&gt;&lt;span&gt;&amp;#160;observation gap between GRACE and GRACE-FO&lt;/span&gt;&lt;span&gt;,&lt;/span&gt;&lt;span&gt;&amp;#160;&lt;/span&gt;&lt;span&gt;and&amp;#160;&lt;/span&gt;&lt;span&gt;apparent&lt;/span&gt;&lt;span&gt;&amp;#160;&lt;/span&gt;&lt;span&gt;recent&amp;#160;&lt;/span&gt;&lt;span&gt;drifts in&amp;#160;&lt;/span&gt;&lt;span&gt;other&amp;#160;&lt;/span&gt;&lt;span&gt;observation systems&lt;/span&gt;&lt;span&gt;.&amp;#160;&lt;/span&gt;&lt;span&gt;Here, we&lt;/span&gt;&lt;span&gt;&amp;#160;present&amp;#160;&lt;/span&gt;&lt;span&gt;a statistical&lt;/span&gt;&lt;span&gt;-&lt;/span&gt;&lt;span&gt;model-&lt;/span&gt;&lt;span&gt;based&amp;#160;&lt;/span&gt;&lt;span&gt;SLB&amp;#160;&lt;/span&gt;&lt;span&gt;from observations&lt;/span&gt;&lt;span&gt;&amp;#160;for the extended period 2003&amp;#8212;2020&lt;/span&gt;&lt;span&gt;&amp;#160;in a simultaneous inversion&lt;/span&gt;&lt;span&gt;.&amp;#160;&lt;/span&gt;&lt;span&gt;We use&lt;/span&gt;&lt;span&gt;&amp;#160;Argo and in-situ steric sea level change, GRACE&amp;#160;&lt;/span&gt;&lt;span&gt;mass&lt;/span&gt;&lt;span&gt;&amp;#160;change&lt;/span&gt;&lt;span&gt;&amp;#160;as equivalent water height&lt;/span&gt;&lt;span&gt;, satellite altimetry-derived sea surface height change, and a compilation of altimetry and DEM-differencing ice mass change data products&lt;/span&gt;&lt;span&gt;. The Bayesian hierarchical model (BHM)&amp;#160;&lt;/span&gt;&lt;span&gt;solve&lt;/span&gt;&lt;span&gt;s&lt;/span&gt;&lt;span&gt;&amp;#160;for&lt;/span&gt;&lt;span&gt;&amp;#160;the&amp;#160;&lt;/span&gt;&lt;span&gt;spatial and temporal evolution of the&amp;#160;&lt;/span&gt;&lt;span&gt;underlying components of the&amp;#160;&lt;/span&gt;&lt;span&gt;SLB&lt;/span&gt;&lt;span&gt;: land ice mass, land hydrology, ocean manometric sea level and steric sea level.&lt;/span&gt;&lt;span&gt;&amp;#160;&lt;/span&gt;&lt;span&gt;The solution&amp;#160;&lt;/span&gt;&lt;span&gt;provides probability distributions for the time series of&lt;/span&gt;&lt;span&gt;&amp;#160;each component&amp;#8217;s contribution to the sea-level budget at&amp;#160;&lt;/span&gt;&lt;span&gt;each mesh node, integrating to&amp;#160;&lt;/span&gt;&lt;span&gt;catchment and sub-ocean basin scale&lt;/span&gt;&lt;span&gt;&amp;#160;and&lt;/span&gt;&lt;span&gt;&amp;#160;the&lt;/span&gt;&lt;span&gt;&amp;#160;global-mean.&amp;#160;&lt;/span&gt;&lt;span&gt;Thus&lt;/span&gt;&lt;span&gt;&amp;#160;the probabilistic solution allows&lt;/span&gt;&lt;span&gt;&amp;#160;interrogation of where the largest uncertainties remain.&lt;/span&gt;&lt;span&gt;&amp;#160;&lt;/span&gt;&lt;span&gt;We will discuss the component contributions&amp;#160;&lt;/span&gt;&lt;span&gt;from this solution,&amp;#160;&lt;/span&gt;&lt;span&gt;their uncertainties&lt;/span&gt;&lt;span&gt;, and where and why these differ from other SLB approaches&lt;/span&gt;&lt;span&gt;.&lt;/span&gt;&lt;span&gt;&amp;#160;&lt;/span&gt;&lt;span&gt;In addition, the BHM can be run both backward (hindcast) and forward (forecast) in time to provide calibrated projections for each process and the integral both globally and regionally.&lt;/span&gt;&lt;/span&gt;&lt;span&gt;&amp;#160;&lt;/span&gt;&lt;/p&gt;