“…As experience is gained, application of state estimation is expanding from drawing inferences from sampling the estimates akin to observations to quantitatively analyzing processes by utilizing the complete physics embodied in the model. Examples of such include analyses of property budgets that are closed without unresolved components (e.g., Buckley et al, 2015;Piecuch et al, 2017;Ponte and Piecuch, 2018), tracing origins and fate of ocean water masses (e.g., Fukumori et al, 2004;Gao et al, 2011;Qu et al, 2013) and quantifying causal mechanisms controlling the ocean (e.g., Fukumori et al, 2015;Pillar et al, 2016Pillar et al, , 2018Jones et al, 2018;Smith and Heimbach, 2019). The model's adjoint offers a unique tool in such efforts by providing an efficient means to evaluate physical dependencies among different quantities of interest.…”