期刊名称：Journal of Advances in Modeling Earth Systems
电子版ISSN：1942-2466
出版年度：2021
卷号：13
期号：5
页码：e2020MS002436
DOI：10.1029/2020MS002436
出版社：John Wiley & Sons, Ltd.
摘要：Interior oceanic motions occur predominantly along, rather than across, the neutral tangent plane. These planes do not link together to form well-defined surfaces, so oceanographers use approximately neutral surfaces. To date, the most accurate such surface is the ω -surface, but its practical utility was limited because its numerical implementation was slow and sometimes unstable. This work upgrades the speed, robustness, and utility of ω -surfaces. First, we switch from solving an overdetermined matrix problem by minimal least squares, to solving an exactly determined matrix problem, obtained either by the normal equations (multiplication by the matrix's transpose) or by discretizing Poisson's equation derived from the original optimization problem by the calculus of variations. This reduces the computational complexity, roughly from to , where N is the number of grid points in the surface. Second, we update the surface's vertical position by solving a nonlinear equation in each water column, rather than assuming the stratification is vertically uniform. This reduces the number of iterations required for convergence by an order of magnitude and eliminates the need for a damping factor that stabilized the original software. Additionally, we add “wetting” capacity, whereby incrops and outcrops are reincorporated into the surface should they become neutrally linked as iterations proceed. The new algorithm computes an ω -surface in a 1,440 by 720 gridded ocean in roughly 15 s, down from roughly 11 h for the original software. We also provide two simple methods to label an ω -surface with a (neutral) density value. Plain Language Abstract In the deep ocean interior, the circulation is much simpler than a fully three-dimensional flow, because density places a strong constraint on the flow: water “wants” to be neutrally buoyant with its environment. As such, the deep ocean is well described as a stack of two-dimensional surfaces, flowing within (rather than across) these surfaces. Because seawater's density is a nonlinear function of salinity, temperature, and pressure, these surfaces do not exist in reality: they can only be approximated. Oceanographers have been approximating these surfaces for nearly a century, but for half of that time it was not known exactly what surface was being approximated. Only in the past decade has an algorithm existed to numerically approximate these surfaces with great accuracy. However, that algorithm was computationally slow and occasionally unstable, greatly limiting the practical use of these approximate-yet-accurate surfaces. We have overhauled the algorithm, making it over 2,500 times faster on a typical modern oceanic data set (having one data point every quarter degree of latitude or longitude). Many oceanographic discoveries rely upon these types of approximate surfaces for their analyses. Our work enables such a pace of discovery to continue into the modern era of big ocean data.
