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.

中文翻译：

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查找近似中性曲面的算法改进

内部海洋运动主要沿中性切平面而不是沿中性切平面发生。这些平面不会链接在一起以形成轮廓分明的表面，因此海洋学家会使用近似中性的表面。迄今为止，最精确的此类表面是ω-表面，但其实际应用受到限制，因为其数值实现缓慢且有时不稳定。这项工作提高了ω的速度，鲁棒性和实用性表面。首先，我们从通过最小最小二乘求解超定矩阵问题，转向通过正则方程（通过矩阵转置的乘法）或通过微积分离散化从原始优化问题派生的泊松方程而获得的精确确定的矩阵问题。变化。这样可以降低计算复杂度，大约从到，其中N是曲面中的网格点数。其次，我们通过求解每个水柱中的非线性方程来更新表面的垂直位置，而不是假设分层在垂直方向上是均匀的。这将收敛所需的迭代次数减少了一个数量级，并且不需要使原始软件稳定的阻尼因子。此外，我们增加了“润湿”能力，从而使在反复进行时中性联系起来的露头和露头被重新结合到地表中。新算法可在大约15 s的时间内，在1,440 x 720网格海洋中计算ω-曲面，而原始软件的计算时间约为11 h。我们还提供了两种简单的方法来用（中性）密度值标记ω-曲面。