论文标题
从位置不确定性到物理上约束的协方差通货膨胀
Physically Constrained Covariance Inflation from Location Uncertainty
论文作者
论文摘要
最初在\ cite {memin2013fluidfd}中引入的``位置不确定性''的概念的动机，寻求在每个预测时间步骤的状态变量的``位置''''位置。进一步考虑了Brenier的定理\ cite {Brenier1991}，断言同一域上两个正密度场的差异可以通过传输图来表示，因此扰动被证明可以始终如一地定义了来自原始PDE的SPDE。随之而来的是，一定数量的每一个时间步骤都保存。值得注意的是，可以从这种扰动方案中恢复了盐\ cite {Holm2015VariationalPf}和Lu \ cite {Memin2013fluidfd，Resseguier2016GeophySicalFu}的衍生物。尽管如此，它仍然开放了更广泛的适用性，因为它不明确依赖拉格朗日力学或牛顿的武力定律。为了说明，提出了热浅水方程的随机版。
Motivated by the concept of ``location uncertainty", initially introduced in \cite{Memin2013FluidFD}, a scheme is sought to perturb the ``location" of a state variable at every forecast time step. Further considering Brenier's theorem \cite{Brenier1991}, asserting that the difference of two positive density fields on the same domain can be represented by a transportation map, perturbations are demonstrated to consistently define a SPDE from the original PDE. It ensues that certain quantities, up to the user, are conserved at every time step. Remarkably, derivations following both the SALT \cite{Holm2015VariationalPF} and LU \cite{Memin2013FluidFD, Resseguier2016GeophysicalFU} settings, can be recovered from this perturbation scheme. Still, it opens broader applicability since it does not explicitly rely on Lagrangian mechanics or Newton's laws of force. For illustration, a stochastic version of the thermal shallow water equation is presented.
