Using transient tracers: the regularization problem
Using transient tracers: the regularization problem
复制标题
使用瞬态跟踪器：正则化问题
DOI：
10.1111/j.1600-0889.1987.tb00207.x
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发表时间：
1987
期刊：
影响因子：
2.3
通讯作者：
C. Wunsch
中科院分区：
文献类型：
--
作者：
C. Wunsch
推导流体性质，速度，混合，和边界条件从现实的示踪剂观测的一般问题制定和攻击。重点是海洋瞬态示踪剂，但同样的问题元素出现在许多其他领域，包括气象学，医学和化学工程。很明显，使用示踪剂，瞬态或以其他方式，需要在某个阶段的对流/扩散方程的解决方案eitherupstream，或向后的时间，或两者兼而有之，其不稳定的情况下臭名昭著，因为扩散过程逐步破坏信息的“前进”的方向。我们给出了一个一维空间和一维时间的简单有限差分形式的例子。这个问题是“向后”运行的，但是通过线性规划来解决它。线性规划也被证明对稳定和不稳定的正问题和反问题有几个潜在的优点：答案的形式知识很容易使用;数据的不确定性被容纳;浓度的正性约束是隐含的;稀疏软件是可用的;最佳观测策略的问题由对偶解来解决;和反向问题的强不稳定性得到抑制。DOI：10.1111/j.1600-0889.1987.tb00207.x
The generic problem of deducing fluid properties, velocity, mixing, and boundary conditionsfrom realistic tracer observations is formulated and attacked. The focus is on oceanic transienttracers, but the same problem elements appear in many other fields including meteorology,medicine and chemical engineering. It becomes clear that use of tracers, transient orotherwise, requires at some stage the solution of the advection/diffusion equation eitherupstream, or backwards in time, or both, a situation notorious for its instability becausediffusive processes progressively destroy information in the “forward” direction. We consideran example in simple finite difference form for one space dimension and time. The problem isrun “backwards”, but regularized by solving it through linear programming. Linear programmingis shown also to have several potential advantages for stable and unstable forwardproblems, and the inverse problem: knowledge of the form of the answer is easily used; datauncertainty is accommodated; the positivity constraints on concentrations are implicit; sparsesystem software is available; questions of best observational strategy are addressed by the dualsolution ; and the strong instabilities of the inverse and backwards problems are suppressed. DOI: 10.1111/j.1600-0889.1987.tb00207.x