CMG Collaborative Research: Particle Filters and Ecological Models (PFEM): Application of chainless Monte-Carlo methods to mapping the ecology of the North Pacific Ocean

智力优势。世界海洋生态系统对年际和十年期气候变率的动态响应的特点是变化率（如初级生产率和出口生产率）或群落结构的变化。如果不增加生态系统模型的复杂性，就很难对群落结构的这些变化进行建模。当生态系统模型必须反映世界海洋一个区域到另一个区域的群落变化时，也存在类似的局限性。本研究的工作假设是，数据同化技术的进步，耦合物理-生物模拟和高性能计算将有助于构建生态模型的参数估计地图，以反映这些变化的物种和群落结构。使用遥感海洋颜色和原位观测的参数估计是特别具有挑战性的，因为状态和/或测量函数是高度非线性的，并且过程状态的后验分布不是高斯分布。在过去十年左右的时间里，一些数据同化技术已被用于海洋物理学和海洋地球化学的耦合模型，但其中大多数依赖于弱非线性和高斯系统（如变分法，EnergyKalman滤波器）或过于昂贵（如粒子滤波器）。在粒子方法中，人们估计粒子系综的概率密度（通过观察修改的模型的实例）。这通常通过贝叶斯构造来完成，而精确度所需的恢复则通过马尔可夫链蒙特卡罗来完成。对于大规模系统，该过程可能非常昂贵，因为颗粒的数量可能需要很大，并且因为MCMC可能具有过多的排斥分数。这项研究将采用新开发的方法，其中的概率密度直接采样，没有贝叶斯步骤，并在没有诉诸马尔可夫链的情况下进行重新排序。针对变分法和马尔可夫链蒙特-卡罗粒子方法在求解状态维数很高的非线性、非高斯系统时的不足，设计了一种无链蒙特-卡罗粒子滤波器.这些无链方法在较小的系统中表现良好。其目的是产生空间和时间变化的参数估计的生态模型的中等复杂性耦合到混合层模型，在北太平洋海盆遥感表面叶绿素a观测同化的基础上。参数值将被解释在物种分布和养分循环方面。该项目将评估这一耦合模式模拟观测到的季节至年际变化的能力，评估其对强迫的敏感性，并将结果与海洋生态考虑联系起来。新的资料同化技术将广泛应用于海洋学和应用数学交叉学科中出现的高度非线性高维问题。对误差估计的审查将导致对遥感观测的信息内容进行定量评估，并有助于规划未来的观测方案。耦合模式模拟的结果应为评估气候变化的影响提供有用的信息。粒子方法是非线性滤波领域的一个重大进展，在科学和工程中有着广泛的应用。在教育方面，该项目将为未来的科学家提供跨学科建模和数据同化领域的培训。

Intellectual Merit. Dynamic response of the world ocean ecosystem to interannual and decadal climate variability has been characterized by changes either in rates (e.g. rate of primary and export production) or in community structure. These changes in community structure cannot be easily modeled without introducing additional complexity in the ecosystem model. Similar limitations exist when ecosystem models have to reflect changes in the community from one region of the world ocean to another. The working hypothesis of this study is that advances in data assimilation techniques, coupled physical-biological modeling and high performance computing will help construct maps of parameter estimates for ecological models that will reflect these changes in species and community structure.Parameter estimation using remotely sensed ocean color and in situ observations is especially challenging since the state and/or measurement functions are highly non-linear, and the posterior distribution of the process states is not Gaussian. Several data assimilation techniques have been utilized in the last decade or so for coupled models of ocean physics and biogeochemistry but most of them rely on weakly non-linear and Gaussian systems (e.g. variational methods, Ensemble Kalman Filters) or are prohibitively expensive (e.g. particle filters). In particle methods one estimates the probability density of an ensemble of particles (instances of the model modified by observations). This is usually done by a Bayesian construction, with the resampling needed for accuracy done by Markov chain Monte Carlo. For large-scale systems this procedure can be prohibitively expensive, because the number of particles may need to be substantial and because the MCMC may have an excessive fraction of rejections. This study will employ newly-developed methods, where the probability density is sampled directly, without a Bayesian step, and where the resampling is done without recourse to Markov chains. A chainless Monte-Carlo particle filter is designed to overcome the shortcomings of variational methods and Markov chain Monte-Carlo particle methods for highly nonlinear, non-Gaussian systems with very high state dimensions. These chainless methods have performed well in smaller systems. The aim is to produce spatially and temporally varying parameter estimates for an ecological model of medium complexity coupled to a mixed layer model, based on assimilation of remotely-sensed surface chlorophyll-a observations in the north Pacific basin. Parameter values will be interpreted in terms of species distribution and nutrient cycling. This project will evaluate the ability of this coupled model to simulate observed seasonal to interannual variability, evaluate its sensitivity to forcing, and relate the results to considerations of ocean ecology.Broader Impact. The new data assimilation techniques will be broadly applicable to the highly nonlinear high dimensional problems that appear in interdisciplinary oceanography and applied mathematics. Examination of error estimates will lead to quantitative assessment of the information content of remotely sensed observations, and facilitate planning of future observing programs. The results of the coupled model simulations should provide useful information for assessment of the impact of climate change. The particle methods will be a significant advance in the state of the nonlinear filtering art, and be widely applicable in science and engineering. On the educational side, the project will provide training for future scientists in the field of interdisciplinary modeling and data assimilation.