A Bayesian Algorithm for Reconstructing Climate Anomalies in Space and Time. Part I: Development and Applications to Paleoclimate Reconstruction Problems
A Bayesian Algorithm for Reconstructing Climate Anomalies in Space and Time. Part I: Development and Applications to Paleoclimate Reconstruction Problems
复制标题
重建时空气候异常的贝叶斯算法。
DOI：
10.1175/2009jcli3015.1
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发表时间：
2010
影响因子：
4.9
通讯作者：
P. Huybers
中科院分区：
文献类型：
--
作者：
M. Tingley;P. Huybers
从重叠的仪器和气候代理时间序列数据集中重建气候场的空间格局是一个重要的统计问题。需要将代理观测转换为气候场的估计，而且观测到的时间序列在空间上不是均匀分布的事实，使分析进一步复杂化。目前解决这一问题的主要方法是基于在“校准”间隔内估计代理时间序列和仪器时间序列之间的完整协方差矩阵，然后在线性回归的背景下使用该协方差矩阵来预测在仪器覆盖之前几年代理观测中缺失的仪器值。通过指定气候场的空间协方差和时间演变的参数形式，以及描述数据类型与相应的气候场真值之间关系的“观测方程”，提出了解决这一问题的一种根本不同的方法。采用层次贝叶斯模型来吸收代理和仪器数据集，并在规则的空间网格上估计所有模式参数和气候场随时间的概率分布。该方法的输出包括对气候场和模式参数的完整协方差结构的估计，以及估计不同代理时间序列效用的诊断。在破坏了一些时间序列以模拟代理观测后，使用仪器表面温度数据集演示了该方法。结果与使用正则化期望最大化算法获得的结果进行了比较，在这些实验中，贝叶斯算法以更高的技巧产生重建。第2部分将更详细地探讨这两种方法背后的假设以及将每种方法应用于简单代理数据集的结果。
Reconstructing the spatial pattern of a climate field through time from a dataset of overlapping instrumental and climate proxy time series is a nontrivial statistical problem. The need to transform the proxy observations into estimates of the climate field, and the fact that the observed time series are not uniformly distributed in space, further complicate the analysis. Current leading approaches to this problem are based on estimating the full covariance matrix between the proxy time series and instrumental time series over a ‘‘calibration’’ interval and then using this covariance matrix in the context of a linear regression to predict the missing instrumental values from the proxy observations for years prior to instrumental coverage. A fundamentally different approach to this problem is formulated by specifying parametric forms for the spatial covariance and temporal evolution of the climate field, as well as ‘‘observation equations’’ describing the relationship between the data types and the corresponding true values of the climate field. A hierarchical Bayesian model is used to assimilate both proxy and instrumental datasets and to estimate the probability distribution of all model parameters and the climate field through time on a regular spatial grid. The output from this approach includes an estimate of the full covariance structure of the climate field and model parameters as well as diagnostics that estimate the utility of the different proxy time series. This methodology is demonstrated using an instrumental surface temperature dataset after corrupting a number of the time series to mimic proxy observations. The results are compared to those achieved using the regularized expectation‐maximization algorithm, and in these experiments the Bayesian algorithm produces reconstructions with greater skill. The assumptions underlying these two methodologies and the results of applying each to simple surrogate datasets are explored in greater detail in Part II.