Collaborative Research: CMG: Gridded Analyses of Large Multi-Scale Climate Data Sets with Ensemble Representation of Uncertainty

了解过去的气候变率和预测未来的气候变化需要长期的观测气候场记录。然而，过去的观测通常是嘈杂的，在时间和空间上采样不规则，有很大的空间差距。对所分析领域的不确定度的改进表示将在气候学研究中极为有用。为了帮助满足这一需求，该项目将继续研究一种系统的、可靠的方法，从空白的气候数据中产生分析场。要采取的方法是尝试融合两种计算效率高的方法，以处理不同尺度上的可变性。两种方法中的第一种是在气候研究中发展起来的，它使用对系统误差协方差矩阵的低秩近似。该方法主要重建气候场的大尺度特征，因而忽略了大部分的小尺度变率。第二种方法源于地质统计学中的贝叶斯估计，它将全局估计协方差的强度与非平稳局部估计相结合；它不仅表示由于观测噪声和采样缺陷引起的不确定性，而且表示由于未知协方差关系引起的不确定性。这些方法是独立开发的，它们的耦合用于实际气候学应用或在集合历史分析中表示不确定性尚未完成。要使这种方法适用于现实的气候问题，需要进行理论研究。如果成功，项目的结果将开发一种有效的数值算法，适用于非常大的、不同的、不规则间隔的气候数据集：a)在不同尺度上重建变异性；b)在规则的时空网格上产生平均分析场；C)产生一种方法来产生等可能分析场的集合（一个集合），它反映了平均分析场的不确定性。然后，该方法将应用于对当前气候学研究很重要的海洋和陆地气候数据集。这些结果还将为创建气候模拟集合的初始条件提供更好的技术，允许更好地估计气候变化预测中的不确定性。实施新方法的软件和由此产生的气候数据集将向公众开放。

Understanding past climate variability and predicting future climate changes requires long records of observed climate fields. However, observations from the past are typically noisy and irregularly sampled in time and space, with large spatial gaps. Improved representations of the uncertainty in analyzed fields would be extremely useful in climatological research. To help meet this need, this project will pursue research into a systematic and robust method of producing an analyzed field from gappy climate data. The approach to be taken is to attempt to fuse two computationally efficient approaches that address variability at different scales. The first of the two methods was developed in climate research and uses a low-rank approximation to the system error covariance matrix. The method reconstructs mainly large-scale features of a climate field and hence misses most of small-scale variability. The second approach stems from Bayesian estimation in geostatistics that combines the strength of a globally estimated covariance with nonstationary local estimates; it represents the uncertainty not only due to the observational noise and sampling deficiencies, but also uncertainty due to unknown covariance relationships. The methods have been developed independently and their coupling for a practical climatological application or representing uncertainty in a historical analysis by ensemble has yet to be accomplished. To make this approach work for realistic climate problems requires the theoretical research proposedIf successful, the result of the project will the development of an efficient numerical algorithm suitable for very large, disparate, irregularly spaced climatological data sets that a) reconstructs variability on different scales, b) produces an average analysis field over a regular spatio-temporal grid and, c) yields a method to produce a collection of equally likely analysis fields (an ensemble) which reflects the uncertainty in the average analysis field. The method will then be applied to data sets of marine and land climate important to current climatological research. The results will also provide a better technique for creating the initial conditions for climate simulation ensembles, permitting better estimation of uncertainty in predictions of climate variation. Software implementing the new approach and the climate data sets derived from it will be made publicly available.