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A spectral approach to estimating the timescale-dependent uncertainty of paleoclimate records – Part 1: Theoretical concept
Climate of the Past ( IF 3.8 ) Pub Date : 2020-08-11 , DOI: 10.5194/cp-16-1469-2020
Torben Kunz , Andrew M. Dolman , Thomas Laepple

Proxy records represent an invaluable source of information for reconstructing past climatic variations, but they are associated with considerable uncertainties. For a systematic quantification of these reconstruction errors, however, knowledge is required not only of their individual sources but also of their auto-correlation structure as this determines the timescale dependence of their magnitude, an issue that has been often ignored until now. Here a spectral approach to uncertainty analysis is provided for paleoclimate reconstructions obtained from single sediment proxy records. The formulation in the spectral domain rather than the time domain allows for an explicit demonstration and quantification of the timescale dependence that is inherent in any proxy-based reconstruction uncertainty. This study is published in two parts. In this first part, the theoretical concept is presented, and analytic expressions are derived for the power spectral density of the reconstruction error of sediment proxy records. The underlying model takes into account the spectral structure of the climate signal, seasonal and orbital variations, bioturbation, sampling of a finite number of signal carriers, and uncorrelated measurement noise, and it includes the effects of spectral aliasing and leakage. The uncertainty estimation method, based upon this model, is illustrated by simple examples. In the second part of this study, published separately, the method is implemented in an application-oriented context, and more detailed examples are presented.

中文翻译:

一种光谱方法来估计古气候记录的时间尺度相关不确定性 第1部分:理论概念

代理记录是重建过去的气候变化的宝贵信息来源,但它们具有很大的不确定性。但是,要对这些重建误差进行系统的量化,不仅需要了解其各个来源,而且还需要了解其自相关结构,因为这决定了其规模对时间尺度的依赖性,这一问题至今一直被人们忽略。在这里,从单一沉积物替代记录获得的古气候重建提供了一种不确定性分析的光谱方法。在频谱域而不是时域中的表述允许对任何基于代理的重构不确定性中固有的时标依赖性进行明确的演示和量化。这项研究分为两个部分。在第一部分中,提出了理论概念,并得出了沉积物替代记录重建误差的功率谱密度的解析表达式。基本模型考虑了气候信号的频谱结构,季节和轨道变化,生物扰动,有限数量的信号载波采样以及不相关的测量噪声,其中包括频谱混叠和泄漏的影响。通过简单的例子说明了基于该模型的不确定性估计方法。在本研究的第二部分(单独出版)中,该方法在面向应用程序的上下文中实现,并提供了更详细的示例。推导了沉积物替代记录重建误差的功率谱密度解析表达式。基本模型考虑了气候信号的频谱结构,季节和轨道变化,生物扰动,有限数量的信号载波采样以及不相关的测量噪声,其中包括频谱混叠和泄漏的影响。通过简单的例子说明了基于该模型的不确定性估计方法。在本研究的第二部分(单独出版)中,该方法在面向应用程序的上下文中实现,并提供了更详细的示例。推导了沉积物替代记录重建误差的功率谱密度解析表达式。基本模型考虑了气候信号的频谱结构,季节和轨道变化,生物扰动,有限数量的信号载波采样以及不相关的测量噪声,其中包括频谱混叠和泄漏的影响。通过简单的例子说明了基于该模型的不确定性估计方法。在本研究的第二部分(单独出版)中,该方法在面向应用程序的上下文中实现,并提供了更详细的示例。和不相关的测量噪声,其中包括频谱混叠和泄漏的影响。通过简单的例子说明了基于该模型的不确定性估计方法。在本研究的第二部分(单独出版)中,该方法在面向应用程序的上下文中实现,并提供了更详细的示例。和不相关的测量噪声,其中包括频谱混叠和泄漏的影响。通过简单的例子说明了基于该模型的不确定性估计方法。在本研究的第二部分(单独出版)中,该方法在面向应用程序的上下文中实现,并提供了更详细的示例。
更新日期:2020-08-20
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