Abstract. Characterizing the variability across timescales is important to understand the underlying dynamics of the Earth system. It remains challenging to do so from paleoclimate archives since they are more than often irregular and traditional methods to produce timescale-dependent estimates of variability such as the classical periodogram and the multitaper spectrum generally require regular time sampling. We have compared those traditional methods using interpolation with interpolation-free methods, namely the Lomb-Scargle periodogram and the first-order Haar structure function. The ability of those methods to produce timescale-dependent estimates of variability when applied to irregular data was evaluated in a comparative framework using surrogate paleo-proxy data generated with realistic sampling. The metric we chose to compare them is the scaling exponent, i.e. the linear slope in log-transformed coordinates, since it summarizes the behaviour of the variability across timescales. We found that for scaling estimates in irregular timeseries, the interpolation-free methods are to be preferred over the methods requiring interpolation as they allow for the utilization of the information from shorter timescale which are particularly affected by the irregularity. In addition, our results suggest that the Haar structure function is the safer choice of interpolation-free method since the Lomb-Scargle periodogram is unreliable when the underlying process generating the timeseries is not stationary. Given that we cannot know a priori what kind of scaling behaviour is contained in a paleoclimate timeseries, and that it is also possible that this changes as a function of timescale, it is a desirable characteristic for the method to handle both stationary and non-stationary cases alike.

中文翻译：

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古气候时间序列中气候变化的时标相关标度估算技术比较

摘要。跨时标表征变化对了解地球系统的基本动力学很重要。从古气候档案库中做到这一点仍然具有挑战性，因为它们不但经常是不规则的，而且传统的方法还需要时间尺度相关的可变性估计，例如经典的周期图和多锥度谱，通常需要定期的时间采样。我们将那些使用插值的传统方法与无插值方法（即Lomb-Scargle周期图和一阶Haar结构函数）进行了比较。在比较框架中，使用通过实际采样生成的替代古代理数据，评估了将这些方法应用于不规则数据时产生时间依赖于时标的可变性估计的能力。我们选择比较它们的度量标准是缩放指数，即对数转换坐标中的线性斜率，因为它总结了跨时标的可变性行为。我们发现，对于按比例缩放不规则时间序列中的估计值，与需要插值的方法相比，无插值方法将是首选方法，因为它们允许利用更短时间尺度的信息，而该时间尺度尤其受不规则性影响。此外，我们的结果表明，当生成时间序列的基础过程不稳定时，Lomb-Scargle周期图不可靠，因此Haar结构函数是无插值方法的较安全选择。鉴于我们无法先验地知道古气候时间序列中包含哪种缩放行为，