Near-surface air temperature is one of the most widely studied hydroclimatic variables, as both its regular and extremal behaviors are of paramount importance to human life. Following the global warming observed in the past decades and the advent of the anthropogenic climate change debate, interest in temperature’s variability and extremes has been rising. It has since become clear that it is imperative not only to identify the exact shape of the temperature’s distribution tails, but also to understand their temporal evolution. Here, we investigate the stochastic behavior of near-surface air temperature using the newly developed estimation tool of Knowable (K-)moments. K-moments, because of their property to substitute higher-order deviations from the mean with the distribution function, enable reliable estimation and an effective alternative to order statistics and, particularly for the outliers-prone distribution tails. We compile a large set of daily timeseries (30–200 years) of average, maximum and minimum air temperature, which we standardize with respect to the monthly variability of each record. Our focus is placed on the maximum and minimum temperatures, because they are more reliably measured than the average, yet very rarely analyzed in the literature. We examine segments of each timeseries using consecutive rolling 30-year periods, from which we extract extreme values corresponding to specific return period levels. Results suggest that the average and minimum temperature tend to increase, while overall the maximum temperature is slightly decreasing. Furthermore, we model the temperature timeseries as a filtered Hurst-Kolmogorov process and use Monte Carlo simulation to produce synthetic records with similar stochastic properties through the explicit Symmetric Moving Average scheme. We subsequently evaluate how the patterns observed in the longest records can be reproduced by the synthetic series.

近地表空气温度是研究最广泛的水文气候变量之一，因为其规则行为和极端行为对人类生活至关重要。在过去几十年中观察到全球变暖以及人为气候变化辩论的到来之后，人们对温度的变化性和极端性的兴趣不断上升。此后变得很清楚，不仅必须确定温度分布尾部的确切形状，而且还必须了解它们的时间演变。在这里，我们使用新开发的已知（K-）矩估算工具调查近地表气温的随机行为。K矩，因为它们具有用分布函数代替均值的高阶偏差的特性，能够进行可靠的估计，并且可以有效替代订单统计信息，尤其是对于那些容易出现异常值的分布尾部的情况。我们编制了大量的平均，最高和最低气温的每日时间序列（30-200年），我们针对每个记录的每月可变性进行标准化。我们将重点放在最高和最低温度上，因为它们比平均温度更可靠地进行测量，但在文献中很少进行分析。我们使用连续的30年滚动周期检查每个时间序列的细分，然后从中提取对应于特定回报期水平的极值。结果表明，平均温度和最低温度趋于增加，而总体最高温度则略有下降。此外，我们将温度时间序列建模为经过滤波的Hurst-Kolmogorov过程，并使用蒙特卡罗模拟通过显式对称移动平均方案生成具有相似随机属性的合成记录。随后，我们评估了如何通过合成系列再现最长记录中观察到的模式。