The Hurst Phenomenon in Error Estimates Related to Atmospheric Turbulence
The Hurst Phenomenon in Error Estimates Related to Atmospheric Turbulence
复制标题
与大气湍流相关的误差估计中的赫斯特现象
DOI：
--
复制
发表时间：
2018
影响因子：
4.3
通讯作者：
M. Chamecki
中科院分区：
文献类型：
--
作者：
N. Dias;Bianca Luhm Crivellaro;M. Chamecki
Hurst现象是一个著名的长期持续性特征，由E。1950年代的赫斯特在风洞、大气和河流中测量的湍流时间序列中的几个案例中也发现了这种情况。在这里，我们进行了系统的调查的赫斯特系数H值在大气近地层数据，其影响的随机误差的估计。我们证明了通常H > 0.5H>0.5，这意味着积分时标不存在（在统计意义上）。由于积分时标存在于用于估计随机误差的Lumley-Panofsky方程中，这具有重要的实际后果。我们估计H在两个主要的方式：（1）与最近提出的过滤方法估计的随机误差（$$H_p$$Hp）的扩展，和（2）与经典的重新标度的范围介绍了赫斯特（$$H_R$$HR）。其他估计，尝试，但发现不太能够捕捉大尺度的湍流的统计行为。使用三个微气象活动的数据，我们发现，一阶和二阶湍流统计显示赫斯特现象。通常，对于相同的数据集，$$H_R$$HR大于$$H_p$$Hp，这就提出了一个问题，即这些估计量中的一个，甚至两个，可能是有偏差的。对于相对误差，我们发现，估计的误差与我们所采用的方法，我们称之为宽松的过滤方法，并考虑到赫斯特现象的发生，是大于过滤方法和经典的Lumley-Panofsky估计。最后，我们发现H和Obukhov稳定性参数之间没有明显的关系。然而，相对误差，表现出稳定性的依赖性，特别是在不稳定条件下的运动学动量通量的误差的情况下，和运动学感热通量在稳定条件下。
The Hurst phenomenon is a well-known feature of long-range persistence first observed in hydrological and geophysical time series by E. Hurst in the 1950s. It has also been found in several cases in turbulence time series measured in the wind tunnel, the atmosphere, and in rivers. Here, we conduct a systematic investigation of the value of the Hurst coefficient H in atmospheric surface-layer data, and its impact on the estimation of random errors. We show that usually $$H > 0.5$$H>0.5, which implies the non-existence (in the statistical sense) of the integral time scale. Since the integral time scale is present in the Lumley–Panofsky equation for the estimation of random errors, this has important practical consequences. We estimated H in two principal ways: (1) with an extension of the recently proposed filtering method to estimate the random error ($$H_p$$Hp), and (2) with the classical rescaled range introduced by Hurst ($$H_R$$HR). Other estimators were tried but were found less able to capture the statistical behaviour of the large scales of turbulence. Using data from three micrometeorological campaigns we found that both first- and second-order turbulence statistics display the Hurst phenomenon. Usually, $$H_R$$HR is larger than $$H_p$$Hp for the same dataset, raising the question that one, or even both, of these estimators, may be biased. For the relative error, we found that the errors estimated with the approach adopted by us, that we call the relaxed filtering method, and that takes into account the occurrence of the Hurst phenomenon, are larger than both the filtering method and the classical Lumley–Panofsky estimates. Finally, we found that there is no apparent relationship between H and the Obukhov stability parameter. The relative errors, however, do show stability dependence, particularly in the case of the error of the kinematic momentum flux in unstable conditions, and that of the kinematic sensible heat flux in stable conditions.
影响因子：
3.3
作者：
Caccia, DC;Percival, D;Bassingthwaighte, JB
通讯作者：
Bassingthwaighte, JB