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Are atmospheric surface layer flows ergodic?
Author(s) -
Higgins Chad W.,
Katul Gabriel G.,
Froidevaux Martin,
Simeonov Valentin,
Parlange Marc B.
Publication year - 2013
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1002/grl.50642
Subject(s) - ergodicity , ergodic theory , statistical physics , planetary boundary layer , turbulence , scalar (mathematics) , boundary layer , meteorology , environmental science , mathematics , physics , mechanics , statistics , mathematical analysis , geometry
The transposition of atmospheric turbulence statistics from the time domain, as conventionally sampled in field experiments, is explained by the so‐called ergodic hypothesis. In micrometeorology, this hypothesis assumes that the time average of a measured flow variable represents an ensemble of independent realizations from similar meteorological states and boundary conditions. That is, the averaging duration must be sufficiently long to include a large number of independent realizations of the sampled flow variable so as to represent the ensemble. While the validity of the ergodic hypothesis for turbulence has been confirmed in laboratory experiments, and numerical simulations for idealized conditions, evidence for its validity in the atmospheric surface layer (ASL), especially for nonideal conditions, continues to defy experimental efforts. There is some urgency to make progress on this problem given the proliferation of tall tower scalar concentration networks aimed at constraining climate models yet are impacted by nonideal conditions at the land surface. Recent advancements in water vapor concentration lidar measurements that simultaneously sample spatial and temporal series in the ASL are used to investigate the validity of the ergodic hypothesis for the first time. It is shown that ergodicity is valid in a strict sense above uniform surfaces away from abrupt surface transitions. Surprisingly, ergodicity may be used to infer the ensemble concentration statistics of a composite grass‐lake system using only water vapor concentration measurements collected above the sharp transition delineating the lake from the grass surface.

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