A STUDY OF SPECTRA, STRUCTURE AND CORRELATION FUNCTIONS AND THEIR IMPLICATIONS FOR THE STATIONARITY OF SURFACE-LAYER TURBULENCE NELSON L. DIAS ⋆ , MARCELO CHAMECKI and AKEMI KAN LEMMA – Laboratory for Environmental Monitoring and Modeling Analysis, UFPR/IAPAR/SIMEPAR, PO Box 19100 CEP 81531-990, Curitiba PR, Brazil CRISTHIANE M. P. OKAWA Civil Engineering Department, State Univeristy of Maringá, Maringá PR, Brazil (Received in final form 11 February 2003) Abstract. The related concepts of stationarity and the existence and values of integral time scales are central to the ability of analyzing micrometeorological data within the framework of Monin– Obukhov similarity theory. Not only does the theory strongly hinge on the stationarity assumption, the estimation of turbulence moments and their accuracies are dependent on the values of the corres- pondent integral time scales. In spite of the general importance of these concepts, there are relatively few studies concerned with them. Moreover, although each turbulence variable has its own integral scale, this fact is often overlooked when numerical values are estimated. In this work we study three daytime events of surface inversion formation, that is, events where a nonstationary period is clearly present. Our analysis reveals a low-frequency component in the temperature data that is not totally removed by a simple (but often used in turbulence data analysis) first-order recursive filter. This component has to be filtered out in the frequency domain, after which we are able to recover similarity between temperature and humidity statistical descriptors (in this case, the structure function). After applying a simple criterion to estimate numerical values of the integral time scales, we are able to assess the relationships between the existence of integral scales and the stationarity of the corresponding process. Finally, we find out that in the case of second-order moments the Sarmanov theorem does not always apply. The implications for accuracy estimates of these moments are then briefly discussed. Keywords: Integral scale, Low-frequency turbulence, Spectral analysis, Stationarity, Temperature- humidity similarity. 1. Introduction In turbulence theory, the term ‘integral scale’ is often employed to mean two different concepts. It can be used to denote the time or length scales at which turbulence is produced (Tennekes and Lumley, 1972, p. 20; Hinze, 1975, p. 224), and related to maxima in the turbulence kinetic energy (or some scalar) spectrum, or else defined statistically by means of the autocorrelation function of a given stationary stochastic process. In simple situations it is reasonable to expect the two ⋆ E-mail: nldias@ufpr.br Boundary-Layer Meteorology 110: 165–189, 2004. © 2003 Kluwer Academic Publishers. Printed in the Netherlands.