Power spectra and cospectra for wind and scalars in a disturbed surface layer at the base of an advective inversion

This paper reports power spectra and cospectra of wind speed and several scalars measured at two heights near the base of an advective inversion. The inversion had formed over a paddy field downwind of an extensive dry region. Winds over the paddy field were variable in strength and direction, as a result of convective motions in the atmospheric boundary layer passing over from the dry region upwind. Fetch over the rice was large enough that advective effects on the transport processes were small at the upper level and negligible at the lower level. Results from the lower level are interpreted in terms of a horizontally homogeneous, but disturbed, surface layer. Power spectra of longitudinal and lateral velocity were substantially enhanced at low frequencies. The resulting vertical motions added only a small amount to the spectrum of vertical velocity but this strongly affected scalar power spectra and cospectra. These were all substantially enhanced over a range of low frequencies. We also found that differences in lower boundary conditions cause differences among scalar spectra at low frequencies. Our analysis shows that the spectra and cospectra have three components, characterized by different scaling regimes. We call these the ILS (inner-layer scaling), OLS (outer-layer scaling) and CS (combined scaling) components. Of these, the CS component had not previously been identified. We identify CS components of spectra by their independence of height and frequency. Spectra with these characteristics had been predicted by Kader and Yaglom for a layer of the atmosphere where spectral matching between ILS and OLS was proposed. However, we find that the velocity and scalar scales used by Kader and Yaglom do not fit our results and that their concept of a matching layer is incompatible with our application. An alternative basis for this behaviour and alternative scales are proposed. We compare our decomposition of spectra into ILS, CS and OLS components with an extended form of Townsend's hypothesis, in which wind and scalar fluctuations are divided into `active' and `inactive' components. We find the schemes are compatible if we identify all OLS spectral components as inactive, and all CS and ILS components as active. By extending the implications of our results to ordinary unstable daytime conditions, we predict that classical Monin-Obukhov similarity theory should be modified. We find that the height of the convective boundary layer is an important parameter when describing transport processes near the ground, and that the scalar scale in the ILS part of the spectrum, which includes the inertial subrange, is proportional to observation height times the local mean scalar gradient, and not the Monin-Obukhov scalar scale parameter. The former depends on two stability parameters: the Monin-Obukhov stability parameter and the ratio of the inner-layer and outer-layer velocity scales. The outer-layer scale can reflect disturbances by topographically-induced eddying as well as by convective motions.