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The complex structure of a typical stratus cloud base height (or profile) time series is analyzed with respect to the variability of its fluctuations and their correlations at all experimentally observed temporal scales. Due to the underlying processes that create these time series, they are expected to have multiscaling properties. For obtaining reliable measures of these scaling properties, different methods of statistical analysis are used herein : power spectral density, detrended fluctuation analysis, and multifractal analysis. This broad set of diagnostic techniques is applied to a typical stratus cloud base height (CBH) data set; data were obtained from the Southern Great Plains site of the Atmospheric Radiation Measurement Program of the Department of Energy from a Belfort Laser Ceilometer. First, we demonstrate that this CBH time series is a nonstationary signal with stationary increments. Further, two scaling regimes are found, although the characteristic laws are quite similar ones. Next, the multi-affine scaling properties are confirmed. The scaling properties of the cloud base height profile of such a continental stratus are found to be similar to those of the marine cloud base height profiles studied by us previously. Some physical interpretation in terms of anomalous diffusion (or fractional random walk) is given for the continental case.

This work reports a quantitative assessment of propagation losses for the frequency band 2110–2170 MHz under evaporation and surface‐based ducts conditions. Flat‐underlying‐surface and elevated‐terrain cases are studied. The calculations are based on the parabolic approximation to the wave equation in conjunction with finite‐element and Fourier split‐step techniques. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 42: 390–394, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20314

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The scaling ranges of time correlations in the cloud base height records of marine boundary layer stratocumulus are studied applying the Detrended Fluctuation Analysis statistical method. We have found that time dependent variations in the evolution of the α exponent reflect the diurnal dynamics of cloud base height fluctuations in the marine boundary layer. In general, a more stable structure of the boundary layer corresponds to a lower value of the α -indicator, i.e. larger anti-persistence, thus a set of fluctuations tending to induce a greater stability of the stratocumulus. In contrast, during periods of higher instability in the marine boundary, less anti-persistent (more persistent like) behavior of the system drags it out of equilibrium, corresponding to larger α values. From an analysis of the frequency spectrum, the stratocumulus base height evolution is found to be a non-stationary process with stationary increments. The occurrence of these statistics in cloud base height fluctuations suggests the usefulness of similar studies for the radiation transfer dynamics modeling.

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A hydraulic jump (Fig. 1) is a jet stream accompanied by the formation of an eddy zone, according to the current viewpoint. One of the main problems of a hydraulic calculation of such streams is to establish the distribution law of the mean velocity over the cross section of the flow, depth of water within the eddy zone and at its end, and the length of this zone. Investigations by many authors show that the flow within the hydraulic jump both in a horizontal and sloping channel corresponds to the model of flow in a plane turbulent wall jet [1] in which the vertical velocity distribution obeys the SchlichtIng relation [1,2] for the main part of the jet. The jet character of flow in hydraulic structures enables us to approach the solution of many problems in this area from positions of the theory of turbulent jets propagating in a bounded space. Here it is assumed that the cross sections are plane and the pressure of the fluid is distributed over the depth of the flow according to the law of hydrostatics.To determine the regularities of change of the average free surface in the entire eddy zone and length of the eddy of the free jump, the equations of motion of a fluid in the boundary layer following from the Reynolds system of equations of motion are used [3]. As a result of solving these equations, with the assumptions adopted above, the following relations associating the depth of the flow h with the longitudinal coordinate x coinciding with the bottom of the flow are obtained:for i ~ 0.12 ~a (h --hi)

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