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The temporal variability of global irradiance estimated from daily satellite data and numerical models has been compared for different spans of time. According to the time scale considered, a different behaviour can be expected for each climate. Indeed, for all climates and at small scale, the persistence decreases as this scale increases, but the mediterranean climate, and its continental variety, shows higher persistence than oceanic climate. The probabilities of maintaining the values of irradiance after a certain period of time have been used as a first approximation to analyse the quality of each source, according to the climate. In addition, probability distributions corresponding to variations of clearness indices measured at several stations located in different climate zones have been compared with those obtained from satellite and modelling estimations. For this work, daily radiation data from the reanalysis carried out by the European Centre for Medium-Range Weather Forecasts and from the Satellite Application Facilities on climate monitoring have been used for mainland Spain. According to the results, the temporal series estimation of irradiance is more accurate when using satellite data, independent of the climate considered. In fact, the coefficients of determination corresponding to the locations studied are always above 0.92 in the case of satellite data, while this coefficient decreases to 0.69 for some cases of the numerical model. This conclusion is more evident in oceanic climates, where the most important errors can be observed. Indeed, in this case, the RRMSE derived from the CM-SAF estimations is 20.93%, while in the numerical model, it is 48.33%. Analysis of the probabilities corresponding to variations in the clearness indices also shows a better behaviour of the satellite-derived estimates for oceanic climate. For the standard mediterranean climate, the satellite also provides better results, though the numerical model improves significantly. In fact, for continental climate, both sources offer similar outcomes.

This paper deals the study of variability and intermittency of solar irradiation using an analogy with the turbulence and thus making use of some methodologies used in the study of intermittency of the turbulence. An analysis of the shape of the PDFs corresponding to the increments in the clearness and transmittance indexes, for direct and global radiations, is presented. In addition a study of the relations between the scaling exponents of the structure functions of the clearness and transmittance indexes and the orders of these structure functions has been carried out. According to the study, the range of relative variability is due to changes in the atmospheric components that play a role in the attenuation of solar irradiation. This range of variability is higher in the case of the global irradiation than in the case of the direct. Moreover, the multifractality is showed more intense in sites where, due to local effects, sharper variations in the radiation can be expected, as the case of deserts.

The shape of the curves relating the scaling exponents of the structure functions to the order of these functions is shown to distinguish the Dow Jones index from other stock market indices. We conclude from the shape differences that the information-loss rate for the Dow Jones index is reduced at smaller time scales, while it grows for other indices. This anomaly is due to the construction of the index, in particular to its dependence on a single market parameter: price. Prices are subject to turbulence bursts, which act against full development of turbulence.

We show the relationship between the intermittency of turbulence and the type of stratification for different atmospheric situations during the SABLES98 field campaign. With this objective, we first demonstrate the scaling behaviour of the velocity structure functions corresponding to these situations; next, we analyze the curvature of the scaling exponents of the velocity structure functions versus the order of these functions (ζ p vs. p), where ζ p are the exponents of the power relation for the velocity structure function with respect to the scale. It can be proved that this curve must be concave, under the assumption that the incompressible approximation does not break down at high Reynolds numbers. The physical significance of this kind of curvature is that the energy dissipation rate increases as the scale of the turbulent eddies diminishes (intermittency in the usual sense). However, the constraints imposed by stability, preventing full development of the turbulence, allow the function ζ p versus p to show any type of curvature. In this case, waves of high frequency trapped by the stability, or bursts of turbulence caused by the breaking up of internal waves, may produce a redistribution of energy throughout the scaling range. Due to this redistribution, the variation with the scale of the energy dissipation rate may be smaller (decreasing the intermittency) and, even in more stable situations, this rate may diminish (instead of increasing) as the scale diminishes (convex form of the curve ζ p vs. p).

Data from the SABLES98 experimental campaign (Cuxart et al., 2000) have been used in order to study the relationship of the probability distribution of velocity increments (PDFs) to the scale and the degree of stability. This connection is demonstrated by means of the velocity structure functions and the PDFs of the velocity increments. Using the hypothesis of local similarity, so that the third order structure function scaling exponent is one, the inertial range in the Kolmogorov sense has been identified for different conditions, obtaining the velocity structure function scaling exponents for several orders. The degree of intermittency in the energy cascade is measured through these exponents and compared with the forcing intermittency revealed through the evolution of flatness with scale. The role of non-homogeneity in the turbulence structure is further analysed using Extended Self Similarity (ESS). A criterion to identify the inertial range and to show the scale independence of the relative exponents is described. Finally, using least-squares fits, the values of some parameters have been obtained which are able to characterize intermittency according to different models.

This article analyzes the possibility of applying a GOY theoretical model to atmospheric boundary layer data. Bearing this in mind, relative scaling exponents of velocity structure functions are used to compare the model with the data under study. In the model, these exponents are set based on two parameters (q and δ), which are appropriate to define the model that better features a certain atmospheric state. From these scaling exponents, the gap between 2-D and 3-D turbulence is observed in the model, depending on the fact that δ is higher or lower than unity, respectively. Atmospheric data corresponding to very different states of stratification stability have been analyzed. For convective or near-neutral situations (usually associated to 3-D turbulence), it is possible to find parameters q and δ to define a model that fits the measured data. More stable situations can be featured by GOY models with higher values of δ. However, it is clear that it is impossible to represent nocturnal situations of strong stable stratification (with a more similar behaviour to 2-D) with this type of model.