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Three common stochastic tools, the climacogram i.e. variance of the time averaged process over averaging time scale, the autocovariance function and the power spectrum are compared to each other to assess each one's advantages and disadvantages in stochastic modelling and statistical inference. Although in theory, all three are equivalent to each other (transformations one another expressing second order stochastic properties), in practical application their ability to characterize a geophysical process and their utility as statistical estimators may vary. In the analysis both Markovian and non Markovian stochastic processes, which have exponential and power-type autocovariances, respectively, are used. It is shown that, due to high bias in autocovariance estimation, as well as effects of process discretization and finite sample size, the power spectrum is also prone to bias and discretization errors as well as high uncertainty, which may misrepresent the process behaviour (e.g. Hurst phenomenon) if not taken into account. Moreover, it is shown that the classical climacogram estimator has small error as well as an expected value always positive, well-behaved and close to its mode (most probable value), all of which are important advantages in stochastic model building. In contrast, the power spectrum and the autocovariance do not have some of these properties. Therefore, when building a stochastic model, it seems beneficial to start from the climacogram, rather than the power spectrum or the autocovariance. The results are illustrated by a real world application based on the analysis of a long time series of high-frequency turbulent flow measurements.

To seek stochastic analogies in key processes related to the hydrological cycle, an extended collection of several billions of records from hundred thousands of worldwide stations is used in this work. The examined processes are the near-surface hourly temperature, dew point, relative humidity, sea level pressure, and atmospheric wind speed, as well as the hourly/daily streamflow and precipitation. Through the use of robust stochastic metrics such as the K-moments and a second-order climacogram (i.e., variance of the averaged process vs. scale), it is found that several stochastic similarities exist in both the marginal structure, in terms of the first four moments, and in the second-order dependence structure. Stochastic similarities are also detected among the examined processes, forming a specific hierarchy among their marginal and dependence structures, similar to the one in the hydrological cycle. Finally, similarities are also traced to the isotropic and nearly Gaussian turbulence, as analyzed through extensive lab recordings of grid turbulence and of turbulent buoyant jet along the axis, which resembles the turbulent shear and buoyant regime that dominates and drives the hydrological-cycle processes in the boundary layer. The results are found to be consistent with other studies in literature such as solar radiation, ocean waves, and evaporation, and they can be also justified by the principle of maximum entropy. Therefore, they allow for the development of a universal stochastic view of the hydrological-cycle under the Hurst–Kolmogorov dynamics, with marginal structures extending from nearly Gaussian to Pareto-type tail behavior, and with dependence structures exhibiting roughness (fractal) behavior at small scales, long-term persistence at large scales, and a transient behavior at intermediate scales.

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In individuals with IGT, vinegar ingestion before a mixed meal results in an enhancement of muscle blood flow, an improvement of glucose uptake by the forearm muscle and a reduction of postprandial hyperinsulinaemia and hypertriglyceridaemia. From this point of view, vinegar may be considered beneficial for improving insulin resistance and metabolic abnormalities in the atherogenic prediabetic state.

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Background and Aims. Vinegar has been shown to have a glucose-lowering effect in patients with glucose abnormalities. However, the mechanisms of this effect are still obscure. The aim of this randomised, crossover study was to investigate the effect of vinegar on glucose metabolism in muscle which is the most important tissue for insulin-stimulated glucose disposal. Materials and Methods. Eleven subjects with DM2 consumed vinegar or placebo (at random order on two separate days, a week apart), before a mixed meal. Plasma glucose, insulin, triglycerides, nonesterified fatty acids (NEFA), and glycerol were measured preprandially and at 30–60 min for 300 min postprandially from the radial artery and from a forearm vein. Muscle blood flow was measured with strain-gauge plethysmography. Glucose uptake was calculated as the arteriovenous difference of glucose multiplied by blood flow. Results. Vinegar compared to placebo (1) increased forearm glucose uptake (p = 0.0357), (2) decreased plasma glucose (p = 0.0279), insulin (p = 0.0457), and triglycerides (p = 0.0439), and (3) did not change NEFA and glycerol. Conclusions. In DM2 vinegar reduces postprandial hyperglycaemia, hyperinsulinaemia, and hypertriglyceridaemia without affecting lipolysis. Vinegar's effect on carbohydrate metabolism may be partly accounted for by an increase in glucose uptake, demonstrating an improvement in insulin action in skeletal muscle. This trial is registered with Clinicaltrials.gov NCT02309424.