One of the most intriguing facets of the climate system is that it exhibits variability across all temporal and spatial scales; pronounced examples are temperature and precipitation. The structure of this variability, however, is not arbitrary. Over certain spatial and temporal ranges, it can be described by scaling relationships in the form of power laws in probability density distributions and autocorrelation functions. These scaling relationships can be quantified by scaling exponents which measure how the variability changes across scales and how the intensity changes with frequency of occurrence. Scaling determines the relative magnitudes and persistence of natural climate fluctuations. Here, we review various scaling mechanisms and their relevance for the climate system. We show observational evidence of scaling and discuss the application of scaling properties and methods in trend detection, climate sensitivity analyses, and climate prediction.Plain Language Summary Climate variables are related over long times and large distances. This shows up as correlations for averages on long intervals or between distant areas. An important finding is that the majority of correlations in climate can be described by a simple mathematical relationship. We present such correlations for temperature on long times. Similarly, the intensity of precipitation events depends on their frequency in a simple manner. A useful concept is scaling where a scale denotes the width of an average. Scaling says that averages on different scales are related by a simple function-mathematically, this is a power law with the scaling exponent as a characteristic number. Scaling has impacts on predictability, temperature trends, and the assessment of future climate changes caused by anthropogenic forcing.

This article aims at providing a comprehensive survey of recent developments in the field of integer-valued time series modelling, paying particular attention to models obtained as discrete counterparts of conventional autoregressive moving average and bilinear models, and based on the concept of thinning. Such models have proven to be useful in the analysis of many real-world applications ranging from economy and finance to medicine. We review the literature of the most relevant thinning operators proposed in the analysis of univariate and multivariate integer-valued time series with either finite or infinite support. Finally, we also outline and discuss possible directions of future research.

The authors prospectively studied the value of clinical and neurophysiologic measurements in assessing progression in ALS. Motor unit number estimation (MUNE) and the neurophysiologic index (NI) were significantly correlated with ADM strength (maximal voluntary isometric contraction force in the abductor digiti minimi muscle [MVIC-ADM]). MUNE and the NI were reliable, but the NI showed a lower variation. On assessing progression at 3, 6, and 12 months, MUNE, NI, and MVIC-ADM showed the highest rate of change. The NI is a potentially useful new neurophysiologic measurement.

Abstract. The analysis of trends in air temperature observations is one of the most common activities in climate change studies. This work examines the changes in daily mean air temperature over Central Europe using quantile regression, which allows the estimation of trends, not only in the mean but in all parts of the data distribution. A bootstrap procedure is applied for assessing uncertainty on the derived slopes and the resulting distributions are summarised via clustering. The results show considerable spatial diversity over the central European region. A distinct behaviour is found for lower (5 %) and upper (95 %) quantiles, with higher trends around 0.15 • C decade −1 at the 5 % quantile and around 0.20 • C decade −1 at the 95 % quantile, the largest trends (>0.2 • C decade −1 ) occurring in the Alps.

Recebido em 6/3/09; aceito em 30/7/09; publicado na web em 11/1/10 AIR POLLUTION AND EMERGENCY ADMISSIONS FOR CARDIORESPIRATORY DISEASES IN LISBON (PORTUGAL).Daily records of hospital admissions due to cardiorespiratory diseases and levels of PM 10 , SO 2 , CO, NO, NO 2 , and O 3 were collected from 1999-2004 to evaluate the relationship between air pollution and morbidity in Lisbon. Generalised additive Poisson regression models were adopted, controlling for temperature, humidity, and both short and long-term seasonality. Significant positive associations, lagged by 1 or 2 days, were found between markers of traffic-related pollution (CO and NO 2 ) and cardiocirculatory diseases in all age groups. Increased childhood emergency admissions for respiratory illness were significantly correlated with the 1-day lagged SO 2 levels coming from industrial activities.