Abstract. Reliable reference profiles and estimates of variability are a necessity for a variety of processes relating to ENVISAT including the development of key aspects and inputs for the operational processor for the Michelson Interferometer for Passive Atmospheric Sounding. MIPAS reference atmospheres have therefore been produced in two forms, namely standard atmospheres for modelling and error analysis for typical atmospheric situations and the IG2 seasonal climatologies for initial guess profiles used as part of the operational processing. The reference states cover 36 species on a common altitude, pressure, and temperature grid from 0 to 120 km, and include both means and estimates of variability (maximum, minimum and one sigma values). This paper describes V3.1 of the standard atmospheres and V4.0 of the IG2 atmospheres which are the current versions of the reference atmospheres. Particular attention is paid to the MIPAS operational geophysical products (pressure/temperature, H2O, O3, CH4, N2O, HNO3 and NO2) and to CO2 whose mixing ratio is required for the retrieval of pressure and temperature. A dynamic representation of CO2 is presented which shows the presence of CO2 gradients in the troposphere and the lower stratosphere. Since these atmospheres have been produced independently of MIPAS data, it is also possible to compare the data to the MIPAS operational products and derive valuable information on both the reference atmospheres and on MIPAS data products themselves. This process has been performed for V4.61/V4.62 data from the year 2003 as part of the MIPAS validation activity. It is demonstrated that the agreement between the MIPAS mean data and the reference atmospheres is very good in mid-latitudes and the tropics, verifying these data to first order. There is also reasonable agreement in standard deviations between the IG2 atmospheres and the corresponding sigmas calculated from the MIPAS data. Knowledge of tropospheric concentrations of CH4 and N2O is used to examine the accuracy of the MIPAS data and their susceptibility to cloud effects. It is shown that for the highest accuracy, MIPAS data should be filtered with cloud index values of 2.5 for N2O and 3.5 for CH4. Once such filtering has been performed, the MIPAS data for these species appear to be accurate to within 10% in the upper troposphere. The use of cloud index data in combination with MIPAS data is recommended for studies of the polar winter stratosphere and the upper troposphere/lower stratosphere.

Mandelbrot introduced the concept of fractals to describe the non-Euclidean shape of many aspects of the natural world. In the time series context, he proposed the use of fractional Brownian motion (fBm) to model non-negligible temporal persistence, the 'Joseph Effect'; and Lévy flights to quantify large discontinuities, the 'Noah Effect'. In space physics, both effects are manifested in the intermittency and long-range correlation which are by now well-established features of geomagnetic indices and their solar wind drivers. In order to capture and quantify the Noah and Joseph effects in one compact model, we propose the application of the 'bridging' fractional Lévy motion (fLm) to space physics. We perform an initial evaluation of some previous scaling results in this paradigm, and show how fLm can model the previously observed exponents. We suggest some new directions for the future.

We analyse the distributions of the number of goals scored by home teams, away teams, and the total scored in the match, in domestic football games from 169 countries between 1999 and 2001. The probability density functions (PDFs) of goals scored cannot be fitted over their entire ranges by Poisson or negative binomial distributions; here, we compare the PDFs with those arising from extremal statistics. In addition, we show that it is sufficient to model English top division and FA Cup matches in the seasons of 1970/71 to 2000/01 on Poisson or negative binomial distributions, as reported in analyses of earlier seasons, and that these are not consistent with extremal statistics.Comment: 7 pages, 3 figure

Abstract. Whilst direct observations of internal transport in accretion disksare not yet possible, measurement of the energy emitted from accreting astrophysical systems can provide useful information on the physical mechanisms at work. Here we examine the unbroken multi-year time variation of the total X-ray flux from three sources: Cygnus X-1, the microquasar GRS 1915+105, and for comparison the nonaccreting Crab nebula. To complement previous analyses, we demonstrate that the application of advanced statistical methods to these observational time-series reveals important contrasts in the nature and scaling properties of the transport processes operating within these sources. We find the Crab signal resembles Gaussian noise; the Cygnus X-1 signal is a leptokurtic random walk whose self-similar properties persist on timescales up to three years; and the GRS 1915+105 signal is similar to that from Cygnus X-1, but with self-similarity extending possibly to only a few days. This evidence of self-similarity provides a robust quantitative characterisation of anomalous transport occuring within the systems.