SUMMARYThe influence matrix is used in ordinary least-squares applications for monitoring statistical multipleregression analyses. Concepts related to the influence matrix provide diagnostics on the influence of individual data on the analysis-the analysis change that would occur by leaving one observation out, and the effective information content (degrees of freedom for signal) in any sub-set of the analysed data. In this paper, the corresponding concepts have been derived in the context of linear statistical data assimilation in numerical weather prediction. An approximate method to compute the diagonal elements of the influence matrix (the selfsensitivities) has been developed for a large-dimension variational data assimilation system (the four-dimensional variational system of the European Centre for Medium-Range Weather Forecasts). Results show that, in the boreal spring 2003 operational system, 15% of the global influence is due to the assimilated observations in any one analysis, and the complementary 85% is the influence of the prior (background) information, a short-range forecast containing information from earlier assimilated observations. About 25% of the observational information is currently provided by surface-based observing systems, and 75% by satellite systems.Low-influence data points usually occur in data-rich areas, while high-influence data points are in data-sparse areas or in dynamically active regions. Background-error correlations also play an important role: high correlation diminishes the observation influence and amplifies the importance of the surrounding real and pseudo observations (prior information in observation space). Incorrect specifications of background and observation-error covariance matrices can be identified, interpreted and better understood by the use of influence-matrix diagnostics for the variety of observation types and observed variables used in the data assimilation system.

This study presents a new simple approach for combining empirical with raw (i.e., not bias corrected) coupled model ensemble forecasts in order to make more skillful interval forecasts of ENSO. A Bayesian normal model has been used to combine empirical and raw coupled model December SST Nifio-3.4 index forecasts started at the end of the preceding July (5-month lead time). The empirical forecasts were obtained by linear regression between December and the preceding July Nino-3.4 index values over the period 1950-2001. Coupled model ensemble forecasts for the period 1987-99 were provided by ECMWF, as part of the Development of a European Multimodel Ensemble System for Seasonal to Interannual Prediction (DEMETER) project. Empirical and raw coupled model ensemble forecasts alone have similar mean absolute error forecast skill score, compared to climatological forecasts, of around 50% over the period 1987-99. The combined forecast gives an increased skill score of 74% and provides a well-calibrated and reliable estimate of forecast uncertainty.

Seasons are the complex nonlinear response of the physical climate system to regular annual solar forcing. There is no a priori reason why they should remain fixed/invariant from year to year, as is often assumed in climate studies when extracting the seasonal component. The widely used econometric variant of Census Method II Seasonal Adjustment Program (X-11), which allows for year-to-year variations in seasonal shape, is shown here to have some advantages for diagnosing climate variability. The X-11 procedure is applied to the monthly mean Niño-3.4 sea surface temperature (SST) index and global gridded NCEP-NCAR reanalyses of 2-m surface air temperature. The resulting seasonal component shows statistically significant interannual variations over many parts of the globe. By taking these variations in seasonality into account, it is shown that one can define less ambiguous ENSO indices. Furthermore, using the X-11 seasonal adjustment approach, it is shown that the three cold ENSO episodes after 1998 are due to an increase in amplitude of seasonality rather than being three distinct La Niña events. Globally, variations in the seasonal component represent a substantial fraction of the year-to-year variability in monthly mean temperatures. In addition, strong teleconnections can be discerned between the magnitude of seasonal variations across the globe. It might be possible to exploit such relationships to improve the skill of seasonal climate forecasts.

The Indian summer monsoon rainfall is the net result of an ensemble of synoptic disturbances, many of which are extremely intense. Sporadic systems often bring extreme amounts of rain over only a few days, which can have sizable impacts on the estimated seasonal mean rainfall. The statistics of these outlier events are presented both for observed and model-simulated daily rainfall for the summers of 1986 to 1989. The extreme events cause the wet-day probability distribution of daily rainfall to be far from Gaussian, especially along the coastal regions of eastern and northwestern India. The gamma and Weibull distributions provide good fits to the wetday rainfall distribution, whereas the lognormal distribution is too skewed. The impact of extreme events on estimates of space and time averages can be reduced by nonlinearly transforming the daily rainfall amounts. The square root transformation is shown to improve the predictability of ensemble forecasts of the mean Indian rainfall for June 1986-89.

Subjective tests for the assessment of the quality of experience (QoE) are typically run with a pool of subjects providing their opinion scores using a 5-point scale. The subjects' mean opinion score (MOS) is generally assumed as the best estimation of the average score in the target population. Indeed, for a large enough sample, we may assume that the mean of the variations across the subjects approaches zero, but this is not the case for the limited number of subjects typically considered in subjective tests. In this paper, we propose an approach based on generalized linear models (GLMs) for estimation of the population average QoE. The motivating dataset is composed of the individual scores assigned by 25 subjects to a set of gaming videos evaluated under different resolutions and compression ratios. The approach recognizes the multinomial nature of the data and allows for correlation between scores of the same subject. The resulting estimated average QoE is shown to follow more credible patterns than the MOS, particularly for higher bitrates, for which the model estimates present more coherent behavior. Similar convincing results are found on a second dataset, showing the validity of the approach.