Estimation Of Error Statistics Research Articles

Multi-year objective analyses of warm season ground-level ozone and PM<sub>2.5</sub> over North America using real-time observations and Canadian operational air quality models

Abstract. Multi-year objective analyses (OA) on a high spatiotemporal resolution for the warm season period (1 May to 31 October) for ground-level ozone and for fine particulate matter (diameter less than 2.5 microns (PM2.5)) are presented. The OA used in this study combines model outputs from the Canadian air quality forecast suite with US and Canadian observations from various air quality surface monitoring networks. The analyses are based on an optimal interpolation (OI) with capabilities for adaptive error statistics for ozone and PM2.5 and an explicit bias correction scheme for the PM2.5 analyses. The estimation of error statistics has been computed using a modified version of the Hollingsworth–Lönnberg (H–L) method. The error statistics are "tuned" using a χ2 (chi-square) diagnostic, a semi-empirical procedure that provides significantly better verification than without tuning. Successful cross-validation experiments were performed with an OA setup using 90% of data observations to build the objective analyses and with the remainder left out as an independent set of data for verification purposes. Furthermore, comparisons with other external sources of information (global models and PM2.5 satellite surface-derived or ground-based measurements) show reasonable agreement. The multi-year analyses obtained provide relatively high precision with an absolute yearly averaged systematic error of less than 0.6 ppbv (parts per billion by volume) and 0.7 μg m−3 (micrograms per cubic meter) for ozone and PM2.5, respectively, and a random error generally less than 9 ppbv for ozone and under 12 μg m−3 for PM2.5. This paper focuses on two applications: (1) presenting long-term averages of OA and analysis increments as a form of summer climatology; and (2) analyzing long-term (decadal) trends and inter-annual fluctuations using OA outputs. The results show that high percentiles of ozone and PM2.5 were both following a general decreasing trend in North America, with the eastern part of the United States showing the most widespread decrease, likely due to more effective pollution controls. Some locations, however, exhibited an increasing trend in the mean ozone and PM2.5, such as the northwestern part of North America (northwest US and Alberta). Conversely, the low percentiles are generally rising for ozone, which may be linked to the intercontinental transport of increased emissions from emerging countries. After removing the decadal trend, the inter-annual fluctuations of the high percentiles are largely explained by the temperature fluctuations for ozone and to a lesser extent by precipitation fluctuations for PM2.5. More interesting is the economic short-term change (as expressed by the variation of the US gross domestic product growth rate), which explains 37% of the total variance of inter-annual fluctuations of PM2.5 and 15% in the case of ozone.

The Evolution of Dispersion Spectra and the Evaluation of Model Differences in an Ensemble Estimation of Error Statistics for a Limited-Area Analysis

Abstract An ensemble of limited-area forecasts has been obtained by integrating the Aire Limitée Adaptation Dynamique Développement International (ALADIN) limited-area model, in cold-starting mode, from an ensemble of Action de Recherche Petite Echelle Grande Echelle (ARPEGE) global analyses and forecasts. This permits error covariances of the ALADIN 6-h forecast and of the ARPEGE analysis to be estimated. These two fields may be combined in a future ALADIN analysis. The evolution of dispersion spectra is first studied in a perfect model framework. The ARPEGE analysis reduces the large-scale dispersion of the ARPEGE background by extracting some information from observations. Then, the digital filter initialization reduces the small-scale dispersion by removing the noise caused by interpolation of the ARPEGE analysis onto the ALADIN grid. Finally, the ALADIN 6-h forecast strongly increases the small-scale dispersion, in accordance with its ability to represent small-scale processes. Some model error contributions are then studied. The variances of the differences between the ALADIN and ARPEGE forecasts, which are started from the same ARPEGE analysis, are of smaller scale than are the ALADIN and ARPEGE perfect model dispersions. The small-scale part of these ARPEGE–ALADIN model differences is shown to correspond to structures that are represented by ALADIN and not by ARPEGE. Therefore, this part may be added to the ARPEGE analysis dispersion. The residual large-scale part is more ambiguous, but it may be added to the ALADIN dispersion; this may reflect some effects of the coupling inaccuracies, and strengthen (in a future ALADIN analysis) the use of the large-scale information from the ARPEGE analysis.

Sea surface topography fields of the tropical Pacific from data assimilation

Time series of maps of monthly tropical Pacific dynamic topography anomalies from 1979 through 1985 were constructed by means of assimilation of tide gauge and expendable bathythermograph (XBT) data into a linear model driven by observed winds. Estimates of error statistics were calculated and compared to actual differences between hindcasts and observations. Four experiments were performed as follows: one with no assimilation, one with assimiation of sea level anomaly data from eight selected island tide gauge stations, one with assimilation of dynamic height anomalies derived from XBT data, and one with both XBT and tide gauge data assimilated. Data from seven additional tide gauge stations were withheld from the assimilation process and used for verification in all four experiments. Statistical objective maps based on data alone were also constructed for comparison purposes. The dynamic response of the model without assimilation was, in general, weaker than the observed response. Assimilation resulted in enhanced signal amplitude in all three assimilation experiments. RMS amplitudes of statistical objective maps were only strong near observing points. In large data‐void regions these maps show amplitudes even weaker than the wind‐driven model without assimilation. With few exceptions the error estimates generated by the Kaiman filter appeared quite reasonable. Since the error processes cannot be assumed to be white or stationary, we could find no straightforward way to test the formal statistical hypothesis that the time series of differences between the filter output and the actual observations were drawn from a population with statistics given by the Kaiman filter estimates. The autocovariance of the innovation sequence, i.e., the sequence of differences between forecasts before assimilation and observations, has long been used as an indicator of how close a filter is to optimality. We found that the best filter we could devise was still short of the goal of producing a white innovation sequence. In this and earlier studies, little sensitivity has been found to the parameters under our direct control. Extensive changes in the assumed error statistics make only marginal differences. The same is true for long time and space scale behavior of different models with richer physics and finer resolution. Better data assimilation results will probably require relaxation of the assumptions of stationarity and serial independence of the errors. Formulation of such detailed noise models will require longer time series, with the attendant problems of matching very different data sets.

Modeling Broadcast Teletext Systems for Analysis and Computer Simulation Studies

An isomorphism is derived between a typical bandpass broadcast television system to be used in transmitting teletext data and its complex baseband equivalent representation for use in analysis and computer simulations. The distortions introduced by a multipath channel are discussed. The complex noise process is modeled by a mixture of Gaussian and impulsive noise, and the parameters of the noise model are derived. The video signal-to-noise ratio SNR TV is related to other parameters such as the input noise variance, output noise power, and the carrier-to-noise density ratio. A complete simulation model for broadcast television transmission and reception is shown in block diagram form. The remaining components of the computer simulation model are briefly discussed and references given. These include topics such as amplitude control, computer generation of ensembles of complex impulse responses, simulation of synchronous, quasi-synchronous and envelope detectors, bit slicers, bit synchronizers, error-correcting codes, estimation of error statistics and bit error rates, and adaptive equalization. Validation is also briefly noted with references. Several examples of simulation results are given. Some of the implementation details, simulation results, and a flow diagram of the simulation program are provided. This teletext computer simulation model appears to be the most complete one created to this time and has been used extensively in performance analyses to evaluate new designs and gain insights into design improvements.