A comparison of two postprocessing approaches as part of the HEavy Precipitation forecast Postprocessing over India (HEPPI) project.

<p>Accurate predictions of heavy precipitation in India are vital for impact-orientated forecasting, and an essential requirement for mitigating the impact of damaging flood events. Operational forecasts from non-convection-permitting models can have large biases in the intensities and spatial structure of heavy precipitation, and while convection-permitting models can reduce biases, their operational use over large areas is not yet feasible. Statistical postprocessing can reduce these biases for relatively little computational cost, but few studies have focused on postprocessing monsoonal rainfall and the associated severe flooding events. As part of the Weather and Climate Science for Service Partnership India (WCSSP India), the HEavy Precipitation Forecast Postprocessing over India (HEPPI) project assesses the value of multiple postprocessing methods in this context. </p><p>Here, we present an evaluation of two postprocessing approaches to determine their suitability for heavy rainfall in India: Univariate Quantile Mapping (UQM) and Ensemble Model Output Statistics (EMOS). For each method, we apply the statistical postprocessing to daily precipitation in the NCMWF 12km forecast for the 2018 and 2019 monsoon seasons individually at each grid cell within the forecast. UQM leads by construction to rainfall distributions close to the observed ones, while EMOS optimises the spread of the postprocessed ensemble without guaranteeing realistic rainfall distributions. The choice of method is therefore to some degree dependent on end user requirements.</p><p>We use three rainfall observation data sets and different parametric distributions for UQM to determine the best setup. Mixed distributions, where gamma distributions are fitted separately to the bottom 90% and the top 10% of rainfall events are found to be the best choice because they are a better fit for the high rainfall values.</p><p>In several case studies, an overestimation of west coast rainfall in the forecasts is corrected by UQM. Although errors linked to forecasting rainfall in the wrong location or where no rainfall has been observed at all cannot be corrected by local statistical postprocessing, the overall forecast performance is improved by the UQM approach adopted here.</p><p>As in UQM, we use multiple observational datasets to determine the best EMOS setup. We select the gamma distribution, due to its suitability for both low and heavy rainfall events. Unlike in UQM, mixed distributions are unnecessary as the distribution is fitted across ensemble members at each timestep. EMOS and UQM are verified against observations and compared to each other using a variety of metrics including case studies, the Receiver Operating Characteristic and the Continuous Rank Probability Score.</p><p> </p><p> </p><p> </p><p> </p>

The application of new distribution in determining extreme hydrologic events such as floods

In hydrology, statistics of extremes play an important role in the use of time series analysis as well as in planning, design and operation of hydrotechnical structures and water systems. In particular, probability distributions are used to estimate and forecast floods. However, in order to use distributions, the data must be random, with a change-point and should not have a trend. Unfortunately, the data being analyzed are not independent, which is very often due to the anthropogenic impact, among other factors. In situations where various processes generate rainfall and floods in river basins, the use of mixed distributions is recommended. However, an accurate estimation of multiple parameters derived from a mixture of distributions can be difficult, which is the biggest disadvantage of this approach. Therefore, as an alternative, we propose a new extension of the GEV distribution – the Dual Gamma Generalized Extreme Value Distribution (GGEV) developed by Nascimento, Bourguignony and Leão (2016). We compared this distribution with selected 3-parameter distributions: Pearson type III, Log-Normal, Weibull and Generalized Extreme Value. In addition, various methods of estimating 3-parameter distributions were used. As a case study, rivers from Poland and the Czech Republic were investigated, because this has a significant impact on water management in the Upper Oder basin due to the strategic water reservoirs and other hydrotechnical constructions, either existing or planned. Currently, there are no clearly indicated distributions for the Upper Oder basin. Therefore, our aim was to approximate them. Two methods were used, namely the Annual Maximum (AM) and the Peaks Over Threshold (POT). In the latter case, two methods for determining the threshold were used, namely: the Mean of the Annual Maximum River Flows (MAMRF) and the Hill plot. Hence, the basic 3-parameter Weibull distribution, with parameters estimated using the modified method of moments and the maximum likelihood estimation, yielded a better fit to the observation series in the AM and POT methods. For the AM and POT (MAMRF, Hill plot) methods, the GGEV turned out to be the best-fitted distribution according to the Mean Absolute Relative Error (MARE). The GGEV distribution can be used as an alternative to mixed distributions in various samples, both homogeneous and heterogeneous. This distribution turned out to be the best fit especially for the sample whose independence is affected by the presence of a GGEV water reservoir.

Quantization for a Mixture of Uniform Distributions Associated with Probability Vectors

The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability distribution by a discrete distribution. Mixtures of probability distributions, also known as mixed distributions, are an exciting new area for optimal quantization. In this paper, we investigate the optimal quantization for three different mixed distributions generated by uniform distributions associated with probability vectors.

Application of queueing models with abandonment for Call Center congestion analysis

This paper studies and applies queueing systems to Call Centers regarding the possibility of customer abandonment from the system before being served due to their impatience in waiting for a service. Call Centers are service organizations that predominantly serve customers via phone calls. One of the main concerns in managing them is to provide quality service at a minimum cost. Noticing the quality of services offered is expressed by customers, for example by abandonment from the queue. This paper shows that the M/M/c+G analytical queueing models with abandonment, with patience time represented by generic distributions (particularly mixed distributions), are more effective than the M/M/c+M analytical queueing models with abandonment, with Exponential patience, commonly used to evaluate congestion problems in Call Centers and support sizing and operational decisions in these systems. We conducted a study using data extracted from a Bank Call Center located in Israel and the parameters and some performance measures are determined based on this data. These sampling measures are compared with the same measures achieved by the M/M/c+M and M/M/c+G analytical queueing models considered in this research, which use parameters obtained empirically and the mixed and non-mixed distributions based on Exponential and Lognormal to represent user patience. An experimental discrete simulation model was also used to explore an alternative scenario, showing the potential of using the approaches based on analytical models with abandonment for Call Center analysis.