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This chapter is dedicated to the comparison of three well-known models that apply to multiple (that is, simultaneous) collisions: Moreau's law, the binary collision law, and the LZB model. First a brief recall of these three models and of their numerical implementation is done. Then an analysis based on numerical simulations, where the LZB outcome is considered as the reference outcome, is made. It is shown that Moreau's law and the binary collision model possess good prediction capabilities in some few "extreme" cases. The comparisons are made for free chains of aligned grains, and for chains impacting a wall. The elasticity coefficient, restitution coefficients, mass ratios and contact equivalent stiffnesses are used as varying parameters.

The overall objective of this study is to improve the forecasting accuracy of the precipitation in the Singapore region by means of both rainfall forecasting and nowcasting. Numerical Weather Predication (NWP) and radar‐based rainfall nowcasting are two important sources for quantitative precipitation forecast. In this paper, an attempt to combine rainfall prediction from a high‐resolution mesoscale weather model and a radar‐based rainfall model was performed. Two rainfall forecasting methods were selected and examined: (i) the weather research and forecasting model (WRF); and (ii) a translation model (TM). The WRF model, at a high spatial resolution, was run over the domain of interest using the Global Forecast System data as initializing fields. Some heavy rainfall events were selected from data record and used to test the forecast capability of WRF and TM. Results obtained from TM and WRF were then combined together to form an ensemble rainfall forecasting model, by assigning weights of 0.7 and 0.3 weights to TM and WRF, respectively. This paper presented results from WRF and TM, and the resulting ensemble rainfall forecasting; comparisons with station data were conducted as well. It was shown that results from WRF are very useful as advisory of anticipated heavy rainfall events, whereas those from TM, which used information of rain cells already appearing on the radar screen, were more accurate for rainfall nowcasting as expected. The ensemble rainfall forecasting compares reasonably well with the station observation data. Copyright © 2012 John Wiley & Sons, Ltd.