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Asher B. Siebert and M. Neil Ward


A statistical simulation framework is developed to explore the future frequencies of threshold-crossing events, focusing here on low seasonal rainfall totals. Global change (GC) is represented by a trend on the seasonal mean rainfall total. Natural decadal to multidecadal variability (MDV) is represented by an autoregressive process. Interannual variability (IV) of seasonal totals is represented by white noise with either a normal or skew normal distribution consistent with parameters observed in the historical record at the location being modeled. Monte Carlo simulations are undertaken for various combinations of the above components, and the authors evaluate the extent to which future event frequencies can be estimated from the statistics of previous years. The sample of four study locations used to illustrate the approach is drawn from the Millennium Villages Project in Africa, where the potential of index insurance as a development and adaptation tool has been considered, thereby bringing a targeted problem setting to the analyses. The simulations highlight a number of general principles. For example, it is shown that a 10% change in the mean rainfall can lead to a change of order times 2 in the number of threshold-crossing low seasonal rainfall totals, even without invoking any change in the characteristics of the IV. The magnitudes of change are also shown to be sensitive to the threshold studied, as well as to site-specific climate features (here, coefficient of variation and skewness). The framework developed permits quantification of how, especially in the near term (of order 30 years), MDV can strongly add to uncertainty about future event frequencies. Therefore, statistical treatment of estimated MDV magnitudes will often be a key input to optimal risk management, with further enhancements expected through explicit MDV forecasts. The results highlight the importance of finding optimal ways to update climate statistics such as event thresholds, in the presence of GC and MDV.

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Brian J. Thompson, Georgy B. Parrent, John H. Ward, and Bruce Justii


Recently a new instrument termed the laser fog disdrometer was introduced by Silverman, Thompson and Ward. As implied by the name, the function of the instrument is the determination of the size distribution of fog droplets. In design, operation and analysis this instrument represents a significant departure from the customary approaches to the problem. The basic principle of the instrument may be summarized as follows: by suitably storing the diffraction pattern associated with a droplet, both the precise size and location of the droplet may be determined. This principle can be utilized to obtain size distributions without disturbing the statistics of the sample, i.e., finite volumes may be sampled without dilution.

Originally, the data were read directly from the diffraction pattern. This type of readout is subject to two fundamental difficulties: 1) the geometry of droplets is difficult to ascertain except for simple structures; 2) if several droplets are relatively near each other in the sample volume, the resultant diffraction pattern is difficult to interpret. This first consideration does not represent a severe limitation for this application; however, it would be a serious limitation in other applications where non-spherical droplets exist. Both of these restrictions, however, are removed by the present readout technique. Physically, the new readout is based on the realization that the diffraction patterns stored by the instrument are, in fact, a new kind of hologram. Hence, the stored diffraction pattern can be used to create a real three-dimensional image of the sample volume. Since the image is fixed in time, the volume may be explored at will and the size and shape of each particle as well as its position relative to the other particles in the sample may be determined. In the present paper the concept and design of the disdrometer is reviewed and the new readout technique is discussed from both a theoretical and experimental point of view. Typical experimental results are also illustrated.

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