This project focused on the temporal and spatial structure of rain with an emphasis on smaller scales most relevant to urban flood forecasting and to agricultural concerns of soil erosion. There were also many significant findings applicable to much larger scales particularly with regard to the effect of measurement scale and statistical heterogeneity so important for scaling of rainfall observations and of computer model outputs as well as for satellite communications. Specifically, we

• found that steadier, light rain decorrelates spatially faster than does the convective rain, but in both cases the 2D spatial correlation functions are anisotropic, perhaps reflecting an asymmetry in the physical processes influencing the rain reaching the ground not accounted for in numerical microphysical models.
• found that the variability of probability drop-size distributions increased with the expansion of the network size L because the network acts to integrate the variance from smallest wavelengths to those comparable to the network size L so that as L increases, so does the variability.
• found that network observations are affected by the length of the temporal interval over which measurements are combined as well as by the size of the network. When the observation interval is small, only network size matters. Networks then act as high-pass filters that distort both the spatial correlation function and, consequently, the variance spectrum. However, when the observation interval becomes large, advection enhances the contributions from longer wavelengths, leading to a distortion of correlation function and the associated variance spectrum. There is no known way to correct for this.
• found that, in contrast to network measurements which act as high-pass filters, remote sensing instruments act as low-pass filters, thus complicating comparisons between the two sets of observations. However, sometimes the network-observed spatial correlation function can be corrected to become a good estimate of the intrinsic spatial correlation function that can yield a variance spectrum that can then be spatially low-pass filtered in a manner appropriate for the remote sensor so that ground-based observations.
• found that while the variability of the rainfall rate depends upon the variability of the drop size distribution, it is only most significant for small domains. However, over dimensions of 1 km and larger, it is only the variability of total number of drops that determines the variability of the rainfall rate with the role of the drop size distribution only being to provide a mean drop size.
• found a physically based method independent of statistical models for evaluating whether a set of data in rain is statistically suitable (wide-sense stationary or WSS) for accurate rainfall scaling.
• found correlated rainfall spatial structures in 13 hours of rain even over areas as small as only an 11 cm x 11 cm grid. Such fine structures are particularly relevant to soil erosion (a multi-billion-dollar problem world-wide every year) because of the kinetic energy and impact power of the with the total number of drops rather than drop size playing the crucial role. Therefore, in future studies of rain it is recommended that the total number of drops be retained as a crucial variable.
• found a new technique to study the problem of satellite communication site diversity performance utilizing only a single location’s drop size distribution measurement. Site diversity is one of the few fade mitigation techniques that are actively explored to overcome the serious fading condition encountered in high frequency satellite communication, particularly over tropical regions. However, the study of site diversity performance is very limited over tropical regions due to unavailability of simultaneous fade measurements from two or more locations as well lack of data on spatial rain pattern from radar measurements. Using this new approach, the effects of frequency, elevation angle and site separation on diversity gain show agreement with those derived independently using radar measurements in Singapore. The study indicates that the developed method provides a significant improvement over the inappropriate application of existing standard models to the tropics because of the different nature of tropical rain.

These findings indicate that new directions for research to include a survey of when WSS is applicable over a wide range of meteorological conditions.  In addition, it is obvious that time and space are not independent variables so that further research is required to better document their relationship in different meteorological conditions. Moreover, rain structures vary not only over time and two dimensions, but also over three spatial dimensions. Little is currently known about such 3-D structures. Yet they likely play an important role in the evolution of rain.

Last Modified: 10/02/2018
Modified by: Arthur R Jameson