Variance Reduction Factor Research Articles

Uncertainty Quantification of Mean-Areal Radar-Rainfall Estimates

Abstract The most common rainfall measuring sensor for validation of radar-rainfall products is the rain gauge. However, the difference between area-rainfall and rain gauge point-rainfall estimates imposes additional noise in the radar–rain gauge difference statistics, which should not be interpreted as radar error. A methodology is proposed to quantify the radar-rainfall error variance by separating the variance of the rain gauge area-point rainfall difference from the variance of radar–rain gauge ratio. The error in this research is defined as the ratio of the “true” rainfall to the estimated mean-areal rainfall by radar and rain gauge. Both radar and rain gauge multiplicative errors are assumed to be stochastic variables, lognormally distributed, with zero covariance. The rain gauge area-point difference variance is quantified based on the areal-rainfall variance reduction factor evaluated in the logarithmic domain. The statistical method described here has two distinct characteristics: first, it propo...

Transformation of point rainfall to areal rainfall: Intensity-duration-frequency curves

Abstract Current approaches to constructing catchment intensity-duration-frequency (IDF) curves are dominated by the use of empirically-derived areal reduction factors (ARFs). In this paper we present an alternative methodology which is based on the spatial correlation structure of rainfall. It represents an attempt to link current scientific theories of space-time rainfall fields with design methods. The starting point is to derive the parent distribution of catchment average rainfall intensity from that of point rainfall intensity. The parameters of the two parent distributions are related through a variance reduction factor which is a function of the spatial correlation structure of rainfall and catchment area. Assuming that the parent distribution is of the “exponential type”, it is then transformed to an extreme value distribution of the Gumbel type. The crucial step is to match the parameters of the extreme rainfall distribution derived above, for the particular case of zero catchment area, with those of empirical point IDF curves which have also been fitted to the Gumbel distribution. With this match, the proposed theory then naturally generalises to yield catchment IDF curves for catchments of any size, and for rainfall of any spatial correlation structure. The new catchment IDF curves have the attractive property that, with a minimum number of assumptions, they can reproduce a range of observed properties of catchment rainfall. For example, not only the mean and the standard deviation of extreme rainfall, but also its coefficient of variation, decrease with increasing catchment area. We also find that computed ARFs using the new approach depend not only on catchment area and storm duration, but also on the return period. We estimate ARFs using the new methodology for two major observed storms in Austria, and find that these estimates compare favourably with our understanding of the rainfall generating mechanisms associated with these two particular storm types.

A Model of a Closed-Loop Conveyor with Random Material Flow

Abstract A closed-loop conveyor with one loading station and one unloading station is considered. The material arriving at the unloading station is modeled as a stationary stochastic process. An analytical solution for the probability distribution of the material flow leaving the unloading station is presented. It is shown that the storage feature of the closed loop can be utilized to smooth the random fluctuations present in the input flow. This smoothing is quantified by the variance reduction factor, which is the ratio of the variances of output flow and input flow. The variance reduction factor is related to the conveyor capacity and a linear decision rule for unloading.