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  • Author or Editor: Witold F. Krajewski x
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Emmanouil N. Anagnostou, Witold F. Krajewski, and James Smith


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 proposes a range-dependent formulation for the error variance, and second, the error variance estimates are relative to the mean rainfall at the radar product grids. Two months of radar and rain gauge data from the Melbourne, Florida, WSR-88D are used to illustrate the proposed method. The study concentrates on hourly rainfall accumulations at 2- and 4-km grid resolutions. Results show that the area-point difference in rain gauge rainfall contributes up to 60% of the variance observed in radar–rain gauge differences, depending on the radar grid size, the location of the sampling point in the grid, and the distance from the radar.

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Piotr A. Lewandowski, William E. Eichinger, Anton Kruger, and Witold F. Krajewski


A significant scale gap between radar and in situ measurements of rainfall using rain gauges and disdrometers indicates a pressing need for improved knowledge of rainfall variability at the spatial scales below those of today’s operational radar rainfall products, that is, ∼1–4 km. Lidar technology has the potential to fulfill this need, but there has been inconsistency in the literature pertaining to quantitative observations of rain using lidar. Several publications have stated that light scattering properties of raindrops could not be correlated with rain rates, while other papers have demonstrated the existence of such relationships. This note provides empirical evidence in support of the latter claim.

The authors conducted a simple experiment using a near-horizontal-pointing elastic lidar to observe rain in Iowa City, Iowa, in the fall of 2005. The lidar signal was used to estimate rainfall quantities that were subsequently compared with independent estimates of the same quantities obtained from an optical disdrometer that was placed about 370 m from the lidar, ∼10 m below the lidar beam. To perform the conversion from the raw lidar signal, the authors used an optical geometry-based procedure to estimate optical extinction data. A theoretical relationship between extinction coefficients and rain rates was derived based on a theoretical drop size distribution. The parameters of the relationship were found through a best-fit procedure using lidar and disdrometer data. The results show that the lidar-derived rain rates correspond to those obtained from the optical disdrometer with a root-mean-square difference of 55%.

The authors conclude that although a great deal remains to be done to improve the inversion algorithm, lidar measurements of rain are possible and warrant further studies. Lidars deployed in conjunction with disdrometers can provide high spatial (<5 m) and temporal (<1 min disdrometer, ∼1 s lidar) resolution data over a relatively long distance for rainfall measurements (1–2 km in the case of the University of Iowa lidar).

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