Influence of small scale rainfall variability on standard comparison tools between radar and rain gauge data
Introduction
The most commonly used rainfall measurement devices are tipping bucket rain gauges, disdrometers, weather radars and (passive or active) sensors onboard satellites. In this paper we focus on the observation scale gap between the two first devices which are considered here as point measurements and weather radars. A rain gauge typically collects rainfall at ground level over a circular area with a diameter of 20 cm and the sample area of operational disdrometers is roughly 50 cm2 whereas a radar scans the atmosphere over a volume whose projected area is roughly 1 km2 (for standard C-band radar operated by most of the western Europe meteorological national services). Hence observation scales differ with a ratio of approximately 107 between the two devices. A basic consequence (e.g. Wilson and Brandes, 1979), is that direct comparison of the outputs of the two sensors is at least problematic.
Standard comparisons between rain gauge and radar rainfall measurements are based on scatter plots, rain rate curves, cumulative rainfall depth curves, and the computation of various scores such as normalized bias, correlation coefficient, root mean square errors, Nash–Sutcliffe coefficient etc. (see e.g., Diss et al., 2009, Emmanuel et al., 2012, Figueras i Ventura et al., 2012, Krajewski et al., 2010, Moreau et al., 2009). Despite usually being mentioned the issue of the representativeness of point measurement (i.e. disdrometer or rain gauge) with regard to average measurements (i.e. radar) is basically not taken into account and its influence on the standard scores is not assessed. Furthermore the authors who addressed it either to separate instrumental errors from representativeness errors (Ciach and Krajewski, 1999, Ciach et al., 2003, Zhang et al., 2007, Moreau et al., 2009), or to introduce an additional score taking into account an estimation of the representativeness error (Emmanuel et al., 2012, Jaffrain and Berne, 2012) all rely on a geostatistical framework which may tend to underestimate rainfall variability and especially the extremes. Indeed this framework assumes that the rainfall field or a transform of it is Gaussian, which does not enable to fully take into account the fact that the extremes of rainfalls exhibit a power law behaviour as it has been shown by various authors (Schertzer et al., 2010, Hubert, 2001, Ladoy et al., 1993, de Lima and Grasman, 1999, Schertzer and Lovejoy, 1992).
In this paper we suggest to revisit how the representativeness issue is taken into account in standard comparison tools between point measurement devices (disdrometers or rain gauges) and radar rainfall measurements by explicitly modelling the small scale rainfall variability with the help of Universal Multifractals (Schertzer and Lovejoy, 1987). They rely on the physically based notion of scale-invariance and on the idea that rainfall is generated through a multiplicative cascade process. They have been extensively used to analyse and simulate geophysical fields extremely variable over wide range of scales (see Schertzer and Lovejoy, 2011 for a recent review). The issue of instrumental errors is not addressed in this paper.
The standard comparison tools are first presented and implemented on 4 rainfall events over the Seine-Saint-Denis County for which radar and rain gauge measurements are available (Section 2). A downscaling process is then suggested and validated with two dense networks of point measurement devices (disdrometers or rain gauges) (Section 3). Finally the influence of small scale rainfall variability on the standard scores is assessed and discussed (Section 5).
Section snippets
Rainfall data in Seine-Saint-Denis (France)
The first data set used in this paper consists in the rainfall measured by 26 tipping bucket rain gauges distributed over the 236 km2 Seine-Saint-Denis County (North-East of Paris). The rain gauges are operated by the Direction Eau et Assainissement (the local authority in charge of urban drainage). The temporal resolution is 5 min. For each rain gauge the data is compared with the corresponding radar pixel of the French radar mosaic of Météo-France whose resolution is 1 km in space and 5 min in
Methodology
In this paper we suggest to bridge the scale gap between radar and point (disdrometer or rain gauge) measurements with the help of a downscaling process based on the framework of Universal Multifractals (UM) (Schertzer and Lovejoy, 1987, Schertzer and Lovejoy, 2011 for a recent review). The UM framework is indeed convenient to achieve this, because its basic assumption is that rainfall is generated through a space–time cascade process meaning that the downscaling simply consists in extending
Methodology
The aim of this section is to estimate the expected values of the scores if neither radar nor rain gauges were affected by instrumental error, and the deviations from the optimum values were only due to the small scale rainfall variability. We will also investigate the related issue of the variations of the scores depending on where the rain gauges are located within their respective radar pixel. We remind that the studied data set is made of the rainfall output of 26 rain gauges and their
Conclusion
In this paper the issue of representativeness of point measurement with regard to larger scale measurements is revisited in the context of comparison between rain gauge and radar rainfall measurement. More precisely the influence the small scale rainfall variability occurring below the radar observation scale (1 km in space and 5 min in time here) on the standard comparison scores is investigated. It appears that this influence is twofold. First the target values of the scores are not the optimum
Acknowledgements
The authors acknowledge Météo-France and especially Pierre Tabary and Valérie Vogt, and the “Direction Eau et Assainissement” of Seine-Saint-Denis and especially Natalija Stancic and François Chaumeau, for providing respectively the radar rainfall estimates and the rain gauges data in an easily exploitable format. The authors greatly acknowledge partial financial support from the Chair “Hydrology for Resilient Cities” (sponsored by Veolia) of Ecole des Ponts ParisTech, and the EU INTERREG
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