Elsevier

Atmospheric Research

Volume 138, 1 March 2014, Pages 125-138
Atmospheric Research

Influence of small scale rainfall variability on standard comparison tools between radar and rain gauge data

https://doi.org/10.1016/j.atmosres.2013.11.008Get rights and content

Highlights

  • Observation scale gap between radar and rain gauge is investigated.

  • Standard comparisons are revisited in the light of small scale rainfall variability.

  • A downscaling process is validated using dense network of point measurement device.

  • New target values and uncertainty ranges are estimated for standard comparison scores.

Abstract

Rain gauges and weather radars do not measure rainfall at the same scale; roughly 20 cm for the former and 1 km for the latter. This significant scale gap is not taken into account by standard comparison tools (e.g. cumulative depth curves, normalized bias, RMSE) despite the fact that rainfall is recognized to exhibit extreme variability at all scales. In this paper we suggest to revisit the debate of the representativeness of point measurement by explicitly modelling small scale rainfall variability with the help of Universal Multifractals. First the downscaling process is validated with the help of a dense networks of 16 disdrometers (in Lausanne, Switzerland), and one of 16 rain gauges (Bradford, United Kingdom) both located within a 1 km2 area. Second this downscaling process is used to evaluate the impact of small scale (i.e. sub-radar pixel) rainfall variability on the standard indicators. This is done with rainfall data from the Seine-Saint-Denis County (France). Although not explaining all the observed differences, it appears that this impact is significant which suggests changing some usual practice.

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

References (39)

  • J.-F. Royer et al.

    Multifractal analysis of the evolution of simulated precipitation over France in a climate scenario

    C. R. Geosci.

    (2008)
  • D. Schertzer et al.

    Hard and soft multifractal processes

    Physica A

    (1992)
  • S. Verrier et al.

    Multifractal analysis of African monsoon rain fields, taking into account the zero rain-rate problem

    J. Hydrol.

    (2010)
  • A. Biaou et al.

    Analyse multifractale des précipitations dans un scénario GIEC du CNRM

  • J.M. Chambers et al.

    A method for simulating stable random variables

    J. Am. Stat. Assoc.

    (1976)
  • L. de Montera et al.

    The effect of rain–no rain intermittency on the estimation of the universal multifractals model parameters

    J. Hydrometeorol.

    (2009)
  • E.M. Douglas et al.

    Probable maximum precipitation estimation using multifractals: application in the eastern United States

    J. Hydrometeorol.

    (2003)
  • J. Figueras i Ventura et al.

    Long-term monitoring of French polarimetric radar data quality and evaluation of several polarimetric quantitative precipitation estimators in ideal conditions for operational implementation at C-band

    Q. J. R. Meteorol. Soc.

    (2012)
  • A. Gires et al.

    Analyses multifractales et spatio-temporelles des precipitations du modele Meso-NH et des donnees radar

    Hydrol. Sci. J.

    (2011)
  • Cited by (65)

    • Coupled prediction of flash flood response and debris flow occurrence: Application on an alpine extreme flood event

      2018, Journal of Hydrology
      Citation Excerpt :

      We refer to Marra et al. (2014) for a detailed description of algorithms and correction procedures. The assessment of radar rainfall estimation accuracy has been performed by comparison with rain gauge data from 14 stations and it has been carried out on the event-cumulated values in order to minimize the sampling errors between rain gauges and radar pixel (Gires et al., 2014; Peleg et al., 2013). Fig. 2 shows a scatter plot of the event rainfall accumulation as observed by gauges and co-located radar pixels.

    • Multifractal characterisation of a simulated surface flow: A case study with Multi-Hydro in Jouy-en-Josas, France

      2018, Journal of Hydrology
      Citation Excerpt :

      For three events the data recorded with the help of a rain gauge operated by the SIAVB located a few hundred meters south of the catchment at the “Bassin des Bas Près” is also available. Because of (i) the standard 0.2 mm discretization issue of the tipping bucket rain gauge (data is number of tips equal to 0.2 mm) which prevents it from providing reliable intensity, (ii) the gap between the observation scales of the two measuring devices (see Gires et al., 2014b, for an in-depth analysis of this issue) and (iii) the fact that the rain gauge is furthermore outside of the catchment; it is not possible to use the rain gauge data for other purpose than a rough check of the accuracy of radar data. It is done by comparing the cumulative volumes of rainfall for each studied event which are displayed in Table 1 along with their main features.

    View all citing articles on Scopus
    View full text