Spatial variability of extreme rainfall at radar subpixel scale

Extreme rainfall is quantified in engineering practice using Intensity–Duration–Frequency curves (IDF) that are traditionally derived from rain-gauges and more recently also from remote sensing instruments, such as weather radars. These instruments measure rainfall at different spatial scales: rain-gauge samples rainfall at the point scale while weather radar averages precipitation on a relatively large area, generally around 1 km2. As such, a radar derived IDF curve is representative of the mean areal rainfall over a given radar pixel and neglects the within-pixel rainfall variability. In this study, we quantify subpixel variability of extreme rainfall by using a novel space-time rainfall generator (STREAP model) that downscales in space the rainfall within a given radar pixel. The study was conducted using a unique radar data record (23 years) and a very dense rain-gauge network in the Eastern Mediterranean area (northern Israel). Radar-IDF curves, together with an ensemble of point-based IDF curves representing the radar subpixel extreme rainfall variability, were developed fitting Generalized Extreme Value (GEV) distributions to annual rainfall maxima. It was found that the mean areal extreme rainfall derived from the radar underestimate most of the extreme values computed for point locations within the radar pixel (on average, ?70%). The subpixel variability of rainfall extreme was found to increase with longer return periods and shorter durations (e.g. from a maximum variability of 10% for a return period of 2 years and a duration of 4 h to 30% for 50 years return period and 20 min duration). For the longer return periods, a considerable enhancement of extreme rainfall variability was found when stochastic (natural) climate variability was taken into account. Bounding the range of the subpixel extreme rainfall derived from radar-IDF can be of a major importance for different applications that require very local estimates of rainfall extremes.

[1]  U. Shamir,et al.  The characteristic time scale for basin hydrological response using radar data , 2001 .

[2]  N. Jensen,et al.  Spatial Variability of Rainfall: variations within a single radar pixel , 2005 .

[3]  Henrik Madsen,et al.  Quantification of the spatial variability of rainfall based on a dense network of rain gauges , 2010 .

[4]  Demetris Koutsoyiannis,et al.  A mathematical framework for studying rainfall intensity-duration-frequency relationships , 1998 .

[5]  A stochastic model of space‐time variability of mesoscale rainfall: Statistics of spatial averages , 2003 .

[6]  Modelling the Space-Time Structure of Precipitation and its Impact on Basin Response , 2013 .

[7]  J. Arblaster,et al.  Assessing trends in observed and modelled climate extremes over Australia in relation to future projections , 2007 .

[8]  Christian Onof,et al.  Quantifying the impact of small scale unmeasured rainfall variability on urban runoff through multifractal downscaling: A case study , 2012 .

[9]  P. Moran.  The Interpretation of Statistical Maps , 1948 .

[10]  Nadav Peleg,et al.  Radar subpixel-scale rainfall variability and uncertainty: lessons learned from observations of a dense rain-gauge network , 2013 .

[11]  H. Leijnse,et al.  Sensitivity of power functions to aggregation: Bias and uncertainty in radar rainfall retrieval , 2014 .

[12]  C. Price,et al.  Flash flood prediction using an uncalibrated hydrological model and radar rainfall data in a Mediterranean watershed under changing hydrological conditions , 2010 .

[13]  Remko Uijlenhoet,et al.  Geostatistical simulation of two‐dimensional fields of raindrop size distributions at the meso‐γ scale , 2009 .

[14]  J. R. Wallis,et al.  Correction to "Some statistics useful in regional frequency analysis" by J. R. M. Hosking and J. R. Wallis In the paper "Some statistics useful in regional frequency , 1995 .

[15]  Witold F. Krajewski,et al.  An analysis of small-scale rainfall variability in different climatic regimes , 2003 .

[16]  Witold F. Krajewski,et al.  Analysis and modeling of spatial correlation structure in small-scale rainfall in Central Oklahoma , 2006 .

[17]  Efrat Morin,et al.  Spatial characteristics of radar-derived convective rain cells over southern Israel , 2006 .

[18]  R. Weingartner,et al.  Inter-annual variability of runoff and climate within the Upper Rhine River basin, 1808–2007 , 2011 .

[19]  R. Geary,et al.  The Contiguity Ratio and Statistical Mapping , 1954 .

[20]  W. Krajewski,et al.  On the estimation of radar rainfall error variance , 1999 .

[21]  Watted,et al.  Critical review of the evolution of the design storm event concept , 2013 .

[22]  G. Pegram,et al.  Downscaling rainfields in space and time, using the String of Beads model in time series mode , 2001 .

[23]  Robust estimates of climate-induced hydrological change in a temperate mountainous region , 2013, Climatic Change.

[24]  G. Pegram,et al.  High resolution space–time modelling of rainfall: the “String of Beads” model , 2001 .

[25]  C. Svensson,et al.  Review of methods for deriving areal reduction factors: Review of ARF methods , 2010 .

[26]  Jose M. Mejia,et al.  On the transformation of point rainfall to areal rainfall , 1974 .

[27]  R. Moore,et al.  Rainfall and sampling uncertainties: A rain gauge perspective , 2008 .

[28]  W. E. Watt,et al.  Design storms for urban drainage design , 1984 .

[29]  H. Madsen,et al.  Assessing future climatic changes of rainfall extremes at small spatio-temporal scales , 2013, Climatic Change.

[30]  M. Borga,et al.  Estimation of debris flow triggering rainfall: Influence of rain gauge density and interpolation methods , 2015 .

[31]  B. Efron.  Bootstrap Methods: Another Look at the Jackknife , 1979 .

[32]  Matthew A. Lackner,et al.  Probability distributions for offshore wind speeds , 2009 .

[33]  Marco Gabella,et al.  Radar-based quantitative precipitation estimation over Mediterranean and dry climate regimes , 2007 .

[34]  M. Parlange,et al.  Statistics of extremes in hydrology , 2002 .

[35]  Witold F. Krajewski,et al.  Initial Validation of the Global Precipitation Climatology Project Monthly Rainfall over the United States , 2000 .

[36]  A. Jenkinson.  The frequency distribution of the annual maximum (or minimum) values of meteorological elements , 1955 .

[37]  Karl Auerswald,et al.  Spatial variability of rainfall on a sub‐kilometre scale , 2009 .

[38]  Alexis Berne,et al.  Quantification of the Small-Scale Spatial Structure of the Raindrop Size Distribution from a Network of Disdrometers , 2012 .

[39]  D. Schertzer,et al.  Impact of spatial and temporal resolution of rainfall inputs on urban hydrodynamic modelling outputs: A multi-catchment investigation , 2015 .

[40]  D. Sharon,et al.  The distribution of rainfall intensity in Israel, its regional and seasonal variations and its climatological evaluation , 1986 .

[41]  Alexis Berne,et al.  Statistical analysis of rainfall intermittency at small spatial and temporal scales , 2011 .

[42]  R. Allen,et al.  Considerations for the use of radar-derived precipitation estimates in determining return intervals for extreme areal precipitation amounts , 2005 .

[43]  J. Olsson,et al.  Climate change impact assessment on urban rainfall extremes and urban drainage: Methods and shortcomings , 2012 .

[44]  Francesco Marra,et al.  Radar rainfall estimation for the identification of debris-flow occurrence thresholds , 2014 .

[45]  Peter Molnar,et al.  On the effects of small scale space–time variability of rainfall on basin flood response , 2014 .

[46]  Murugesu Sivapalan,et al.  Transformation of point rainfall to areal rainfall: Intensity-duration-frequency curves , 1998 .

[47]  Lorenzo Marchi,et al.  Impact of uncertainty in rainfall estimation on the identification of rainfall thresholds for debris flow occurrence , 2014 .

[48]  Witold F. Krajewski,et al.  RADAR-Rainfall Uncertainties , 2010 .

[49]  Francesco Marra,et al.  Use of radar QPE for the derivation of Intensity–Duration–Frequency curves in a range of climatic regimes , 2015 .

[50]  S. Coles,et al.  An Introduction to Statistical Modeling of Extreme Values , 2001 .

[51]  A. Berne,et al.  Stochastic Simulation of Intermittent DSD Fields in Time , 2012 .

[52]  J. R. Wallis,et al.  Regional Frequency Analysis: An Approach Based on L-Moments , 1997 .

[53]  I. Rodríguez‐Iturbe,et al.  The design of rainfall networks in time and space , 1974 .

[54]  S. Rocky Durrans,et al.  Estimation of Depth-Area Relationships using Radar-Rainfall Data , 2002 .

[55]  D. Schertzer,et al.  Multifractal analysis of a semi-distributed urban hydrological model , 2013 .

[56]  Marc B. Parlange,et al.  STATISTICS OF EXTREMES: MODELING ECOLOGICAL DISTURBANCES , 2005 .

[57]  Remko Uijlenhoet,et al.  Extreme value modeling of areal rainfall from weather radar , 2010 .

[58]  Nadav Peleg,et al.  Stochastic convective rain‐field simulation using a high‐resolution synoptically conditioned weather generator (HiReS‐WG) , 2014 .

[59]  J. R. Wallis,et al.  Some statistics useful in regional frequency analysis , 1993 .

[60]  R. García-Bartual,et al.  Estimating maximum expected short-duration rainfall intensities from extreme convective storms , 2001 .

[61]  Aart Overeem,et al.  Extreme rainfall analysis and estimation of depth‐duration‐frequency curves using weather radar , 2009 .

[62]  F. Napolitano,et al.  On the use of radar reflectivity for estimation of the areal reduction factor , 2006 .

[63]  Thomas L. Bell,et al.  A space‐time stochastic model of rainfall for satellite remote‐sensing studies , 1987 .

[64]  Daniele Veneziano,et al.  The areal reduction factor: A multifractal analysis , 2005 .

[65]  Yu Zhang,et al.  On the use of radar-based quantitative precipitation estimates for precipitation frequency analysis , 2015 .

[66]  Taha B. M. J. Ouarda,et al.  Probability distributions of wind speed in the UAE , 2015 .

[67]  Peter Molnar,et al.  A stochastic model for high‐resolution space‐time precipitation simulation , 2013 .

[68]  Nadav Peleg,et al.  Convective rain cells: Radar-derived spatiotemporal characteristics and synoptic patterns over the eastern Mediterranean , 2012 .

[69]  Jonathan R. M. Hosking,et al.  The four-parameter kappa distribution , 1994, IBM J. Res. Dev..

[70]  Jose Maliekal,et al.  The Uncertainty of Simple Spatial Averages Using Rain Gauge Networks , 1995 .

[71]  Mark W. Shephard,et al.  An integrated approach for identifying homogeneous regions of extreme rainfall events and estimating IDF curves in Southern Ontario, Canada: Incorporating radar observations , 2015 .