Quantifying the impact of small scale unmeasured rainfall variability on urban runoff through multifractal downscaling: A case study

Summary This paper aims at quantifying the uncertainty on urban runoff associated with the unmeasured small scale rainfall variability, i.e. at a resolution finer than 1 km × 1 km × 5 min which is usually available with C-band radar networks. A case study is done on the 900 ha urban catchment of Cranbrook (London). A frontal and a convective rainfall event are analysed. An ensemble prediction approach is implemented, that is to say an ensemble of realistic downscaled rainfall fields is generated with the help of universal multifractals, and the corresponding ensemble of hydrographs is simulated. It appears that the uncertainty on the simulated peak flow is significant, reaching for some conduits 25% and 40% respectively for the frontal and the convective events. The flow corresponding the 90% quantile, the one simulated with radar distributed rainfall, and the spatial resolution are power law related.

[1]  Shaun Lovejoy,et al.  Causal space‐time multifractal processes: Predictability and forecasting of rain fields , 1996 .

[2]  A. Gires,et al.  Analyses multifractales et spatio-temporelles des précipitations du modèle Méso-NH et des données radar , 2011 .

[3]  L. Barthès,et al.  Multifractal analysis of African monsoon rain fields, taking into account the zero rain-rate problem , 2010 .

[4]  L. Barthès,et al.  The Effect of Rain–No Rain Intermittency on the Estimation of the Universal Multifractals Model Parameters , 2009 .

[5]  Shaun Lovejoy,et al.  Multifractal methods applied to rain forecast using radar data , 2007 .

[6]  Julien Lhomme,et al.  Applying a GIS-based geomorphological routing model in urban catchments , 2004 .

[7]  Shaun Lovejoy,et al.  Nonlinear Processes in Geophysics Scaling and multifractal fields in the solid earth and topography , 2008 .

[8]  D. Schertzer,et al.  Scaling turbulent atmospheric stratification. III: Space–time stratification of passive scalars from lidar data , 2008 .

[9]  D. Nykanen.  Linkages between Orographic Forcing and the Scaling Properties of Convective Rainfall in Mountainous Regions , 2008 .

[10]  Shaun Lovejoy,et al.  Multifractal Cascade Dynamics and Turbulent Intermittency , 1997 .

[11]  Guido Vaes,et al.  Towards a roadmap for use of radar rainfall data in urban drainage , 2004 .

[12]  Edward C. Waymire,et al.  A statistical analysis of mesoscale rainfall as a random cascade , 1993 .

[13]  Dušan Prodanović,et al.  Overland flow and pathway analysis for modelling of urban pluvial flooding , 2009 .

[14]  Nicola Rebora,et al.  A comparison of stochastic models for spatial rainfall downscaling , 2003 .

[15]  D. Schertzer,et al.  The simulation of universal multifractals. , 1993 .

[16]  Daniel Schertzer,et al.  Multifractal analysis of the evolution of simulated precipitation over France in a climate scenario , 2008 .

[17]  Shaun Lovejoy,et al.  Universal Multifractals: Theory and Observations for Rain and Clouds , 1993 .

[18]  R. Deidda.  Rainfall downscaling in a space‐time multifractal framework , 2000 .

[19]  Theo G. Schmitt,et al.  Analysis and modeling of flooding in urban drainage systems , 2004 .

[20]  Shaun Lovejoy,et al.  Multifractals, Generalized Scale Invariance and Complexity in Geophysics , 2011, International Journal of Bifurcation and Chaos in Applied Sciences and Engineering.

[21]  W. Eichinger,et al.  Multiscaling analysis of high resolution space-time lidar-rainfall , 2009 .

[22]  Nicola Rebora,et al.  Rainfall downscaling and flood forecasting: a case study in the Mediterranean area , 2006 .

[23]  Patrick Arnaud,et al.  Influence of rainfall spatial variability on flood prediction , 2002 .

[24]  D. Schertzer,et al.  Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes , 1987 .

[25]  Merab Menabde,et al.  Multiscaling properties of rainfall and bounded random cascades , 1997 .

[26]  D. Schertzer,et al.  Influence of the zero-rainfall on the assessment of the multifractal parameters , 2012 .

[27]  Johan Grasman,et al.  Multifractal analysis of 15-min and daily rainfall from a semi-arid region in Portugal , 1999 .

[28]  D. A. Woolhiser,et al.  Impact of small-scale spatial rainfall variability on runoff modeling , 1995 .

[29]  Nicola Rebora,et al.  RainFARM: Rainfall Downscaling by a Filtered Autoregressive Model , 2006 .

[30]  Philip B. Bedient,et al.  Assessing urban hydrologic prediction accuracy through event reconstruction , 2004 .

[31]  Vijay P. Singh,et al.  Effect of spatial and temporal variability in rainfall and watershed characteristics on stream flow hydrograph , 1997 .

[32]  C. Maksimovic,et al.  Sensitivity analysis of surface runoff generation in urban flood forecasting. , 2010, Water science and technology : a journal of the International Association on Water Pollution Research.

[33]  Dawn Harrison,et al.  Improving precipitation estimates from weather radar using quality control and correction techniques , 2000 .

[34]  François G. Schmitt,et al.  Modeling of rainfall time series using two-state renewal processes and multifractals , 1998 .

[35]  D. Schertzer,et al.  The HYDROP experiment: an empirical method for the determination of the continuum limit in rain , 2001 .

[36]  Giuseppe T. Aronica,et al.  Studying the hydrological response of urban catchments using a semi-distributed linear non-linear model , 2000 .

[37]  Daniel Schertzer,et al.  No monsters, no miracles: in nonlinear sciences hydrology is not an outlier! , 2010 .

[38]  Merab Menabde,et al.  Factors affecting multiscaling analysis of rainfall time series , 1997 .

[39]  C. Mallows,et al.  A Method for Simulating Stable Random Variables , 1976 .

[40]  Shaun Lovejoy,et al.  On the simulation of continuous in scale universal multifractals, part I: Spatially continuous processes , 2010, Comput. Geosci..

[41]  Victor Koren,et al.  Runoff response to spatial variability in precipitation: an analysis of observed data , 2004 .

[42]  A. Kolmogorov.  A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number , 1962, Journal of Fluid Mechanics.

[43]  Jonas Olsson,et al.  Multifractal analysis of daily spatial rainfall distributions , 1996 .

[44]  J. Olsson.  Statistical atmospheric downscaling of short-term extreme rainfall by neural networks , 2001 .

[45]  Vijay P. Singh,et al.  The influence of the pattern of moving rainstorms on overland flow , 2002 .

[46]  Daniel Harris,et al.  Orographic influences on the multiscale statistical properties of precipitation , 2003 .

[47]  Thomas M. Over,et al.  A space‐time theory of mesoscale rainfall using random cascades , 1996 .

[48]  S. Lovejoy,et al.  - 1-An Introduction to Stochastic Multifractal Fields , 2004 .

[49]  E. Foufoula‐Georgiou,et al.  Incorporating the spatio-temporal distribution of rainfall and basin geomorphology into nonlinear analyses of streamflow dynamics , 2005 .