Multivariate distributed ensemble generator: A new scheme for ensemble radar precipitation estimation over temperate maritime climate

Summary It is broadly recognized that large uncertainties are associated with radar rainfall (RR) estimates, which could propagate in the hydrologic forecast system and contaminate its final outcomes. Ensemble generation of probable true rainfall is an elegant and practical solution to characterize the uncertainty of RR estimates and behavior in the hydrologic forecast system. In this study, we have proposed a fully formulated uncertainty model that can statistically quantify the characteristics of the RR errors and their spatial and temporal structure, which is a novel method of its kind in the radar data uncertainty field. The error model is established based on the distribution of gauge rainfall conditioned on radar rainfall (GR|RR). It’s spatial and temporal dependencies are simulated based on the t-copula function. With this proposed error model, a Multivariate Distributed Ensemble Generator (MDEG) driven by the copula and autoregressive filter is designed and applied in the Brue catchment (135 km 2 ), an extensively gauged site in the United Kingdom. The products from MDEG include a time series of ensemble rainfall fields with each of them representing a probable true rainfall. A series of tests show that the ensemble fields generated by MDEG have realistically maintained the spatial and temporal structure of the random error in RR as they have relatively low mean absolute errors (MAEs) of spatio-temporal correlation towards the observed ones. In addition, the results show that the simulated uncertainty bands derived by the 500 realizations of ensemble rainfall encompass most of the reference rain gauge measurements, indicating that the proposed scheme is statistically reliable.

[1]  V. Isham,et al.  Design of the HYREX raingauge network , 2000 .

[2]  Keith Beven,et al.  Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology , 2001 .

[3]  Mark L. Morrissey,et al.  Using sparse raingages to test satellite‐based rainfall algorithms , 1991 .

[4]  Noel A Cressie,et al.  Statistics for Spatial Data. , 1992 .

[5]  Anne-Catherine Favre,et al.  Importance of Tail Dependence in Bivariate Frequency Analysis , 2007 .

[6]  Roman Krzysztofowicz,et al.  The case for probabilistic forecasting in hydrology , 2001 .

[7]  Dawei Han,et al.  Sensitivity and uncertainty analysis of mesoscale model downscaled hydro‐meteorological variables for discharge prediction , 2014 .

[8]  Grzegorz J. Ciach,et al.  Local Random Errors in Tipping-Bucket Rain Gauge Measurements , 2003 .

[9]  Yannick Malevergne,et al.  Testing the Gaussian copula hypothesis for financial assets dependences , 2001, cond-mat/0111310.

[10]  Witold F. Krajewski,et al.  A Monte Carlo Study of rainfall sampling effect on a distributed catchment model , 1991 .

[11]  András Bárdossy,et al.  Copula‐based uncertainty modelling: application to multisensor precipitation estimates , 2010 .

[12]  Mario R. Melchiori.  Which Archimedean Copula is the Right One? , 2003 .

[13]  Konstantine P. Georgakakos,et al.  Impacts of parametric and radar rainfall uncertainty on the ensemble streamflow simulations of a distributed hydrologic model , 2004 .

[14]  Konstantine P. Georgakakos,et al.  A methodology for assessing the utility of distributed model forecast applications in an operational environment , 2003 .

[15]  M. Borga,et al.  Long‐term assessment of bias adjustment in radar rainfall estimation , 2002 .

[16]  M. L. Morrissey,et al.  Comparison of Two Satellite-based Rainfall Algorithms Using Pacific Atoll Raingage Data , 1993 .

[17]  Witold F. Krajewski,et al.  Radar–Rain Gauge Comparisons under Observational Uncertainties , 1999 .

[18]  Rafael Schmidt,et al.  Tail dependence for elliptically contoured distributions , 2002, Math. Methods Oper. Res..

[19]  D. B. Preston.  Spectral Analysis and Time Series , 1983 .

[20]  Anthony G. Barnston.  An Empirical Method of Estimating Raingage and Radar Rainfall Measurement Bias and Resolution , 1991 .

[21]  Massimiliano Zappa,et al.  Flash-flood early warning using weather radar data: from nowcasting to forecasting , 2013 .

[22]  R. Mantilla,et al.  Impact of radar‐rainfall error structure on estimated flood magnitude across scales: An investigation based on a parsimonious distributed hydrological model , 2012 .

[23]  Eric Bouyé,et al.  Copulas for Finance - A Reading Guide and Some Applications , 2000 .

[24]  Witold F. Krajewski,et al.  Towards probabilistic forecasting of flash floods: The combined effects of uncertainty in radar-rainfall and flash flood guidance , 2010 .

[25]  E. Habib,et al.  Application of a radar‐rainfall uncertainty model to the NWS multi‐sensor precipitation estimator products , 2013 .

[26]  András Bárdossy,et al.  Conditional simulation of remotely sensed rainfall data using a non-Gaussian v-transformed copula , 2010 .

[27]  Roman Krzysztofowicz,et al.  Bayesian theory of probabilistic forecasting via deterministic hydrologic model , 1999 .

[28]  Witold F. Krajewski,et al.  A method for filtering out raingauge representativeness errors from the verification distributions of radar and raingauge rainfall , 2004 .

[29]  J. M. Bevan,et al.  Rank Correlation Methods , 1949 .

[30]  Kurt K. Benke,et al.  Parameter uncertainty, sensitivity analysis and prediction error in a water-balance hydrological model , 2008, Math. Comput. Model..

[31]  G. Villarini,et al.  Product-Error-Driven Uncertainty Model for Probabilistic Quantitative Precipitation Estimation with NEXRAD Data , 2007 .

[32]  R. Moore,et al.  Accuracy of rainfall measurement for scales of hydrological interest , 2000 .

[33]  Emmanouil N. Anagnostou,et al.  Uncertainty Quantification of Mean-Areal Radar-Rainfall Estimates , 1999 .

[34]  Dawei Han,et al.  The impact of raindrop drift in a three-dimensional wind field on a radar–gauge rainfall comparison , 2013 .

[35]  Qingyun Duan,et al.  An integrated hydrologic Bayesian multimodel combination framework: Confronting input, parameter, and model structural uncertainty in hydrologic prediction , 2006 .

[36]  Carlo De Michele,et al.  Extremes in Nature : an approach using Copulas , 2007 .

[37]  V. Singh,et al.  Copula‐based spatio‐temporal patterns of precipitation extremes in China , 2013 .

[38]  Alexis Berne,et al.  Toward an error model for radar quantitative precipitation estimation in the Cevennes-Vivarais region, France ERAD 2006 , 2010 .

[39]  Dawei Han,et al.  Appraisal of SMOS soil moisture at a catchment scale in a temperate maritime climate , 2013 .

[40]  B. Bobée,et al.  Multivariate hydrological frequency analysis using copulas , 2004 .

[41]  A. Bárdossy,et al.  Geostatistical interpolation using copulas , 2008 .

[42]  Emad Habib,et al.  Analysis of radar-rainfall error characteristics and implications for streamflow simulation uncertainty , 2008 .

[43]  M. Kendall.  Rank Correlation Methods , 1949 .

[44]  Alberto Montanari,et al.  Large sample behaviors of the generalized likelihood uncertainty estimation (GLUE) in assessing the uncertainty of rainfall‐runoff simulations , 2005 .

[45]  S. Sorooshian,et al.  A Shuffled Complex Evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters , 2002 .

[46]  D. Neeleman,et al.  A Monte-Carlo study , 1973 .

[47]  Qi Zhang,et al.  Parameter and modeling uncertainty simulated by GLUE and a formal Bayesian method for a conceptual hydrological model , 2010 .

[48]  H. Joe.  Multivariate models and dependence concepts , 1998 .

[49]  Dawei Han,et al.  Machine Learning Techniques for Downscaling SMOS Satellite Soil Moisture Using MODIS Land Surface Temperature for Hydrological Application , 2013, Water Resources Management.

[50]  Miguel A. Rico-Ramirez,et al.  Rainfall Estimation with an Operational Polarimetric C-band Radar in the UK: Comparison with a Gauge Network and Error Analysis , 2011 .

[51]  Dawei Han,et al.  Modelling radar-rainfall estimation uncertainties using elliptical and Archimedean copulas with different marginal distributions , 2014 .

[52]  Witold F. Krajewski,et al.  Synthesis of radar rainfall data , 1985 .

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

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

[55]  K. Schröter,et al.  Implications of radar rainfall estimates uncertainty on distributed hydrological model predictions , 2011 .

[56]  Vijay P. Singh,et al.  Copula-based risk evaluation of droughts across the Pearl River basin, China , 2012, Theoretical and Applied Climatology.

[57]  A. Seed.  A Dynamic and Spatial Scaling Approach to Advection Forecasting , 2001 .

[58]  Torben O. Sonnenborg,et al.  Impact of Precipitation Spatial Resolution on the Hydrological Response of an Integrated Distributed Water Resources Model , 2011 .

[59]  K. Beven.  Rainfall-Runoff Modelling: The Primer , 2012 .

[60]  Ian Cluckie,et al.  Bright‐band detection from radar vertical reflectivity profiles , 2007 .

[61]  Timothy C. Coburn,et al.  Geostatistics for Natural Resources Evaluation , 2000, Technometrics.

[62]  R. Nelsen.  An Introduction to Copulas , 1998 .

[63]  U. Germann,et al.  REAL—Ensemble radar precipitation estimation for hydrology in a mountainous region , 2009 .

[64]  M. Sklar.  Fonctions de repartition a n dimensions et leurs marges , 1959 .

[65]  Witold F. Krajewski,et al.  Product‐error‐driven generator of probable rainfall conditioned on WSR‐88D precipitation estimates , 2009 .

[66]  Renzo Rosso,et al.  Extremes in Nature , 2007 .

[67]  James Xu,et al.  Statistical modelling and inference for multivariate and longitudinal discrete response data , 1996 .