Statistical analysis of error propagation from radar rainfall to hydrological models

Hydrology and Earth System Sciences Open Access Ocean Science Open Access Solid Earth Open Access The Cryosphere Open Access Hydrol. Earth Syst. Sci., 17, 1445–1453, 2013 www.hydrol-earth-syst-sci.net/17/1445/2013/ doi:10.5194/hess-17-1445-2013 © Author(s) 2013. CC Attribution 3.0 License. cess Model Development Statistical analysis of error propagation from radar rainfall to hydrological models D. Zhu1 , D. Z. Peng2 , and I. D. Cluckie1 1 Department of Civil Engineering, Swansea University, Swansea, UK 2 College of Water Sciences, Beijing Normal University, Beijing, China Correspondence to: D. Z. Peng () Received: 6 August 2012 – Published in Hydrol. Earth Syst. Sci. Discuss.: 10 September 2012 Revised: 22 March 2013 – Accepted: 25 March 2013 – Published: 17 April 2013 Abstract. This study attempts to characterise the manner with which inherent error in radar rainfall estimates input influence the character of the stream flow simulation uncertainty in validated hydrological modelling. An artificial statistical error model described by Gaussian distribution was developed to generate realisations of possible combinations of normalised errors and normalised bias to reflect the identified radar error and temporal dependence. These realisations were embedded in the 5 km/15 min UK Nimrod radar rainfall data and used to generate ensembles of stream flow simulations using three different hydrological models with varying degrees of complexity, which consists of a fully distributed physically-based model MIKE SHE, a semidistributed, lumped model TOPMODEL and the unit hydrograph model PRTF. These models were built for this purpose and applied to the Upper Medway Catchment (220 km2 ) in South-East England. The results show that the normalised bias of the radar rainfall estimates was enhanced in the simulated stream flow and also the dominate factor that had a significant impact on stream flow simulations. This preliminary radar-error-generation model could be developed more rigorously and comprehensively for the error characteristics of weather radars for quantitative measurement of rainfall. 1 Introduction Recently, the advances of radar rainfall estimates with high spatial and temporal resolution have demonstrated the prospect of improving the accuracy of rainfall inputs on which the accuracy of stream flow simulation and realtime flood forecasting through hydrological models depends. There is a wide range of studies which have focused on using weather radars for quantitative measurement of rainfall in various hydrological models in order to evaluate the radar performance in different hydrological applications, especially in flood forecasting (Collier and Knowles, 1986; Owens, 1986; Cluckie and Owens, 1987; Cluckie et al., 1989; Bell and Moore, 1998a, b; Borga, 2001; Carpenter et al., 2001; Tachikawa et al., 2002; Hossain et al., 2004; Reichel et al., 2008; Zhu and Cluckie, 2011); in particular, the value of radar-based data from the UK Nimrod system has been highlighted repeatedly, for example, in two severe flooding events during 1998 (at Easter over the Midlands and in late October over Wales), estimates of surface rainfall derived from radar data provided evidence of the extent and severity of the rainfall events. However, the advantage of the weather radar rainfall estimates has been limited by a variety of sources of uncertainty in the radar reflectivity process, including random and systematic errors such as the hardware calibration, which acquires accurate measurements of transmitted power, bandwidth, antenna gain, wavelength and pulse width (ProbertJones, 1962; Battan, 1973), the deflection of the radar beam (anomalous propagation), non-meteorological echoes (clutter), signal attenuation, orographic enhancement, radar beam overshooting, variation of the vertical profile of reflectivity (VPR), extrapolation of the measurements to the ground, drop size distribution, Z-R relationship, sampling effects and bright band, all of which can be referred to in the numerous discussions on radar rainfall estimation errors (Harrold et al., 1974; Browning, 1978; Wilson and Brandes, 1979; Duncan et al., 1993; Fabry et al., 1992, 1994; Kitchen, 1997; Krajewski and Smith, 2002; Rico-Ramirez et al., 2007). Published by Copernicus Publications on behalf of the European Geosciences Union. 1446 D. Zhu et al.: Statistical analysis of error propagation from radar rainfall to hydrological models More importantly, all these radar-related errors cannot be separated from the model errors when radar rainfall estimates are inputted to the hydrological models, and therefore the added benefit of radar rainfall data was devalued. Although corresponding correction techniques can be applied to improve the quality of the radar rainfall estimation (Collier et al., 1983; Hardaker et al., 1995; Collier, 1996; Fulton et al., 1998; Harrison et al., 2000), the radar rainfall estimates are always at risk of being contaminated by the error from different sources due to a great deal of uncertainty. Therefore, some studies have been conducted to analyse the impact of radar rainfall estimation errors on hydrological applications. Collier and Knowles (1986) suggested that the impact of the errors in the precipitation estimation on the rainfall-runoff process varies, in specific circumstances, the errors will be less in the flow simulation, but in other circumstances, the error will be magnified. In addition, Wyss et al. (1990) argued that the errors in runoff predictions are more significantly caused by the errors introduced in the transformation of rainfall to runoff than the errors of radarestimated precipitation input. Winchell et al. (1998) concluded that the errors in radar rainfall estimates can be separated into two categories: the errors come from the conversion of reflectivity to rainfall and the errors due to the misrepresentation of rainfall field in spatial and temporal domain. And he pointed out that infiltration-excess runoff generation is much more sensitive than saturation-excess runoff generation to both types of precipitation uncertainty, and the decrease of spatial and temporal resolution will result in the significant reduction of predicted flow in the infiltration-excess runoff model. Pessoa et al. (1993), Vieux and Bedient (1998) and Morin et al. (2005) analysed influence of various Z-R relationships upon simulated hydrographs and indicated that the differences can be significant. Borga (2002) selected different elevation scan angles to evaluate the impact of VPR on the catchment stream flow through a lumped hydrological model. Vivoni et al. (2007) presented the propagation of radar rainfall nowcasting error to flood forecasts in the context of distributed hydrological simulations over a range of catchment size or scales. The above mentioned studies have only focused on individual sources of the radar error. However, in practical applications, separating and estimating t (...truncated)