Anteproyecto

Rainfall uncertainty in hydrological modelling: An evaluation of multiplicative error models
Hilary McMillana, , , Bethanna Jacksonb, Martyn Clarka, Dmitri Kavetskic and Ross Woodsa
a National Institute of Water and Atmospheric Research, Christchurch, New Zealand
b School of Geography, Environment and Earth Sciences, Victoria University of Wellington, New Zealand
c School of Engineering,University of Newcastle, Callaghan, Australia
Received 5 August 2010;  
revised 18 January 2011;  
accepted 21 January 2011.  
This manuscript was handled by A. Bardossy, Editor-in-Chief, with the assistance of Attilio Castellarin, Associate Editor. 
Available online 27 January 2011. 

Summary
This paper presents an investigation of rainfall error models used in hydrological model calibrationand prediction. Traditional calibration methods assume input error to be negligible: an assumption which can lead to bias in parameter estimation and compromise model predictions. In response, a growing number of studies now specify an error model for rainfall input, usually simple in form due to both difficulties in understanding sampling errors in rainfall, and to computational constraintsduring parameter estimation. Such rainfall error models have not typically been validated against experimental evidence. In this study we use data from a dense gauge/radar network in the Mahurangi catchment (New Zealand) to directly evaluate the form of basic statistical rainfall error models. For this catchment, our results confirm the suitability of a multiplicative error formulation for correctingmean catchment rainfall values during high-rainfall periods (e.g., intensities over 1 mm/h); or for longer timesteps at any rainfall intensity (timestep 1 day or greater). We show that the popular lognormal multiplier distribution provides a relatively close approximation to the true error characteristics but does not capture the distribution tails, especially during heavy rainfall where inputerrors would have important consequences for runoff prediction. Our research highlights the dependency of rainfall error structure on the data timestep.
Research highlights
► Rainfall error analysis to construct input error structures for hydrological models. ► Dense raingauge network and high-resolution radar used. ► Multiplicative error formulation found to be suitable. ► Popular lognormal fitdoes not capture tails of multiplier distribution. ► Dependency of rainfall error structure on model timestep.
Keywords: Hydrology; Rainfall; Radar; Error models; Input uncertainty
Article Outline
1. 
Introduction
2. 
Sources of rainfall input uncertainty in hydrological models
3. 
Error models for rainfall measurements
4. 
Site and campaign description
5. 
Analysis
5.1. Rainfall state5.1.1. Raingauges
5.1.2. Radar
5.2. Rainfall quantity
5.2.1. Distributions of rainfall totals
5.2.2. Raingauge vs. radar data
5.2.3. Consistency in rainfall profiles
6. 
Discussion and conclusions
Acknowledgements
References
1. Introduction
Adequate characterization of rainfall inputs is fundamental to success in rainfall–runoff modelling: no model, however well-founded in physicaltheory or empirically justified by past performance, can produce accurate runoff predictions if forced with inaccurate rainfall data (e.g., Beven, 2004). The impact of rainfall errors on predicted flow has been highlighted by many authors, including (Sun et al., 2000),(Kavetski et al., 2002), (Kavetski et al., 2006a), (Bárdossy and Das, 2008) and (Moulin et al., 2009). From a management perspective,inaccuracies in rainfall inputs directly compromise model predictions and hence also compromise robust decision-making on water and risk management options. An accurate statistical representation of rainfall errors has potential for real-time bias correction and uncertainty estimation of streamflow forecasts. Furthermore, errors in rainfall reduce our ability to identify other sources of error...