A ROBUST METHOD OF EVALUATING COASTAL NUMERICAL MODELS : THE GLUE APPROACH

Sophisticated numerical models play an important role in forecasting beach erosion at high risk sites along NSW coastlines. These models contain free parameters that require calibration to available field data and little guidance (beyond the adoption of the default values provided) is presently available to inform the selection of best-fit parameter values. In practice, the means of calibrating erosion models through the optimisation of these parameters often lacks a sufficient consideration of parameter compensation for model error, the impacts of parameter interdependence and parameter-induced model uncertainty. The Generalised Likelihood Uncertainty Estimation (GLUE) method has been previously employed in the field of hydrology and has proven to be a conceptually simple and efficient method to evaluate model sensitivity to parameters, optimum calibrated parameter values and parameter uncertainty. This paper describes the application of the GLUE method to the XBeach storm erosion model, using data from a site in Italy where the XBeach model has been previously applied without such a rigorous calibration method. The results presented demonstrate the more generic effectiveness of GLUE in enhancing the performance of coastal numerical models. The sensitivity of XBeach to each trailed free parameter is determined in a rigorous and transparent manner, and parameter-induced uncertainty bounds are obtained. This enables the modeller to better quantify model skill in predicting observed and potential future erosion. Introduction A number of sites (‘hotspots’) have been identified along the NSW coastline which are susceptible to coastal erosion events and the ability to forecast the potential impact of storm events at these sites would greatly improve the effectiveness coastal protection and emergency response (NSW Office of Environment and Heritage, 2003). To assist coastal managers in the identification of marine storm risk, a number of international projects (Ciavola et al., 2011; Stockdon et al., 2012) have incorporated coastal erosion models into on-line tools which provide real-time beach erosion forecasts. These forecasts must be accompanied by information on prediction uncertainty to allow decision makers to act with confidence, especially when rapid forecasting requires the use of imperfect input data (Plant and Holland, 2011; Kinsela and Hanslow, 2013). To give accurate representations of uncertainty bounds, modellers must be able to reliably calibrate models, recognise model limitations and identify areas in which the physics of the real-world system are not adequately resolved. Several studies have attempted to examine the sources of model uncertainty present in coastal engineering forecasts. Errors propagating through morphological response forecasts have been examined (Baart et al., 2011), with a focus on quantifying uncertainty in input data. A large body of work to-date on the quantification of uncertainty bounds for numerical modelling used in coastal engineering has focused on 2 providing probabilistic estimates of storm erosion (Callaghan et al., 2008; Pender and Karunarathna, 2013). These studies often incorporate Monte Carlo sampling of storm characteristics combined with bootstrapping methods to produce estimates of storm erosion demand spanning a range of time scales (Callaghan et al., 2013; Li et al., 2014). Importantly, such an approach assumes that uncertainties stemming from the model itself are effectively negligible, once the initial calibration process has been completed (Li et al., 2013). It is important in uncertainty estimation to be aware of model structural errors and limit these to ensure that the model is performing optimally. As such, calibration of model free parameters is vital before quantifying model performance. In reality, this crucial calibration process is often approached in a somewhat ‘ad hoc’ fashion, often due to the complex and non-linear interaction of parameters. Algorithms have been applied to simpler models with fewer free parameters, searching through the parameter space to find optimal parameter values by minimizing discrepancies between model results and observational data (Plant, 2004; Ruessink et al., 2007; Dubarbier et al., 2015). Models like XBeach (eXtreme Beach behaviour model) have tended to be analysed in a less rigorous way due to the large number of free model parameters and longer run times. XBeach, a process-based model, is the current `state-of-the-art' model used to predict changes in coastal morphology arising due to storms (Roelvink et al., 2009). Most documented calibrations of XBeach have used modeller experience and one-at-atime variation to determine sensitive parameters, and have varied these selected parameters by only a few values in order to determine the ‘optimal’ parameter set using a skill measure (Roelvink et al., 2009; Harley et al., 2011; Splinter and Palmsten, 2012; Callaghan et al., 2013; Pender and Karunarathna, 2013; Stockdon et al., 2014). A brief examination of these 6 example studies reveals that in each a different parameter subset was found to be sensitive. Few studies (Vousdoukas et al., 2012) have rigorously trailed a broad range of XBeach parameter combinations and values, and no generalised techniques have been applied to examine the impact of model uncertainty due to parameter selection. The Generalised Likelihood Uncertainty Estimation (GLUE) method (formally presented in (Beven and Binley, 1992)) has the potential to address a number of the shortcomings identified above. It is a Monte Carlo based method that provides parameter sensitivity information, reliable parameter values and uncertainty estimation. The GLUE method is based upon the concept of ‘equifinality’, the idea that multiple parameter combinations may produce model runs equally skilful as estimators of observed morphological change in the system (Freer et al., 1996; Beven, 2006). This can be due to the complex and often non-linear interaction between model parameters (Yates et al., 2009), over-parameterization without sufficient observational data to inform parameter selection (Beven, 2006) and, errors in the observational data and model structure. These errors can be termed ‘epistemic’, referring to a lack of knowledge of the system within the model (Efstratiadis and Koutsoyiannis, 2010; Beven and Binley, 2014). For instance, the complex three-dimensional morphology may not be captured in the two-dimensional beach profile surveys, the observational data may not be collected immediately before/after the event allowing sediment transport to occur outside of the model simulation time, or the model may be formulated in such a way that overly simplifies the physics in the system (Dubarbier et al., 2015). Recognizing this, the modeller’s focus is then shifted to finding the most