Regionalised spatiotemporal rainfall and temperature models for flood studies in the Basque Country, Spain

Abstract

A spatial-temporal point process model of rainfall is fitted to data taken from three homogeneous regions in the Basque Country, Spain. The model is the superposition of two spatial-temporal Neyman-Scott processes, in which rain cells are modelled as discs with radii that follow exponential distributions. In addition, the model includes a parameter for the radius of storm discs, so that rain only occurs when both a cell and a storm disc overlap a point. The model is fitted to data for each month, taken from each of the three homogeneous regions, using a modified method of moments procedure that ensures a smooth seasonal variation in the parameter estimates. <br><br> Daily temperature data from twenty three sites are used to fit a stochastic temperature model. A principal component analysis of the maximum daily temperatures across the sites indicates that 92% of the variance is explained by the first component, implying that this component can be used to account for spatial variation. A harmonic equation with autoregressive error terms is fitted to the first principal component. The temperature model is obtained by regressing the maximum daily temperature on the first principal component, an indicator variable for the region, and altitude. This, together with scaling and a regression model of temperature range, enables hourly temperatures to be predicted. Rainfall is included as an explanatory variable but has only a marginal influence when predicting temperatures. <br><br> A distributed model (TETIS; Francés et al., 2007) is calibrated for a selected catchment. Five hundred years of data are simulated using the rainfall and temperature models and used as input to the calibrated TETIS model to obtain simulated discharges to compare with observed discharges. Kolmogorov-Smirnov tests indicate that there is no significant difference in the distributions of observed and simulated maximum flows at the same sites, thus supporting the use of the spatiotemporal models for the intended application

Downscaling future precipitation extremes to urban hydrology scales using a spatio-temporal Neyman–Scott weather generator

“…Rodríguez-Iturbe et al (1987a, b) developed the stochastic point process model in a way to better characterize and describe the precipitation process at the event level. Implementations of the stochastic point process models for spatio-temporal precipitation seem to work satisfactorily at temporal resolutions down to 1 h (Cowpertwait and O'Connell, 1997;Cowpertwait, 2006;Burton et al, 2008Burton et al, , 2010aCowpertwait et al, 2013). Also, downscaling to finer resolution than 1 h is inherently problematic as the scaling properties change below this point (Nguyen et al, 2002;Molnar and Burlando, 2008).…”

“…At the daily level, the Neyman-Scott rectangular pulses (NSRP) and the spatio-temporal Neyman-Scott rectangular pulses (STNSRP) models (Burton et al, 2008(Burton et al, , 2010aCowpertwait et al, 2013) have shown good skill in downscaling point precipitation extremes. This applies for individual gauges (Sunyer et al, 2012) as well as for spatially averaged precipitation covering large areas considered to have a uniform climate described by relatively few gauges (e.g.…”

“…This applies for individual gauges (Sunyer et al, 2012) as well as for spatially averaged precipitation covering large areas considered to have a uniform climate described by relatively few gauges (e.g. five gauges for a 4000 km 2 basin in the Pyrenees; Burton et al, 2010a; three gauges used to calibrate a regional model covering a catchment of 342 km 2 in the Basque Country; Cowpertwait et al, 2013). This is, however, inadequate in urban hydrology where the rainfall dynamics that cause the effects under study occur on much smaller time and space scales.…”

“…WGs can take different forms (Cowpertwait, 2006;Vrac et al, 2007;Burton et al, 2008;Arnbjerg-Nielsen and Onof, 2009;Chen et al, 2010;Cowpertwait et al, 2013) but they generally work by analysing observed precipitation (and possibly other weather-related variables) and use the obtained statistics to create artificial stochastic precipitation (or weather) time series that replicate the behaviour of the observations with respect to these statistics (Maraun et al, 2010;Sunyer et al, 2012). Perturbation of the WG to yield output time series representing future climates is then possible by application of climate change factors calculated from output from RCMs (operation at too large space scales and timescales) to relevant parameters of the WG (that operates at the right space scales and timescale).…”