Regionalised spatiotemporal rainfall and temperature models for flood studies in the Basque Country, Spain
A spatiotemporal 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 spatiotemporal 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.
Daily temperature data from 23 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.
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.