Effects of parameter perturbation on daily precipitation models in Southern Spain using the NAO index

The effects of the North Atlantic Oscillation (NAO) on a second order-mixed exponential stochastic model (MC2ME) of daily precipitation were detected for 33 weather stations located in southern Spain. The stations exhibit a wide range of elevations and distance from the Atlantic Ocean and consequently have large variations of mean annual precipitation and mean annual number of wet days. Annually, periodic parameters were obtained by numerical maximum likelihood fitting of Fourier series utilizing 54 years of concurrent data for each station. NAO effects were determined by perturbing these parameters by functions of the NAO Index. The Akaike information criterion (AIC) was used to select the appropriate number of Fourier harmonics for each parameter and to determine if the non-stationary model with perturbed parameters was superior to the annually periodic model. Likelihood ratio tests showed that improvements in log likelihood functions by NAO perturbations of the logits of transition probabilities and the periodic function of the mean of the mixed exponential were highly significant. Improvements in the log likelihood functions were obtained by perturbing only during the winter months. Limited goodness of fit analyses by simulations showed that the NAO perturbations led to increased variance of annual precipitation and greater ranges of annual maximum and minimum precipitation as compared to simulations with annually periodic parameters.