## 1. Introduction

Seasonal forecast of hydrometeorological variables, such as rainfall, temperature and discharge has been the object of numerous studies, and different approaches have been proposed and developed over the years. Seasonal forecasts can be deterministic (point forecast representing our best guess) or probabilistic (it provides the forecast in terms of probability of exceedance which reflects a range of possible values for the variable of interest), can be statistical in nature or based on numerical models. For an overview, the interested reader is referred to Palmer and Anderson (1994), Carson (1998), Goddard *et al.* (2001), and Troccoli (2010), among others.

Seasonal forecasts are founded on the principle that large-scale surface processes evolve slowly, providing predictability to the atmospheric component at seasonal time scales (Palmer and Anderson, 1994; Anderson, 2000). These forecasts can have large societal and economic repercussions, ranging from the energy sector to the insurance/reinsurance industry, from crop production to water resources management (Hansen *et al.*, 2000; Alaton *et al.*, 2002; Hamlet *et al.*, 2002; Jewson and Caballero, 2003; Cantelaube and Terres, 2005; Abawi *et al.*, 2007; Benth *et al.*, 2007; Harrison *et al.*, 2007; Nelson *et al.*, 2007; Troccoli, 2007; Kumar, 2010; de Oliveira Cardoso *et al.*, 2010). Our improved seasonal forecasts would contribute to more efficient management of natural resources, improved productivity and more accurate pricing of weather-related quantities.

Seasonal forecasts do not exhibit the same skill for all the meteorological variables and every area of the globe. Recently, Lavers *et al.* (2009) examined the skill of eight seasonal climate forecast models in forecasting rainfall and temperature, and found that these models exhibit significant skill in long-lead times only for temperature and for the equatorial Pacific Ocean. On the other hand, there is a very limited skill in rainfall forecast beyond one month, in particular at the mid-latitudes (see also Anderson, 2000; Doblas-Reyes *et al.*, 2000; Graham *et al.*, 2000; Vizard *et al.*, 2005; and Alessandri *et al.*, 2011, among others).

In this study, we follow an empirically based approach and develop statistical models to provide at-site probabilistic seasonal rainfall forecasts for the Bucharest-Filaret (Romania) station. While the largest potential rainfall predictability over Europe is for spring (Nranković *et al.*, 1994; Doblas-Reyes *et al.*, 2000; Graham *et al.*, 2000; Lloyd-Hughes and Saunders, 2002), we develop models for all the seasons and compare forecast performance across them. Moreover, while in most of the cases linear regression is used to relate predictand and predictors (see Mason and Baddour, 2007; for a recent overview), we move away from statistical models using distributions from the exponential family (e.g. Gaussian, exponential) and consider a more general set of models. We also include nonlinear dependencies in the relation between covariates and predictand (see also Lo *et al.* (2007) and Maia and Meinke (2010) for nonlinear probabilistic approaches).

The basic idea is to use covariates available prior to the onset of the season to forecast, and use them to predict the values of the parameters of the selected probability distribution. By relating the parameters and the predictors, we obtain the forecast distribution for a given season (see Serinaldi (2011) for a recent example). The probabilistic forecasts represent the last of a set of steps we need to go through and related to answering the following questions:

- 1.What are the appropriate probability distributions, predictors and their relation to the parameters of the probability distribution?
- 2.Can these models be used to forecast seasonal rainfall? Do they perform better than naïve forecasts (e.g. the rainfall value for the previous year)?

These are all questions we address in this study. Rather than focusing on a single model, we show that there is not a single ‘best’ model from a statistical standpoint. The final model depends on whether we focus on individual seasons, or consider the rainfall time series as continuous and account for seasonal changes. Model selection (both in terms of predictors and their functional dependence on distribution's parameters) depends on the penalty rule we apply, the likelihood-based evaluation criterion, and whether we select a more or less parsimonious model. Apart from the differences in statistical structure of the forecast system, we also highlight how the forecast accuracy of these models depends on the performance measure used. Nonetheless, even though there is not a single model that is unequivocally better than the others, we provide general recommendations based on performance and parsimony.

This paper is organized as follows. In Section 2, we describe the data, the statistical procedures for covariate and model selections, and provide an overview of the different measures used to quantify the forecast performance. Section 3 describes the results of our analyses, followed by a summary and conclusions, which are presented in Section 4.