OPERATIVA INADECUADA

Abstract Stochastic rainfall generators aim to reproduce the main statis-

tical features of rainfall occurrence and intensity at small spatial and tem- poral scales. Used to simulate long-term synthetic rainfall series, they are recognized as suitable for use with impact analysis in the fields of water, agricultural, and ecological management.

While many stochastic rainfall generators have been developed in the last decades and applied in regions with contrasted climates, only a few of them have been developed and used in intertropical regions. The largely convection-driven rainfall in the intertropical belt presents properties that need to be specifically considered and included in stochastic rainfall genera- tors. These include (i) a strong rainfall intermittency, (ii) high variability of intensities within storms, (iii) strong spatiotemporal correlation of intensities, and (iv) a marked seasonality that affects the statistical properties of storms (i.e. occurrence, intensity). In addition, intertropical storms are among the most powerful on Earth, and an intensification of the most extreme ones is already observed in some regions, tied to global warming.

In this paper, improvements for an existing statistico-dynamic rainfall generator that models convective storm systems in the intertropical zone are presented. Notable improvements include (i) the ability to model the occurrence of precipitation events via a model based on the distribution of the inter-event time parameter, (ii) an improved temporal disaggregation scheme that better represents the rainfall distribution at all sub-event scales, and (iii) the use of covariates that reflect seasonal changes in precipitation occurrence and marginal distribution parameters. Extreme values are explic- itly considered in the distribution of storm event intensities. In this study, the simulator is implemented in the Sahelian region, specifically in south- west Niger. The simulator is calibrated and the simulations validated using 28 years of 5-minute precipitation data from the 30 rain gauge AMMA- CATCH network. The simulation is used to generate both large propagative systems and smaller local convective precipitation. Results show that the improvements in the simulator coherently represent the local climatology. The simulator can be used to generate scenarios for hydrological and agri- cultural impact studies with a more accurate representation of convective precipitation characteristics.

Authors Catherine Wilcox, Claire Aly, Th´eo Vischel, G´er´emy Panthou, Juliette Blanchet, Guillaume Quantin, Thierry Lebel

3.3

Introduction

Stochastic rainfall generators aim to simulate realistic rainfall series by re- producing key statistical features that characterize rainfall variability. Com- monly modeled elements include rainfall occurrence, intensity, and depen- dence structures in time and/or space. As stochastic rainfall generators are suitable for generating long-term rainfall sequences at fine resolutions, they are useful in many applications: conducting risk assessment studies to esti- mate the return periods of very rare events (Evin et al., 2018; Arnaud et al., 2016); and assessment of rainfall estimation uncertainties and their propaga- tion into impact models (Renard et al., 2011; Borgomeo et al., 2014), to name a few. These statistical models are complementary to physical atmospheric or climate models as they can be used in climate change impact studies as a means to downscale and disaggregate coarse-resolution climate model rain- fall outputs (Wilks, 2010; Sørup et al., 2016; Peres and Cancelliere, 2018). For these reasons, stochastic rainfall models are recognized as useful tools in numerous areas of environmental sciences for which rainfall is of major influence, for instance hydrology, agronomy, and ecology.

While many stochastic rainfall generators have been developed over the last decades (see Wilks and Wilby (1999); Ailliot et al. (2015); Vu et al. (2018); Loveridge and Rahman (2018) for a review) and applied in regions with contrasted climates, only a few of them have been used in intertropical regions. A first reason is that the tropics are sparsely-monitored regions, a factor which limits the possibility to infer the statistical parameters of stochastic rainfall generators, especially for rainfall properties at sub-daily scales. A second reason is that the intertropical belt presents specific rainfall characteristics that are rarely considered and included in stochastic rainfall generators. Precipitation events in the tropics are mainly, if not exclusively, due to convective storms. These storms can be very localized due to local convection processes, but mostly are long life cycle propagative convective systems sometimes referred to as mesoscale convective systems (MCS). They are largely driven by synoptic atmospheric processes that take place in re- gional climate systems such as seasonal monsoons.

storms is a markedly strong seasonality. The movement of the intertropical convergence zone (ITCZ) provokes strong trends on convective storm devel- opment and propagation. These dynamics generate strong seasonal signals that are generally consistent from one year to another, but that are also susceptible to evolve or cycle over time.

In addition, intertropical storms are some of the most powerful on the Earth (Zipser et al., 2006), and an intensification of the most extreme ones is already observed in some regions in the Tropics, tied to global warming (Tay- lor et al., 2017; Tan et al., 2015). MCSs have been shown to be associated with extreme rainfall events (Schumacher and Johnson, 2005). This under- lines the need to specifically treat extreme intensities in rainfall generators in this region.

Given the nature of convective systems, tropical storms are character- ized by a strong intermittency of rainfall, a high variability of intensities within storms, and a strong correlation of intensities in time and space. An appropriate rainfall generator for tropical storms would thus need to simu- late spatio-temporal rain fields and not independent single site precipitation series.

Among the variety of stochastic rainfall generators, those aiming at simu- lating spatiotemporal rainfall fields are often divided in two classes: multi-site and random fields models. The first are an extension of single-site stochas- tic models over several distant locations (often corresponding to rain-gages). They are mainly based on non-parametric resampling methods, on paramet- ric point processes based on the successive use of statistical rainfall occur- rence and a statistical rainfall amount model, or on cluster point processes (Cowpertwait et al., 1996; Wilks, 1998). The second category focuses on con- tinuously simulating (on regular grids) the spatial variability of rainfall. This

family includes rain cell models (F´eral et al., 2003), scale invariance models

(Serinaldi, 2010; Lombardo et al., 2017; Raut et al., 2018) and meta-Gaussian random fields (Benoit and Mariethoz, 2017). The latter group of models - meta-Gaussian fields - is considered in this paper as a suitable method for modeling the spatiotemporal properties of convective storm systems in the intertropical zone.

Some promising developments in rain field modeling have been made in other regions. Peleg and Morin (2014)’s model produced both convective storm cells and areas of low-intensity rainfall. Oriani et al. (2017) and Singer and Michaelides (2017) conditioned their models’ parameters on factors such as elevation and weather state. Lee (2018) improved methods of spatial cor-

relation for the copula method of modeling marginal distributions. Baxevani

and Lennartsson (2015) and B´ardossy and Pegram (2016) developed Gaus-

sian field precipitation models that are dependent on both space and time. Regarding extreme events, Baxevani and Lennartsson (2015) and Evin et al. (2018) proposed modeling precipitation magnitudes with a gamma dis- tribution for smaller values and a generalized pareto distribution (GPD) for larger values (for Baxevani and Lennartsson (2015), above a given thresh- old; for Evin et al. (2018), with a transition function as developed in Naveau et al. (2016)). Wilks (1999) evaluated various marginal distributions for their ability to reproduce extreme event characteristics.

A selection of stochastic rainfall generators have been developed and/or applied to modeling rain fields in the intertropical zone. Some, as in Cowden et al. (2008), provided stochastically generated series of rainfall amounts, but without a spatial structure, a potentially significant criteria for impact studies in the intertropical zone (Carney et al., 2008). Others provided only the occurrence of wet and dry days without rainfall amounts (Jimoh and Webster, 1999; Robertson et al., 2004). Several rain field simulations were developed for the intertropical zone based on the the Global Atmospheric Research Program Atlantic Tropical Experiment (GATE) dataset, including Valdes et al. (1990), Bell (1987), Ferraris et al 2003, and Over and Gupta (1994). The spatial structure of seasonal storms in Mexico City was evaluated in Bouvier et al. (2003).

A stochastic simulator developed for the Sahelian region of West Africa was initially presented in Lebel et al. (1998). Guillot and Lebel (1999a), Guil- lot and Lebel (1999b), and Balme et al. (2006) provided further developments for the spatial and temporal disaggregation respectively, and Onibon et al. (2004) proposed the Gibbs sampling method for the simulation of marginal distribution values. Vischel et al. (2009) explored point conditioning meth- ods for the model. The above articles demonstrated that the precipitation model accurately reproduce both the spatial distribution and marginal dis- tribution of precipitation events, an important characteristic for evaluating hydrological impacts (Troutman, 1983; Wilson et al., 1979). It also treated the problems of spatial and temporal disaggregation separately.

The rainfall simulator in its state for Vischel et al. (2009) did not take into account a few key variables, notably extreme values, the frequency of precipi- tation events, and the seasonal precipitation signal. The model also produced sub-event intensities that were stronger than those found in the record, an effect linked to the temporal disaggregation method. The choice of temporal

disaggregation method and the resulting synthetic hyetograph has direct im- pacts on simulated hydrological outputs (Lambourne and Stephenson, 1987). Building on the rainfall simulator described in Vischel et al. (2009), this paper demonstrates recent advances in stochastically generating convective storm events. We propose an improved version named ”Stochastorm” that models additional phenomena pertinent to the intertropical zone and relevant for driving impact models. Notable improvements in this paper include (i) the ability to model the occurrence of precipitation events via modeling the distribution of the inter-event time, (ii) the explicit consideration of extreme values in the distribution of storm event intensities, and (iii) an improved temporal-disaggregation scheme that better represents the rainfall distribu- tion at all sub-event scales. The seasonality of the rainfall properties is taken into account by adding covariates that reflect seasonal changes in precipi- tation occurrence and marginal distribution parameters. In this study, the simulator is implemented in the Sahelian region, specifically over the AMMA-

CATCH Observatory that covers an area of 10,000 km2 _{in southwest Niger}

and provides 28 years of 5-minute precipitation data from the 30 recording rain gauges.