Statistical analysis of rainfall event features using the Self Organizing Map with application to Northern Tunisia

The use of artificial neural networks in problems related to water resources, hydrology and meteorology has received steadily increasing interest over the last decade or so. In this study, the methodology proposed to analyse rainfall features and to investigate the relationships with global climate change is based on  the use of Self-Organizing Map (SOM) and presents a generic character.

As a first step, daily winter precipitation of northern Tunisia, collected between 1960-2009 over 70 rain gauge stations, are transformed into separate events. This separation is based on the determination of the minimun inter-event time (dry interval) between two independent and consecutive rain events. Six rainfall event features (i.e., average rain event accululation, average event duration, seasonnal accumulation, number of rainy day…) are thus extracted for each of the (70 stations x 50 winter seasons).

In the second step, SOM is applied to analyse the six rainfall features. The SOM is an unsupervised learning algorithm, used as a technique vector quantization, allowing the modeling of probability density functions. It divides the set of multidimensional data (vectors of six features in our case) into clusters. As in k-means, rainfall stations and years with similar characteristics are grouped in a cluster represented by its centroid point named referent. SOM enables moreover the projection of high-dimensional data onto a low dimensional (usually two-dimensional) discrete lattice of neurons as an output layer (map space). The structure of the neurons in the map and the cost function used for its training, ensure that neighboring neurons in the map space are associated with neighboring referents in the initial space. This conservation of the topology allows the analysis of multidimensional nonlinear relationships between the six selected descriptors by visualizing their projection in the map space.

For a better representation of the input dataset a 16×20 neurons map is used. But a such number may complicate the synthesis of some spatial or temporal specificities. So, this large number of neurons is aggregated into a smaller number of clusters. For that an hierarchical agglomerative clustering (HAC)  is applied in the third step. This hierachical process is initiated by accepting each neuron as a separate cluster. Then, at each stage of the algorithm, similar clusters, using Ward distance, are combined in pairs.

The fourth step allows to determine the final number of clusters by using visually-based method known as data image. This consists of mapping the dissimilarity matrix of the referents into an image framework where each pixel reflects the magnitude of each value. Here rows and columns can be reordered based on hierarchical clustering of the referents The blocs observed along the diagonal of each image represents the clusters.

Finaly the northern Tunisia winter precipitation are classified into four rainfall situations from the driest to the wettest while also taking into account the rainfall day frequency during the season and rainfall event types. The projection of external climatic variables on the map will make it possible to analyse the links between the four observed rain regimes and the global climate.