## 2 Study Area and Observation  
New Zealand is an island country located in the southwestern Pacific Ocean, east of the Australian continent, between 34\({}^{\circ}\) to 47\({}^{\circ}\) S and between 164\({}^{\circ}\) to 179\({}^{\circ}\) E, with an area of 270,000 km\({}^{2}\). It consists of two main islands presenting a northeast-southwest oriented shape. The North Island is mainly characterized by plains but it also presents mountains reaching a maximum altitude of more than 2700 m a.s.l. Conversely, the South Island is mainly mountainous, with the Southern Alps reaching an altitude of 3764 m (Figure 1). Generally, New Zealand's weather patterns reflect those of the oceanic mid-latitude locations [36; 37], but it is also affected by some physical factors [38]. The first factor is the location of the country in the Pacific Ocean, which influences air circulation and seasonal climate. The air masses coming from the tropical zones of the Pacific lead to a humid weather, with fresh summers and mild winters, and temperatures oscillating between 18 \({}^{\circ}\)C and 21 \({}^{\circ}\)C, although snow and frost occur as a consequence of the oceanic currents from Antarctica. The presence of the mountains in the eastern side of the North Island and of the 750-km long, over 3000-m high Southern Alps traversing the South Island constitutes the second factor affecting air circulation and determining New Zealand's climate [39; 40]. As a result, large differences in the rainfall volumes occur even over short distances between the mountain areas and the eastward plans. Moreover, summers in the northern part of the North Island are influenced by the westerly wind perturbations [38]. Finally, although more than 2000 km divide New Zealand from the Australian continent, this significantly influences New Zealand seasonal climate because of the cyclogenesis region moving through the Tasman Sea which is responsible for the significant differences in the  
Figure 1: Geographic localisation of New Zealand and the selected 294 rain gauges (blue dots) over a digital elevation model (DEM). precipitation amount occurring over short distances especially in the South Island [41; 42; 43; 44]. Clear sky conditions in winter lead to considerable surface cooling, which, in turn, results in stable lower atmospheric conditions. This has an impact eastward since it prevents the western airflow from significantly affecting New Zealand. On the contrary, large convective hot air masses coming across the Tasman Sea cause robust airflow affecting New Zealand in summer [25]. New Zealand's climate has been carefully described by The National Institute of Water and Atmosphere Research (NIWA) of New Zealand [45]. According to NIWA, warm, humid summers and mild winters affect the North Island, in which winter is the rainiest period of the year, while summer and autumn are characterized by tropical storms and intense precipitation. The Central Region of the North Island is the least affected by winds that heavily sweep many areas of the country. Stable, dry, and warm summers with unstable cool winters are typical of this region. The south-west part of the North Island does not present many climate extremes with a stable weather in summer, which is usually warm, and at the beginning of autumn and unsettled, although not very cold, winters. The sunniest area of New Zealand is the northern part of the South Island, characterised by warm, dry and stable summer. In the western side of the South Island is affected by extreme yearly precipitation higher than average, although occasional dry spells my occur between the end of the summer and the winter months. The eastern and inland areas of the South Island are characterized by low mean annual rainfall and by long dry episodes in the summer season. With the aim to perform a spatial analysis of the rainfall in New Zealand, monthly observations have been extracted from the NIWA database for the period 1951-2012.