## 1 Introduction  
Groundwater, amounting to 23.4 million km\({}^{3}\), is the second largest resource of freshwater in the world, after glaciers and permanent ice caps with a volume of 32.9 million km\({}^{3}\), and the only widely accessible fresh water source [1; 2; 3]. In the time of global water scarcity, groundwater is under high stress, especially in urban and semi-urban areas where not only global warming influences its quantity, but also many artificial factors have a negative effect on the available volume of groundwater [4]. To manage this precious resource properly, we have to know how much water exists in the aquifer. For that, we need long-term groundwater level observations, which are important for effective and sustainable water management, geoengineering as well as for a reliable freshwater supply. Based on the data gathered during the observation period we can define and describe natural and artificial factors influencing groundwater levels resulting in water resource quantity estimations and predictions. As longer observation periods are favorable for reliable statistical analysis and predictions in Earth sciences, we used the longest time series accessible to us in Wroclaw, Poland.  
Groundwater level fluctuations are indicative for changes in the quantity of water stored underground. Mid and long term analysis of groundwater level fluctuations refer to a specific cycle called water year or hydrological year (HY). It is the annual cycle that is associated with the natural progression of the hydrological seasons and depends on climate conditions and differs in different regions of the world (in Poland its duration is from 1 November until 31 October).  
Groundwater level fluctuations in undisturbed conditions depend on the geological setting and the permeability of the unsaturated (vadose) zone as well as on precipitation, air temperature, air moisture and insolation (Figure 1). These factors can be easily measured with sensitive automated sensors nowadays. In urban and semi-urban areas, there are many unmeasurable factors influencing the groundwater level that can disturb its seasonal (cyclic) nature (e.g., regulated water streams, surface pavements, drainage). By combining mathematics, signal processing, hydrogeology, and meteorology, some new opportunities for long-term analysis of groundwater fluctuation can be derived. There are key questions to be answered: (i) does the groundwater level in a semi-urban area behave in a similar way every hydrological year and season? (ii) is the predefined duration of the hydrogeological year still valid in this semi-urban area? and (iii) are there any anomalies in the groundwater level fluctuations and what are the reasons for that? Thus, to develop a model for anomaly detection and future prediction of relationships between groundwater level, precipitation and temperature seems to be imperative. However, a precise relationship is unknown and also depends on the specific properties of a given area semi-urban part of a large city. This paper is an introduction to this kind of complex analysis and introduces methods well known from other applications that can be implemented for the groundwater level. Based on the example of one observation well in the city of Wroclaw, data, first observations, preliminary analysis, and conclusions are presented. Reasons for choosing this single observation well are that it's the city's well with the longest nearly uninterrupted observation period, its location within the semi-urban area of Wroclaw (Figures 2 and 3), and the fact that the methods described had to be tested and evaluated first, before including additional wells with long term observations.