Hydrological analysis of a karst system via Ensemble Kalman Filter

The subject is a hydrological analysis of a karst system using the instruments of the data assimilation field of study, in particular the Ensemble Kalman Filter. In particular, the analysed system is the karst complex of Bossea-Artesinera, located in the south of Piedmont. The aim is to characterize the response of the aquifer in response to a meteoric precipitation. To do this we used a response initially composed by an infiltration coefficient and an instantaneous unitary hydrogram (IUH). So, the response of the system can be modelled using a number of state parameters, and an output can be calculated from them as an outcoming rate flow. Since is impossible to access most of the underground aquifer, a statistical approach has been followed via Ensemble Kalman Filter and later Ensemble Smoother with multiple data acquisition. We possess two sources of information, both incomplete: the model and the observations, both usually in a discrete form. We know the equations governing the dynamical, time-dependent model but not the value of its parameters, while the observations we have measured are affected by an error and are available only at specific times. So, we can forecast the model until we reach the time of an observation, then we can use the observation to update the model parameters to stay stuck to the reality of the system as much as we can. We start the model with an ensemble of state vectors with values randomly extracted, then the model is updated using the available measures. In the end the stochastic ensemble representation of each parameter will converge to its real statistical moments. In the thesis works we use daily data of meteoric precipitations, air temperature (collected at the Borello weather station by ARPA Piemonte) and rate flow (collected at the Bossea Scientific Station) along the chosen model of the system. Some flood events, according to the data, are selected and analysed separately. The model chosen is composed of a vector of four main parts: •??Infiltration coefficients, one per day •??IUH, the response of a unitary income, considered as a vector of values or a parametric form, •??Snow Melting, a model derived to consider the stored snow and the subsequent melting contribution in terms of water equivalent: it identifies the snow events according to temperature data and then estimate the snow melting time and volume •??A rate flow due to previous rainfalls events, which decreases over time, named flow rate B An ensemble of state vectors comprehending all the necessary parameters is generated and updated using the available data, and eventually converges to the result. The collected data are analysed trying to define a typical response of the system capable of predicting the behaviour of the aquifer with a certain approximation. In this sense, the events are divided into spring events and summer-autumn events, due to the marked differences in seasonal responses. The different components of the model were analysed one by one, trying to identify the recurring patterns. Average responses were defined in terms of IUH and a recurring trend in the infiltration coefficient during the year. To this has been added a rough assessment of snow melting and rate flow B as general behaviour, although it is impossible to speak of recurring patterns. In this way it was possible to define a signature of the system whose validity was tested in terms of Nash-Sutcliffe efficiency and forecast of the total outgoing volumes.