Analysis of Continuous Time Series in Urban Hydrology: Filling Gaps and Data Reconstitution

We analyse flow rates and quality (conductivity, temperature, pH, turbidity) of urban dis- charges during dry and storm weather conditions. Missing data are present in these time series. If the length of a missing interval is short (up to 10 or 15 minutes), then simple techniques (linear interpolation or splines for example) are very effective to fulfill them. When the weather is dry and the missing data interval is longer (some hours or more), we propose a method to rebuild the missing information. First, we cluster the observed -full- dry days to identify their common properties and their variability. Then, we use a linear combination of the centers of the clusters as corner functions to fill the gaps of days with missing data. Numerical results on real dataset show the superiority of the new method with respect to a method based on an empirical clustering.