Generating rainfall fields using principal components (PC) decomposition of the covariance matrix: a case study in Mexico City

Risk assessment and water resources management need to get a reliable estimation not only of the temporal distribution of the rainfall events, but also of their spatial extension. Data provided by dense rain gauges network or meteorological radar are generally not long enough to supply consistent information on a given area. Using Principal Components (PC) decomposition of the correlation matrix may generate rainfall fields, in order to expand or create available data. Features of the model ensure quick simulation, because the orthogonality of the eigenvectors of the correlation matrix allows separating the time and space generation. This model was applied to an 11 year daily rainfall sample of 49 raingauges, bounded within a rectangular frame of nearly 2500 km^2 around Mexico City. In order to account for seasonality effect, only rainfields from June to September were selected. The observed rainfields may have some important intermittence in space, since a lot of them do not cover more than half the reference area. First, it is shown that the distributions of the main characteristics of both the observed and generated rainfields are very close together, which means that the model is able to deal with spatial intermittence. Then, rainfields were generated using a better resolution grid (713 points instead of 49): the so-obtained rainfields feature more chaotic structures which could be coherent with what would be observed at a smaller scale on radar images, as it will be analyzed furthermore. So this kind of model could also suit for the spatial scaling effects. This model may be easily calibrated on the basis of both time-series at a given point and a correlation matrix. The former are generally readily available, the latter may be drawn from a short period where meteorological radar images are available. Furthermore, it could be applied to any given finite duration.