In open water systems, water levels, flows, transports, mixing, etc. all depend on gravitational, externalmechanical, and external-thermodynamic forcing. In practical applications of hydrodynamic numerical models, and especially when an accurate representation is desired for relatively small spatial and temporal scales (order of 1 km or less, and 10 minutes or less, for example), it has often proved to be impossible to obtain data of this external forcing with a sufficiently detailed resolution. As a result, these data must be interpolated appropriately to the much finer spatial and temporal grids of the numerical model.
Recently a method was developed for the construction of synthetic time series. In this method physical/statistical properties can be prescribed within an interpolation of observed samples. In this way, a synthetic/interpolated time series is highly consistent with the actual physical process. A special feature of the method is that ensembles of consistent synthetic series can be generated and the variability in such an ensemble represents uncertainties.
In this case, the suitability of the method was tested for the interpolation of wind speed fluctuations. To obtain statistic properties of these fluctuations, an observed data set with 1-minute wind-speed samples was statistically analysed. The wind-speed fluctuations were identified as the residuals of a regression model for the long(er) term temporal variations. The statistical analysis revealed that these fluctuations can be modelled as a random process (close to Gaussian) with an exponential auto-covariance function.
The resulting (analytical) model which has been identified for the observed wind speed fluctuations was used to generate an ensemble of synthetic time series. Together with the marginal distribution and auto-covariance function, a sparse subset of observations was prescribed as well. In this way the situation is emulated in which the original time series of 1 minute samples must be reproduced from a sparse subset of 10 minute samples. |
