Stochastic Generation of Wind Patterns over Lake Geneva
Lake Geneva (length 74 km on the long east-west axis, surface area 562 km2, volume 89 km3) is a freshwater lake bordered by Switzerland and France. The lake’s hydrodynamics are forced principally by wind and seasonality, with inflows and the Coriolis effect playing relatively minor roles. Of the major forcings, wind is highly variable due to the rapid changes in topography around the lake, with mountains in the east and relatively gentle landscapes in the west. Numerous field investigations have revealed that the lake’s currents, which are dominated by the wind, are likewise highly variable. In particular, analysis of field measurements of Lake Geneva’s wind and currents found that the lake’s currents during the summer stratification period are consistent with diurnal winds and long-fetch synoptic events. Obviously, a quantitative understanding of the wind forcing is a prerequisite for evaluating the current patterns in the lake. Hourly wind patterns (produced using the non-hydrostatic, fully compressible COSMO model) at 10 m above the lake were provided by MeteoSuisse (the Swiss meteorological service) on a 2.2 km2 grid for 2009-2010. These patterns were categorized using the k-means data-mining method, with each pattern assigned an arbitrary integer index 1, 2, 3, etc., along with the pattern's frequency. For later use, all wind fields corresponding to a given pattern were grouped into bins. It was found that the index frequencies could be approximated by a Poisson distribution with a characteristic temporal autocorrelation time of around 15-20 hours. More specifically, the wind pattern autocorrelation has an initial rapid, power law-like decline ( αt, where α ≈ 0.8 and t is the lag in hours) for about 24 hours, then a slow decay. The main features of this behavior (Poisson process with a power-law autocorrelation) were captured by an integer auto-regressive process, the INAR(1) model. This model was used as a stochastic generator of wind-pattern indices, i.e., the INAR(1) model produces a sequence of integers, each of which corresponds to a wind pattern. For a given index, the aforementioned binned COSMO wind fields were sampled randomly to produce the stochastic wind-field sequence.