Sampling Statistics of Atmospheric Observations



After having specified the basic vocabulary for simple statistics, which is recapitulated for N independent observations in section two, and which leads to the concept degrees of freedom equal to N, we proceed to the statistics of consecutive events that are correlated over finite times, i.e. having a ‘memory’ measured in terms of the integral time scale ��. In section three we determine what we call the effective degrees of freedom �� for the case where there are many observations over a period of duration ��. In this case, �� is smaller than N. The analysis is generalized in section four to include a simple equation for the ratio ��/N irrespective of the sampling rate. Finally, in section five we present, as our major contribution, a theoretical model for ��/N when we have intermittent sampling of an otherwise continuous signal. The model is applied to a time series of wind speed in specified wind direction sectors. The time series is intermittently and randomly interrupted when the wind direction gets out of the specified sector. Copyright © 2002 John Wiley & Sons, Ltd.