Some Effects of Finite Sample Size and Persistence on Meteorological Statistics. Part I: Autocorrelations

Abstract

Time series of meteorological variables typically exhibit a pronounced annual cycle and persistence and samples are of finite size. This paper analyses the impact of these complicating features on certain statistics computed from the time series. The presence of an annual cycle means that statistics are nonstationary unless computed from multiyear samples of limited duration. Persistence leads to lack of independence of observations. Large amplitude weather (high frequency) events induce natural variability at low frequencies, known as climatic noise, that is enhanced by the presence of persistence. This natural variability should be, taken into account when estimating population statistics from a finite sample, but generally this has not been done in meteorology. A number of studies in meteorology have computed statistics from daily data by 1) removing the annual cycle; 2) computing second moment statistics over each individual season; and 3) averaging the second moment statistics over all years... Abstract Time series of meteorological variables typically exhibit a pronounced annual cycle and persistence and samples are of finite size. This paper analyses the impact of these complicating features on certain statistics computed from the time series. The presence of an annual cycle means that statistics are nonstationary unless computed from multiyear samples of limited duration. Persistence leads to lack of independence of observations. Large amplitude weather (high frequency) events induce natural variability at low frequencies, known as climatic noise, that is enhanced by the presence of persistence. This natural variability should be, taken into account when estimating population statistics from a finite sample, but generally this has not been done in meteorology. A number of studies in meteorology have computed statistics from daily data by 1) removing the annual cycle; 2) computing second moment statistics over each individual season; and 3) averaging the second moment statistics over all years...