One possible means of approximating the statistical moments at length scales smaller than the directly measured scales is to use scaling properties of the moments. By scaling we mean that dependence of a statistic on length scale can be written as a power law. If a statistic of a particular field is shown to exhibit scaling without scale breaks, then the small-scale statistics can be inferred from a measurement of larger scale statistics and knowledge of the scaling exponent. Many statistics characterizing properties of turbulent fluid flows have been shown to exhibit scaling. Several previous studies exploring the horizontal spatial variability of water vapor fields as measured by aircraft and satellite based instruments have found statistics of water vapor to exhibit scaling across both large and small scales. Recently, Kahn and Teixeira's (2009) investigation of water vapor variance scaling from the Atmospheric Infrared Sounder (AIRS) aboard NASA'a Aqua satellite showed scaling with very weak or no scale breaks at length scales >150km and suggested that observations from AIRS could be extended to smaller scales if there were no scale breaks below 150km.
Resolving the issue of the applicability of scaling relationships at length scales below 150 km requires a data set of significantly higher spatial resolution than AIRS. A few studies have considered scaling at these smaller length scales but most have been limited in number of cases studied or to particular atmospheric phenomena. Our study investigates scaling relationships in the statistics of measured water vapor at the 396 m level of the 447 m WLEF tower (Davis et al. 2003). Water vapor measurements are obtained from a high-frequency calibrated infrared gas analyzer. Taylor's hypothesis is used to convert the time dimension of the tower time series to a spatial dimension so that spatial variability may be considered. In particular we analyze one hour subsets of time series data sampled at 10 Hz by computing "poor man's" variance spectra and fitting exponents to these spectra. The set of length scales which can be assessed using this method is limited by the length of the time series and the mean horizontal wind velocity, however many one hour time series allow assessment of scaling in excess 30 km.
The observed scaling exponents for water vapor variance computed from the WLEF time series agree well with the previous study of variance scaling using AIRS retrievals as well as with other studies. By partitioning our tall tower observations and analysis into mid-day within boundary layer observations and nocturnal above boundary layer observations, the statistics of the two regimes become evident. We will conjecture as to the relevant physical mechanisms setting the scaling exponents in these two regimes.