2006 AMS Remote Sensing Lecture: Raindrop size distributions: lies, damn lies and statistics

Much of what “we know” about raindrop size distributions is based on questionable treatment of the observations. This includes incomplete portrayal of the data in graphical presentations and ad hoc analysis procedures. This lecture examines the subject to elucidate:

Lies – in the incomplete presentation of the data in the usual semi-log plots, involving omissions and leading to the famous “hockey-stick” effect;

Damn lies – in the “fitting” of distribution functions to the observations, where use of arbitrarily-chosen functions and moment methods (with their inherent bias) for estimating parameters leads to results that often represent neither the data samples nor the underlying population correctly; and

Statistics – as a basis for more accurate presentation and more rigorous analysis of the data, including tests to determine whether a particular function is appropriate for the data and fitting methods with little or no bias.

Data plotting and analysis procedures that should lead to improved descriptions of the observed drop-size distributions will be outlined. The need for unbiased fitting procedures that can incorporate interest in bulk quantities such as liquid water concentration will be highlighted.